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11 

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1 


MONTHLY  NOTICES 


OF  THE 


ROYAL    ASTRONOMICAL    SOCIETY. 


Vol.  XL VII.    No.  i.    November  1886. 


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MONTHLY   NOTICES 


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ROYAL  ASTRONOMICAL  SOCIETY, 


CONTAINING 


PAPERS,    ABSTRACTS    OP    PAPERS,    AND 

REPORTS  OF  THE  PROCEEDINGS 

OP  THE  SOCIETY 


FROM  NOVEMBER    1886   TO   NOVEMBER   1887. 


VOL.  XLVIL 


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LONDON : 
ROYAL    ASTRONOMICAL    SOCIETY 

BUBLINGTON   HOUSE,   W. 
1887. 


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1  ^  -y^N 


MONTHLY   NOTICES 

OF  THE 

EOYAL    ASTKONOMICAL    SOCIETY. 


Vol.  XLVII.  November  12,  1886.  No.  1 


J.  W.  L.  Glaisher,  M  A.,  F.R.S.,  President,  in  the  Chair. 

Maurice  Loewy,  the  Observatory,  Pari* ;  ami 
G.  Sporer,  Astrophysical  Observatory,  Potsdam, 

were  balloted  for  and  duly  elected  Associates  of  the  Society. 


A  Reply  to  Mr.  Neison's  Strictures  on  Delaunay's  Method  of  De- 
termlning  the  Planetary  Perturbations  of  the  Moon.  By 
G.  W.  Hill. 

For  several  years  past  Mr.  Neison  has  been  maintaining  in 
the  Monthly  Notices  and  Memoirs  of  the  Society  that  Deiaunay's 
investigation  of  the  two  long  period  inequalities  in  the  Moon's 
motion  arising  from  the  action  of  Venus  is  seriously  defective, 
on  account  of  the  omission  by  him  of  a  certain  class  of  terms'. 
In  the  Monthly  Notices  for  last  June  there  appears  a  long  article 
by  him  upholding  this  view ;  to  this  I  wish  more  especially  to 
direct  attention. 

At  the  outset  I  may  be  allowed  to  say  that  all  this  criticism 
is  without  foundation.  It  appears  to  arise,  partly  from  the  very 
confused  conception  Mr.  Neison  seems  to  have  of  the  nature  of 
Deiaunay's  method,  and  partly  because  he  fails  to  notice  that 
Delaunay,  after  setting  the  degree  of  approximation  he  wishes 
to  attain,  always  rigorously  adheres  to  it.  If  we  were  obliged 
to  admit  the  validity  of  all  the  statements  in  this  article,  an  easy 
corollary  from  them  would  be  that  Lagrange's  general  method 
of  the  variation  of  arbitrary  constants  in  the  problems  of 
mechanics  was  a  blunder.  Now,  I  think  that  no  one  acquainted 
with  this  method  could,  for  a  moment  even,  entertain  such  a 

B 


2  Mr.  Hilly  Reply  to  Mr.  Neison's  xlvii.  i, 

proposition.  Hence  we  may  conclude  there  is  some  flaw  in  the 
reasoning  of  this  Paper.  But  this  mast  be  substantiated  by 
noticing  seriatim  the  objectionable  points. 

In  the  first  place,  why  bring  forward  Hansen's  published 
values  of  the  coefficients  of  these  inequalities  for  the  purpose  of 
throwing  discredit  upon  Delaunay's  values,  when  their  author, 
himself,  virtually  confesses  he  has  no  confidence  in  them,  by 
saying  he  had  computed  them  in  two  different  ways,  and  found 
essentially  different  results  ?  And,  to  the  very  end  of  his  life, 
he  appears  never  to  have  been  able  to  find  out  whether  one  of 
these  results  was  right,  and  which  it  was,  or  whether  both  were 
wrong.  It  would  be  an  amusing  circumstance  should  it  turn 
out  that  the  set  of  values,  withheld  from  publication  by  Hansen, 
were  identical  with  those  of  Delaunay. 

There  is  some  inexactitude  in  Mr.  Neison' s  statement,  re- 
garding the  degree  of  approximation  adopted  by  Delaunay  in 
calculating  the  coefficient  whose  argument  is  8Z"  —  13Z'.  In  this 
connection  we  note  that,  on  account  of  the  close  proximity  of 
the  Moon  to  the  Earth,  a  planet  cannot  produce  in  her  motion 
inequalities  of  the  same  order  with  those  it  produces  in  the  Earth, 
but  that  they  are  only  of  the  order  of  these  multiplied  by  the 
solar  disturbing  force  ;  and  this  is  as  true  of  the  indirect  action 
as  of  the  direct.  Now,  on  referring  to  Delaunay's  work,  we  see 
that  he  has  considered,  not  only  the  term  of  the  lowest  order  in 
each  portion  of  the  coefficient,  but  also  multiples  of  this  by  m2. 
Hence,  it  is  correct  to  say  that  he  has  considered  terms  of  the 
order  of  the  mass  of  Venus  multiplied  by  the  square  of  the  solar 
disturbing  force,  but  not  those  multiplied  by  the  cube  of  the 
latter. 

Mr.  Neison  regards  the  evidence  adduced  in  his  earliest  Paper, 
as  conclusively  establishing  the  omission  by  Delaunay  of  a  certain 
class  of  terms.  But  what  was  this  evidence  ?  Simply,  that 
Hansen  was  at  variance  with  Delaunay.  Now,  since  Hansen 
was  as  much  at  variance  with  himself  as  he  was  with  Delaunay, 
what  weight  ought  to  be  attributed  to  this  evidence  ?  Then, 
Mr.  Neison  believes  that  certain  discrepancies  between  results, 
obtained  on  the  one  hand  by  himself,  and,  on  the  other,  by  M. 
Gogou  and  myself,  have  their  origin  in  the  same  cause.  Now, 
if  Hansen's  investigation  and  also  Mr.  Neison's  were  accessible, 
this  point  could  be  immediately  pronounced  upon;  but  since 
they  are  not,  it  appears  useless  to  speculate  on  the  matter. 

Mr.  Neison  says  (p.  416),  "  He  (Delaunay)  substitutes  the 
preceding  value  for  the  term  in  the  disturbing  function  with  the 
argument  '( in  the  differential  equation  and  integrates."  This 
does  not  correctly  represent  what  Delaunay  does.  For  he  sub- 
stitutes in  the  differential  equation  not  only  the  term  factored  by 
cos  £,  but  also  the  non-periodic  portion  of  R:  to  wit,  in  the 
memoir  of  1862,  the  terms 

/*  ,     /rt=ri  .  3  «.  225  „h'    /31    Q71  ,\W'H 
2a        a'*L4    8         $4     n      \32     32     /"'J 


Nov.  1886.  Strictures  on  Delaunay's  Method.  3 

and,  in  the  memoir  of  1863,  the  terms 

2tt        o'»L4    2         S       8     J 

The  terms  differ  in  the  two  cases,  because  the  degree  of 
approximation  aimed  at  requires  the  preservation  of  different 
terms  with  allowable  neglect  of  all  the  rest.  From  this  non- 
periodic  portion  of  B  results,  in  both  cases,  much  the  larger  part 
of  the  two  inequalities  considered.  Mr.  Neison's  failure  to  note 
this  completely  invalidates  his  argument  on  the  two  following 
pages,  by  which  he  attempts  to  prove  the  incompleteness  of 
Delaunay's  procedure.  And,  in  this  connection,  it  may  be  noted 
that  it  is  not  necessary  that  the  coefficient  in  (38)  should  vanish 
identically  in  order  to  prove  Delaunay  right;  it  is  necessary 
only  that  it  should  turn  out  of  such  an  order  of  sroallness  as  to 
prove  that  the  adopted  degree  of  approximation  had  been 
attained. 

On  p.  417  it  is  said  that  the  coefficients  B  and  B'  "only 
differ  by  small  quantities,  unimportant  for  the  present  purpose." 
So  far  from  this  being  the  case,  the  difference  B'  —  B  constitutes 
one  portion  of  the  terms  which  Mr.  Neison,  all  along,  has  been 
asserting  were  neglected  by  Delaunay. 

That  Delaunay,  in  treating  the  two  Venus  inequalities,  dis- 
carded his  own  method,  and  employed  the  old  one  recommended 
by  Poisson,  is  erroneously  stated  on  p.  423.  The  fact  is  that 
the  method  followed  is  the  same  as  that  he  had  used  in  deriving 
the  solar  perturbations.  Next,  Delaunay  is  found  fault  with 
(p.  424)  because  he  confines  himself  to  calculating  in  B  the  term 
which  has  the  argument  of  the  particular  inequality  he  is  dealing 
with ;  while  it  is  plain  that  there  are  a  multitude  of  terms  in  B, 
having  other  arguments,  which  could  contribute  to  the  value  of 
the  coefficient  sought.  This  is  true,  but  Delaunay's  reasons  for 
passing  by  these  terms  are  quite  evident.  In  the  first  place,  it 
must  be  remembered  that  his  final  expression  for  the  inequality 
is  a  formula  of  substitution,  which  must  be  made,  not  only  in 
the  mean  longitude  of  the  Moon,  but  also  in  the  equation  of  the 
centre,  in  the  evection,  variation,  and  in  all  the  inequalities 
arising  from  solar  action.  Hence,  Delaunay's  method  of  treat- 
ment enables  him  to  obtain,  with  very  little  additional  labour, 
all  the  terms  in  the  expression  for  the  true  longitude  which 
involve  the  very  small  divisor  arising  from  the  slow  motion  of 
the  argument  which  he  is  considering ;  and  that  whatever  may 
be  their  arguments.  And,  secondly,  while  the  terms  in  B, 
having  other  arguments,  which  would  be  treated  by  Delaunay 
as  giving  rise  each  to  a  distinct  transformation,  can,  in  a  strict 
sense,  add  something  to  the  coefficient  of  the  inequality  in  the 
true  longitude,  practically  these  terms  are  insensible ;  for,  al- 
though they  may  be  of  the  same  order,  before  integration,  as 
the  quantities  retained,  they  are  altogether  independent  of  the 
excessively  small  divisor  which  arises  from  the  slow  motion  of 

b  2 


4  Mr.  Hilly  Reply  to  Mr.  Neison' s  xlyii.  i, 

the  argument  of  the  inequality.  As  illustrating  this  point,  it 
may  be  remarked  that,  in  the  case  of  the  two  Venus  inequalities 
in  question,  we  get  such  relatively  largo  coefficients  as  16"  and 
o""27  only  by  multiplying  the  corresponding  terms  in  R  by 
factors  which  are  about  15,000,000  iu  the  first,  and  10,000,000 
in  the  second  inequality.  Hence,  if  there  are  other  terms,  which, 
rigorously  ought  to  be  added  to  the  preceding  values,  but  which, 
while  in  other  respects  of  the  same  order  of  smallness,  have 
factors  not  much  exceeding  unity,  it  is  very  apparent  they  may 
be  neglected. 

In  the  next  place  we  find  Delaunay  charged  with  neglecting 
every  term  of  the  solar  perturbations  save  the  term  of  the  lowest 
order  in  the  variation  in  calculating  the  proper  form  for  E». 
And  it  is  said  that  his  development  "in  no  sense  depends  on  his 
method  of  transformed  elements,  though  made  to  appear  as  if  it 
does ;  nor  does  it  differ  in  any  way  from  the  values  hitherto 
employed  by  astronomers  save  in  being  somewhat  less  complete." 
These  statements  misrepresent  Delaunay.  He  arranges  under 
four  different  heads  the  transformations  made  by  him,  and  they 
involve  no  less  than  16  out  of  the  57  operations  of  his  first 
volume,  besides  4  complementary  ones.  And  whether  the  amount 
of  work  in  this  be  regarded  as  much  or  little,  I  have  ascertained 
that  it  is  precisely  sufficient  to  obtain  the  degree  of  approximation 
he  proposes  in  the  coefficients  B,  viz.,  to  terms  involving  m2. 
Carrying  the  approximation  farther  could  only  have  afforded 
him  terms  of  a  higher  order.  It  is,  of  course,  open  to  Mr. 
Neison  to  say  he  deems  this  degree  of  approximation  insufficient ; 
and  nothing  can  be  said  in  opposition.  But  this  is  very  different 
from  saying  Delaunay  has  committed  errors.  Again,  I  am  not 
aware  of  the  existence  of  any  published  investigation  in  which 
the  degree  of  approximation  is  greater. 

The  reasoning  Mr.  Neison  employs  to  show  that  Delaunay 
deserts,  in  this  investigation,  his  own  method  and  returns  to  the 
old  method  recommended  by  Poisson,  is  certainly  very  strange. 
He  notes  that  the  differential  equation  used  has  nothing  in  it  to 
distinguish  it  from  the  corresponding  one  which  Poisson  would 
have  used.  But  from  what  circumstance  does  this  state  of  things 
arise  ?  Simply  because  it  is  Delaunay's  habit  to  omit,  in  the 
statement  of  his  equations,  every  term  which  gives  rise,  in  the 
final  result,  only  to  terms  of  a  higher  order  than  he  has  agreed 
to  retain.  The  factors  in  question,  in  Delaunay's  method,  can 
be  expressed  only  as  infinite  series ;  it  is  necessary,  therefore,  to 
cut  them  off  at  some  point,  and  he  determines  this  point  in  the 
way  just  stated.  If  reference  is  made  to  the  same  equation,  in 
the  memoir  where  Delaunay  treats  the  other  Venus  inequality, 
it  will  be  found  to  be  duly  distinguished  by  the  presence  of 
additional  terms,  Delaunay  writing  as  many  as  are  just  sufficient 
for  his  purpose. 

Mr.  Neison  next  notices  two  assumptions,  which  he  says  have 
been  made  by  Delaunay  in  his  integration. 


Nov.  1SS6.  Strictures  on  Delaunaifs  Method.  5 

2  dR 

The  first  is  that  the  factor      ,  which  multiplies  — ,  is  treated 

aw  dl 

as  if  it  were  constant.     Bet  here  he  forgets  that,  with  Delaunay, 

at  this  stage  of  the  work,  the  symbols  a,  e,  y,  /,  g,  and  A,  denote 

quantities  which  have  no  solar  perturbations ;  and  that,  conse- 

quently,  the  deviation  of       from  a  constant  has  the  mass  of  the 

an 

planet  as  a  factor.     Thus,  as  - ..-  already  has   this   factor,  the 

fit 

additional  terms,  which  would  in  this  manner  arise,  would  have 
the  square  of  the  mass  of  the  planet  as  factor  ;  these,  as  all  other 
investigators,  Delaunay  expressly  neglects. 

With  regard  to  the  second  assumption,  in  reference  to  which 
Mr.  Neison  makes  what  he  thinks  his  chief  point  against 
Delaunay,  let  us  consider  what  is  the  essential  difference  between 
Delaunay's  method  and  that  employed  by  the  earlier  investi- 
gators. Delaunay  said  to  himself,  Do  not  let  us  go  back  to  the 
elements  of  the  Keplerian  ellipse  every  time  we  have  to  consider 
the  action  of  a  new  force  on  the  Moon,  but  let  us  determine  our 
new  wave  of  motion  in  such  a  way  that  it  may  be  superposed  on 
the  curve  which  the  Moon  would  describe  under  the  action  of  all 
the  forces  previously  considered,  instead  of  on  the  Keplerian 
ellipse.  At  any  stage  of  progress,  in  expressing  the  Moon's 
co-ordinates,  there  must,  of  necessity,  appear  in  them  six  arbitrary 
constants  which  have  been  introduced  by  integration.  Let  us 
take  these  as  variables,  instead  of  the  six  elements  of  the  Kep- 
lerian ellipse.  This  course  demands  that  the  differential  equations 
employed  by  the  earlier  investigators  should  be  somewhat  modi- 
fied. The  modification  appears  as  a  change  in  the  values  of  the 
quantities  which  Poisson  denoted  generally  by  the  symbol  [a,  6]. 
Now,  just  as  it  would  be  absurd  to  maintain  that  the  elements 
of  the  Keplerian  ellipse  suffer  perturbations  from  the  action  of  a 
centrobaric  Earth,  so  it  is  absurd  to  maintain  that  the  quantities 
ff>  e>  Ti  h  9  and  hj  employed  by  Delaunay  after  he  has  got  through 
with  the  solar  perturbations  and  has  arrived  at  the  treatment  of 
the  planetary  perturbations,  and  which  are  the  elements  of  the 
curve  which  would  be  described  by  the  Moon  under  the  combined 
action  of  the  Earth  and  Sun,  suffer  perturbations  from  the  latter 
body.  Yet  Mr.  Neison's  argument,  when  divested  of  its  ob- 
scurities, is  seen  to  be  nothing  more  or  less  than  a  plea  that 
these  quantities  do  suffer  perturbations  from  the  Sun. 

To  make  the  matter  plainer,  let  us  suppose  that  Delaunay, 
groping  about  in  the  dark,  had  fallen  upon  the  Poissonian 
equations,  and,  thinking  them  to  be  his  own,  had  used  them  as 
such;  and,  moreover,  on  making  his  substitutions,  had  made 
them  only  in  the  elliptic  portion  of  the  co-ordinates.  Then  be 
would  have  committed  the  very  error  Mr.  Neison  lays  to  his 
charge.  But  since  he  uses  equations  suitably  modified  to  the 
new  signification  of  the  quantities  a,  e,  &c,  and,  moreover, 
makis    his   substitutions   in   the  complete  expressions   for  the 


6  Mr.  Uill t  Reply  to  Mr.  Neison's  xlvu.  i, 

Moon's  co-ordinates,  and  not  in  the  elliptic  portion  only,  as  the 
earlier  investigators  do,  is  it  not  plain  that,  by  these  two  modi- 
fications, he  obtains  terms  which  he  would  not  have  obtained  in 
the  former  supposed  case  ?  Now  these  terms,  in  sum,  are  pre- 
cisely equivalent  to  those  Mr.  Neison  accuses  him  of  neglecting 
by  omitting  to  include  B'"  in  his  disturbing  function.  Thus  it 
is  seen  that  Delaunay  takes  account  of  B'"  in  an  indirect  manner, 
the  peculiar  nature  of  his  method  absolving  him  from  considering 
the  terms  arising  from  B'"  as  a  separate  class. 

Perhaps  the  matter  will  be  clearer  still  if  we  say  that,  just 
as  in  determining  the  solar  perturbations  we  have  no  class  of 
terms  of  the  order  of  the  product  of  the  mass  of  the  Earth  by 
the  mass  of  the  Sun,  simply  because  the  Earth's  action  is  con- 
sidered as  the  principal  force,  so  when  we  come  to  treat  the 
planetary  perturbations  by  Delau nay's  method,  there  is  no 
special  class  of  terms  of  the  order  of  the  product  of  the  Sun's 
mass  by  the  planet's  mass,  for  the  reason  that  here  the  combined 
actions  of  the  Earth  and  Sun  are  regarded  as  forming  the  prin- 
cipal force. 

Next  we  must  not  pass  over  without  notice  the  quite 
erroneous  method  Mr.  Neison  proposes  (pp.  430, 431)  for  getting 
the  proper  expressions  for  the  Poissonian  quantities  [a,  6]  ; 
viz.,  by  substituting  for  the  elements  in  the  expressions  proper 
to  the  older  form  of  the  differential  equations  their  complete 
values  as  functions  of  the  time,  and  then  neglecting  all  the 
periodic  terms.  It  is  very  certain  this  procedure  will  not  give 
the  same  values  as  Delaunay  has,  who  obtains  them  by  taking 
the  partial  derivatives  of  a,  e,  and  y  with  respect  to  the  elements 
Lj  0,  and  H,  which  are  the  conjugates  of  Z,  g>  and  //. 

Mr.  Neison  is  not  content  with  what  he  has  already  said  to 
establish  the  serious  imperfection  of  Delaunay's  method,  but 
fortifies  himself  in  the  belief  of  it  by  a  new  line  of  argument 
(pp.  432-437),  where  he  gives  his  conception  of  the  essential 
nature  of  Delaunay's  transformations.  But  his  argument  is 
fatally  vitiated  because  he  will  have  it  that  the  transformations 
in  question  are  rigorously  linear  in  their  operation.  Thus,  to 
illustrate,  suppose  Delaunay  has 

Operation  I. 
Replace  a0  by  ax  +/,(cr„  f>  &c.) 

Operation  2. 
Replace  <r,  by  a.,  +/2(fl2,  c.,}  &c.) 

(I  use  the  subscripts,  which  Delaunay  has  not,  that  my  meaning 
may  be  clear.)  According  to  Mr.  Neison's  way  of  looking  at 
things,  these  two  operations  are  equivalent  to 

Replace  aQ  l>y  a2  +/,(a2,  e9  &c.)  +/2(«2,  e2f  &c.) 


Nov.  1886.  Strictures  on  Delaunay*  8  Method.  7 

Thus  be  fails  to  see  that  Delaunay  intends  the  al7  tinder  the 
functional  sign  /„  to  be  eliminated  by  the  substitution  of 
Operation  2,  as  well  as  the  ax  which  is  outside  of  it.  In  conse- 
quence he  misses  all  the  terms  which  are  of  the  order  of  the 
product  of  fx  by/2. 

Now,  suppose  that/j  belongs  to  an  operation  which  is  con- 
cerned with  solar  perturbations,  and  f2  to  one  concerned  with 
planetary  perturbations.  Then  Mr.  Neison,  by  his  erroneous 
interpretation  of  Delaunay 's  processes,  fails  to  get  some  terms 
of  the  order  of  the  product  of  the  masses  of  the  Sun  and 
planet,  which,  nevertheless,  Delaunay  has.  Now,  these  are  the 
very  terms  Delaunay  is  accused  of  neglecting.  And,  what  is 
sufficiently  singular,  Mr.  Neison  appears  to  regard  the  symbols 
0,  e,  &c.j  which  are  nnder  the  functional  signs  /,,  /2,  &c,  as 
having  everywhere  throughout  the  whole  series  of  operations  the 
same  signification,  and  as  being  absolute  constants  ;  so  that,  for 
him,  all  the  fs  are  explicit  functions  of  the  time. 

There  is  another  way  in  which  Mr.  Neison' s  error  may  be 
illustrated.  Suppose  we  write  one  of  the  differential  equations 
of  the  Moon's  motion  in  rectangular  co-ordinates,  thus 

*   rfaS-^'+^f'  \r>jf\  .  .  .  +  <£»* +*«**■+&*, 

at*       dx      dx  dx  ax  ax  ax 

where  So  denotes  the  potential  of  the  force  exerted  by  a  centro- 
baric  Earth  ;  and  the  portion  of  the  disturbing  function  due  to 
solar  action  has  been  broken  into  a  nnmber  of  parts  B/0),  efR{l\ 
e?*R{t\  <fcc.,  severally  proportional  to  the  various  powers  of  the 
solar  eccentricity  e' ;  and  /3R0  is  the  portion  due  to  the  figure  of 
the  Earth,  /3  being  a  constant  which  measures  the  deviation  of 
the  Earth  from  a  centrobaric  body  ;  in  fine,  ?/i"R1,  is  the  portion 
due  to  the  action  of  a  planet  whose  mass  is  m".  Then 
Delaunay's  way  of  proceeding  is  very  similar  to  this :  he  first 
ascertains  what  would  be  the  expressions  for  the  Moon's  co- 
ordinates were  R,0)  the  complete  distui'bing  function,  by  making 
variable  the  a,  e,  y,  Z,  g,  and  h  which  appear  in  the  elliptic 
formuke ;  he  then  transposes  R(0)  over  to  the  left  member  of  the 
equation,  and  the  potential  of  the  principal  force  is  now  no 
longer  Q0  but  Q0  +  R(0) ;  he  then  proceeds  to  treat  e'R(n  as  if  it 
alone  constituted  the  whole  of  the  disturbing  function,  using  the 
elements  a,  e,  y,  Z,  g,  and  h,  which  stand  in  his  last  expressions 
for  the  co-ordinates  as  variables,  not  those  which  belong  to  the 
elliptic  expressions.  When  this  is  done,  e'R;,)  is  transferred  to 
the  left  member,  and  the  potential  of  the  principal  force  is  now 
80  +  R(0)  +  6/R(l),  and  the  work  is  continued  as  before. 

Now,  Mr.  Neison  admits  the  legitimacy  of  all  this  as  long  as 
we  are  dealing  with  the  portions  of  the  disturbing  function 
which  arise  from  solar  action ;  but  says  that,  the  moment  wo 
arrive  at  the  term  m"R,,  all  changes.  Then  certain  ghosts,  as 
it  were,  of  the  portions  R(0),  e'R01,  &c,  unbidden  return  to  the 


8  Mr.  Bryant,  On  XLYir.  i, 

right  member  and  trouble  tbe  portion  m^R^  Thus  we  have 
the  strange  spectacle  of  forces  figuring  at  once  as  principal  and 
as  disturbing.  Mr.  Stock  well  made  a  precisely  similar  objection 
to  my  elaboration  of  tbe  inequalities  dne  to  the  figure  of  the 
Earth,  which  was  disposed  of  by  Prof.  Adams  in  a  single 
sentence. 

If  all  this  be  true,  what  becomes  of  the  assertion,  often 
reiterated,  that,  when  the  differential  equations  are  written 
down,  all  the  rest  is  a  pure  question  of  analysis  ?  On  Mr. 
Neison's  and  Mr.  Stock  well's  view,  the  analyst,  who  does  the 
integrating,  needs  an  astronomical  or  mechanical  prompter  at  his 
elbow  to  inform  him  of  the  exact  physical  import  of  tke 
constants  /3  or  m",  otherwise  he  will  infallibly  go  wrong. 

Washington, 

1886,  Oct.  14. 


On  Kepler's  Problem.     By  Robert  Bryant,  B.A.,  B.Sc. 

The  solutions  of  this  problem  are  usually  given  with  a  view  of 
obtaining  the  eccentric  anomaly  directly  from  a  series  expanded 
in  powers  of  the  eccentricity,  the  application  of  which  is  in 
general  very  laborious. 

The  use  of  the  differential  formula 


dM    1—  e  cosh' 

when  an  approximate  value  of  E  in  a  planetary  orbit  is  known, 
involves  less  labour,  while  the  results  converge  with  great 
rapidity. 

The  two  following  series  are  given  as  readily  offering  the 
required  approximate  value  of  E  in  a  planetary  orbit,  when  one 
application  of  the  differential  formula  usually  gives  the  eccentric 
anomaly  with  sufficient  accuracy.  The  series  are  so  simple  and 
so  readily  present  themselves  that  they  have  probably  been  given 
before,  but  I  have  not  met  with  them. 

We  have  M=E  —  e  sin  E  with  M  and  e,  given  to  find  E. 

Lagrange's  theorem  may  be  concisely  expressed  thus : 


ll=0 


the  interpretation  of  which  when  w  =  o  is  obvious. 
If  we  expand  sin  E  and  cos  E,  we  obtain 


t'    ■     >r/_       -    •    -n#v    .  e3 


sin  E  =  sin  M  +  e  sin  M  cos  M  +     sin  M(2  —  3  sincM)  +     sin  M  cosM(3  -  8  sin*M) 

+      sin  M  (24  — 136  sin  31  + 125  sin4  M)  +   .... 
24 

cos E« cos  M  —  esin*M  —  3  -  sin'McosM—    fc  sin- M  ("1  —  4  sin2  M) 

2  3 

-f  5r*sin'-,MccsM(i2-4sin'M)+    .... 

9A 


Nov.  1886.  Kepler'*  Problem.  9 

These  series  are  generally  unsuifced  for  the  evaluation  of  E ; 
bat  if  we  multiply  them  by  sin  M  and  cos  M  respectively,  we 
get  on  addition 

cos(E-M)  =  l-r%in-M-r»sin2McosM-c4  sin* M (36 -49 sin* M) 

2  24 

or 

sin2 1  (E  -M)« -^1M  (*  +2«cos  M)+  e*  sin'M  (36-49  sin2M)      (A) 

4  24 

m  r*  si  n2  M  ( t  +  2  f  cog  M j  +  *«  fc.n  M  gin  3  M  near]y  (Bj 

If,  as  Mr.  Glaisher  lias  suggested  to  me,  we  extract  the 
square  root  of  each  side  of  (A),  we  get 

sinA(E  — M)  =  Aetin3I  -  1  +<?co*M+   -  (30  — 43  sin- M)  J  nearly 

-  4  <rsin  M  { 1  +  c  cos  M  +  5 f  ^-^  }  nearly  (C) 

In  (B)  and  (C)  the  term  involving  sin  3  M  may  be  neglected 
in  obtaining  an  approximate  value  of  E. 

Again,  in  the  above  expression  for  Lagrange's  theorem,  if  for 
a  particular  value  of  n  we  can  make  the  quantity  within  the 
brackets  constant,  the  corresponding  term  in/  (y)  will  vanish. 

Aa  the  form  of  the  function  /  is  completely  at  our  disposal, 
avc  may  for  a  particular  value  of  n  put 

9 1- ;"/'(-)  =  const. 
or 

In  the  present  case  $  (M)  =  sin  M. 
If  n  =  i,  we  derive  but  little  assistance. 
If  «  =  2,  we  gct/(M)  =  cotM  (omitting  a  constant  multi- 
plier), and  e2  will  not  appear  in  our  result. 

/(  oosM       ,  nM 

2smiM  2 

which  is  too  complicated  to  assist  us. 

For  values  of  n  greater  than  3  /  (M)  is  equally  unsuitable. 
Expanding,  then,  cot  E,  we  get 

cot  E  ^  cot  M  —         r  +  r„  sin  M  +  '  sin-  M 
bin  al     6  3 

(& 
—      sin  M  (27  sin2  M— 20)  .... 
40 

■-  «.     +      sin  M  nearly  (D) 


io  Mr.  Bryant,  On  Kepler's  Problem*  xlvii.  I, 

The  introduction  of  the  term  in  e3  is  easily  effected,  and 
when  M  falls  near  ±  900,  it  is  better  to  consider  it,  in  which 
case  it  is  evident  that  the  terms  involving  e4  and  e5  are  very 
small. 

In  the  first  formula  the  sign  of  E— M  is  the  same  as  that  of 
sin  M. 

In  the  second  formula,  E  >  or  <  1800,  according  as 
M  >  or  <  1800.  This  fact  and  the  sign  of  cot  E  are  sufficient 
to  determine  the  quadrant  in  which  E  is  to  be  taken. 

The  following  example  will  sufficiently  illustrate  the  deduc- 
tion of  E  by  the  methods  above  mentioned : 

Suppose  M  =  25o°  for  the  planet  Eurynome  (79),  for  which 
c=  [9-29078]. 


Formula  C 

Formula  D 

4 

96990 

e 

92908 

sin  M 

-  9'973o 

Addition  log 

0*1962* 

e 

92908 

cos  M 

~9'534i 

cos  M 

-9*5341 

02433 

e  cos  M 

-88249 

cos  M— e 

-97303 

1-1751 

sinM 

-  99730 

1 

00300* 

cotE 

97573 

I  +  c  cos  M 

£  c  sin  M 

-89628 

E 

2400  14' 

sin$(E-M) 

-89328 

J(E-M) 

-4°  55' 

E-M 

-9    5° 

E 

240  10 

Having  obtained  an  approximate  value  of  E,  we  shall  bo 
greatly  assisted  in  obtaining  its  true  value  by  considerations 
such  as  the  following. 

In  the  first  series  the  principal  term  neglected  depends  on 

sin  M      .  **  — -  ,  or  sin  3  M,  which  in  this  case  is  positive.   Hence 
sin  M 

the  deduced  value  of  E  is  too  small. 

In  the  second  series  .the  principal  term  neglected  depends  on 
sin  M,  which  in  this  case  is  negative.  Hence  the  deduced  value 
of  cot  E  is  too  great,  and  since  E  lies  in  the  third  quadrant,  it 
follows  that  E  is  too  small. 

If  we  then  increase  E  by  a  few  minutes  of  arc,  we  can  work 
the  results  side  by  side  with  but  little  extra  labour,  the  requisite 
logarithms  being  taken  out  at  the  same  entry. 

The  correct  value  of  K  being  unknown,  the  values  adopted 
were  2400  14/  and  2400  20'.  With  these  the  calculation  is  as 
follows : — 

*  From  Zcch's  Tafeln  dcr  Additions'  und  Sttbtractionslogarithmen. 


Nov.  1886.  Mr.  Knott,  Note  on  y  Equulei.  11 

e        9-29078  9-29078 

sinE     -9*93855  -993898 

Radius  in  minutes        3*53627  3*53627 

tf  sin  E  —  276560  —  276603 

Natural  number  —  582'9i  «  -90  42'*9i  —  583'*49  =  —9°  43'*49 

E  2400  14'  2400  207 

Deduced  value  of  M  249    56-91  250     3*49 

<ZM  +309  -3-49 

We  have  thus,  it  will  be  seen,  overstepped  the  trne  value  of 
E  in  our  estimate. 
We  have  also 

I  —  e  cos  E  0*04430  00441 6 

dll  +048996  —054283 

dE  +2^790  -3'- 153 

E  2400  16*790  2400  i6'*847 

The  mean  of  these  differs  from  the  trne  value  of  E  by  only 
o//-3i.     Using  seven  figure  logs  we  find  E  =  2400  16'  49"*4i. 


Note  on  the  Star  y  Equulei.    By  George  Knott,  B.A.,  LL.B. 

In  the  spring  of  last  year  Mr.  Hind  pointed  out  to  me  that, 
in  view  of  the  Proper  Motion  of  the  star  y  Equulei,  there  was 
ground  for  the  inference  that  a  small  11  mag.  companion, 
detected  by  me  in  July  1867,  was  in  physical  connection  with 
it.  I  have  been  hoping  accordingly  to  obtain  further  measures 
of  the  pair,  but  have  failed  doing  so  until  the  present  month. 

I  give  below  the  results  of  the  measures  hitherto  obtained  by 
myself,  together  with  a  set  by  Mr.  Burnham  at  an  intermediate 
epoch  : 


// 


1867-52 

p«=  27683 

B  =  2i73 

Knott. 

186757 

27685 

^•089 



1871-61 

277-62 

1875 



187772 

2745 

2-1 

Burnham. 

188683 

27376 

2058 

Knott. 

188684 

272-70 

The  measures  of  1871*61  were  taken  under  unfavourable  cir- 
cumstances, as  appears  from  the  note  : — "  B  only  to  be  seen  on 
the  most  careful  scrutiny ;  obs.  most  difficult."  At  my  last 
epoch  clouds  came  over  before  any  measures  of  distance  could  be 
obtained.  Mr.  Burnham  adds  another  small  star,  12  mag., 
which  I  have  not  yet  seen.  His  co-ordinates  for  it  are : 
P=  io°-o,  D  =  4i//*3,  Ep.  187772.  It  seems  desirable  that  this 
star  should  be  re-measured. 


:I2  •  Mr.  Gore,  On  the  Orbit  xlvii.  i, 

If  now  we  take*  the  Proper  Motion  values  assigned  by 
Prof.  Anwers,  viz.: — in  R.A.  +  os,oo22  and  in  Decl.— o"*i67, 
and  starting  from  the  epoch  1867*54  compute  the  present  values 
of  P.  and  D.  on  the  assumption  that  the  companion  does  not 
share  in  the  motion  of  the  principal  star,  we  get  P  =  32i0#72, 
D  =  4//,428.  A  comparison  of  these  numbers  with  my  latest 
measures  points  distinctly  to  the  conclusion  that  a  physical 
connection  subsists  between  the  objects.  The  series  of  measures 
as  a  whole  appears  further  to  indicate  a  slight  but  decided 
decrease  in  the  angle  of  position  of  the  companion  in  nineteen 
years,  while  no  change  would  seem  to  have  taken  place  in  the 
distance. 

Knowks  Lodge,  Ci'ckficld:  1886,  November  10. 


On  the  Orbit  o/S  1757.     By  J.  E.  Gore. 

I  have  computed  the  orbit  of  this  binary  star,  by  means  of 
the  graphical  method,  and  find  the  following  provisional 
elements : 

Elements  of  2  1757. 

P  =*  340'38  years.  £  «  89°  45'. 

T  =  1 77881.  \  «  203°i4'. 

e  «  02425.  a  s=  2"*25. 

7  =  45°  51'. 


n  « 

+  i°o53 

r. 

[nparison  between  the  recorded  observa- 
:omputed  from  the  above  elements  : 

0 
100 

9e 

1075 

90—9g 
-075 

Po 

// 

I  60 

PC 

1-38 

Po-PC 

// 
+  0'2 

195 

18-55 

+  095 

144 

i'45 

—  o*o 

24*  X 

230 

+  I'IO 

i'5 

149 

+  o-oi 

239 

246 

-070 

154 

1*50 

+  004 

25-5 

276 

—  2IO 

r66 

i*53 

+  013 

294 

29*1 

+  030 

1  64 

i'54 

+  010 

310 

321 

—  no 

«7 

1  60 

+  010 

360 

361 

—  010 

174 

163 

+  0"II 

37*4 

37*4 

O'OO 

1  67 

166 

-rOOl 

37  9 

375 

+  040 

17 

r66 

+  0-04 

388 

3875 

+  005 

— 

1  69 

■ — 

409 

388 

+  2TO 

— 

169 

— 

437 

40*2 

+  3-50 

189 

171 

+  018 

408 

417 

—090 

202 

174 

-1  028 

Epoch.  Observer. 

1825-37  Struve 
182982 

1832-39  Smyth 

183338  Struve 

I835-37 

1836-42  .     „ 

183848  Smyth 

1841-38  Miidler 

1842*39  Dawes 

184252  Smyth 

1843-45  Dawes 

184351  Kaiser 

184472  0.  Struve 

184588  Mailer 

*  I  am  indebted  for  these  numbers  to  Mr.  Hind. 


NOV.  l886.                                         0/2  1757.  JJ; 

Epoch.     Obscrrer.                            $Q            *c          0o-0c  pQ  p,,  p„— -p*3 

185038    O.  Struve                 48%  468       +200  185  1*82  +0-03 

18523S    Smyth                     517  489       +  280  2-0  r88  +0*12 

1853*09    Midler                     522  496       +  2-6o  2-05  189  +0*16 

'85373    Jacob  48-0  5025     —225  214  1*89  +0*25 

'854*37    Madler                     501  5085     -075  2*  16  1-90  +0*26 

185531        „                           513  518       -0-5  17  193  -023 

185632        „                          518  5275     -095  15  195  -045 

1856-42    Morton                     51-9  5285     -095  201  195  +0*06 

1S5688    Secchi  529  5335  -0*45  184  1*95  — o-ii 

lS57'29    Morton  54*2  537       +05  200  197  +0*03 

185S08    Jacob  528  5445  -165  176  1-98  — 0-22 

1858*37     Madler                     547  54*6       +01  1*91  198  —0-07 

1859*36        ,.                         53  7  555      -i'8  «'8*  202  -0-20 

186034  Dawes                      54-3  564       -21  2-31  203  +0*28 

186035  „  534  56-4  -300  208  203  +0-05 

186332    Dembowski              590  5896     +004  2*01  209  -o*c8 

1865-97            „  60-4  6ro       -o-6  209  2-13  -004 

186601     O.  Struve  6o*8  6103  -0-23  2-34  214  +020 

1867-27    Talmage  63-7  621       +1*6  260  2-16  +044 

1868-30    Dembowtfki  627  62*8  —01  2*04  218  —014 

186922    Briinnow  63*4  6353  —0*13  2*59  220  +039 

186924    Talmage  643  63-53  +  077  —  2-20  — 

1870*15     Dembowski  63-5  642  —07  2-03  222  —019 

1870-37     Talmage  64-1  643  -0-2  200  222  -0-22 

1871-19    Dembowski  63*4  64-9  —15  213  2*24  -o*u 

187233     Wilson  &Stabroke  648  657  -09  230  2*25  +005 

1872-37     Talmage  673  65-73  +1*57  —  225  — 

187323     Wilson  &  Seabroke  640  66*45  —  2*45  2*°5  227  -0*22 

l873'35         »             »  65°  66*53  -153  200  227  -027 

187432          „            .,,  655  67-25  -175  2*15  228  -013 

187432    Talmage  69*8  6725  +255    (ro8)?  228  (-1-20)? 

1874*41     Wilson  &  Seabroke  64*2  67-31  -3*11  2- 16  228  —0-12 

1 8753 1     Schiaparclli  66*6  67*8  — 1*2  200  229  —0*29 

1876-36    Wilson  &  Seabroke  67*2  68*45  —  *'25  2'1S  2  3°  -0-15 

1876-41          „             „  665  68-48  —198  221  230  -0-09 

187940    Hall  689  70*5  —  i*6o  2-33  235  -0*02 

1879470  Schiaparelli  67-98  705  -2*52  2-462  2*35  +0*112 

1882467          „  6938  7243  -305  2'3'4  2'42  -0106 

1883-21    Engelmann  7044  728  -236  2623  2-43  +0193 


X4  Mr*  Sherman,  On  Bright  xlvii.  i, 

The  formulas  for  calculation  of  an  ephemeris  are  as  follows  : 

(i)    u- 13-89  sin  «=  +i°o57  (^-177881), 

(2)  tan  £V=  1-28  tan  £«, 

(3)  tan  (0C- 890  45') - 06965  tan  (V  +  2030  14'). 

(4)  p=2"-25  (1-0-2425  cos  10  — -(V+2°31-I4'2; 

w    V  *K  *  3  'cost*c-  89°45') 

where  u  is  the  eccentric  anomaly,  and  V  the  true  anomaly  for 
the  epoch  t>  0C  the  required  position  angle,  and  p  the  distance. 
The  position  of  the  star  is  for  18860 

R.A.  i3h  28m  29s 
+  o°  16'  6". 

It  is  Lalande  25087,  and  lies  closely  np  £  Virginis.  .  It  was 
estimated  7m  by  Lalande,  and  7*0  at  Cordoba.  According  to 
Strove  the  magnitudes  of  the  components  are  7*8  and  8*9. 

The  orbit  has  been  previously  computed  by  Casey,  who  finds 
a  period  of  401*0  years,  with  T  =  1797-42,  and  e  =  0*5079. 

BaUysodare,  Co.  Stigo  : 

1 886,  Oct.  14. 


Beply  to  certain  Questions  raised  before  the  Royal  Astronomical 
Society  at  the  Meeting  on  1886,  March  12,  concerning  the  matter 
detailed  in  a  Taper  entitled  "  Bright  Lines  in  Stellar  Spectra" 

,     By  0.  T.  Sherman. 

(Communicated  by  the  Secretaries.) 

The  object  of  the  method  employed  is  to  render  the  image  of 
the  bright  line  light  as  broad  and  intense  as  may  be,  and  the 
intensity  of  the  background  light  a  minimum.  A  successful 
application  is  presented  in  the  spectrum  of  Nova  Andromeda?, 
which  is  shown  in  an  adjoining  cut.*     Along  a  faint  bluish  line 


J£50(K),I*74{K) 
Portion  of  the  Spectrum  of  Nora  Andromedse. 

there  were   seen  bright  stellar  images  surrounded  by  a  haze. 
These  were  termed  bright  lines. 

In  practice  the  background  light  is  often  sufficiently  intense 

*  The  haze  surrounding  the  stellar  image  is  somewhat  exaggerated  in  the 
drawing. 


Nov.  1886.  Lines  in  Stellar  Spectra.  15 

to  cut  down  the  haze  surrounding  the  point,  so  that  the  image 
appears  as  a  bright  knot,  fuzzy  or  sharply  bounded,  beading  or 
embedded  in  the  bright  linear  spectrum.  Such  is  the  case  with 
ft  Lyrce  or  y  Cassiopeice,  as  seen  with  the  means  at  command. 

One  has  to  distinguish  between  bright  line,  bright  back- 
ground space,  and  mere  disturbance  in  the  light  of  the  spectrum. 
The  principle  upon  which  the  discrimination  is  made  is  that  the 
bright  background  space  being  the  effect  of  contrast  remains 
constant  in  both  place  and  intensity.  The  disturbance  in  the 
light  of  the  star  is  constant  in  neither  intensity  nor  position. 
The  bright  line  is  constant  in  place  but  not  in  intensity. 
For  each  star,  therefore,  an  extended  series  of  observations  is 
necessary. 

The  first  remarks  made  concern  (a)  the  adjustment  of  the 
instrument ;  (b)  the  action  of  the  lines  ;  (c)  the  position  of  the 
cylindrical  lens. 

(a)  "  First, '  previous  to  each  night's  work,  the  instrument 
was  adjusted  upon  the  Sun ;  a  solar  spot  when  possible  being 
brought  sharply  in  focus  on  the  jaws  of  the  slit.'  This  would 
seem  a  proper  and  necessary  adjustment,  and  would  suffice  for 
the  centre  of  the  spectrum  ;  but  for  the  extreme  rays,  especially 
the  blue  and  violet,  the  spectroscope  would  not  be  in  the  proper 
focus  of  the  equatorial.  There  is  a  paragraph  in  Mr.  Sherman's 
Paper  which  at  least  suggests  that  the  extreme  ends  of  the 
spectrum  suffered  in  this  way.  ..."  The  adjustments  of  the 
spectroscope  were  such  as  to  give  good  definition  for  the  solar 
spectrum.  It  was  presumed  they  wonld  also  for  the  stellar. 
The  adjustments  have  been  regarded.  Also  two-thirds  of  the 
lines  announced  for  y  CassiopeicB  lie  between  D3  and  H  y(1),*  a 
space  not  encroaching  very  far  on  the  extreme  ends  of  the 
spectrum.     It  is  thought  the  remark  will  hold  generally  true. 

(b)  "  There  is  a  paragraph  in  Mr.  Sherman's  Paper  which 
at  least  suggests  that  the  extreme  ends  of  the  spectrum  suffered 
in  this  way :  '  At  the  red  end,  under  a  sharp  focus,  they '  (the 
bright  lines)  '  stand  out  the  full  breadth  of  the  spectrum,  bearing 
somewhat  the  same  relation  to  the  background  as  the  prominences 
to  the  solar  spectrum.  In  the  brighter  portion  of  the  spectrum 
they* are  cut  down  to  bright  star  points.  At  the  blue  end  they 
become  more  distinct,  bub  not  so  sharp  as  at  the  red.  At  times 
they  shine  with  almost  a  metallic  brilliancy  ;  at  other  times  they 
are  faint,  faded,  and  easily  passed  over.  Certain  sets  appear  to 
be  prominent  at  times ;  others  at  other  times.'  It  seems  very 
difficult  to  believe  that  this  can  be  a  description  of  true  stellar 
bright  lines,  while  it  is  quite  conceivable  that  lines  due  to  some 
instrumental  effect  might  present  just  such  an  appearance  in  a 
spectroscope,  adjusted  as  Mr.  Sherman's  seems  to  have  been,  only 
for  the  centre  of  the  spectrum.  ..." 

There  are  at  least  two  other  observers  who  agree  as  to  the 

*  American  Journal  of  Science,  Dec.  188^ 


1 6  Mr.  Sherman,  On  Bright  xlvii.  i, 

action  of  the  bright  line.  A  note  taken  from  the  Astronomisclie 
Nachrichten,  Nos.  2651-2652,  is  copied  from  the  Observatory  of 
April,  1885. 

"  Variations  in  the  Spectrum  of  /?  Isyrce.— In  the  summer  and 
antnmn  of  1883,  Dr.  N.  de  Konkoly  and  Herr  E.  von  Gothard 
detected  a  certain  amount  of  variability  in  the  C,  D3  and  F  lines 
in  the  spectra  of  y  Cassiopeia  and  /3  Lyrce,  in  which  they  are  fre- 
quently seen  to  shine  as  bright  lines.  Daring  1884,  Herr  von 
Gothard  has  followed  np  his  investigations  and  observed  the 
spectrum  of  /3  Lyrce  on  thirty  nights.  On  nine  of  these  occasions 
the  D3  line  was  seen  to  be  more  or  less  bright.  On  July  13  it 
was  even  described  as  *  almost  dazzling  * ;  on  several  other  nights 
its  presence  was  only  suspected ;  on  ten  nights  no  trace  of  it  was 
seen,  so  that  it  presented  on  different  occasions  every  possible 
degree  of  change  of  brightness  from  great  brilliancy  down  to  total 
disappearance.  The  C  line  was  also  seen  to  be  reversed  on  many 
occasions,  and  was  frequently  very  brilliant,  bnt  on  others  it  was 
only  faint,  was  difficult  to  see,  or  was  evidently  a  dark  line.  The 
F  line  was  not  so  often  noticed  to  appear  bright ;  its  reversal 
would  naturally  be  less  easily  observed  than  that  of  C  or  Ds.  Herr 
von  Gothard  was  not  able  to  satisfactorily  determine  the  length 
of  the  period  of  variability ;  it  was  evidently  very  short,  and  a 
period  of  about  seven  days  seemed  to  suit  the  observations  fairly 
well.  It  should  be  added  that  the  three  lines  appear  to  vary  in 
perfect  accord  with  each  other  „  .  .  ." 

Again,  "  both  show  bright  lines  of  hydrogen  and  helium,  so 
that  the  peculiarity  of  their  condition  probably  consists  in  the 
unusual  extent  and  intense  ignition  of  their  chromospheric  sur- 
roundings. But  this  condition  is  subject  to  fluctuations.  The 
brilliant  rays  indicative  of  it  died  out  during  nine  years,  1874- 
1883...."* 

Again,  the  bright  lines  of  the  solar  chromosphere  show  a 
similar  variation  in  both  visibility  and  frequency,  as  is  shown  in 
the  frequency  and  maximum  brilliancy  numbers  in  Young's 
"  Catalogue  of  Bright  Lines  in  the  Spectrum  of  the  Solar 
Atmosphere."  t 

Again,  one  might  appeal  to  our  knowledge  derived  from 
"  new  "  or  "  temporary  "  stare — for  example,  the  changes  in  the 
spectrum  of  T  Coronce.% 

Again,  a  similar  action  is  not  entirely  unknown  even  in 
laboratory  work.  For  the  sake  of  an  example  we  quote,  §  "  When 
the  carbonic  acid  is  displaced  by  hydrogen,  the  hydrogen  lines 
appear,  the  hydro-carbon  flame  and  the  triple  sets  remaining 
bright,  but  in  this  gas  the  flame  group  at  4310  is  particularly 
well  marked,  and  the  carbon  line  at  4266  keeps  flashing  in  occa- 

*  History  of  Astronomy  during  the  Nineteenth  Century,  Clerke,  p.  420. 
f  American  Journal  of  Science,  Nov.  1872. 

t  History  of  Astronomy  during  the  Nineteenth  Century,  Clerke,  p.  422. 
$  On  the  Origin  of  the  Hydro-Carbon  Flame  Spectrum,  Profs.  G.  I).  Live- 
ing  and  J.  Dewar,  IVoc.  Roy.  Soc.  Vol.  34,  1 882-1883,  p.  429. 


Nov.  1886.  Lines  in  Stellar  Spectra.  17 

sionalhj."  Or,  in  general,  examples  might  be  drawn  from  the 
whole  range  of  phenomena  showing  change  in  spectra  depending 
upon  temperature  or  upon  mechanical  mixture  with  some  other 
gas* 

(c)  "  Particularly  as  he  placed  his  cylindrical  lens  not  before 
the  slit,  nor  even  in  the  viewing  telescope,  but  between  the  eye- 
piece and  his  eye." 

The  cylindrical  lens  need  have  and- properly  has  no  place  in 
the  arrangement.  Used  at  the  commencement  of  the  work,  it 
has  long  since  been  abandoned.  As  bearing  on  the  point,  how- 
ever, the  following  quotation  which  has  come  to  my  knowledge 
within  a  day  or  two  is  no+  withont  interest.  It  comes  from  ono 
who,  having  searched  in  the  same  field  without  being  satisfied, 
makes  suggestions  for  those  that  follow,  "and  to  ask  others 
with  greater  optical  power  to  search  for  the  lines,  taking  the 
precaution  to  use  the  cylitidrical  lens  close  to  the  eye,  and  not  to 
apply  it  to  the  instrument  nntil  the  rays  to  be  examined  uro 
absolutely  in  focus  on  the  slit,  if  a  slit  is  used.  It  is  possible 
scintillation  may  help  matters."  t 

Under  the  second  head  is  treated  (a)  the  width  of  the  Blit ; 
(&)  the  accuracy  of  the  measures  ;  (c)  the  generality  of  the 
appearances ;  (d)  the  fact  that  they  have  not  been  observed 
before. 

Second  (a).  "Mr.  Sherman  used,  an  unusually  wide  slit, 
1 5™*"  or  more.'  1  think  most  stellar  spectroscopics  will  pro- 
nounce this  to  have  been  fully  100  times  too  wide.  5mm"  in 
the  focus  of  the  3-inch  object-glass  would  correspond  to  6'  of 
arc.  It  seems  hard  to  see  what  purpose  a  slit  of  so  great  a 
width  would  serve,  and  in  what  essential  feature  it  differed  from 
no  slit  at  all." 

It  practically  is  no  slit  at  all.  A  glance  at  the  quotation  just 
above  is  not  without  interest.  However  wide  the  metallic  jaws 
may  be,  the  practical  slit  is  the  stellar  diffraction  shield  for  an 
eight-inch  glass,  about  three  seconds  of  aro  in  diameter.  % 

(6)  "  And  it  is  also  difficult  to  place  much  confidence  in 
measures  made  with  so  wide  a  slit,  especially  as  the  collimator 
only  measures  6  inches  in  focal  length,  so  that  no  stress  can  be 
laid  upon  the  correspondence  between  the  bright  lines  observed 
and  those  seen  in  the  solar  chromosphere." 

Since  the  practical  slit  is  three  seconds  in  place  of  six 
minutes,  it  is  hoped  that  this  objection  falls.  The  light  of  the 
shield  fades  off  rapidly  towards  the  edge,  leaving  a  sharp  central 
point  to  be  set  upon,  or  a  fuzzy  disc  to  be  bisected.  The 
measures  seem  therefore,  in  point  of  accuracy,  comparable  with 

*  See  the  work  of  Profs.  Liveing  and  Dewar,  Proc.  Roy.  Soc.  Vols.  27  and  36. 

t  Note  on  Bright  Lines  in  the  Spectra  of  Stars  and  Nebulae.  By  J.  Norman 
Lockyer.    Proc.  Roy.  Soc  Vol.  27,  p.  51. 

X  Hermann  Strove,  M6m.  de  l'Acad.  Imperial e  des  Sciences  de  St.  Peters- 
bonrg,  VII*  Sene,  Tome  XXX.  No.  8.  Airy,  Transactions  of  the  Cambridge 
Philosophical  Society,  Vol.  V.  part  iii. 

C 


i8  Mr.  Sherman,  Bright  Lines  in  Stellar  Spectra,      xlyii.  r, 

there  obtainable  with  a  slit  somewhat  less  in  width  than  the 
stellar  diffraction  image,  and  some  stress  seems  due  to  their 
approximate  agreement  with  the  solar  atmospheric  lines.  A 
greater  conditioning  circumstance  seems  to  be  the  use  of  a  thick 

(e)  "  The  most  suspicions  circumstance  of  all,  however,  is,  I 
think,  that  so  far  Mr.  Sherman  has  never  failed  to  see  bright 
lines  in  any  star  which  he  has  examined I  have  had  occa- 
sion to  notice  on  more  than  one  occasion  that  a  stellar  spectrum 
which  is  fnll  of  dark  lines  or  bands  may,  when  badly  seen,  give 
a  very  perfect  illusion  of  bright  lines ;  the  dark  lines  escaping 
recognition  as  such,  bnt  producing  their  effect  by  making  the 
parts  of  tbe  spectrum  most  free  from  them  shine  ont  by  contrast 
like  a  veritable  chromospheric  spectrum." 

The  method  by  which  it  was  hoped  to  distinguish  between 
bright  background  space  is  already  explained.  It  was  hasty  to 
claim  bright  lines  for  numerous  stars.  The  announcement 
should  have  awaited  the  completion  of  the  series  of  observations. 
Credence  for  the  statement  withont  snch  a  series  cannot  be 
asked,  bat  it  is  asked  that  the  result  of  tbe  series  be  awaited, 

(d)  "  And  that  though  '  sometimes  they  shine  with  almost 
metallic  brilliancy,'  yet  no  previous  observer  has  detected  them," 

The  spectroscopic  arrangement  is  considerably  different  from 
that  usually  employed.  Although  no  assertion  of  the  existence 
of  the  lines  has  reached  me,  there  is  at  least  one  who  has 
suspected  them,  as  the  following  quotation  shows  :*  "  Two  years 
ago  (1876)  I  searched  for  indications  of  a  large  chromosphere  in 
the  easo  of  o  Lyrte  and  some  other  stars.  I  believe  I  had  glimpses  of 
bright  lines  at  F  and  b,  bnt  if  this  discussion  [between  Kuggins 
and  Stone]  had  not  arisen  I  should  have  still  hesitated  to  mention 
this,  as  I  bad  been  hoping  for  an  increase  of  optical  power." 

In  closing  one  may  perhaps  draw  attention  to  this  fact,  that 
the  result  is  not  at  variance  with  our  best  knowledge  of  stellar 
constitution.  Sneaking  of  the  lesson  to  be  learned  from 
1'  (krVKa,  a  recent  writer  says  :  "  No  clear  dividing  line  can  be 
dtHWO  between  stars  and  nebulss,  but  that  in  what  are  called 
planetary  nebnhe  on  the  one  side  and  in  '  gaseous  stars  '  (those 
giving  a  spectrum  of  bright  lines)  on  the  other,  we  meet  with 
transitional  forms  serving  to  bridge  the  gap  "f  between  the  faintly 
locent  nebula  and  the  highly-finished  star,  and  among  the  stars 
themselves  one  may  readily  pursue  every  value  of  tbe  ratio 
ng  the  relation  between  the  light  from  the  stellar  nucleus 
IH  a  the  stellar  atmosphere.  While  the  arrangement  which 
v. : ,  1        ig  oat  the  absorption  lines  will  hide  all  but  the  brightest 

'  ■  gaseous  lines,  the  method  just  described  is,  I  think, 
MnpBg  ont  those  lines  which  belong  to  the  gaseous  envelope. 

Us  on  Bright  Lines  in  (he  Spectra  of  Start  and  Kebulie.   By  J.  Norman 
Lockjtr.    Roe.  B*y.  80c.  Vol.  27,  p.  5a 

1         ijtj  of  Ajrtrononi *  during  the  Ximteeulh  Centuiy,  Clerke,  pp.  422-423. 


Nov.  1886.        Eev.  A.  Cortie,  Spectra  of  Sun-spots.  19 


Bands  observed  in  Hie  Spectra  of  Sun-spots  at  Stonyhurst 
Observatory.    By  the  Rev.  A.  Cortie,  S.J. 

(Communicated  by  the  Rev.  8.  J.  Perry.) 

There  are  three  kinds  of  bands  which  have  been  observed 
in  the  spectra  of  Sun-spots.  The  first,  which  is  a  certain  fuzzy 
appearance  surrounding  the  widened  portions  of  the  dark  lines, 
has  been  very  frequently  seen,  and  is  only  a  particular  phase  of 
the  widening  of  the  line.  The  second  is  an  intensifying  of  the 
general  absorption  due  to  a  Sun- spot  in  particular  parts  of  the 
spectrum.  The  third  is  the  appearance  of  real  bands  in  the 
selective  absorption  due  to  a  spot.  The  present  paper  contains 
some  observations  of  each  of  these  kinds  of  bands. 

With  regard  to  the  hazy  appearance  or  fuzziness  surround- 
ing a  widened  line,  it  is  usually  and  most  easily  observed  on  tho 
D  lines,  although  not  peculiar  to  them.  In  a  spot  in  the  S.  F. 
quadrant  of  the  Sun  observed  on  November  15,  1883,  the  widen- 
ing of  all  the  lines,  instead  of  a  dark  and  distinct  thickening  of 
the  same,  presented  the  appearance  of  a  penumbral  shade  at 
either  side  of  the  dark  central  line.  But  this  haziness  has  been 
most  markedly  attached  to  the  D  lines  on  several  occasions. 
Thus  on  September  29,  1884,  and  on  January  14,  1886,  these 
two  lines  were  not  only  widened  and  fuzzy,  but  were  also 
reversed  in  one  portion  of  their  length.  Sometimes  the  haze 
exists  surrounding  the  lines,  while  the  lines  themselves  are  not 
widened,  as  on  October  2  and  3  of  the  present  year  in,  a  small 
spot.  In  the  part  of  the  spectrum  between  D  and  C,  Angstrom 
gives  a  line  as  due  to  No-  at  6160*23  a  little  more  refrangible 
than  a  strong  Qa  line  at  6160*40.  This  Na  line  is  drawn  as 
double  in  the  maps  of  Fievez  and  Piazzi  Smyth,  and  with  good 
definition,  and  using  a  dispersion  of  twelve  prisms,  it  has  been 
usually  so  seen.  This  double  is  always  remarkably  widened  in 
the  spectra  of  spots,  and,  moreover,  the  widening  is  of  the 
nature  of  the  fuzzy  band  seen  at  times  in  connection  with  the 
D  lines.  If  a  moderate  dispersion  of  six  prisms  be  used,  it 
appears  as  if  the  Qa  line  adjoining  this  faint  double  was  con- 
siderably widened  and  displaced  towards  the  violet.  But  on 
using  a  great  dispersion  the  widening  is  seen  to  be  principally 
due  to  these  faint  Na  lines,  although  the  thick  Qa  line  is  usually 
also  affected.  On  June  25,  1885,  and  on  January  14,  1886,  tho 
widened  Qa  line  was  seen  running  through  the  haze  due  to  these 
Na  lines.  In  the  small  spot  of  October  2  of  the  present  year, 
the  band  due  to  these  lines  was  at  least  one-tenth  metre  in 
breadth.  Finally  it  may  be  mentioned  in  connection  with  the 
D  lines,  that  when  the  widening  on  the  two  sides  is  unequal,  the 
balance  is  almost  invariably  in  favour  of  the  violet  or  more  re- 
frangible side  of  the  lines. 

c  2 


20  llev.  A.  Cor  tie,  Bands  observed  xlvii.  i, 

The  second  kind  of  band  is  dae  to  the  intensifying  of  tho 
general  absorption  in  particular  parts  of  the  spectrum  of  Sun- 
spots.  This  phenomenon  has  only  been  observed  on  four  occa- 
sions during  the  conrse  of  as  many  years  of  observation.  On 
May  11,  1884,  the  general  absorption  of  a  large  spot  N  P  had  a 
blurred  appearance  in  the  red  end,  and  besides  was  so  dark 
that  it  almost  masked  the  selective  absorption,  rendering  it  very 
difficult  of  observation.  The  same  appearance  was  seen  on 
May  18  of  tho  same  year  in  a  black  spot  S  P.  Again,  on 
June  25,  1885,  the  lines  about  6172*5  were  masked  by  this 
blurring  effect  ;  and,  finally,  on  February  6,  1886,  the  relative 
darkness  of  the  general  absorption  in  the  red  end  was  much 
more  intense  than  in  the  rest  of  the  spectrum.  This  last 
observation  was  made  between  2  and  3  p.m.  in  a  hazy  sky.  In 
the  Greenwich  observations  of  tho  great  Sun-spot  of  Novem- 
ber 19,  1882,  it  is  noted  that  "  the  general  absorption  was  not 
uniform  ;  hero  and  there  there  were  ill-defined  patchos,  notice- 
ably darker  than  the  rest  of  tho  spectrum."  Again,  although 
Prof.  Young,  using  a  Rowland  grating  attached  to  a  23 -inch 
equatorial,  has  succeeded  in  resolving  even  the  band  of  con- 
tinuous shade,  due  to  a  Sun-spot,  into  a  series  of  fine  dark  lines 
with  bright  spaces  (Amver.  Jour.  Science,  vol.  xxvi.  November 
1883),  yet  he  remarks  that  "in  the  red,  even  with  the  highest 
dispersion,  and  under  the  most  favourable  circumstances  of 
vision,  the  spot- spectrum  appears  simply  as  a  continuous  shade, 
crossed  here  and  there  by  widened  and  darkened  lines.1' 

The  last  of  the  three  kinds,  into  which  we  have  divided 
this  phenomeuon  of  spot-bands,  is  perhaps  the  most  important  of 
all,  because  of  its  connection  with  the  selective  absorption  of 
Sun-spots.  Tho  first  recorded  observations  of  these  bands  are 
those  of  Professor  Young  (Nature,  December  12,  1872).  With 
regard  to  their  interpretation  he  states  that  "  they  would  seem 
to  point  to  such  a  reduction  of  temperature  over  the  spot- 
nucleus  as  permits  the  formation  of  gaseous  compounds  by 
elements  elsewhere  dissociated."  In  the  Greenwich  Spectro- 
scopic and  Photographic  Results  for  the  years  1880-83  many 
observations  of  similar  bands  are  recorded  in  the  portion  of  the 
spectrum  from  D  to  P.  At  Stony  hurst  the  spot-spectrum  is 
observed  from  D  to  B.  The  spectroscope  employed  is  an 
automatic  instrument  by  Browning,  and  the  dispersion  generally 
used  is  one  of  twelve  prisms  of  6o°.  Perhaps  the  region  richest 
in  the  various  phenomena  of  the  spectra  of  Sun-spots  in  this 
part  of  the  spectrum  is  that  included  between  A  6370*0  and 
G.  Nine  of  the  lines  have  coincident  bright  lines  in  the  chromo- 
spheric  spectrum  as  mapped  by  Young,  and  there  are  four  dark 
basic  lines.  It  is  in  this  portion  that  the  spot- bands  have  been 
most  frequently  seen,  and  two  of  them  have  been  selected  for 
particular  attention  and  study.  The  bands  were  first  noticed 
on  February  28,  1885,  especially  a  broad  one  lying  between  the 
lines  A  6438-351  and  644929,  and  they  have  been  seen  on  eight 


Nov.  1886.  in  the  Spectra  of  Sun-spot*.  21 

subsequent  occasions.  The  number  of  bands  so  far  reckoned  is 
nine.  Of  these  the  two  more  particularly  studied  are  situated 
the  one  near  X  63800  and  the  other  at  X  6383,  the  positions 
being  fixed  by  accompanying  lines,  and  being-  most  probably 
correct  to  within  one-tenth  metre.  On  May  26  of  the  present 
year  these  two  bands  were  most  distinct  in  a  spot  of  regular 
outline.  The  first  adjoined  the  line  X  6379*99  on  its  less  re- 
frangible side.  The  second  had  no  line  at  its  edges  but  was 
diffused  in  appearance,  although  its  tint  was  somewhat  intensified 
towards  the  red  end.  The  general  appearance  of  these  bands 
resembled  a  fluted  spectrum,  and  some  very  faint  lines  could  be 
traced  from  them  into  the  ordinary  spectrum.  These  two  bands 
were  again  examined  most  carefully  on  July  2nd  and  4th  of  the 
present  year  in  magnificent  definition.  The  general  absorption 
given  by  the  spot  was  one  with  well-defined  edges.  On  the 
former  of  these  dates  the  spot-band  at  X  6379*99  was  joined  on 
to  the  line  as  observed  on  May  26.  Bat  on  the  4th,  when  the 
general  absorption  was  less  intense,  it  no  longer  adjoined  the 
line,  but  was  clearly  separated  from  it.  Moreover,  its  appear- 
ance had  altered,  for  it  seemed  to  be  formed  by  two  or  three 
lines  very  greatly  widened.  The  companion  band  also  seemed 
to  be  composed  of  three  lines  similarly  affected.  But  these 
bands  or  groups  of  lines  were  due  to  the  spot  alone,  for  no  trace 
of  them  could  be  detected  when  the  spot  was  removed  from  the 
slit,  and  they  stood  out  most  clearly  and  distinctly  in  the  darkest 
part  of  the  umbra.  On  the  7  th,  when  the  spot  had  approached 
the  limb,  none  of  the  bands  were  so  distinct  as  formerly,  although 
the  definition  was  equally  good.  Yet  they  were  visible  in  the 
spot,  and  nowhere  else.  In  the  small  spot  of  October  2nd  and  3rd 
no  bands  at  all  could  be  detected  in  the  region  between  X  6379*99 
and  C.  On  the  3rd,  however,  the  lines  at  6242*6  (A°)  and  6305*0 
(Fievez)  had  a  banded  appearance  on  their  more  refrangible 
side,  possibly  due  to  a  displacement  in  that  direction.  It  may 
be  noted,  however,  that  this  line  6305*0  corresponds  to  a  line  in 
Young's  diagram  (loc.  cit.)  marked  at  K  796*2,  which  is  depicted 
as  enormously  widened. 

Finally,  with  regard  to  the  two  bands  selected  as  typical  of 
this  third  class,  this  must  be  remarked,  that  they  occur  in  a 
portion  of  the  spectrum  in  which  Angstrom  marks  no  line,  and 
in  which  the  very  great  dispersion  employed  by  Fievez  and 
Piazzi  Smyth  gave  in  the  first  case  two,  and  in  the  second  three 
faint  lines,  about  the  position  of  the  second  band.  Coincident 
with  the  first  band  there  is  absolutely  no  dark  line  mapped, 
which  is  true  also  for  the  bands  between  X  6438*35  and 
X  6449*29.  This,  coupled  with  the  fact  that  they  appear  only  in 
Sun-spots,  and  there  are  most  intense  in  the  umbra,  shows  them 
to  belong  exclusively  to  Sun-spot  spectra.  They  are  a  pheno- 
menon altogether  distinct  from  the  ordinary  widened,  or 
darkened,  or  obliterated  line  of  such  spectra.  From  fifteen  to 
twenty  such  bands  are  recorded  in  the  Greenwich  observations, 


22  Mr.  Boberts,  Note  on  Pliotograplis  xlvii.  i, 

nine  have  been  seen  at  Stonyhurst,  and  always  in  the  same 
positions.  Even  should  higher  dispersion  resolve  them  into 
lines,  such  clusters  of  greatly  widened  lines  occurring  at  certain 
definite  positions  in  the  spectra  of  some  San-spots  is  a  remark- 
able phenomenon  well  deserving  the  closest  attention. 


Note  on  Photographs  of  Stars  in  Gygnus  taken  in  August  1886. 

By  Isaac  Roberts. 

The  negatives  which  I  now  exhibit  were  taken  with  my 
20-inch  Reflector  on  the  nights  of  August  17,  23,  24,  and  25 
this  year,  and  they  represent  parts  of  the  constellation  Cygnus, 
corresponding  with  those  photographed  by  MM.  Henry  with 
their  13-inch  refractor  in  June  and  August  1885,  copies  of 
which  have  been  presented  to  the  Society  as  well  as  to  some  of 
the  Fellows. 

The  celestial  position  of  the  centre  of  each  plate  is  as 
follows : 

Dccl.  38  12 

35  30 


No.  1 

R.A. 

h     m 
21      2 

3 

t> 

19  45 

4 

it 

19  55 

5 

>t 

20    4 

J* 


II 


It 


37  45 
35  30 


The  enlargements  have  been  made  to  the  scale  corresponding 
with  that  adopted  by  MM.  Henry  so  as  to  facilitate  comparisons 
between  them.  The  time  of  exposure,  namely,  60  minutes,  is 
common  to  all  the  photographs. 

If  we  compare  these  plates  with  those  by  MM.  Henry  there 
are  striking  differences  observable  in  the  sharpness  of  the  margins 
of  the  star  discs,  in  the  density  of  the  images,  and  in  the  number 
of  stars  photographed  in  60  minutes  by  the  two  instruments 
respectively. 

In  the  Henry  plates  the  margins  of  the  stars  are  remarkably 
sharp  and  clearly  defined.  The  brightness  or  density  of  the  images 
also,  whether  the  stars  are  of  the  second  or  of  the  fifteenth 
magnitude,  is  equal  in  all  without  perceptible  gradation.  The 
reflector,  on  the  contrary,  shows  the  margins  somewhat  undefined, 
and  the  stars  of  the  first  to  the  third  magnitude  show  prominently 
diffraction  effects  around  them.  Not  less  noticeable  is  the 
gradation  of  the  light  of  the  stars  between  the  brightest  and  the 
faintest  shown  on  tli9  plates ;  the  gradations  are  such  that  the 
stars  are  ultimately  lost  in  the  colour  of  the  background  or  film, 
and  to  define  their  magnitudes  will  severely  tax  the  powers  of 
classification. 

In  drawing  inferences  from  the  relative  numbers  of  the  stars 


Nov.  1886.  of  Stars  in  Cygnus.  23 

photographed  by  the  two  instruments  in  sixty  minutes,  it  must 
be  remembered  that  besides  the  difference  between  them  in 
principle  and  aperture,  there  may  be  difference  in  the  sensitive- 
ness of  the  plates  used,  also  difference  in  the  atmospheric  con. 
ditions  when  the  photographs  were  taken  as  well  as  difference 
in  the  method  of  developing  the  images ;  but,  subject  to  these 
reservations,  we  may,  in  the  absence  of  more  exact  methods, 
make  approximate  comparisons  by  counting  the  number  of  stars 
on  a  given  area,  such  as  a  square  inch,  on  the  enlarged  photographs 
respectively.  In  this  manner  I  counted  on  one  of  the  reflector 
photographs  109,  93,  and  70,  or  an  average  of  91  stars  on  one 
square  inch.  The  numbers  on  the  corresponding  areas  on  the 
refractor  photograph  were  59,  64,  and  41,  or  an  average  of  55 
stars  on  one  square  inch.  It  therefore  appears  that  the  reflector 
has  over  the  refractor  the  advantage  of  number  in  the  average 
ratio  of  nearly  two  stars  to  one. 

In  view  of  others  entering  upon  the  work  of  photographing 
the  stars,  and  to  save  them  much  waste  of  time  and  resources,  it 
would  be  desirable  to  make  comparisons  between  the  relative 
efficiency  of  existing  refractors  and  reflectors  as  instruments  for 
photographing. 

The  comparisons  might  be  made  in  some  such  manner  as  tha 
following : 

istly.  A  sufficient  number  of  photographic  dry  plates  should 
he  obtained  from  some  reliable  maker.  They  should  be  made- 
from  one  uniform  admixture  of  emulsion,  and  the  plates  distri- 
buted among  those  who  would  engage  in  the  enquiry. 

2ndly.  A  given  number,  such  as  ten,  of  the  plates  should  be 
exposed  for  thirty  minutes  each  on  ten  different  clear  nights 
(one  plate  each  night)  upon  such  sky  spaces  as  may  be  deter- 
mined. 

3rdly.  The  plates  should  be  developed  by  the  same  chemical 
formulse  with  an  immersion  in  the  developer,  say  of  five  minutes. 

4thly.  The  number  of  stars  upon  each  plate  should  be  counted 
and  the  density  of  the  images  noted. 

The  result  would  at  least  be  some  guide  to  those  who  intend 
to  engage  in  photographing  the  stars,  to  enable  them  to  choose* 
their  instruments  and  to  compare  their  work  afterwards.  In 
addition  to  the  information  thus  to  be  obtained,  a  report  upon 
the  driving-clock  used  in  the  experiments  should  be  prepared, 
and  its  errors  given  during  each  exposure  of  the  plates.  An 
accurate  and  reliable  driving-clock  and  gearing  are  absolutely 
essential  in  star  photography,  for  any  appreciable  error  would 
distort  the  star  discs,  and  so  prevent  accurate  micrometrical 
measurements  of  their  relative  positions  being  mad  a, 


24  Jlf/\  Roberts,  Photographs  of  the  Pleiades.         xlvii.  i, 


Xole  on  two  PJiotograpJis  of  the  Nebula*  in  the  Pleiades  taken  in 

October  1886.     By  Isaac  Roberts. 

On  tho  night  of  October  23  (last  month),  I  had  an  oppor- 
tunity of  taking  a  photograph  of  the  Pleiades,  and  intended  to 
expose  the  plate  for  three  honrs  so  as  to  be  able  to  compare  the 
result  with  that  obtained  by  MM.  Henry,  bat  clouds  caused  me 
to  stop  the  exposure  after  eighty-nine  minutes.  The  plate  when 
developed  showed  clearly  that  the  stars  Alcyone,  Maja,  Eleclra, 
and  Merope  are  surrounded  by  nebulfiB,  indications  of  which 
about  three  of  the  stars  arc  shown  on  MM.  Henry's  chart, 
which  is  published  in  the  Annates  de  VObservatoire  de  Paris. 

On  the  following  night  (tho  24th)  I  exposed  another  plate 
for  three  hours,  which,  after  development,  showed  that  not  only 
are  the  stars  which  I  have  just  named  surrounded  by  nebulae, 
but  that  the  nebulosity  extends  in  streamers  and  fleecy  masses, 
till  it  seems  almost  to  fill  the  spaces  between  the  stars,  and  to 
extend  far  beyond  them.  It  suggests  the  probability  that  these 
principal  stars  in  the  Pleiades,  together  with  many  of  the  stare 
around  them,  are  involved  either  directly  or  else  in  sight  align- 
ment with  one  vast  nebula.  The  negatives  and  the  enlargements 
to  six  diameters,  which  I  now  exhibit,  will  enable  yon  to  appre- 
ciate and  to  form  your  own  judgment  as  to  the  credibility  of  the 
evidence  upon  which  these  inferences  rest,  and  I  await  with 
watchfulness  for  a  clear  interval  which  will  enable  me  to  try  an 
exposure  of  five  hours  in  order  to  obtain  more  light  upon  the 
subject. 

The  star  discs  upon  the  photographs  are  somewhat  deformed 
by  refraction  and  uncorrected  instrumental  movements,  but  I 
think  you  will  not  have  much  difficulty  in  mentally  making 
the  corrections  necessary  to  form  accurate  judgment;  and  I 
anticipate  being  able  to  obviate  this  slight  distortion  in  future 
exposures. 


The  Orbit  of  Comet  II,  1883,  discovered  by  Mr.  Ross. 
By  Lieut-General  J.  F.  Tennant,  R.E.,  F.E.S. 

Some  considerable  time  ago  I  made  some  efforts  to  get  a 
satisfactory  orbit  for  this  comet,  but  circumstances  were  un- 
favourable and  I  had  to  give  it  up.  More  recently  I  was  induced 
to  take  it  up  to  see  if  there  were  any  real  departure  from  a  Para- 
bolic Orbit  such  as  Mr.  Bryant  found,  or  whether  his  result  was 
only  due  to  the  selection  he  had  made  of  observations.  My 
conclusion  was  that  there  was  no  real  justification  for  departing 
from  the  parabola.  Then  I  found  that  the  compilers  of  the 
Annuaire  du  Bureau  des  Longitudes  had  adopted  Mr.  Bryant's 


Nov.  1886.        Gen.  Tennant,  Orbit  of  Comet  II. ,  1883.  25 

results,  and  I  made  some  farther  calculations.  I  now  offer 
my  results  for  publication  lest  what  I  think  a  mistake  should 
pass  unnoticed. 

Starting  with  Mr.  Tebbutt's  orbit  as  an  approximation,  I 
computed  an  ephemeris  from  January  10  to  February  6,  1884, 
for  each  Greenwich  noon,  and  with  this  compared  the  whole  of 
the  observations  at  Melbourne,*  Windsor,  and  Madras.  The 
Melbourne  observation  of  January  17  is  affected  with  con- 
siderable error,  and  I  was  obliged  to  reject  it.  The  mean  of 
the  observations  at  Madras  on  January  26,  and  the  observations 
at  Madras  on  January  30,  at  Melbourne  on  February  1,  and 
Windsor  on  February  2,  are  somewhat  discordant,  but  I  have 
not  excluded  them,  as  I  did  not  think  they  would  materially 
affect  my  result.  I  then  proceeded  to  obtain  normal  places,  and 
found  the  error  of  my  ephemeris  to  be 


«     .    _    .  a 


On  Jan.  170  in  R.A.  +51*4    in  Decl.  —34*3 
265  +  39*8  -  26-0 

30-0  +  298  —  24*0 

From  the  places  found  by  applying  these  corrections  to  the 
ephemeris  I  computed  a  parabolic  orbit  with  the  following 
result : 

T  =  Perihelion  Passage  1883,  Dec.  2531928 

log  q  =  94938146 


^11 


-  43  30  48*5] 
Q  ^264  33  135  i-Mean  Equinox,  Jan.  o,  1884 
L«  114  59  03-1) 

which  give  at  the  middle  date 

a<.-a.0=  +  IT2 

0c-/3o--  9"6 

a  result  larger  than  I  had  anticipated  from  the  errors  of  the 
ephemeris  at  the  selected  times. 

By  forming  equations  of  condition  for  the  effects  of  small 
changes  in  the  elements,  I  obtained  the  following  elliptic 
orbit : 

T-1883,  Dec.  25320145 

log  2  =  9-4899874 
e  =  0998044 1 


a 


»-  43  33  168) 
3=264  51  04*0 
L=ii5  03  44-3 


Mean  Equinox,  Jan.  o,  1884. 


*  1  hare  used  the  corrected  observations  in  the  "Astronomische  Xachrichten." 
Those  published  in  the  Monthly  Notices  hare  great  error. 


26  Qm.  Tennant,  Orbit  of  Comet  IL9  1883.        xlyii.  r, 

The  period  would  be  1,986  years,  bat,  of  coarse,  the  deduc- 
tion of  so  long  a  period  from  such  data  is  not  to  be  considered 
as  giving  it  any  certainty. 

Having  the  equations  of  condition  I  proceeded  to  see  what 
would  be  the  most  probable  parabola  from  the  normal  places,  and 
found 

T==  1883,  Dec.  25*319222 
log  q  =  94938953 


41 


»-  43  30  40'4l 
8*264  32  54-4 

L-  114  -3^01-9 


Equinox  as  before. 


5*  *u^\ 

The  errors  at  the  times  of  the  normal  places,  as  obtained  from 
the  equations  of  condition. 


«  .a 


C— 0  at  1st  date  in  R.A.  +  4-43    in  Decl.  +  174 
2nd  —  7'98  +7*42 

3rd  +2*49  —176 

leading  to  a  probable  error  of  +  4"*8  in  the  determination  of 
one  element,  which  seems  possible  enough  when  one  looks  at 
the  individual  observations.  But  it  would  have  been  preferable 
to  give  more  weight  to  the  middle  place,  as  the  observations 
about  the  middle  of  the  apparition  are  the  best. 

On  the  whole  I  think  that  we  have  no  sufficient  data  for 
assigning  elliptic  elements,  and  that  the  parabola  last  given  is 
about  as  good  as  any  which  can  be  deduced  from  the  observa- 
tions, though  the  real  orbit  may  be  an  ellipse  of  long  period. 


Nov.  1886.  Greenwich  Observations  of  Comet 


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Mr.  Lohse,  Observations  of  Comets 


XLVIl.  I, 


Observations  of  Comets  made  at  Mr.  Wigalesicortlis  Observatory 
with  the  1 5*5 -inch  Cooke  Refractor.     By  J.  G.  Lohse. 


Scarborough 
Date  Moan 

Time 

1885         h    m      » 
July   17    II   51  42 


1885         h    m    s 
I>ec.  7      8  37  23 


Comet  1885  a,  Barnard. 

'.  -* 


25  27 


AS 

h 
—  17 


«.*' 


Num. 

of 
Comp, 


m       9 
3  5 179 


»» 


24 


»>      »» 


it 


8  41     2 

9  12  40 
28*  7  35  15 


+ 
+ 


Com!  1885  <7,  Fairy. 

,       i,         h    m        s 
+  248     o  25    954 

+  1  236    23  54  1675 

+ 1  225    23  54  14-91 

+  2  13-6    23  48  5895 


H 
1903 

2338 

21  54 
526 


Comet  1885  f,  Barnard. 


1885  h     m  s 

Dec.  6  11  53  53 

»     7  12  24  15 

„  10  11  11  12 

„  13  12  27  7 

„  28  11  45  o 

:  886 

Jan.  2  10  26  45 


m 


-  43*48 

-  20-87 

-  356 
+  2698 

-1  3255 

-  2295 


// 


-1  139 
-6  21-3 
+  7  382 
+     19*6 

+  485 
-3  597 


h    m        8 

4  14  5779 
4  12  29-90 

4  5  1327 
3  57  33*46 
3  19  5470 

3    8  1397 


+  20  52  438    5 
+  20  40  521  6(6 
+  20  40  51-0    3 
+  20  44  204    7 

+  °4  55  5M  8  8 

+   53  53*2  4 

+  5  21     1-5  9 

+   5  40  316  8 

+   7  4i  531  5,5 

+  8  29  59-7  5 


Adopted  Mean  Places  of  Comparison  Stars  for  18850  and  1886*0. 


a 

1885         h      m       s 
July    17  17     3  2657 

Dec.    7    o  25  2513 
o  33  5256 

24  23  53  5041 

28  23  49     1-35 

23  50  1268 

Dec.  6    4  15  3716 

4  19  5069 
7    4  12  4665 

4     5  '271 
•10    4    5  1271 

13    3  57    235 
28    3  21  2323 

1886 
Jan.   238  3620 


Retln. 

B 
+  2'95 

+  344 


+  296 
+  2-86 


Redn. 


Authority. 


-10  22  158     +    79    B.-W.,  I7h  3. 

(8- 5     mag.     *     con- 
+  20  50  14-0     +  250    nected  with B.W<2  o* 

+  20  48  27-1  j  838^+-  840 


V         2 


+  20  39    29    +  256    B.-W., 23h  1096. 

+  20  41  41  4    +  254  f 9 m&^ * connectedwith 

+  20  42  303 


+  411      +   4  57     89 

+   4  53  io-i 
+  412     +   5  10  129 

+   5  '3  212 

+  412       +    5    13   212 

+  4  13     +   5  40    93 
+  402     +   7  40  59  1 

+  072     +  8  34    6-4 


\  B.B.  VI.  +  20"  5397. 

+    I'4(n  ma*.  *   connected 
j  with  Glaag.  Cat.  1067. 

+    *  "6  f  10  mag.  *    connected 
\  with  Glusg.  Cat.  992. 


Mr.  Wtgglesworth's  Observatory, 

Scarborough  :  10  Nov.,  1SS6. 


+   2-1  Do. 

1   r     Tauri,      Berliner 
+       7\  Jahrb. 

+   5-5    B.B.  VI +  70  510. 

I  A  st.      Nach.      2709 
[4  (Sant,   +  8°  40  + 
Schj.  927-28  +  Glasg. 
748)]. 


Nov.  1886.         at  Mr.  Wiggleswortk's  Observatory.  29 


Notes. 

July  17. — The  comet  is  faint  and  round  ;  it  becomes  gradually 
brighter  towards  the  middle,  but  has  no  real  nucleus.  It 
is  much  fainter  than  on  July  14;  it  was  well  seen  on 
that  day,  but  clouds  came  on  before  an  observation  could 
be  obtained. 

December  24. — Comet  Fabry  is  round  and  has  a  stellar 
nucleus ;  it  is  about  2'  in  diameter,  but  still  faint.  Clouds 
lit  up  by  the  Moon  were  troublesome. 

December  6. — Comet  Barnard  is  faint  and  small.  The  coma 
extends  farther  on  the  following  side  than  in  other 
directions.  The  central  bright  part  appears  granulated, 
and  equals  in  brightness  about  an  nth  mag.  star.  The 
diameter  of  the  comet  is  4  to  5  seconds  in  time. 

December  1  o. — The  comet  is  decidedly  more  extended  on  the 
following  side,  and  about  of  the  same  brightness  as  on 
December  6  and  7.     The  diameter  is  about  7  seconds. 

December  28. — The  comet  was  often  barely  visible  through 
the  faint  clouds  passing.  At  intervals  it  was  snowing 
and  very  stormy.  The  comet  is  elongated  on  the  follow, 
ing  side,  and  the  nucleus  is  brighter  than  that  of  comet  d, 
but  the  latter  seems  to  be  the  larger  one,  though  the 
difference  is  very  small. 

January  2. — The  sky  being  hazy  the  comet  appeared  very 
faint. 

The  observations  were  made  with  a  wire  micrometer  by 
Merz,  kindly  lent  by  Lord  Crawford.  Only  for  the  first  obser- 
vation a  transit  micrometer,  with  a  set  of  fixed  wires,  was  used. 

Refraction  has  always  been  taken  into  account. 

For  the  catalogue  places  of  most  of  the  comparison  stars  I 
am  indebted  to  Dr.  Copeland. 

The  co-ordinates  of  the  Observatory  have  been  taken  from 
the  6-inch  Survey  Map,  and  are : 

Longitude  of  Observatory  =im38ft' 9  west  of  Greenwich. 
Latitude  „  =  +  54°  16'  30". 


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Nor.  1 836.  Phenomena  of  Jupiter's  Satellites.  33 

Remarks, 

March  28.  —  Definition  of  Satellite  L  not  good;  observation  probably  some- 
what late.  IV.  growing  faint  at  14*  37"  26%  and  I  thought  I  could  just 
glimpse  it  agdn  at  14"  39*  20**8.  Satellite  first  noted  at  i6k  28"  47*,  but  I 
was  quite  certain  of  it  57  seconds  later. 

April  1. — Fair  definition ;  satellite  suspected  32  seconds  before  recor-led 
time. 

April  4. — Clear,  but  definition  bad  and  images  tremulous. 
April  22. — Good  definition  and  observation. 

April  24.  --Beautifully  clear  and  definition  excellent;  very  good  observation. 

May  1. — Images  steady  and  definition  excellent ;  good  observation. 

Miy  8. — Images  steady  and  definition  good;  beautifully  clear.  The 
observation  of  the  first  appearance  of  JI.  probably  rather  Ute. 

May  14. — Beautifully  clear  and  definition  good. 

May  15.  -Good  definition,  but  sky  overspread  with  thin  cloud. 

May  21. — Beautifully  clear.  Definition  very  good  at  disappearauce,  but 
images  rather  tremulous  at  reappearance.  Defalcation  of  light  marked  at 
7h  59m  45"9*  Satellite  suspected  a  few  seconds  before  recorded  time  of  first 
appearance. 

May  22. — Definition  excellent  throughout. 

May  31. — Beautifully  clear  and  definition  good. 

June  25. — Definition  fair  at  ingress,  but  not  so  good  at  egress. 

June  26.  —Images  steady,  and  definition  unusually  good. 

June  27.— Beautifully  clear ,  images  steady  and  well  defined ;  good  observa- 
tion. 

June  29. — Bid  definition. 

July  3. — Definition  excellent,  with  clear  sky. 

July  4. — Clear,  but  with  bad  definition. 

July  10.— Fair  definition. 

July  11. — Clear;  definition  fair,  but  images  tremulous. 

July  28.—  Definition  not  good  enough  for  a  higher  power.  Satellite  barely 
visible  as  a  light  spot  at  5h  29™  io\  and  quite  invisible  at  5h  53m  36'.  At 
6 h  32"  30*  pretty  conspicuous  as  a  dark,  not  black,  hazy  spot;  it  had  then 
nearly  reached  mid-transit,  and  was  rather  more  than  half  the  planet's  semi- 
diameter  distant  from  the  planet's  centre.  Clouds  prevented  further  observa- 
tion. 

August  8. — Beautifully  clear,  but  with  poor  definition.  Satellite  III. 
suspected  10  seconds  before  recorded  time  of  first  appearance.  Image  of  I. 
tremulous,  with  bad  definition. 

August  24. — Beautifully  clear,  but  twilight  very  strong.  Sun's  upper 
limb  disappeared  behind  the  horizon  6m  53"  before  the  recorded  time  of  re- 
appearance.    Image  steady  and  definition  good. 

Windsor,  X.S.  Wales:  1886,  Sept.  28. 


HetcaWc  Occulter.     By  R.  S.  Newall,  F.R.S. 

I  lately  designed,  and  had  made  by  a  clever  local  optician,  an 
addition  to  the  eyepiece  of  my  telescope,  which  I  find  of  the 
greatest  advantage  in  examining  the  satellites  of  planets  and 
multiple  stars. 

My  idea  was  to  produce  an  instrument  exactly  the  reverse  of 
Dawes's  solar  eyepiece  ;  that  is,  to  interpose  a  screen  which  shall 
s lint  off  the  bright  object,  and  thus  allow  of  the  faint  com- 
panions being  more  easily  seen,  and,   at  the   same  time,   the. 

D 


34 


Mr.  NewaU,  NewaWs  Occult er. 


XLV1L  I, 


apparatus  must  be  simple  and  capable  of  easy  manipulation  and 
adjustment 

I  had  my  eyepieces  each  fitted  with  a  stop,  that  is,  a  piece  of 
tube  the  same  diameter  as  the  adapter,  into  which  the  eyepiece 
fits,  and  the  stop  is  cat  of  such  length  that  when  the  eyepiece  is 
pushed  in  it  shall  be  in  the  focus  suited  to  my  sight,  so  that  I 
have  no  trouble  in  adjusting. 

The  occnlter  is  a  ring  of  brass,  about  a  quarter  of  an  inch 
thick  and  three-quarters  broad.  It  slips  stiffly  on  to  the  eye- 
piece as  shown  in  the  accompanying  drawing.  The  ring  is  bored 
with  three  holes,  as  in  the  section,  and  into  each  is  fitted  an 
ivory  sphere,  three-eighths  of  an  inch  in  diameter.  They  are 
held  in  place  by  brass  springs,  which  have  a  quarter-inch  hole 
in  each,  to  admit  of  the  movement  in  any  direction  of  a  small 
platinum  wire,  which  passes  through  the  sphere.  On  one  end 
of  the  wire  is  a  disc,  and  on  the  other  a  small  button  or 
handle. 


Fio.  i. 


FlQ.  2. 


By  these  means  the  discs  may  be  placed  in  any  required 
position  to  eclipse  the  object,  or  they  may  be  pushed  to  one  Bide, 
so  as  to  be  entirely  out  of  view ;  and  when  drawn  back  up  to 
the  ivory  sphere  the  ring  can  be  slipped  off  the  tube,  and  the 
eyepiece  is  as  it  was,  having  only  three  holes  in  it  corresponding 
to  those  in  the  ring.  The  centres  of  these  holes  are,  of  course, 
in  the  plane  of  the  focus  of  the  eye-lens,  but  the  spheres  allow 
of  the  discs  being  placed  out  of  focus,  which  is  sometimes  of 
advantage.  One  disc  would  be  quite  enough  for  most  work,  but 
a  spare  one  or  two  may  be  convenient  occasionally a  so  1  made 
mine  with  three  discs  slightly  varying  in  size. 

November  S,  1 886. 


Nov.  1886. 


Mr.  Denning,  Meteor  Streams. 


35 


Distribution  of  Meteor  Streams.     By  W.  F.  Denning. 

I  recently  compiled  a  general  catalogue  of  all  the  meteor 
streams  recorded  in  the  various  publications  which  I  collected 
together  for  the  purpose.  These  include  the  observations  or 
reductions  of  Backhouse,  Bartfay,  Corder,  Denning,  Denza, 
Greg,  Graber,  Herschel,  Heis,  Kobold,  Konkoly,  Kovesligethy, 
Maggi,  Neuinayer,  Sawyer,  Schiaparelli,  Schmidt,  Serpieri, 
Tupman,  Weiss,  Zezioli,  and  many  other  minor  contributors. 

Mr.  Greg's  last  Catalogue  of  1876  was  based  on  850  radiants 
deduced  from  15,000  catalogued  meteors.  At  the  present  time 
we  have  3,035  radiants,  derived  from  more  than  82,000  meteors. 
There  has  been  an  enormous  increase  in  these  observations 
during  the  last  ten  years. 

Upon  analysing  all  the  positions,  I  find  they  exhibit  a  very 
unequal  distribution  amongst  the  constellations,  a  fact  which  is 
unquestionably  due,  partly  to  real  differences,  and,  in  a  less 
decree,  to  the  relatively  excessive  observations  accumulated  in 
certain  months  of  the  year.  In  Right  Ascension  the  3,035 
radiant  points  are  situated  as  follows  : 


0 

I 

RJL 

0 

to     30 

Radiants. 
378 

Per- 
centage. 

12*4 

0 
181 

R.A. 

to 

0 
2IO 

Radiants. 
147 

Per- 
centage. 

48 

31 

if 

60 

449 

I48 

211 

it 

240 

186 

6l 

61 

if 

90 

315 

IO3 

241 

it 

270 

217 

7*2 

91 

»f 

I20 

229 

7*6 

271 

if 

300 

254 

84 

121 

»i 

150 

192 

6-3 

301 

ii 

330 

243 

80 

151 

11 

l8o 

142 

47 

331 

if 

0 

283 

93 

The  meteor  streams  cluster  in  greatest  abundance  between 
i°  and  6o°  of  R.A.  This  is  a  fact  irrespective  of  the  cometary 
showers  of  Andromedes  (Nov.  27)  and  Perseids  (Aug.  10),  which 
fall  in  this  region,  and  might  be  supposed  to  have  induced  the 
singular  condensation  referred  to.  The  zone,  following  it  from 
6i°  to  900,  shows  a  great  decline,  notwithstanding  it  includes 
the  Orionids  (Oct  17-20),  and  the  mass  of  showers  originating 
in  Auriga,  Camelopardus,  and  the  eastern  quarter  of  Taurus. 
And  the  zone,  33 1°  to  o°  preceding  the  region  of  maximum, 
though  rich  in  Aquariads,  Pegasids,  Lacertids,  and  Cepheids, 
exhibits  a  great  deficiency  as  compared  with  it.  The  excess,  so 
decided  in  character,  between  i°  and  6o°  is  distinctly  to  be 
attributed  to  the  Cassiopeids,  a,  /3,  and  y  Andromedes,  Arietids, 
MuBcids,  a  and  /3  Perseids,  Taurids,  <fec,  which,  combined  with 
the  cometary  showers  of  Andromedes  and  Perseids,  swell  the 
aggregate  number  to  an  abnormal  figure. 

The  minimum  proportion  of  showers  is  clearly  indicated 

D  2 


36  Mr.  Vevning,  Distribution  xtvir.  i, 

between  151°  and  aio"  R.A.,  which  does  not  much  exceed  one- 
third  of  those  grouped  between  1°  and  6o°,  the  relative  figures 
being  *8o  and  827. 


iifiiiHIIllilllpilllllltill!!! 

I'm.  I.  —  IHstribtiriim  of  melcir  Btre:im*  in  Kiglit  Ascension. 

In    North    Polnr    Distance   the   showers  are  placed  us    fol- 
lows : 

N.P.n.  Rwllwlt.       Vcr.  N'p.n.  Pad  l.i  11  tt.       P»r- 

o       hi      9  39  13  60      to     69        391         I2'9 


The  maximum  obviously  lies  between  30°  and  49°  N.P.D.,  and 
the  minimum  naturally  occurs  at  the  pole,  inasmuch  as  the  zone 
0°  to  9'  includes  a  much  smaller  area  than  any  other. 

The  distribution    of   the  (.liserved   radiants   in    N.P.D.    is 


Nov.  1886. 


of  Meteor  Streams. 


37 


affected  by  the  differences  in  the  areas  of  the  several  zones  and 
their  relative  degrees  of  visibility.  Though  towards  the  pole  the 
total  space  inclnded  in  the  zones  becomes  less,  yet  this  is  in  a 
large  measure  compensated  for  by  their  more  favourable  position 
and  the  persistency  with  which  they  are  displayed  to  view.  The 
entire  zones,  from  o°  to  490  N.P.D.,  never  fall  below  the  horizon, 
and  such  showers  as  they  present  are  therefore  determinable  at 
any  period  of  the  year  or  time  of  night.  This  applies  specially 
to  English  latitudes,  but  it  also  has  a  general  reference  (with 
perhaps  slight  modification  in  certain  instances)  because  nearly 
all  our  existing  observations  of  shooting  stars  have  been  made  at 
stations  having  considerable  (i.e.  exceeding  350)  north  latitude. 
The  summary  proves  that  while  the  two  zones  embraced  between 
the  parallels  of  300  and  490  N.P.D.  have  the  largest  number 
of  recorded  streams,  the  three  zones  succeeding  towards  the 
equator  exhibit  a  gradual  decline,  though  each  remains  fairly 
prolific.  The  Andromedes,  Perseids,  and  Quadrantids  are 
arranged  between  300  and  490,  while  the  Geminids,  Leonids, 
and  Lyrids,  are  clustered  between  500  and  690  N.P.D.  Con- 
sidering all  the  circumstances,  there  do  not  appear  to  be  great 
inequalities  of  grouping  in  North  Polar  Distance  similar  to  those 
which  undoubtedly  occur  in  Bight  Ascension,  but  the  point 
requires  further  investigation. 

In  considering  the  distribution  of  meteor  streams,  several 
important  conditions  must  not  be  lost  sight  of.  The  bulk  of  the 
observations  have  been  effected  in  the  summer  months,  whence  it 
necessarily  follows  that  such  constellations  as  are  most  favour- 
ably visible  at  this  period  must  certainly  appear  to  exhibit  a 
predominance  of  showers.  I  gave  a  summary  in  the  Monthly 
Notices,  vol.  xxxix.  p.  411,  showing  the  comparative  monthly 
numbers  of  meteors  registered  in  twelve  catalogues,  and  I  have 
now  added  several  others,  the  aggregate  including  82,156  meteors, 
with  the  following  result : 


Month. 

Meteors 
Catalogued. 

Per- 
centage 

January 

2804 

34 

February 

1826 

2  2 

March 

1764 

2' I 

April 

5585 

6-8 

May 

2I20 

2'6 

June 

2353 

2-9 

Month. 

July 

August 

September 

October 

November 

December 


Meteors 
Catalogued. 

Per- 
centage, 

IO670 

121 

3I5I6 

38l 

43<>4 

5*i 

6840 

8*3 

83 '9 

U'3 

4055 

49 

These  numbers  are  derived  from  the  catalogues  of  Corder, 
Denning,  Denza,  Heis,  Konkoly,  Lucas,  Sawyer,  Schmidt, 
Tapman,  Weiss,  Zezioli,  and  the  Italian  Meteoric  Association, 
1869,  1870,  and  1872,  and  some  minor  lists. 

Now,  more  than  one-half  the  total  number  of  observations 
were  obtained  in  July  and  August,  and,  in  point  of  fact,  arc 


38 


Mr.  Denning,  Distribution 


nearly  all  embraced  between  tho  period  from  July  xo  to 
August  15.  The  majority  of  tbe  observations  bare  been  secured 
before  midnight,  and  it  is  therefore  curtain  that  tbe  region  of 
31°  to  6o°  R. A.,  which  ia  for  the  most  part  either  below  tbe 
horizon  or  low  in  the  north-east  at  the  special  epoch  when  the 
largest  number  of  meteors  have  been  recorded,  is  not  rendered 
rich  solely  by  the  abundance  of  observations.  Indeed  the  months 
of  September,  October,  and  November  appear  to  have  funished, 
relatively  to  the  number  of  meteors  catalogued,  hy  far  the 
greatest  number  of    showers    in  this  quarter   of  the   sky.     I 


believe,  therefore,  tbe  great  superabundance  of  streams  about 
Andromeda,  Aries,  and  I'erseu*  is  a  real  one. 

We  must  remember  tbat  the  large  proportion  of  meteora 
catalogued  in  July,  August,  and  later  months  is  far  from  being1 
entirely  due  to  tbe  more  extensive  watches  undertaken  at  those 
times.  It  is  attributable  in  a  great  measure  to  a  real  surplus 
in  tbe  visible  nnmber  of  meteors.  All  regular  workers  in  this 
department  agree  as  to  tbe  far  greater  frequency  of  meteors 
during  the  last  half  of  tbe  year  as  compared  with  tbe  first  half. 
From  my  own  observations,  up  to  the  end  of  1885,  comprising 
7.100  meteors,  I  find  that  the  average  horary  number  for  one 
observer   from   January    to   June  is   695,    and   from  July  to 


Nov.  1 886.  of  Meteor  Streams.  39 

December  12*65,  so  that  the  excess  in  favour  of  the  last  half  of 
the  year  is  nearly  in  the  proportion  of  2  to  1.  From  this  we 
may  conclude  that  both  meteors  and  meteoric  radiants  display 
by  far  the  greatest  profasion  between  July  and  December,  and 
that  the  densest  region  of  radiation  lies  between  i°  and  6o° 
of  R.A.  This  is  indeed  the  most  active  part  of  the  heavens 
even  as  late  as  November,  when  it  is  some  no°  distant  from 
the  apex  of  the  Earth's  way. 

The  known  meteor  streams,  considered  in  respect  to  their  appa- 
rent distribution  upon  the  celestial  vault,  exhibit  special  regions 
of  density  and  scarcity,  not  exactly  regulated  by  the  direction  of 
the  Earth '8  motion.  The  maximum  number  of  showers  is  rarely 
seen  in  that  part  of  the  firmament  towards  which  the  Earth  is 
directed,  though  with  a  perfectly  equal  distribution  of  streams 
this  would  be  expected.  The  richest  showers  usually  come  from 
positions  far  to  the  west  of  the  Earth's  apex,  and  this  is  sufficient 
evidence  that  they  exhibit  a  special  construction  or  grouping 
together.  The  Earth  becomes  alternately  involved  with  rich  and 
tenuous  regions  at  intervals  of  about  six  mouths. 

Bristol:  1 886,  November  9. 


4Q 


Mr.  Marth,  EphemerU  for 


XL VII.  i, 


Ephemeris  far  Physical  Observation* 


Greenwich 
Noon. 


1886 
Dec.    9 

«4 

19 

24 
29 

1887 
Jan.    3 

8 

13 
18 

23 
28 

Feb.    2 

7 
12 

17 
22 

27 
Mar.    4 

9 

14 

'9 

24 
29 

Apr.    3 

8 

13 
18 

23 

28 

May    3 

8 

13 
18 

*3 


Angle  of 

Position  of 

TTsAxia. 


22064 
21*877 
21-694 
21*516 

21'345 


21*182 

-3008 

21*030 

3036 

20*890 

3063 

20*763 

3089 

20*651 

3*  "4 

20*555 

3*139 

20476 

3162 

20416 

3i85 

20*376 

3*206 

2o-3S5 

3225 

20*355 

3242 

20*375 

3*258 

20*416 

-3"27i 

20*476 

3282 

20554 

3290 

20650 

3*295 

20761 

3*297 

20884 

3296 

21*017 

-3292 

21*158 

3285 

21*303 

3*274 

21*451 

3260 

21*598 

3*243 

21741 

3223 

21*879 

-3201 

22*009 

3*177 

22*129 

3151 

22-238 

3124 

22*335 

3096 

Latitude  of 
Karfch      |       Sun 
above  X'*  Equator 

B  B 

o  o 

-2-862  —2*796 

2*893  2-804 

2923  2813 

2*952  2-821 

2-980  2-829 

2836 

2*844 

2852 
2859 

2*866 
2*874 
-2-88i 
2888 
2894 
2901 
2-908 
2914 
■2-920 
2-927 

2*933 

2939 

2*944 

2950 

2956 

2961 

2*966 

2971 

2-976 

2-981 

2-986 

2*991 

2995 

3000 

3004 


Annual 
Parallax. 

A-L. 

-7799 
8-282 

8726 

9127 

9481 

-9784 
10*032 

10*222 
10*351 
10*414 
10*409 
-  IO*332 

io*i8i 

9954 
9649 
9*265 

8-802 
-8261 

7644 
6954 
6  196 

5*375 
4*497 

-3571 
2607 

1*614 

— 0*602 

+  0-418 

1*434 
+  2*434 

3*4o8 

4347 
5242 
608  c 


L-0. 

73°*435 
74*297 

75"9 
75898 
76*630 

77*311 

77*937 
78505 

79012 

79*454 
79*827 

80128 

80*356 

80508 

80582 

80577 

80492 

80*329 

80092 

79782 

79403 
78*961 
78462 

77'9'5 
77*330 
76*716 
76084 

75*444 
74*808 
74188 

73594 

73035 
72520 
72058 


Longitude  of  U'* 
Central  Meridian. 

(878°*95)   <87o°-a7> 
I  II 

34°' 1 5    251^43 
104*86    282-24 

17562    313*10 

24645    34402 

31734      1500 


2829 

9930 
17038 

24153 

31275 
2404 

95*40 
16683 
23832 
30988 
2151 
93*20 
16495 

23675 
308*60 

20*49 

9241 

16435 
236*31 

30828 
20-23 
9216 

16407 

235*93 

30774 

1948 
91*15 

16274 
23425 


4605 

77*16 

10834 

139*59 
170*90 

202-28 

23373 
26526 

29685 

32851 

0*23 

3202 

6386 

9576 

12771 

15970 

19172 

223-76 

25582 

28788 

31993 

351*97 

23*97 

55*93 

8784 

11968 

15146 

183-16 

214*77 


Oorr. 

for 
Phase. 


+  0*264 
•298 

'331 
•362 

•390 

+  O415 

437 

•444 
•465 

•471 
•470 

+  0463 

•450 

*43° 
•404 

•372 

336 
+  0*296 

**54 
•210 

•167 

126 

088 

+  0056 

•030 
on 

+  0*002 

—  0*0OI 

009 

—  0-O26 

•051 
082 
*II9 

161 


Nov.  1886.  Physical  Observations  of  Jupiter.  41 


of  Jupiter  1887.     By  A.  Marth. 


Greenwich 
2foon 

Diameter 
Equat.  |  Polar. 

Difference  of  limbs 
in  A.  B.  |  in  DecL 

JJCICCIp  UI    1IJUU 

Equal  J  in  A.  R. 
preceding  limb 

IlllWUDBt 

1  in  Dec!, 
north  I. 

d 

1 

w 

1886 

// 

« 

■ 

H 

a 

■ 

a 

O 

0 

Dec.      9 

3232 

30-26 

2168 

30*56 

015 

0-009 

002 

7*79 

26969 

14 

32*66 

3058 

2193 

30*88 

•17 

-oio 

•02 

827 

269-57 

19 

3302 

3093 

2'220 

31*22 

•19 

'Oil 

03 

871 

26946 

24 

33*42 

31-30 

2*249 

31*59 

•21 

•013 

•03 

911 

26937 

29 
1887 
Jan.      3 

3384 

3169 

2*280 

3198 

•23 

•014 

•03 

9*47 

269*28 

34*29 

32-11 

2-312 

32*40 

0*25 

0015 

003 

977 

269*19 

8 

3476 

3255 

3*346 

3284 

•27 

016 

•03 

1002 

269*11 

13 

3526 

33*01 

2*38l 

33*31 

-28 

■017 

•03 

10*21 

26902 

18 

3577 

3350 

2-4I7 

3379 

•29 

•018 

•03 

io*34 

26893 

23 

3631 

340I 

2*455 

34*30 

•30 

•018 

•04 

10*40 

268-84 

28 

3687 

34*53 

2*494 

34*82 

•30 

•018 

04 

1040 

268*74 

Feb.     2 

3744 

3506 

2*533 

35*36 

0*30 

o'oi  8 

003 

10-32 

26863 

7 

38*02 

35-60 

2*573 

35'9i 

•30 

•018 

•03 

10-17 

26851 

12 

38*60 

3615 

2-614 

3646 

•29 

018 

•03 

994 

268*37 

17 

3919 

3671 

2654 

3702 

•28 

-017 

03 

964 

26823 

22 

3978 

37*26 

2*693 

37  57 

•26 

016 

•03 

9*26 

268-06 

27 

40-36 

37-80 

2732 

3812 

•24 

•015 

'02 

880 

26786 

Har.    4 

40*92 

3833 

2-769 

38*65 

021 

0014 

002 

826 

267*64 

9 

4146 

3883 

2-804 

39'i6 

18 

*0I2 

•02 

764 

26738 

14 

41-97 

3930 

2837 

39*64 

•15 

•010 

•02 

695 

267*06 

19 

4244 

3974 

2867 

4009 

•12 

•008 

'01 

620 

26667 

24 

42-86 

4014 

2894 

4049 

•09 

006 

'01 

5*38 

266- 14 

29 

43'23 

4049 

2-917 

40*84 

•07 

004 

•01 

4"5i 

26543 

Apr.     3 

4354 

40-78 

2*935 

4114 

0*04 

0*003 

OOO 

360 

26435 

8 

4378 

41-01 

2949 

41*38 

02 

-ooi 

— 

263 

2625 

13 

4396 

41-17 

2959 

41*55 

•01 

•001 

— 

1*64 

2587 

18 

4406 

41*26 

2964 

4165 

on  following 

on  soutl 

1  0-68 

2428 

23 

4409 

4129 

2963 

41-68 

limb 

limb 

052 

1234 

28 

4404 

41*24 

2957 

4164 

O'OI 

0-000 

000 

1*47 

1027 

M*J     3 

4391 

41*12 

2-946 

41*53 

-02 

'OOI 

•00 

2*44 

953 

8 

4372 

4094 

2931 

41*35 

•04 

002 

01 

3'4i 

93*24 

'3 

43*46 

40*70 

2  91 1 

41*10 

•06 

•004 

•01 

4*34 

92*07 

18 

43*14 

40*40 

2888 

4080 

09 

•005 

02 

5'24 

9 1 '3° 

23 

4276 

4005 

2862 

4045 

-12 

007 

'02 

608 

9076 

42 


Mr.  Marth,  Ephemeris  for 


XLVU.  I, 


Greenwich 
Nooti 


1887 
May    28 


June 


July 


Aug. 


.Sept. 


2 

7 
12 

17 
22 

?7 

2 

7 
12 

17 
22 

27 
1 

6 

11 

16 

21 

26 

31 
5 


Angle  of 

Position  of 

X*  Axis. 

P 

22'4l8 

22487 

32*542 
22'582 

22608 

22*619 

22'6l5 

22567 

22564 

22516 

22454 

22*378 

22288 

22*183 

22*064 

21931 

21785 

21*624 

21450 

21*261 

21059 


Latitude  of 
Bartn      |       Sun 
above  %'b  Equator. 

B  B 

3*068        3008 

—  3040   —3*OI2 

3013        3016 


2987 
2061 

2*937 
2915 


3-020 
3023 
3027 

3030 


-2895  -3033 
2*876      3*036 


2859 
2845 

2833 
2823 


3039 
3042 

3045 
3*047 


-2815  -3050 
2809      3*052 


2804 
2-801 
2-800 
2-800 
2*8oi 


3054 

3056 

3058 

3-060 

3061 


-2805  -3063 


Annual 
Parallax. 

A-L. 

6-868 

+  7*586 
8236 
8814 

93l8 

9747 

lO'IOI 

+ 10-380 
10586 
10-721 
10787 
10786 
10720 

+ 10-594 

10-41 1 

io- 1 73 

9-882 

9543 
9159 

8732 
+  8266 


L-O. 

7i°*655 
71317 

71047 
70849 

70*726 

70678 

70705 

70-806 

70981 

71227 

71*542 
71925 
72372 
72880 

73*445 
74065 

74  737 
75-458 
76225 

77034 
77883 


Longitude  of  It's 
Central  Meridian. 
(878°-2s)    (87o°-27) 

I  II 

305°-67  246*29 
1700  27772 
8824    30906 

15938  34030 
23042      11-45 


30I37 
12-24 

8302 

"537i 

22433 
294-88 


4250 

73*47 

10435 

13515 
16587 

19652 


536  227-10 

7577  25762 

14613  28808 

21643  31849 

28669  34885 

35690  19*17 


6708 

13723 

20735 
27744 


4945 
7970 

10902 

140-11 


Corr. 

for 

Phase. 


•205 

—  0250 

•204 
337 

•377 
*4T2 

•443 

-O467 

-486 

•498 
•505 
•505 

•498 
-O486 

•470 

•449 
•424 

395 
'364 

33 1 

—  0297 


The  angle  A — L  is  the  difference  of  the  Jovicentric  longitudes 
of  the  San  and  Earth,  reckoned  in  the  plane  of  Jupiter's  equator 
L — O  +  1800  the  Jovicentric  longitude  of  the  Earth  reckoned 
from  O,  the  point  of  Jupiter'*  vernal  equinox  or  the  point  of  the 
ascendiug  node  of  the  planet's  orbit  on  its  equator.  Two  valnes 
of  the  "  longitude  of  U  's  central  meridian  "  are  given  for  each 
date,  the  first,  computed  with  the  daily  rate  of  rotation  878°* 25, 
being  intended  for  comparing  the  observations  of  the  white  spots 
in  the  neighbourhood  of  the  planet's  equator ;  the  second,  com- 
puted with  the  rate  87o°*27,  for  the  observations  of  the  remnant 
of  the  great  reddish  spot  in  the  planet's  southern  hemisphere. 
The  apparent  irregularities  in  the  motion  of  the  white  equatorial 
spots  leave  it  doubtful  whether  the  adopted  slackened  rate  of 
rotation  will  be  approximately  correct  during  the  approaching 
apparition  of  Jupiter.  But  observers  who  have  instrumental 
and  climatic  opportunities  for  observing  the  spots  assiduously 
can,  after  the  first  observations,  easily  make  allowance  for  any 
changes  of  the  positions  of  the  spots  in  reference  to  the  system  I. 
of  longitudes.     If  the  slackening  of   the  motion  of  the  great 


Nov. 

1886. 

Physical  Observations  of  Jupiter 

» 

43 

Greenwich 
Noon 

Diameter 
Equat.  |  Polar. 

Difference  of  limbs 
in  A.  K.  |  in  Decl. 

Defect  of  illumination. 
Equat.  |  in  A.  R.  ,  in  Di  cl. 
following  limb       touth  I. 

d 

w 

1887 
May  28 

42'33 

39'65 

1 
2832 

40-05 

it 
OI5 

0*009 

11 
002 

086 

9034 

June    2 

4187 

39'2i 

2 '80O 

396i 

Ol8 

OOII 

OO3 

7*57 

9002 

7 

41-37 

3874 

2766 

39*14 

'21 

-OI2 

03 

8*22 

8975 

12 

4084 

3825 

2731 

3864 

•24 

*OI4 

•04 

8*8o 

8952 

17 

40*30 

37*74 

2694 

3813 

•27 

•Ol6 

•04 

9*30 

8933 

22 

3974 

3722 

2657 

376o 

•29 

•OI7 

04 

973  • 

8917 

27 

39*8 

3669 

2'6l9 

3707 

•30 

•Ol8 

•04 

10-09 

8902 

July    2 

3861 

3616 

2582 

3653 

031 

OOl8 

OO4 

10.37 

88-89 

7 

3805 

35*63 

2'545 

3600 

•32 

OI9 

•05 

1057 

8878 

12 

3749 

35  11 

2509 

35*47 

"33 

OI9 

05 

107 1 

88-68 

17 

36*95 

34-60 

2*473 

34*95 

*33 

OI9 

•04 

1077 

8859 

22 

3642 

34*io 

2*439 

34*45 

•32 

•019 

O4 

1077 

88-50 

27 

35*91 

33'62 

2406 

33*96 

31 

OI9 

-04 

10-71 

8843 

Aug.    1 

3541 

33i6 

2'374 

33*49 

030 

OOl8 

OO4 

1058 

8836 

6 

34*94 

3272 

2*344 

3304 

•29 

•OI7 

•04 

10*40 

8829 

11 

3448 

3229 

2-316 

3261 

•27 

•Ol6 

03 

1016 

88-22 

16 

3405 

3189 

2289 

32-20 

25 

OIS 

03 

9*87 

88-15 

21 

3365 

31*51 

2-264 

3181 

•23 

OI4 

•03 

9*53 

8808 

26 

33  26 

31*15 

2*241 

31*44 

•21 

•OI3 

03 

9*15 

8801 

3* 

32  91 

3081 

2-219 

3110 

•19 

OI2 

•02 

972 

87*94 

Sept.    5 

32'57 

30*50 

2-199 

3078 

017 

OOIO 

0*02 

9-26 

8787 

reddish  spot  should  be  maintained,  its  place  will  be  found  near 
the  zero  meridian  of  the  system  XL  of  longitudes.  The  periods 
of  rotation  corresponding  to  the  adopted  rates  are 

h    m       s 
I.  daily  rate  878°-25  period  9  50  15*88 

II.  870°27  9  55  4063 

The  differences  of  successive  values  in  the  two  columns  for 
"  Longitude,  Ac,"  amount  for  the  intervals  of  five  days  to  12 
rotations  in  addition  to  the  differences  directly  deduced,  so  that, 
for  instance,  the  differences  of  the  values  for  Dec.  14  and  Dec.  9 
are  439o°7i  and  435o°'8i.  The  addition  of  the  correction  for 
phase  "  to  the  longitude  of  "U  's  central  meridian  "  gives  the 
longitude  of  the  meridian  which  bisects  the  illuminated  disc.  A 
list  of  Greenwich  times  when  their  longitude  is  o°  will  be  found 
further  on. 

The  diameters  of  the  disc,  etc.,  depend  on  the  same  assumed 
values  as  in  the  ephemeris  for  the  preceding  app  arition.  The 
formulae  employed  may  be  found  in  vol.  xlv.  p.  508. 


44  M*"'  Marth,  Epkrmerufi.tr  xlvii    i, 

Tbe  inclinations  y  and  the  ascending  nodes  T  of  the  orbits  of 
the  four  satellites  of  Jupiter  in  reference  to  the  plane  of  the 
planet's  equator  are  the  following,  the  longitudes  of  the  node* 
being  reckoned  from  0,  the  point  of  the  ascending  node  of 
Jupiter's  orbit  on  the  eqnator : 


SstL 

Sat. 

II. 

S*i. 

III. 

Sat.  IV. 

1*16. 

y. 

r. 

7. 

r. 

T» 

r, 

*/. 

r. 

Not. 

9 

001 18 

295?6 

o?492J 

294?o6 

0*1476 

25°f93 

0*3206 

33°f40 

1887. 
Jan. 

8 

■0117 

2943 

4925 

29217 

I466 

250-67 

3206 

330"5i 

Mar. 

9 

•01 17 

292*9 

•4927 

290-28 

•1455 

25040 

•320S 

33062 

**J 

8 

-01 16 

291-5 

•4928 

28839 

•I444 

250-11 

3203 

33074 

July 

7 

*on6 

290*1 

•4928 

286-50 

•"433 

249-81 

•3200 

330*86 

Sept. 

5 

•0115 

288*6 

4928 

284-60 

-1422 

2*949 

•3*96 

33098 

Nor. 

4 

0-0114 

2870 

O-4928 

28269 

0-141 1 

24915 

0-3191 

33109 

Has  the  eclipse  of  Sat.  IV.  on  May  17,  1886,  which  was  not 
given  by  the  Tables,  bat  the  probable  occurrence  of  which  was 
mentioned  in  toI.  zIt.  p.  509,  not  been  observed  anywhere  ? 

The  following  is  a  list  of  Greenwich  mean  times,  when  tV.e 
sero  meridian  in  the  assumed  two  systems  of  longitudes  will  pass 
the  middle  of  the  illuminated  disc.  To  save  printing,  the  time 
of  only  one  passage  is  given  for  each  day,  and  the  others  most  be 
found  by  interpolation,  or,  if  greater  accuracy  is  not  required,  by 
adding  or  subtracting  9*  5ora  in  the  first  system,  and  9*  56m  iu 
the  second. 


I 

n 

I 

II 

1886 
Dec.     9 

(878°-25) 

h      m 
18  44*2 

(870°-27) 

h      m 
12  550 

1886 
Dec.  25 

(878°-25) 

h      m 
18  268 

(87o°*27) 

h     m 
16    8  8 

10 

14  249 

18  42*2 

26 

14    75 

12     02 

11 

19  55*9 

M  33  7 

27 

19  384 

17  474 

12 

15  366 

20  21  O 

28 

15  190 

13  388 

13 

21     7-6 

16  I2'5 

29 

20  499 

19  26*0 

14 

16  482 

12      39 

30 

16  305 

15  17*4 

IS 

12  28*9 

17  51*2 

31 

12  in 

21    45 

16 

17  598 

13  42*6 

1887 

17 

13  40*5 

19  29'9 

JaD. 

1 

17  420 

16  56-0 

18 

19  11-5 

15  213 

2 

13  226 

12  474 

19 

14  521 

21    85 

3 

18  535 

18  345 

20 

20  23*1 

17     O'O 

4 

14  34*  1 

14  260 

21 

16    37 

12   515 

5 

20    50 

20  13*1 

22 

21  347 

18  387 

6 

15  456 

16    45 

23 

17  15*3 

14  30*  I 

7 

11  262 

"  55  9 

24 

12  559 

20  1 73 

8 

16  570 

17  430 

Nov.  1 836. 

Phytic 

nl  C 

)bserva 

Hon*  nfjttfriter. 

4. 

i287 
Jan.     9 

I 
(878°-25) 

h      m 

12  376 

II 

(87o°-27) 

h      m 
13  34*4 

(8; 

1887 

Feb.   13           1 

] 

l$c 

h 
18 

w 

•25)     ( 

m              1 

397        1 

II 

87o°-27) 

h     m 

7  263 

IO 

18    85 

19 

215 

14 

»4 

202        1 

13  176 

II 

13  49*o 

15 

12-9 

15 

10 

06 

19    4'5 

12 

19  199 

11 

43 

16 

"5  3i'3        1 

14  558 

13 

15    04 

16 

5i*4 

17 

11 

117 

ro  47  1 

14 

10  41*0 

12 

428 

18 

16 

424 

16  340 

15 

16  1 1-8 

18 

298 

19 

12 

228 

12  25  4 

16 

I0h5  conj. 

of  U  with 

20 

17 

535        > 

18  121 

*8m  W.B.  14,  in 

21 

»3 

339        i 

14    34 

*  o'2  north  of  limb. 

22 

19 

46        ] 

19  50-3 

— 

11  52-4 

H 

21*2 

23 

14  45'o 

15  4i  5 

«7 

17  232 

10 

12  6 

24 

10 

254        1 

[i  327 

18 

13    37 

15 

596 

25 

15  56o 

17  196 

'9 

18  346 

11 

510 

26 

11 

36'5        1 

13  108 

20 

14  151 

17 

380 

27 

17 

71         i 

'8  577 

21 

19  459 

13  294 

28 

12 

475 

14  489 

22 

15  264 

19 

164 

March     1 

18 

181         i 

to  40  2 

23 

11     70 

15 

7-8 

2 

13 

5*5 

16  270 

24 

16  377 

10 

591 

3 

9 

38'9 

r2  182 

25 

12  183 

16 

46' 2 

4 

«5 

95        1 

rS    51 

26 

17  490 

12 

37*5 

5 

10 

499 

^3  56  3 

27 

13  296 

18 

245 

6 

16 

205 

9  475 

28 

19    03 

«4 

159 

7 

12 

09         1 

15  343 

29 

14  40  8 

20 

2-9 

8 

17 

3i'5         1 

[i  255 

30 

20  116 

15  542 

9 

13 

118         i 

'7  123 

3« 

15  521 

11 

455 

10 

8 

522         l 

'3    3  6 

Feb.      i 

11  326 

17 

325 

11 

'4 

22  8 

8  54-8 

2 

17    3  3 

13 

238 

12 

ro 

32         1 

[4  41  6 

3 

12  438 

19 

io-S 

13 

'5  33  7        1 

[o  32  8 

4 

18  145 

15 

21 

14 

11 

141         1 

[6  196 

5 

13  55o 

10 

534 

15 

16 

447         1 

12  108 

6 

19  258 

16 

40-4 

16 

[2 

250 

S     19 

7 

15    62 

12 

317 

17 

s 

54         1 

13  48  7 

8 

10  467 

iS 

186 

18 

13 

360 

9  399 

9 

16  174 

14 

99 

19 

9 

163         1 

15  267 

10 

11  579 

10 

12 

20 

14 

469         i 

(I   179 

n 

17  286 

'5 

48- 1 

21 

10 

272 

17    47 

12 

13    90 

11 

39'4 

22 

>5 

57-S 

12  55  8 

46 

Mr.  Marth, 

Ephemeris 

M 

XLVII.  I, 

i887 

March    23 

I 
(878*25) 

h      m 
II    38'1 

II 

(870*27) 

h      ni 
8  470 

1887 
April   30 

1 

(878°-25) 

h      m 
14  246 

11 

(87o°'27) 
)i     m 
/    IO     II 

24 

17      87 

14  338 

May 

1 

IO     49 

5  523 

25 

12  490 

10  250 

2 

5  45  3 

11  391 

26 

8  294 

16  117 

3 

11   159 

7  303 

27 

13  599 

12    2-9 

4 

6  56*3 

13  172 

28 

9  40  2 

7  54"  1 

5 

12  269 

9    84 

29 

15  10-8 

13  408 

6 

8    73 

14  55  2 

30 

10  511 

9  32° 

7 

13  379 

10  46-5 

3i 

16  21'6 

15  188 

8 

9  i8'3 

6  377 

April    1 

12    20 

11     99 

9 

14  490 

12  245 

2 

7  42*3 

7     11 

10 

10  294 

8  158 

3 

13  128 

12  479 

11 

6    98 

14    27 

4 

8  53-2 

8  09-o 

12 

11  405 

9  539 

5 

14  237 

14  258 

13 

7  209 

5  45*2 

6 

10    40 

10  169 

14 

12    51*6 

n  321 

7 

15  34*6 

6    81 

15 

8  320 

7  233 

8 

11  149 

11  54'8 

16 

14    27 

13    IO-2 

9 

6  553 

7  460 

17 

9  43*  1 

9     15 

10 

12  258 

13  328 

18 

5  236 

14  484 

11 

8    61 

9  239 

19 

10  543 

10  397 

12 

13  36  6 

15  107 

20 

6348 

6  310 

13 

9  170 

11     1-9 

21 

12    55 

12  180 

14 

14  475 

6  530 

22 

7  46  0 

8    93 

15 

10  279 

12  398 

23 

13  167 

13  56*2 

16 

6    82 

8  309 

24 

8  57'2 

9  47  5 

17 

n  387 

14  177 

25 

14  279 

5  388 

18 

7  191 

10    89 

26 

10    84 

11  258 

«9 

12  496 

6    00 

27 

5  489 

7  17-2 

20 

8  30-0 

11  468 

28 

11   197 

13    4*2 

21 

14    05 

7  380 

29 

7      0-2 

8  5-s 

22 

9  408 

13  247 

30 

12   30*9 

14  425 

23 

15  11-4 

9  159 

3i 

8  11  5 

10  338 

24 

10  517 

15    27 

June 

1 

13  423 

6  25-2 

25 

6  32*1 

10  53  9 

2 

9  22*8 

12    I2'2 

26 

12    27 

6  451 

3 

5    33 

8    36 

27 

7  43*o 

12  319 

4 

10  34- 1 

13  507 

28 

13  I3'6 

8  23- 1 

5 

6  147 

9  420 

29 

8  540 

14    9*9 

6 

"  45*5 

5  334 

Nov.  1886. 

Plysi( 

ra 7  Observation*  of  Jupiter. 

4 

1887 

June  7 

I 

(878°-25) 

b      m 
7  26"  I 

JI 
(87o°-27) 

b      m 
II   20'5 

1887 
July   15 

I 

(878°-25) 
h      m 
IO  26*2 

IT 

(87o°-27) 
b     m 
12  483 

8 

12   569 

7  ii"9 

16 

6 

69 

8  39  8 

9 

8  375 

12  590 

17 

11 

380 

4  3i'4 

10 

14    8-4 

8  503 

18 

7 

187 

10  187 

11 

9  489 

14  374 

19 

12 

498 

6  103 

12 

5  295 

10  28-9 

20 

8 

306 

•  1 1  57'6 

13 

u     0-4 

6  20- 3 

21 

4 

113 

7  49  2 

14 

6  410 

12    74 

22 

9  42  4 

13  3^-6 

'5 

12  11-9 

7  588 

23 

5 

232 

9  28  1 

16 

7  525 

13  460 

24 

10 

543 

5  '97 

17 

'3  234 

9  374 

25 

6 

35o 

11     71 

18 

9    40 

5  288 

26 

12 

6*2 

6  587 

19 

14  349 

11   160 

27 

7  46'9 

12  46*0 

20 

10  156 

7     7*4 

28 

13 

181 

8  376 

21 

5  562 

12  546 

29 

8 

588 

4  292 

22 

11  271 

8  46- 1 

3o 

4  39'6 

10  16*6 

23 

7     78 

14  33  3 

31 

10 

10-8 

6    82 

24 

12  38  7 

10  247 

Aug.     1 

5 

51*5 

11  55  6 

25 

8  194 

6  16-2 

2 

11 

227 

7  47  2 

26 

13  50'3 

12    34 

3 

7 

35 

3  388 

27 

9  3io 

7  549 

4 

12 

347 

9  26-2 

28 

5  n-6 

13  42  r 

5 

8 

154 

5  179 

29 

10  42-6 

9  33 "6 

6 

3 

56*2 

11     53 

30 

6  233 

5  251 

7 

9 

274 

6  56  9 

July     1 

»  543 

11  12-3 

8 

5 

8-2 

12  44  3 

2 

7  350 

7    38 

9 

10 

394 

8  359 

3 

13    60 

12  511 

10 

6 

20'2 

4  27  6 

4 

8  467 

8  426 

11 

11 

5M 

10  150 

5 

14  17  7 

14  29  9 

12 

7 

322 

6    6-4 

6 

9  584 

10  214 

»3 

13 

3*4 

11  541 

7 

5  39  1 

6  12-9 

14 

8 

442 

7  45  7 

8 

II    101 

12    0-2 

15 

4  250 

3  373 

9 

6  508 

7  517 

16 

9 

562 

9  24  3 

10 

12  21-9 

13  390 

17 

5  37o 

5  164 

11 

8    2-6 

9  305 

18 

11 

82 

11    3*9 

12 

13  33*6 

5   22*1 

19 

6 

490 

6  555 

13 

9  144 

11    9*4 

20 

12 

20-2 

12  43  0 

H 

4  55* 

7    0'9 

21 

8 

10 

8  346 

46 


i887 

March    23 

(878°-25> 

h      in 
II    38  I 

24 

17     87 

25 

12  490 

26 

8  29-4 

27 

13  599 

28 

9  40  2 

29 

15  jo-8 

30 

10  511 

31 

16  21*6 

April    1 

12    20 

2 

7  423 

3 

13  128 

4 

8  532 

5 

14  237 

6 

10    4*0 

7 

»5  34*6 

8 

11  149 

9 

6  553 

10 

12  25-8 

11 

8    61 

12 

13  366 

13 

9  170 

14 

14  475 

IS 

10  279 

16 

6    8-2 

17 

11  387 

18 

7  191 

19 

12  49-6 

20 

8  30-0 

21 

14    05 

22 

9  408 

23 

15  114 

24 

10  517 

25 

6  32*1 

26 

12    27 

27 

7  430 

28 

13  136 

29 

8  540 

.  Marth, 

Ephemeris 

for 

XLV1I.  1 

II 

(87o°-27) 

h      m 

8  470 

1887 
April  30 

I 

(878°-25) 

b      m 
14  246 

II 

(87o°-27) 

h      m 
/    IO     II 

14  33'8 

Maj 

1 

10    49 

5  52'3 

10  250 

2 

5  45*3 

11  391 

16  117 

3 

II  159 

7  30'3 

12     2-9 

4 

6563 

13  172 

7  54'  1 

5 

12    26*9 

9    84 

13  408 

6 

8    73 

14  55'2 

9  32*o 

7 

13  379 

10  465 

15  188 

8 

9  183 

6  377 

11     99 

9 

14  490 

12  245 

7     ri 

10 

10  294 

8  158 

12  479 

11 

6    98 

14    27 

8  390 

12 

11  405 

9  53  9 

14  25  8 

'3 

7  20*9 

5  45'2 

10  16-9 

14 

12    516 

11  32-1 

6    81 

15 

8  32  0 

7  233 

11  548 

16 

14   27 

13  10-2 

7  46  0 

17 

9  43' 1 

9    1  "5 

13  32'8 

18 

5  236 

14  48-4 

9  239 

19 

10  543 

10  397 

15  107 

20 

6  348 

6  31*0 

11     19 

21 

12     55 

12  i8*o 

6  530 

22 

7  460 

8    9*3 

12  398 

23 

13  167 

13  5^*2 

8  309 

24 

8  572 

9  475 

14  177 

25 

14  279 

5  388 

10    89 

26 

10    8-4 

11  258 

6    00 

27 

5  489 

7  17-2 

11  468 

28 

11  197 

13     4*2 

7  380 

29 

7      0'2 

85-5 

13  247 

30 

12   30*9 

14  425 

9  159 

3i 

8  115 

10  338 

15    27 

June 

1 

13   423 

6  25*2 

10  539 

2 

9  22'8 

12    12*2 

6  451 

3 

5    33 

8    36 

12  319 

4 

10  34- 1 

13  507 

8  23- 1 

5 

6  147 

9  42*0 

14    99 

6 

»  45*5 

5  33*4 

Nov.  1886. 

Physical  Observations  of  Jupiter. 

4 

1887 

June  7 

I 

(8780-25) 

b      m 
7  261 

II 

(870°-27) 
h      m 
II   205 

1887 
July   15 

I 
(878°-25) 

h      m 
IO  26'2 

II 

(87o°-27) 
h     01 
12  483 

8 

12  569 

7   11-9 

16 

6    6-9 

8  39  8 

9 

8  375 

12   590 

17 

II   380 

4  3''4 

10 

14    84 

8  503 

18 

7  187 

10  187 

11 

9  489 

14  374 

19 

12  498 

6  103 

12 

5  295 

10  289 

20 

8  306 

•  11  576 

13 

11     0-4 

6  20  3 

21 

4  H'3 

7  492 

14 

6  410 

12    74 

22 

9  42  4 

13  3^6 

15 

12  ii*9 

7  588 

23 

5  232 

9  28  1 

16 

7  525 

13  460 

24 

10  54  3 

5  197 

17 

13  234 

9  374 

25 

6  350 

11     71 

18 

9    40 

5  288 

26 

12     6*2 

6587 

19 

14  349 

11   160 

27 

7  469 

12  46-0 

20 

10  156 

7     7"4 

28 

13  181 

8  37*6 

21 

5  562 

12  54  6 

29 

8  588 

4  292 

22 

11  271 

8  46-1 

3° 

4  39'6 

10  i6*6 

23 

7     78 

14  333 

31 

10  108 

6    8-2 

24 

12  38  7 

10  247 

Aug.      1 

5  51*5 

11  556 

25 

8  194 

6  16-2 

2 

11  227 

7  47*2 

26 

13  5o-3 

12    34 

3 

7    35 

3  388 

27 

9  310 

7  549 

4 

12  34  7 

9  26-2 

28 

5  ir6 

13  42  1 

5 

8  154 

5  179 

29 

10  42-6 

9  33'6 

6 

3  56*2 

»     5*3 

30 

6  233 

5  251 

7 

9  27  4 

6  56  9 

July      1 

"  543 

11  123 

8 

5    82 

12  443 

2 

7  35o 

7    3*8 

9 

10  394 

8  359 

3 

13    60 

12  511 

10 

6  202 

4  276 

4 

8  467 

8  426 

11 

11  514 

10  150 

5 

14  177 

14  299 

12 

7  322 

6    6-4 

6 

9  58-4 

10  214 

13 

13    34 

ll  541 

7 

5  39'  1 

6  12-9 

14 

8  44-2 

7  45  7 

8 

11  1 01 

12      0'2 

15 

4  250 

3  37*3 

9 

6  508 

7  517 

16 

9  562 

9  243 

10 

12  219 

13  390 

17 

5  37o 

5  164 

11 

8    26 

9  305 

18 

11     8-2 

11    39 

12 

13  33*6 

5   22' I 

19 

6  490 

6  555 

13 

9  '44 

11     94 

20 

12   20'2 

12  43  0 

H 

4  55*1 

7     o*9 

21 

8     10 

8  346 

50  Dr.  Copeland,  On  Hartwig's  xlvii.  2, 

showed  that  the  spectrnm  had  little  or  nothing  in  common  with 
the  brilliant  spectrum  of  Schmidt's  Nova  Oygni  in  its  earlier 
stages.  The  spectrnm  was  continuous  from  end  to  end,  and 
only  on  close  examination  could  slight  condensations  indicative 
of  bright  lines  be  detected.  The  spectrum  was  not  considered 
to  differ  strikingly  from  that  of  the  nebula. 

September  2  was  cloudy,  but  a  clear  interval  shortly  after 
midnight  on  the  3rd  enabled  Lord  Crawford  and  the  writer  to 
examine  the  Nova  critically  with  the  15 -inch  Equatorial ;  it  was 
then  seen  that  following  the  new  star,  a  little  to  the  north,  was 
a  nebulous  object.  Naturally  concluding  that  this  might  be  the 
nucleus  of  the  Great  Nebula,  the  relative  position  of  the  objects 
was  measured  with  the  micrometer,  and  they  were  also  connected 
with  an  i.il  magnitude  star  some  o\  seconds  preceding.  On 
comparing  tne  interval  between  this  latter  star  and  the  nebula 
with  a  rough  measure  taken  at  Birr  Castle  on  October  25,  1851, 
it  was  possible  to  announce  on  September  5,  in  Circular  98, 
"  that  tne  Nova  is  most  probably  situated  some  i'*6  preceding, 
and  5"  south  of  the  old  nucleus,  which  is  much  overpowered  by 
the  light  of  the  star."  To  test  this  conclusion  the  measurements 
were  repeated  from  time  to  time  as  occasion  offered,  the  place 
of  Nova  being  at  the  same  time  determined  with  the  Transit  Circle. 
The  following  is  a  summary  of  the  results  for  each  night : — 


Dec.  1886. 


Nova  Andromeda. 


5* 


1 


«     v© 


N      *•    v©      N 


w      W      N     VO     00      ON  fi 


N 


O 

5 

• 

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co 

• 

w   10  Q 

o\  p  * 

"b 

-H 

W 

w 

• 

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On 

in  to  **■ 

to 

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w 

ww»* 

w 

1 

f 

1   1   1 

1 

W 

*b 

+ 

^  vp     w    vp     3>    IO 

10    *•    **•    *■    **•    **• 


00 

to 
to 


+     +     +      +     +     + 


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w 
I 


3 
O 


<l 


to    be 

-h    2  b   1  b    J         ^ 

7      **      n  OvOsOSQ^^wMwwwwQwPts^ 

1    1  A.  1    1    ii5  +  +  +  +  +  +  e  +  «  + 

**  O  3  2 


co 


I 

to 


o 

j  -H 

O  »0  00  Q 

3  5vo  pv  5\ 

J  >  ^  ^ 

«  "  2  w 

A  «  ~  w 


ON     t^     N 


*b 

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3" 


o 

■H 
w      w     00      N      10     xn 

00     7*     **    vp    vo    vo 

00    vb   vb   vb   vb   vb 

W         W         W         W         w         m 


to 

o 

to 


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i 

3 


10 

o  ©    *   •     **>    CO 

£*«         •     vo     vo 

a 

s 


vp 


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w      M       M      N 

VO     vo     VO     5 
W      «      «     7$ 


s 


VO 


M 

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0 

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vo 

co 

w 

to 

On 

CO 

w 

M 

to 

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w 

to 

co 

CO 

to 

co 

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^» 

d 

vO 

r^ 

t^ 

t*» 

t^ 

*>• 

1 

a 

w 

to 

w 

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to   t^    ~ 

•*     .^ 

+J  to 

su  00 

00 


fO     O^     N     O 


^     »     N       ON     M       £* 
ww  v* 


ON 


£ 


to 

•*-< 

Pi 

00 

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o 

00 

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OQ 

w 

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S     CO 

(3  "S 


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52  Dr.  Copeland,  On  Hartwig's  xlvii.  2r 

Meridian  Observations  of  Nova  Andromeda  with  (he  %-inch  Transit  Circle. 


Apparent  a 

Red. 

Apparent  6. 

Bed. 

Observer, 

1885. 
Sept.    3 

h  m       s 

0  36  3086 

8                  °      '« 
-411          +40  38 

24-8 

// 
—  104 

L.B. 

10 

3085 

-423 

■  •• 

•  •  • 

n 

15 

3no 

-430 

286 

-14-8 

u 

19 

3106 

-4'35 

294 

-159 

i> 

25 

31*11 

-442 
Mean  Equinox 

18850. 

30'5 

-177 

38  144 

»» 

1885. 

Sept.     3 

a 
h  m       8 
O  36  26  75 

0 
+  40 

10 

2662 

•  •  • 

15 

2680 

138 

19 

2671 

135 

25 

2669 

128 

od  the  mean  of  which  is  based  the  following  table  : — 

Mean  Places  1885-0.    (Berliner  Jahrbuch.) 

a  & 

h  m       e  o      t        11 

iij  mag.  star  o  36  17-14  +40  37  585 

Nova  Andr.  o  36  26-71  +40  38  136 

Neb.  nucleus  o  36  2808  +40  38  181 

13  mag.  star.  o  36  2859  +40  35  380 

11  mag.  star  o  36  3469  +40  34  411 

Observers :  L.  B.  =  Br.  Ludwig  Becker ;  R.  C.  =  Ralph  Copeland. 

The  mean  errors  of  the  micrometrical  measures  are  deriveJ 
from  a  comparison  of  the  original  readings. 

The  relative  position  of  the  nucleus  of  the  Great  Nebula  and 
the  1 1  ^-magnitude  star  preceding  is  shown  directly  in  1  ;  but  it 
also  results  from  the  sum  of  2  and  3,  which  give 

Aa  Ad 

1 1  Jra  star  to  nebula  —  iof,,983  ±  o"030         — 19"-  64  ±  o"-42 

which  combined  with  1  affords  the  mean  value 

Aa  A* 

lijra  star  to  nebula  —  I08'898±08,OI9         —  I9"'47±o"*I& 

These  quantities  having  been  more  frequently  measured  at 
various  observatories  than  any  other  feature  connected  with  the 


Dec.  1886.                      Nova  Andromeda.  53 

nebula,  the  earlier  observations  are  here  collected  and  brought 
op  to  1885-0. 

Pos.          Precession.    Distance.  Aa*8850"   ±8 


O        #  §  It  ■  // 


IW»  1836.  Oct.  13 j       gl  I2.2       +J.3      I2|..24     _Io883     _I9X>5 

^Oct.  2f"e't ..    ,85!:}       83  +'3  —639    -479 

D'Arrest,§  1863,  Aug.  12  Ao=  - 1 1**26  —  1 128 

1865,  July  30  Aa  =  - 1 1'  60  —  1 1  -62 

H.  Vafd.1  1866,  Oct.  19  )  _  10*07     -I0'« 

Aa--io*79,  A8«~i9"-4f  +I3  -10507         1935 

Of  these  reanlts  those  by  Lord  Bosse  and  D'Arrest,  from  the 
nature  of  the  apparatus  employed,  are  much  less  accurate  than 
the  others.  The  remaining  observations,  although  somewhat 
discordant,  show  a  great  relative  fixity  in  the  two  objects,  the 
A8  alone  indicating  a  slight  possibility  of  progressive  change. 

The  Spectrum. 

As  will  be  seen  further  on,  the  New  Star  was  of  about  the 
8£  magnitude  when  first  observed  at  Dun  Echt  on  Sept.  1, 1885. 
It  was  therefore  a  priori  fairly  within  range  of  the  spectroscope; 
the  weather,  however,  only  permitted  a  brief  examination,  chiefly 
by  looking  through  a  prism  into  the  eyepiece,  with  the  results 
already  mentioned,  that  the  spectrum  was  continuous,  with  feeble 
traces  of  bright  lines,  and  much  resembled  that  of  the  Great 
Nebula.  The  star  was  "  yellowish  "  in  colour  on  this  night,  and 
"fall  yellow"  on  Sept.  3.  It  was  not  until  the  10th  that  a 
settled  fine  night  permitted  a  close  spectroscopic  examination. 
With  the  unmagnified  dispersion  of  a  direct- vision  Vogel  spec- 
troscope the  spectrum  extended  from  W.L.  67ommm  to  453mmm, 
or  from  between  B  and  C  to  half-way  between  F  and  G.  When 
the  spectrum  was  sufficiently  narrow  all  the  colours  were  visible, 
with  a  suspicion  of  brighter  points  in  the  line.  An  attempt  was 
made  to  measure  these  with  the  Grubb  spectroscope  and  a  flint 
prism  of  only  400  refracting  angle.  This  instrumental  change 
-cut  down  the  spectrum  to  the  limits  of  6oonunniand  456mmm,with 
a  maximum  at  544'4mmm  and  "  a  suspicion  of  a  bright  line,  but 
hardly  more,"  at  482"2mmm.  With  the  same  apparatus  the 
spectrum  appeared  quite  continuous  on  Sept.  11,  but  again  showed 
traces  of  bands  on  the  13th,  and  was  slightly  banded  on  the  15th. 
Traces  of  a  condensation  of  light  were  seen  at  W.L.  47  r6mmm  on 
•Sept.  20. 

*  Annate*  der  K.  Sternwarte,  Miinchen,  vol.  xxxii.  (1869),  p.  306. 
f  Melanges  Mathemaiiques  et  Astronomiques,  vol.  iii.  p.  571. 
%  Phil.  Trans.,  1861,  p.  700.  §  Sidcrvm  Nebulosorum  Obs. 

II  Beobachtungen  von  Nebefflecken,  &c,  Leipzig,  1867,  p.  65. 


54  2)r*  Copeland,  On  Harturig's  xlvii.  2, 

By  the  end  of  September  a  special  acute  prism  of  only  15  ° 
angle  was  received  from  Mr.  Hilger.  This  had  been  made  with 
a  view  to  obtaining  a  very  short  and  relatively  bright  spectrum, 
in  which  it  might  be  possible  to  measure  the  positions  of  the 
brighter  bands.  But  by  this  time  Nova  had  fallen  to  about  9*8 
magnitude,  so  that,  in  spite  of  the  very  low  dispersion,  only 
traces  of  two  brighter  points  towards  the  yellow  end  of  the 
spectrum  could  be  made  out  on  September  30,  the  rest  of  the 
spectrum  appearing  absolutely  continuous.  On  October  1,  by 
taking  every  precaution  in  the  way  of  moderating  the  illumina- 
tion, and  protecting  the  eyes  from  all  extraneous  light  with  a 
black  cloth,  these  two  lines  and  a  still  fainter  one  were  measured 
with  a  power  of  7  on  the  viewing  telescope.  The  measures  and 
wave-lengths  are : — 


Screw. 

W.L. 

Means. 

r       p 

mmm. 

mmm. 

Band  1 

52  257 

5571 

546-8 

49 

541-8 

4'6 

541*5 

Band  2 

5*  54*3 

510*  1 

5140 

694 

5^9*5 

58*1 

5124 

Band  3 

51  231 

493*1 

489*2 

169 

489-9 

5'8 

484*5 

Bed  end 

52  487 

575*8 

575*8 

Violet  end 

50  67-2 

4676 

467-6 

Respecting  the  discordancy  of  these  measures  it  must  be 
noted  that,  since  one  revolution  of  the  tangent-screw  covers  io' 
of  arc,  the  whole  visible  spectrum  was  but  slightly  more  than 
18'  in  length  ;  the  measures  for  the  three  bands,  therefore,  range 
over  2/,i,  i'*5,  and  i'*7  respectively,  arcs  which  cannot  be  con- 
sidered excessive  for  so  low  a  power  as  7  diameters,  on  such 
ill-defined  objects.  Indeed,  the  task  of  measuring  these  feeble 
bands  might  fairly  be  compared  with  that  of  attempting  to  fix 
the  azimuths  of  three  terrestrial  objects  in  dim  twilight  with  a 
theodolite  of  which  the  telescope  magnified  seven  times.  Part 
of  the  inaccuracy  is  also  probably  due  to  the  indeterminateness 
of  the  bands  themselves. 

Making  due  allowance  for  this  uncertainty,  it  seems  probable 
that  the  three  " bright"  bands  of  wave-lengths,  546*8,  514*0, 
and  489-2,  are  identical  with  the  three  brightest  bands  afterwards 
measured  with  the  same  apparatus  in  Mr.  Gore's  Nova  Orionis, 
of  which  the  brightest  parts  were  at  wave-lengths  542  8,  516*2, 
and  494  4  *     The  trace  of  a  condensation  of  light  at  W.L.  471*6- 

*  Monthly  Notices,  vol.  xlvi.  p.  1 10. 


Dec.  1886.  Nova  Andromeda.  55 

seen  on  September  20  agrees  well  with  the  bright  line  in  Nova 
Ononis  at  W.L.  472*2 ;  while  the  maximum  of  light  in  Nova 
Andromeda  at  544*4  on  September  10  is  closely  in  accord  with 
that  for  the  star  in  Orion  at  542*8.  The  only  really  discordant 
item  is  tbe  point  laid  down  at  482*2  on  September  10,  which 
does  not  correspond  to  any  known  bright  band  in  the  Bpectra  of 
variable  stars ;  it  was,  however,  entered  in  the  note-book,  in  the 
terms  already  stated,  as  "  a  suspicion  of  a  bright  hue,  but  hardly 
more."  But  if  it  does  roughly  represent  tbe  position  of  a  "bright " 
line  actually  visible  in  the  spectroscope,  one  would  feel  inclined 
to  regard  it  as  a  trace  of  the  F  line.*  On  October  2  tbe  spectrum 
presented  the  same  appearance  as  on  tbe  preceding  day.  On 
October  1 9  it  could  be  still  noted  as  continuous,  but  not  uniform, 
with  the  Vogel  spectroscope. 

Although  the  foregoing  results  differ  widely  from  those  ob- 
tained at  Greenwich,  and  also  at  Yale  College,  as  regards  the 
three  chief  lines  the  observer  cannot  doubt  as  to  their  general 
correctness.  The  spectroscope  was  specially  adapted  to  tbe  work, 
the  average  thickness  of  the  prism  traversed  by  the  light  being 
less  than  -^inch,  and  the  object-glasses  of  collimator  and  viewer 
were  cemented  so  as  to  reduce  the  loss  of  light  to  a  minimum. 
The  arrangement  of  the  tangent-screw  is  also  such  that  the 
observer  has  the  least  possible  idea  as  to  the  position  of  the 
lines  measured  until  the  divided  head  is  read  off.  E.g.,  in  this 
particular  instance  of  October  1,  until  the  observations  were 
ended,  the  observer  had  not  the  slightest  suspicion  that  the 
"  red "  end  of  the  spectrum  was  actually  above  the  D  lines. 
Besides,  in  the  case  of  an  object  losing  so  rapidly  its  power  of 
emitting  light,  it  is  quite  possible  that  the  spectrum  may  have 
slightly  varied  from  day  to  day. 

In  conclusion,  it  seems  worthy  of  remark  that  the  spectrum 
described  above  is  the  same  as  that  given  by  any  ordinary 
hydro- carbon  flame,  burning  so  feebly  that  the  spectrum  of  the 
blue  base  of  the  flame  is  just  beginning  to  show  through  the 
continuous  spectrum  afforded  by  the  white  part  of  the  flame. 

Estimations   of  Magnitude. 

The  earlier  estimations  were  made  either  with  the  6-inch 
Simms'  telescope,  power  28,  or  with  a  power  of  24  on  either  of 
the  two  3|-inch  finders  of  the  15-inch  Equatorial.  But  about 
September  10  it  was  found  that  these  low  powers  showed  the 
new  star  relatively  much  brighter  than  did  the  large  telescope, 
and  a  greater  amplification.  On  trial  it  was  found  that  this  was 
because  the  low  powers  failed  to  separate  the  star  sufficiently 
from  the  surrounding  nebulosity ;  the  image,  therefore,  which  was 

*  According  to  Nature,  No.  837,  p.  42,  Mr.  0.  T.  Sherman,  of  Yale 
College  Observatory,  has  seen  the  bright  F  line  in  the  spectrum  of  the  Great 
Andromeda  Nebula. 

*E  4 


.56  Dr.  C&peland,  OnHartwig's  xlvii.  2, 

compared  with  the  neighbouring  stars  was  made  up  of  Nova 
plus  the  denser  part  of  the  nebula.  In  the  15 -inch,  on  the  other 
hand,  Nova9 8  image  was  not  only  quite  distinct  from  that  of  the 
nebular  nucleus,  but  the  remainder  of  the  nebula  could  be  almost 
completely  effaced  by  a  suitable  illumination  of  the  field  of  view. 
Experimenting  in  this  way  on  September  10,  it  turned  out  that 
Nova  seen  with  a  high  power  in  a  bright  red  field  was  of  the  87 
magnitude  by  comparison  with  neighbouring  stars,  or  relatively 
om*8  fainter  than  when  seen  in  the  finder  or  the  6-inch,  which 
showed  it  of  the  7*9  magnitude.  From  this  it  would  seem  that 
the  low  powers  and  dark  field  included  as  much  of  the  surround- 
ing nebulosity  along  with  Nova  as  would  be  equal  to  a  star  of 
the  86  magnitude ;  for  on  Pogson's  scale 

Light  of  8m7  star  +  light  of  8m-6  star-light  of  7""9  star,  nearly. 

After  this  date,  therefore,  all  the  comparisons  were  made  in  a 
field  bright  enough  to  efface  the  diffused  nebulosity,  or,  when  the 
new  star  became  fainter,  with  as  much  light  as  it  would  bear. 
The  estimations  were  made  on  an  arbitrary  scale,  of  which  it  was 
found  that  om'8,  or  rather  om79,  corresponded  to  one  magnitude 
of  Argelander's  scale.  The  following  is  a  list  of  all  the  stars 
used  in  direct  comparison  with  Nova  or  the  nucleus,  or  for  fixing 
the  scale  of  magnitudes ;  in  particular  A  and  B  were  used  in 
checking  the  brightness  of  g,  h,  and  k.  The  places  are  in  part 
brought  up  from  the  Durchmusterung.* 


k 

a  (1885-0.) 
h    m       » 

0  35  55*5 

6  (1885-0.) 
+  40  304 

No.  in  D.M. 

Iu  D.M. 

Magnitude 
Adopted. 

ii'6o 

R 

0  36    79 

40  37  1 

(i3±) 

9 

0  36    97 

40  278 

1063 

B 

0  36  1 28 

40  197 

+  40,145 

90 

91 

h 

0  36  74-9 

40  323 

1095 

I 

0  36  17- 1 

40  380 

ii*6o 

A 

0  36  579 

40  22*8 

+  40,149 

91 

90 

a 

0  39  446 

40   IO7 

+  40,158 

75 

760 

f 

0  39  492 

40  408 

+  40,159 

95 

942 

d 

0  41     2"3 

40  403 

+  40,161 

91 

901 

e 

0  41  251 

40  398 

+  40,162 

91 

918 

The  subjoined  sketch  contains  all  the  D.M.  stars  near  the 

*  R  is  a  small  star  measured  at  Birr  Castle  on  October  28,  1851,  which, 
according  to  M.  Trouvelot  (Comptes  Rendus,  tome  ci.  p.  799),  was  not  visible  at 
Harvard  College  in  1874.  It  is  at  present  (1886,  December  6)  of  the  13th 
magnitude,  and  about  equal  to  star  13,  which  is  also  wanting  in  M.  Trouvelot's 
drawing.  R  appears  as  a  comparatively  bright  star  in  the  reproduction  of 
Mr.  Common's  photograph  in  Nature,  No.  831,  which,  however,  does  not 
give  13. 


Dec.  1886. 


Nova  Andromeda. 


57 


Great  Nebula  as  well  as  those  of  the  foregoing  list,  and  the 
two  small  stars,  11  and  13,  measured  on  October  2,  1885. 


o*  35"       36" 


37' 


38" 


39" 


40m 


41' 


• 

• 

i 

>    • 

1&L3Z 

• 

• 

a. 

• 

ft 

*9 

A 

• 

• 

• 

?  ! 

• 

• 

• 

/• 

• 

+  40°of 


10' 


2& 


30' 


40' 


Stars  near  the  Great  Nebula  in  Andromeda;  Epoch  18850 

+  =  Nova  Andromeda. 

The  stars  g,  B,  A,  I,  and  A  are  respectively  identical  with  a, 
B>  &  7>  and  A  of  Mr.  Stone's  list  in  Monthly  Notices,  vol.  xlvi.  p.  57, 
but  the  magnitudes  differ  considerably  towards  the  fainter  end 
of  the  scale  ;  e.g.,  Mr.  Stone's  ft,  which  is  called  nm'4at  Oxford, 
is  barely  nmo  on  the  Dan  Echt  scale. 

The  following  table  shows  the  resulting  magnitude  of  Nova 
for  each  night  on  which  estimations  were  made : — 


Date. 

G.M.T 

1885,  Sept.    1 

h 

89 

3 

125 

5 

132 

9 

125 

10 

102 

11 

I2*0 

12 

9*2 

13 

•  •  • 

15 

•  •  • 

17 

19 

93 

29 

116 

30 

•  ■  • 

Oct.    2 

129 

4 

103 

Estimations  with 

finder  and  6-inch. 

juagiucuc 

m 

in 

768 

[8'47] 

776 

[8'5S] 

7'84 

[8-63] 

792 

L871] 

7.92 

[870 

885 

897 

877 

917 

949 

941 

975 

983 

991 

10-39 

Date. 

O.M.T. 

1885,  Oct.  5 

h 
13*5 

6 

7'3 

7 

72 

19 

7-8 

Nov.  4 

1 12 

5 

1 18 

7 

I2'I 

30 

lO'I 

Dec.  2 

9-2 

29 

IO'I 

1886,  Jan.  2 

91 

30 

II'2  j 

31 

7'0  , 

Feb.  2 

80 : 

58  Dr.  Oopeland,  On  Hartioig's  xlvii.  2r 

EBtimations  with  Magnitude, 

finder  and  6-Inch.  ju^b-**" 

m  m 

IO47 

IO'47 

IO-47 
IO-91 

io-95 
1095 
1095 
1 1*9 
121* 

130 

135 
1 1  *2  Not  certainly  seen ;  7  j-  hours  west  of  meridian. 

7-0  Just  discernible;  sky  very  clear  •I4m±  . 

80  Not  a  trace  of  Nova  with  15-  inch  aperture. 

These  observations,  plotted  by  themselves  on  cross-lined 
paper,  would  lead  to  the  conclusion  that  Nova  decreased  con- 
tinually but  very  irregularly,  the  light  curve  falling  by  a  suc- 
cession of  steps.  But  on  a  comparison  with  the  results  of  the 
eye-estimations  at  the  HadclhTe  Observatory,  and  the  photometric 
results  of  Prof.  Pritchard,  M.  Charlier,  and  Dr.  Muller,  this 
conclusion  is  not  confirmed,  the  irregularities  disappearing  from 
the  mean  of  all  the  observations.  Even  the  very  slow  decrease 
between  September  5  and  13,  although  confirmed  by  Dr.  Hart- 
wig's  curve  in  Ast.  Nach.,  No.  2690,  is  not  apparent  in  the  mean 
of  the  other  observations.  The  records  agree  best  in  showing 
that  the  star  faded  more  rapidly  at  first  than  in  the  later  stages 
of  its  disappearance. 

The  Visibility  of  the  Nebula. 

It  has  already  been  said  that  the  nucleus  of  the  Great 
Nebula  was  seen  and  measured  on  September  3.  It  was  not 
seen  on  September  1,  but  there  was  so  much  cloud,  and 
attention  was  so  completely  directed  to  the  new  star  and  its 
spectrum,  that  the  relatively  faint  nucleus  may  have  been 
simply  overlooked,  the  more  so  as  the  greater  brilliancy  of  Nova 
on  that  night  must  have  overpowered  it  still  more  than  on  the 
3rd.  From  the  moment  the  nebular  nucleus  was  discerned  a 
look-out  was  naturally  kept  for  the  remaining  features  of  the 
nebula.  By  September  10  a  decrease  of  two  or  three  tenths  of 
a  magnitude  in  Nova  already  permitted  the  innermost  of  Bond's 
dark  lanes  to  be  made  out,  the  remoter  parts  of  the  nebula  at  the 
same  time  presenting  their  usual  appearance.  With  power  307 
the  nucleus  was  estimated  as  2"  in  diam.=  nm  star;  very  sud- 

*  In  dark  field  Nova  about  equal  to  the  nucleus  of  the  nebula,  but  a  red 
field  obliterates  the  nucleus,  leaving  Nova  still  clearly  visible. 


Dec.  1886.  Nova  Andromeda.  59. 

denly  much  brighter  in  the  middle.  With  power  132  it  was 
more  gradually  brighter  in  the  middle.  On  October  5,  with  power 
132,  the  nebula  was  splendidly  visible,  apparently  as  the  observer 
had  known  it  for  more  than  twenty-five  years.  On  November  5, 
1885,  the  night  being  fine  and  the  moon  out  of  the  way,  a  lengthy 
examination  was  made  of  the  nucleus  and  the  new  star  with  eye- 
pieces ranging  from  abont  120  to  600  diameters,  both  with  and 
without  illumination  of  the  field  of  view.  The  lenses  of  the 
lowest  eyepiece  are  adjustable,  bo  that  its  power  varies  to  some 
extent.     The  appearances  may  be  summarised  as  follows  : — 

Without  Illumination. — With  the  lowest  power  the  nucleus 
was  stellar,  and  about  1  magnitude  fainter  than  Nova.  The 
nebulosity  everywhere  extended  far  beyond  the  field  of  view, 
except  where  Bond's  dark  lanes  came  in.  Power  132  showed 
the  nucleus  barely  different  from  a  star  of  the  1  ith  magnitude, 
and  also  with  229  the  nucleus  was  fairly  Btellar,  but  with  307 
this  was  no  longer  the  case,  the  densest  part  appearing  about 
4"  in  diameter.  Increasing  the  power  to  442  rendered  the 
nucleus  slightly  more  diffuse,  and  showed  an  elongation  towards 
Nova.  With  this  eyepiece  Nova  was  still  as  sharp  and  distinct 
as  any  other  star.  Magnified  about  600  times  the  nucleus  was 
seen  as  a  soft  nebulosity  5"  in  diameter. 

With  bright  Illumination  of  the  Field. — With  a  red  field 
sufficiently  bright  to  restrict  the  visible  nebulosity  to  about  20" 
diameter,  the  nucleus  appeared  quite  stellar  and  one  magnitude 
fainter  than  Nova.  This  was  with  the  lowest  eyepiece.  Tried 
in  the  same  way  with  powers  132  and  229  the  nucleus  did  not 
appear  nearly  so  star-like,  and  on  increasing  the  illumination  it 
almost  disappeared,  while  Nova  remained  quite  bright.  With 
power  307,  the  red  illumination  not  being  quite  strong  enough 
to  obliterate  the  nucleus,  a  bright  yellow  field  was  tried  which 
completely  overpowered  the  nucleus,  while  leaving  the  new  star 
brightly  visible.  On  applying  power  442  with  the  same  field, 
the  nucleus  appeared  4"  or  5"  in  diameter,  but  was  very  sensitive 
to  illumination,  being  extremely  difficult  to  distinguish  even 
when  Nova  was  quite  bright.  With  a  power  of  600  it  was  found 
that  the  nucleus  disappeared  before  the  star  n9  preceding. 

The  chief  points  believed  to  be  shown  by  these  experiments 
are : — the  perfectly  stellar  character  of  Nova  and  the  extreme 
sensitiveness  of  the  Great  Nebula  and  its  nucleus  to  illumination. 
It  therefore  seems  but  reasonable  to  conclude  that  the  invisi- 
bility of  the  nebula,  and  even  of  the  nucleus,  on  September  1  was 
solely  due  to  the  overpowering  light  of  the  new  star. 

To  test  this  point  still  further,  a  Zollner's  photometer  was 
attached  to  the  15- inch  on  November  20  of  this  year.  On 
contracting  the  aperture  to  3*6  inches  it  was  found  that  the 
Durchmusterung  star  4*  400  158,  7*5  magnitude,  could  be  most 
perfectly  counterfeited  by  the  artificial  star  of  the  photometer. 
On  bringing  this  artificial  star  in  front  of  the  Great  Nebula,  the 
nucleus  gradually  disappeared  as  the  artificial  star  approached 
it.    In  point  of  fact,  the  nucleus  of  the  Great  Nebula  required 


60  Br.  Copelandy  Nova  Andromeda.  xlvii.  2, 

the  artificial  star  to  be  fully  75"  distant  before  becoming  fairly 
defined.  On  the  other  hand  the  companion  nebula,  M.  32,  bore 
the  comparison  star  very  much  closer,  say  within  15".  Dr.  L. 
Becker  fully  confirmed  this  experiment,  which  was  repeated  by 
recurring  three  times  to  the  D.M.  star.  When  the  artificial 
star  was  placed  exactly  upon  the  nucleus  it  was  surrounded  by 
a  soft  nebulosity,  without  any  distinctive  features.  This  experi- 
ment seems  conclusive  as  to  the  power  of  a  7 ^-magnitude  star 
to  completely  obscure  every  trace  of  the  central  part  of  the 
Great  Nebula  in  Andromeda  without  necessarily  effecting  any 
change  in  the  nebula  itself.*  At  the  same  time,  it  does  not  at 
all  prove  that  no  change  took  place  in  the  nebula,  but  simply 
that  it  was  impossible  to  observe  any  such  change  as  long  as  the 
star  was  shining  brightly.  At  Dun  Echt,  however,  no  traces  of 
a  permanent  change  brought  about  by  the  outburst  of  the  new 
star  have  been  detected  in  the  nebula  since  the  fading  of  the 
star.  Nevertheless,  the  fact  of  the  appearance  of  a  similar  star 
in  the  globular  cluster  M.  80  =  G.  C.  41 73  =  h.  3624,  as  observed 
by  Prof.  Auwers  and  Mr.  Pogson  in  i860,  goes  far  towards 
showing  a  connection  between  these  sudden  outbreaks  and  their 
apparent  surroundings.  This  was  pointed  out  by  the  late 
•C.  G.  Talmage  at  the  conclusion  of  the  reading  of  a  Paper  on  the 
New  Star  at  the  meeting  of  the  British  Association  at  Aberdeen 
in  September  1885,  and  also  forms  the  subject  of  a  communi- 
cation to  the  Astronomische  Nachrichten  (No.  2715) f  by  Prof. 
Auwers.  The  spectrum  of  G.  G.  4173,  moreover,  is  known  to 
be  very  faint  and  continuous  from  the  observations  of  Lieut. -Col. 
Herschel  in  1868  (see  Proc.  Boy.  Soc.,  vol.  xvi.  p.  453),  and  thus 
resembles  that  of  the  Great  Nebula  in  Andromeda.  The  chief 
difference  between  the  two  nebulre  is  that,  while  Sir  J.  Herschel's 
20-foot  telescope  completely  resolved  G.  G.  4173  on  two  occasions 
at  the  Gape  of  Good  Hope,  the  great  northern  nebula  has  never 
shown  more  than  very  doubtful  signs  of  resolvability.  It  may 
be  remarked  that  the  decadence  of  the  Nova  of  i860  was  much 
more  rapid  than  that  of  the  recent  star,  for  Prof.  Auwers' 
figures  show  that  it  fell  3  magnitudes  in  about  twenty  days, 
while  Nova  Andromeda  required  about  eighty  days  to  decrease 
to  the  same  extent. 

With  regard  to  the  reported  occurrence  of  a  fresh  stellar 
outbreak  in  the  nebula  this  autumn  (Astr.  Nach.  No.  2755),  it 
may  be  worth  recording  that  M.  32  was  very  carefully  examined 
on  September  27,  without  anything  being  seen  in  the  Great 
Nebula  that  appeared  worthy  of  remark.     On  October  20,  the 

*  It  has  since  occurred  to  the  writer  that  by  using  the  electric  light  it 
may  be  possible  to  produce  an  artificial  star  sufficiently  bright  to  permit  of 
repeating  this  experiment  with  the  full  aperture  of  a  15-inch  telescope.  By  a 
close  reproduction  of  the  appearance  of  the  star  and  the  nucleus  as  observed 
on  September  3,  1885,  the  brightness  of  the  star  on  that  day  may  even  yet  be 
redetermined  with  some  approach  to  accuracy,  on  the  probable  assumption  that 
the  nucleus  has  not  changed. 

f  See  also  Ast.  Rack.  yol.  liii.  col.  293  ;  vol.  lviii.  col.  374;  and  Monthly 
Notices,  vol.  xxi.  p.  32 


Dec.  1886.       Mr.  Gore,  Formulce  for  Binary  Stars.  61 

distance  of  the  nucleus  from  the  small  star  so  often  mentioned 
was  1 25"*  16,  as  a  result  of  six  settings;  nor  could  a  trace  of 
anything,  except  the  old  nucleus,  be  seen  near  the  centre  of  the 
nebulosity,  with  a  power  of  229  on  the  15 -inch.  The  nebula  was 
also  swept  over  with  the  6-inch  object-glass  prism  on  October  22, 
when  nothing  was  seen  in  the  diffused  image  to  indicate  the 
presence  of  a  star. 

Dun  Echt  Observatory : 
1886,  Dec.  7. 


Formulce  for  Binary  Stars.     By  J.  B.  Gore. 

For  the  following  binary  stars,  of  which  the  observations  are 
not  yet  sufficient  for  the  calculation  of  a  satisfactory  orbit,  I 
have  computed,  by  the  method  of  least  squares,  the  following 
empirical  formulae  for  the  calculation  of  an  ephemeris.  The 
positions  of  the  stars  are  for  i88o"o: — 

23116. 
R.A.  6h  i5"-9,  -ii°  42'. 
Magnitude*  62  and  10. 
e-2i°-89  +  o°-i425  (2- 1850). 
P»4"-I4-o"-oi8  (2-1850). 

45  Geminorum  =  02  165. 
R.A.  7h  im-5,  +  160  8'. 
Magnitudes  5,  107. . 
0=  i27°72- 1°-585  (2-  i85o)-o°-oo8ii  (2- 1850)2. 
P -  3"'6g7  -  o"-0434  (t  - 1850). 

9  Aigus  =  Burnham  10 1 . 
B.A.  7*  46-  I3\  -I3°35'- 

Magnitudes  5,  7. 
0a»29i°-38  +  3°-O44  (2-1875). 
p-o"-5i7  (1875). 

2  1175. 
R.A.  7h  56"- 1,  +40  30'. 

Magnitudes  7*8,  97. 

0«2ii°-i6  +  o°-369  (2-1850). 

P-i"-949(i85o). 

2  1287. 

E.A.  8h  44m'9,  +  120  35'. 

Magnitudes  8,  10*3. 

e=ioo°-83-o°-442  (2-1850). 

P-i"'675  +  o"-oi3  (2-1850). 


62  Mr.  Qore,  Formrdcefor  Binary  Stars.  xr,vir.  2, 

2  1389. 
R.A.  9"  45-5,  +  270  33'. 
Magnitudes  8,  9. 
fl«32i°-87-o°-378  (^-1850). 
p  - 1"*86  +  o"-oo97  (t  - 1850). 

OS  215. 

R.A.  ioh  9"B7,  + 180  20'. 

Magnitudes  7,  7*2. 

0=255°-6o-i°-io3  (^-1850). 

p  -  o"-445  +  o"-oi  16  (t  -  1850). 

2  1879. 

lt.A.  I4b  40n,,4,  +  io°  io\ 

Magnitudes  7*8,  88. 

0  =  54°-64-o°-522  (tf-1850). 

P-o"7i6(i8so). 

Anon.  Herculis  =  Gledhill  528. 

R.A.  i6h  40m-3,  +430  42'. 

Magnitudes  8,  8. 

0«i32°-93-2°-44i  (^-1870). 

P  =  o"'957  (1870)  (distance  diminishing). 

5  2536. 
R.A.  19*  26™  i6«,  +  1 70  32'. 

Magnitudes  8,  11. 
fl=45°-29  +  o°76i  (^-1850). 
p-i"-852. 

OS  437- 
R.A.  2ih  I5m,9,  +31°  56'. 
Magnitudes  7,  10*5  (65,  72  Perrotin,  1885720). 
0  =  62°-53-o°-434  (^-1850). 
p=  i"-34  (1850)  (i"6oo  Perrotin,  1885720). 

72  Pegasi  =  Burnham  720. 

R.A.  23h  28™   +  300  40'. 

Magnitudes  6,  6r. 

B  m  3io°'98  +  2°-229  (t - 1880). 

p«o"*404(i88o). 

Formula  for  most  of  the  other  binary  stars,  computed  by 
Drs.  Doberck  and  Duner,  will  be  found  in  Gledhill's  Handbook 
of  Double  Stars,  and  the  "  Corrections,  Notes,  &c,"  to  this 
excellent  work. 


Dec.  188.6.     Mr.  Maunder,  Mr.  Sherman? s  Observations.  63 

Mr.  Sherman's  Observations  of  Bright  Lines  in  Stellar  Spectra. 

By  E.  W.  Maunder. 

I  fear,  from  Mr.  Sherman's  reply  to  my  former  Paper,  that 
I  was  not  sufficiently  explicit  in  my  critioism  of  his  observations, 
for  he  certainly  seems  to  have  missed  the  point  of  my  remarks. 
Nor  has  he  yet  explained  his  method  of  procedure  in  such  a  way 
that  I  can  understand  it 

His  object  is  "  to  render  the  image  of  the  bright  line  light  as 
broad  and  intense  as  may  be,  and  the  intensity  of  the  background 
light  a  minimum. "  I  see  but  one  way  of  attaining  this  end :  viz., 
by  employing  as  high  a  dispersion  as  the  star  will  bear,  and  by 
making  the  spectrum  as  pure  as  possible  by  the  use  of  a  long 
collimator  and  narrow  slit.  Mr.  Sherman  has  indeed  employed 
a  fairly  high  dispersion,  but  so  far  as  I  can  judge  has  made  no 
effort  to  secure  purity  of  spectrum. 

We  may  take  it  that  the  image  of  a  star  in  the  primary  focus 
of  a  telescope  is  practically  a  point.  The  spectrum  of  a  star  is 
therefore  a  straight  line,  and  as  the  image  of  the  star  has  no  very 
appreciable  breadth  it  is  not  necessary,  in  order  to  see  the  spec- 
trum, to  use  a  slit.  The  star  will,  as  Mr.  Sherman  truly  argues, 
act  as  a  slit  for  itself.  If,  then,  certain  radiations  be  missing  in 
the  star's  light  we  shall  have  the  coloured  line  of  the  star  spec- 
trum broken  by  dark  points,  each  dark  point  being  a  negative 
image  of  the  star.  If  certain  radiations  in  the  star's  light  be 
exceedingly  brilliant  we  shall  have  them  appearing  as  bright 
points  on  the  coloured  line  of  the  star  spectrum,  each  bright 
point  being  an  image  of  the  star;  and  indeed  the  entire 
continuous  spectrum  is  but  a  succession  of  an  infinite  number  of 
various  coloured  images  of  the  star.  By  what  means  then  does 
Mr.  Sherman  secure  that  his  bright  lines  are  of  a  greater  breadth 
than  the  star  spectrum  when  he  uses  no  cylindrical  lens,  and  of 
a  less  breadth  than  the  star  spectrum  when  he  broadens  it  out 
into  a  band  by  the  use  of  a  cylindrical  lens  P*  How  is  it  that  they 
escape  the  broadening  effect  of  the  cylindrical  lens  whilst  the 
spectrum  on  which  they  stand  is  widened  out  ?  It  was  this  point 
in  particular  which  made  me  say  (Monthly  Notices,  vol.  xlvi.  p.  283): 
"  It  seems  very  difficult  to  believe  that  this  can  be  a  description 
of  the  behaviour  of  true  stellar  bright  lines,"  and  not  the  change- 
able flickering  appearance  which  Mr.  Sherman  ascribes  to  them, 
though  I  confess  that,  in  my  view,  added  to  the  unlikelihood  of 
their  being  true  lines.  My  remarks  as  to  the  positions  of  the  slit 
and  cylindrical  lens  were  also  directed  to  this  point,  as  I  thought 
it  possible  that  with  a  slit  badly  adjusted  and  the  cylindrical  lens 
close  to  the  eye,  false  images,  produced  within  the  spectroscope, 
might  present  the  very  appearance  Mr.  Sherman  has  described 
of  long  lines  in  the  red,  and  stellar  points  in  the  green.     Per- 

*  "  At  the  red  end,  under  a  sharp  focus,  they  (the  bright  lines)  stand  out 
the  full  breadth  of  the  spectrum,  bearing  somewhat  the  same  relation  to  the 
background  as  the  prominence  to  the  solar  spectrum.  In  the-  brighter  portion 
of  the  spectrum  they  are  cut  down  to  fine  star-points" 


64  Mr.  Maunder,  Mr.  Sherman9 8  Observations.       xlvii.  2, 

sonally  I  much  prefer  the  use  of  the  cylindrical  lens  before  the 
slit,  but  it  is  not  necessarily  wrong  to  use  it  close  to  the  eye. 

Mr.  Sherman,  whilst  expanding  my  criticism  as  to  the  width 
of  his  slit,  fails  to  see  how  it  affects  his  measures.  His  slit  was 
6'  of  arc  in  width,  the  diffraction  disc  of  his  star  was,  he  adds, 
about  3".  The  slit  was  therefore  120  times  too  wide  at  least,  not 
merely  100  times,  as  I  said.  The  purpose  of  a  slit  in  stellar 
spectroscopy  is  twofold.  It  is  not  necessary  in  order  to  see  the 
spectrum,  bat  it  is  necessary  to  give  it  purity,  and  so  to  bring  up 
fine  lines.  And  it  is  absolutely  essential  for  measures  of  posi- 
tion. Unless  the  slit  is  so  nearly  closed  as  just  to  hold  the  star 
between  its  jaws,  what  guarantee  has  the  observer  that  the  star 
is  not  travelling  about  from  one  side  to  the  other  of  the  slit  P 
And  if  the  star  moves,  the  lines  in  its  spectrum  will  move  too. 
With  a  slit  of  the  width  recorded  by  Mr.  Sherman  no  reliance 
whatsoever  can  be  placed  on  the  positions  he  records  for  the 
lines  he  observed,  unless  he  can  show  that  he  had  some  means 
of  absolutely  fixing  the  star  to  one  particular  and  invariable 
position.  Then  again,  how  did  he  obtain  his  fiducial  points 
for  the  reduction  of  his  observations?  Did  he  allow  the 
light  from  vacuum  tube  or  taper  to  shine  in  through  this 
wide  slit,  thus  practically  observing  the  comparison  spectrum 
through  a  slit  120  times  that  of  the  stellar  spectrum  ?  Sorely  I 
was  right  in  saying  that  such  a  slit  was  practically  no  slit  at  all. 
Mr.  Sherman,  for  all  that  appears,  might  as  well  have  removed 
his  slit  plates  altogether. 

I  infer  from  the  second  paragraph  on  p.  18  in  Mr.  Sherman's 
reply  that  he  wishes  to  withdraw  his  claim  for  some,  if  not  for 
many,  of  the  stars  he  has  examined.  I  felt  sure  that  more  care- 
ful and  continued  observations  would  lead  him  to  that  con- 
clusion. 

;  Finally,  I  have  no  wish  to  say  that  in  every  case  Mr.  Sherman 
has  been  misled.  I  frankly  confess  that  I  do  not  think  his 
observations  look  promising ;  but  since  we  were  both  in  pretty 
close  accord  as  to  our  observations  of  Nova  Andromedce,  he  will, 
I  hope,  acquit  me  of  any  desire  to  pass  a  sweeping  condemnation 
on  his  entire  work. 

With  regard  to  the  numerous  quotations  he  has  made  from 
various  observers,  I  trust  that  he  will  not  do  me  the  injustice  of 
supposing  that  they  were  either  unknown  to  or  ignored  by  me. 
I  do  not,  however,  see  how  they  bear  upon  the  point  at  issue, 
which  is,  not  whether  bright  lines  have  not  been  detected  in  a 
few  special  stellar  spectra,  but  whether  they  form  a  prominent 
but  hitherto  unsuspected  feature  in  every  one  of  fifty  stellar 
spectra  taken  at  random ;  and  whether  true  bright  lines  could 
behave  as  Mr.  Sherman  has  described  his  lines  as  doing,  viz. 
show  themselves  either  as  broader  or  narrower  than  the  general 
stellar  spectrum  of  which  they  formed  a  part. 

Royal  Observatory,  Greenwich: 
1 886,  December  10. 


Dec.  1886.     Greenwich  Observations  of  Comet  f  1886. 


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68  Sydney  Observations  of  Comet  Finlay.  xlyii.  2, 

1886,  Sept.  1. — Comet  seen ;  only  approximate  position  ob- 
tained. 

Sept.  2. — Comet  very  faint  as  close  to  moon;  a  diffused  coma, 
no  decided  nucleus. 

Sept.  8. — Strong  moonlight ;  comet  much  more  condensed 
than  on  Sept.  2.     Coma  small,  about  £'  in  diam. 

Sept.  9. — Comet  much  brighter  even  with  increased  moon* 
light ;  a  suspicion  of  a  nucleus.  Observed  with  a  star  not  in 
catalogue. 

Sept.  10. — Comet  extremely  faint,  and  difficult  to  observe 
owing  to  haze. 

Sept.  14. — Comet  brighter;  a  suspicion  of  a  nucleus. 

Sept.  15. — Comet  much  brighter ;  coma  about  i'  in  diam. 

Sept.  20. — Comet  brighter;  condensed  in  the  centre,  with  a 
very  faint  nucleus. 

Sept.  21. — Comet  bright,  but  no  very  distinct  nucleus,  but 
condensed  in  the  centre.  At  8h  2m  138  S.M.T.  the  centre  of  the 
comet  passed  over  a  9-mag.  star.  The  star  did  not  diminish  in 
brightness,  but  appeared  to  have  a  slight  haze  round  it.  Three 
other  9-mag.  stars  in  the  field.  A  very  faint  nucleus  was  thought 
to  be  seen  in  glimpses ;  but  if  there  at  all  it  must  be  very  faint. 

Sept.  22. — Comet  not  so  bright  as  last  night.  Difference 
of  declination  determined  by  the  circle. 

Sept.  24. — Night  particularly  bad ;  comet  much  fainter  than 
it  has  been.     A  glimpse  of  a  nucleus. 

Sept.  25. — Evening  very  hazy;  haze  stopped  further  observa- 
tions. 

Sept.  28. — Comet  faint ;  coma  diffused,  with  a  faint  nucleus. 

Sept.  29. — Comet  fainter. 

Telescope  n£-inch  Equatorial,  with  filar  micrometer. 

Observations  of  Oomet  discovered  by  Finlay  at  the  Cape,  Sept.  26 r 
1886,  made  at  Sydney  Observatory  urith  the  11  J-incft  Equatorial 
and  filar  micrometer. 

(Communicated  by  H.  C.  Russell,  B.A.,  Government  Astronomer.) 


Date. 

x886. 

Sydney  M.T. 

Star's  Name. 

Difference  of  Comet  from  Star. 
Comet— Star.     Comet— Star. 
BJL                 N.PJX 

No. 

of 

Oomp 

Sept.  30 

h    m   8 
10    0  53 

9391  Cape  Cat.  '80 

m       8 
+ 1  457 

-  7  445" 

I 

Oct.      1 

8  48  47 

9391  Cape  Cat.  '80 

+  4  10-9 

-  5  u-66 

5 

5 

8  26    0 

9504  Cape  Cat.  '80 

+  4  12  70 

+ 13  4092 

6 

11 

9  *7  49 

9766  Cape  Cat.  '80 

-7  51-28 

-  7  5287 

4 

12        8    2  21      9766  Cape  Cat.  '8o      -4  5738     —  6  5978     10 

Sept.  30. — Comet  faint. 

Oct.  5. — Moonlight;  comet  faint. 

Oct.  7. — Comet  observed  with  a  star  not  in  catalogue. 


Dec  1886.  Mr.  Ranyard,  Form  of  the  Area  etc.  69 

Oct.  8. — Comet  brighter.  At  beginning  of  observations  comet 
in  a  straight  line  with  two  9-mag.  stars.  Change  in  B.A.  during 
evening  very  apparent.     Observed  with  a  star  not  in  catalogue. 

Oct.  11. — Evening  very  hazy ;  comet  very  faint. 

Oct.  12. — Comet  feint. 


On  Evidence  with  respect  to  the  Form  of  the  Area  in  the  Heavens 
from  which  the  Meteors  of  November  27,  1885,  appeared  to 
Radiate,    By  A.  C.  Ranyard. 

There  were  a  great  many  observers  of  this  rich  shower,  and 
most  of  them  seem  to  agree  that  the  meteors  did  not  radiate  from 
a  point,  bnt  that  there  was  a  radiant  area  of  some  considerable 
extent.  I  did  not  observe  the  shower  till  well  after  its  maximum 
at  nearly  nine  o'clock  ;  bnt  from  the  forty  or  fifty  meteors  whose 
paths  I  observed,  and  was  able  to  trace  back  upon  the  heavens 
(making  a  mental  estimate  of  the  distance  of  the  radiant,  judged 
from  the  length  of  the  path  and  velocity),  I  thought  that  the 
area  from  which  they  radiated  was  elliptical,  with  its  major  axis 
nearly  north  and  south,  some  120  or  150  long,  and  a  minor  axis  of 
6°  or  8°.  I  mentioned  the  elliptic  shape  of  the  area  I  had  ob- 
served to  Col.  Tupman,  and  he  told  me  that  in  the  chart  of 
paths  he  had  laid  down  the  radiant  area  was  distinctly  elliptical. 
But  as  I  did  not  see  any  reason  for  such  an  elliptic  form  of  the 
area,  I  regarded  the  coincidence  as  merely  accidental,  and  thought 
that  our  results  were  probably  not  founded  on  a  sufficient  number 
of  observed  tracks.  When  Col.  Tupman  described  his  ob- 
servations at  the  evening  meeting  of  the  Society,  he  stated  that 
the  longer  axis  of  the  elliptic  area  observed  by  him  lay  north  and 
south.  This  struck  me  as  an  additional  coincidence,  for  I  felt 
sure  that  I  had  not  mentioned  to  him  the  direction  of  the  axes 
of  the  elliptic  area  observed  by  me ;  but  I  did  not  think  seriously 
of  the  matter  till  a  few  weeks  after,  when  I  saw  a  letter  from 
Prof.  Young  in  Nature  of  December  17,  in  which,  after  de- 
scribing his  observations,  he  says  that  "  the  radiant  was  not  a 
point  but  rather  a  region  about  40  long  north  and  south,  and  20 
wide."  I  then  wrote  to  ask  Prof.  Young  further  about  his  ob- 
servation, and  he  replied  that  the  radiant  region  was  "  an  oval 
area,"  perhaps  a  little  larger  than  he  had  at  first  estimated. 

Recently  during  a  visit  to  the  observatory  at  Nice,  M. 
Perrotin  showed  me  a  map  on  which  he  and  his  assistants  had 
laid  down  the  courses  of  sixty  or  seventy  meteors  they  had  ob- 
served on  the  night  of  November  27.  I  at  once  saw  that  the 
paths  did  not  radiate  from  a  point,  and  without  telling  M.  Per- 
rotin of  the  other  observations,  I  asked  him  to  draw  a  contour 
line  round  the  area  of  radiation.  Both  he  and  M.  Thollon,  who 
was  present,  drew  elliptic  curves  with  the  longer  axis  north  and 
south,  or  rather  inclined  io°  or  150  to  the  west  of  the  north  point. 


7<>  Mr.  Ranyardy  Evidence  with  respect  to  xlyii.  ir 

The  accompanying  woodcut  is  made  from  the  contour  lines  laid 
down  by  M.  Perrotin  and  M.  Thollon  on  a  tracing  from  their 
map. 


There  therefore  appears  to  be  some  very  definite  evidence  that 
the  paths  of  these  meteors  did  radiate  from  an  elongated  area  with 
its  axis  north  and  sonth.  I  have  been  thinking  over  the  possible 
physical  causes  of  such  an  elliptic  area  of  radiation.  If  the  paths 
of  the  meteors  were  all  parallel  they  would  appear  to  meet  in  a 
point.  And  if,  on  entering  the  earth's  atmosphere,  they  were 
deflected  from  their  original  direction,  and  there  was  no  greater 
tendency  to  deflection  in  one  direction  than  in  another,  they 
would,  on  becoming  luminous,  move  in  paths  which  would  be 
symmetrically  arranged  with  respect  to  the  original  direction 
of  motion,  and  an  observer  would  refer  them  to  a  circular  area  of 
radiation  with  its  centre  corresponding  to  the  original  direction 
of  motion  outside  the  earth's  atmosphere.  If  there  were  a  greater 
tendency  to  scattering  or  "  skidding  "  from  the  original  direc- 
tion of  motion  on  entering  the  atmosphere  in  one  direction 
rather  than  in  the  direction  at  right  angles,  the  area  of  radiation 
would  be  elongated  in  the  heavens  in  a  direction  corresponding 
with  the  direction  of  greatest  "  skidding."  The  elliptic  area  of 
radiation  of  the  Biela  meteors  shows  that  their  paths,  at  all 
events  after  they  become  luminous  within  the  earth's  atmosphere,. 


Dec.  1886.      the  Form  of  the  Area  in  the  Heavens  etc.  71 

are  not  parallel,  and  that  there  is  a  greater  tendency  to  deviate 
from  the  mean  direction  to  the  north  and  south  than  to  the  east 
and  west. 

It  has  been  suggested  by  those  who,  like  Sir  Stawell  Ball 
and  Mr.  Proctor,  are  inclined  to  believe  that  meteors  were 
originally  projected  from  the  earth,  that  if  they  were  ejected  in 
slightly  different  directions  they  would  not  return  moving  in 
parallel  paths ;  but  if  their  paths  outside  the  earth's  atmosphere 
were  not  parallel,  their  orbits  and  their  periods  would  be  so  very 
different  that  they  would  not  come  up  to  the  earth  again  in  a 
single  swarm.  We  may  therefore,  I  think,  assume  that  the 
paths  of  the  different  components  of  a  meteoric  swarm  are 
parallel  in  space  before  they  encounter  the  earth's  atmosphere* 
and  that  they  are  deflected  by  reason  of  their  irregular  shapes  after 
they  enter  the  earth's  atmosphere,  and  usually  before  they 
become  luminous,  though  there  is  abundant  evidence  that  such 
deflection  or  "  skidding  "  from  their  original  course  sometimes 
takes  place  after  they  become  luminous.  Professor  Newton, 
Col.  Tupman,  and  Mr.  B.  J.  Hopkins  have  recorded  meteors 
with  curved  paths.  I  have,  on  two  occasions,  seen  meteors  with 
curved  paths,  and  there  is  a  meteor  with  a  very  decidedly  curved 
path  in  the  chart  of  meteor  tracks  observed  at  Greenwich  on  the 
night  of  November  27,  1885,  which  is  given  at  p.  62  of  the 
December  number  of  the  Monthly  Notices  for  1885. 

In  order  to  account  for  the  elliptic  area,  on  the  assumption 
that  the  deflection  from  the  original  path  takes  place  within  the 
earth's  atmosphere,  it  is  necessary  to  find  some  cause  which 
would  account  for  the  deflection  being  greater  in  one  plane  than 
m  the  direction  at  right  angles  to  it.  This  would  be  the  case  if 
there  were  some  arrangement  of  the  particles  in  space  which 
caused  them  to  set  themselves  with  their  longer  axes  north  and 
south.  I  would  suggest  that  if  the  particles  are  magnetic  they 
would,  on  coming  up  to  the  earth,  tend  to  arrange  themselves 
with  their  longer  axes  parallel  to  the  earth's  magnetic  axis.  And 
in  connection  with  this  it  is  worth  noticing  that  the  axis  of  the 
contours  drawn  by  M.  Perrotin  and  M.  Thollon  do  not  point  to 
the  North  Pole,  but  some  120  or  140  to  the  west  of  north,  which 
about  corresponds  to  the  deviation  of  the  magnetic  meridian  at 
Nice. 

Neither  Mr.  Nash  at  Greenwich,  who  seems  to  have  laid  down 
with  great  care  the  tracks  he  gives  in  his  chart, "  principally  from 
observations  made  between  8h  and  9h  3om,"  nor  Mr.  Denning, 
whose  attention  was  attracted  by  the  large  area  of  radiation, 
seem  to  have  noticed  its  elliptic  shape.  But  with  such  slow- 
moving  meteors  as  those  of  the  Biela  swarm,  the  elliptic  shape  of 
the  area  above  referred  to  would  probably  be  missed  by  observers 
who  combined  tracks  laid  down  with  an  interval  of  three  or  four 
hours.  For,  owing  to  the  axial  rotation  of  the  earth,  the  centre 
of  radiation  would  appear  to  shift  rapidly  in  the  heavens  in  a 
direction  nearly  at  right  angles  to  the  longer  axis  of  the  observed 


72  Mr.  Banyard,  Form  of  the  Area  etc.  xltii.  2, 

ellipse.  Thus,  by  combining  observations  separated  by  a  sufficient 
interval  of  time,  a  circular  area  of  radiation  might  be  deduced, 
though  the  true  area  of  radiation  for  any  instant  was  an  ellipse 
of  considerable  ellipticity. 

Mr.  Denning  appears  to  think  that  the  radiant  area  of  this 
shower  was  larger  than  that  usually  observed.  He  says : — "  In 
many  cases  I  found  that  very  accurately  observed  paths  deviated 
several  degrees  from  the  mean.  The  area  of  radiation  must  have 
been  fully  70  in  diameter  to  accommodate  the  discordances  in  the 
flights.  The  centre  was  at  24°+ 440 ;  but  I  saw  several  very  short 
paths  from  a  point  south  of  y  Andromedce."  This  would  seem, 
to  indicate  that  the  radiant  area  was  elongated  in  a  north-westerly 
direction.  Mr.  Denning  adds : — "  I  noted  many  of  the  meteors 
with  the  utmost  care,  in  order  to  assure  myself  of  the  diffuseness 
of  radiation,  and  it  was  found  impossible  to  get  a  sharply  defined 
position.  The  contrary  effect  was  indeed  so  obvious  as  to  arrest 
the  eye  whenever  simultaneous  bursts  of  about  six  or  seven 
meteors  took  place  near  the  radiant.  It  was  then  seen  that  the 
collective  flights  were  not  symmetrical  emanations  from  a  central 
point.  They  rather  appeared  to  be  discharged  in  a  loose,  dis- 
jointed fashion,  from  a  comparatively  large  space  on  the  N.W. 
region  of  y  Andromeda,  and  just  perhaps  enveloping  the  star 
within  its  limits." 

If  the  great  extent  of  the  radiant  area  should  turn  out  to 
be  peculiar  to  this  shower,  it  would  be  evidence  that  the  me- 
teoric particles  of  the  fiiela  stream  are  more  irregular  in  shape 
than  those  of  other  streams.  For  example,  one  can  conceive 
that  they  might  be  elongated  crystalline  forms,  or  a  sponge- 
like meshwork  of  crystals  containing  magnetic  iron,  which  has 
been  torn  into  more  than  usually  irregular  shapes ;  or  the  irregular 
forms  may  be  due  to  exposure  to  heat,  which  has  evaporated 
volatile  substances  from  the  inters/ices  of  crystals  with  a  higher 
melting  point. 

The  size  and  shape  of  the  area  of  radiation  is  well  worthy  of 
careful  examination  during  future  showers,  noting  the  corre- 
sponding star  magnitude  of  the  meteor,  observed  beside  each 
track  laid  down.  Since  the  mass  of  similar-shaped  meteoric 
particles  varies  as  the  cube  of  their  diameter,  while  their  resisting 
surface  varies  as  the  square  of  the  diameter,  we  may  expect  to 
And  the  smaller  particles  heated  to  incandescence  on  entering  the 
atmosphere  more  rapidly,  and  in  a  higher  region,  than  larger 
masses,  and  the  forces  tending  to  deflect  them  from  their  original 
course  bearing  a  larger  proportion  to  the  momentum  the  smaller 
the  particle.  It  is  probable  that  only  the  larger  particles  which 
enter  the  atmosphere  become  visible  as  naked-eye  meteors,  the 
dust-like  particles  being  lost  as  telescopic  meteors,  or  with  a 
sudden  spark,  which,  owing  to  distance  and  atmospherio  absorp- 
tion, may  not  be  visible  even  as  a  telescopio  meteor. 

Some  idea  as  to  the  size  of  meteoric  particles  capable  of  giving 
the  light  of  a  sixth-magnitude  star  may  be  derived  from  the 


Deo.  1886.       Mr.  Hopkins,  On  an  Erratic  Meteor.  73 

consideration  that  a  standard  candle,  seen  at  the  distance  of  a 
mile,  is  only  a  little  brighter  than  a  first-magnitude  star.  Con- 
sequently, without  taking  atmospheric  absorption  into  account, 
an  incandescent  body  at  a  distance  of  100  miles  would  only 
appear  as  a  sixth-magnitude  star  if  it  shone  with  a  light  about 
equal  to  that  of  an  electric  lamp  of  100  candles  power.  As  only 
the  larger  meteors  enter  the  earth's  atmosphere  to  a  depth  of 
below  70  miles  above  the  surface,  it  may  be  assumed  that  few 
of  the  meteors  seen,  except  those  which  appear  in  the  zenith, 
approach  within  100  miles  of  the  observer.  One  may,  conse- 
quently, pretty  safely  assume  that  a  meteor  which  is  just  visible 
to  the  naked  eye  is  larger  than  the  portion  of  the  carbons  which 
is  rendered  incandescent  in  an  arc-light  of  100  candles  power. 
For  a  mass  of  carbon  such  as  is  used  for  electric  lighting  pur- 
poses gives  off  more  light  while  being  driven  into  vapour  than 
other  substances  which  have  been  experimented  upon ;  and  the 
carbon  of  the  electric  light  is  not  exposed  to  the  tremendous 
bombardment  of  cold  air,  which  must  tend  greatly  to  accelerate  the 
disintegration  of  the  meteoric  particles  in  their  passage  through 
the  air,  as  well  as  to  cool  their  surface  by  removing  the  incandes- 
cent matter  as  rapidly  as  it  is  formed.  If  the  above  reasoning  is 
correct,  a  much  greater  amount  of  matter  must  enter  the  Earth's 
atmosphere  during  a  meteoric  shower  than  has  hitherto  been 
supposed.  Such  matter  would  in  time  find  its  way  to  the  Earth's 
surface,  and  when  we  consider  geological  periods  of  time,  would 
have  a  sensible  effect  on  the  growth  of  the  Earth,  and  the  shape 
of  continents. 


Note  on  an  Erratic  Meteor.     By  B.  J.  Hopkins. 

In  November  1885  I  had  the  honour  of  reading  before  the 
Society  a  Paper,  containing  a  series  of  observations  of  mine  of  a 
class  of  meteors  which  from  the  apparent  form  of  their  paths  I 
termed  "  erratic."  I  pointed  out  in  that  Paper  that  the  appear- 
ance of  these  bodies  was  comparatively  rare,  and  in  proof  of  that 
statement  I  may  here  remark  that,  in  a  correspondence  on  the 
subject  which  I  had  with  Mr.  Denning,  he  informed  me  that, 
though  he  had  observed  considerably  over  1,300  meteors  during 
the  year  1885,  only  four  of  them  described  paths  similar  to 
those  mentioned  in  my  Paper  above  referred  to. 

On  account  of  their  being  so  rarely  seen,  I  have  thought 
that  a  few  remarks  upon  one  I  had  the  good  fortune  to  observe 
on  December  4,  18  hrs.,  would  not  be  without  interest ;  particu- 
larly as  the  meteor  presented  not  only  the  peculiarity  of  a  wavy 
path,  but  also  had  that  path  broken  in  two.  The  meteor  re- 
ferred to  was  of  a  brilliant  white  colour,  and  equalled  Jupiter  in 
apparent  magnitude;  it  made  its  appearance  near  v  Ursa 
Majoris,  and  disappeared  between  1  Draconis  and  y  Ursa  Minoris. 


74  Mr.  Hopkins,  On  an  Erratic  Meteor.  xlyii.  2, 

The  first  portion  of  its  flight  extended  from  the  point  of  its 
appearance  to  just  beyond  {  Ursa  Majoris,  where  it  made  a 
slight  curve,  the  convex  side  of  the  curve  being  towards  that 
star ;  at  this  point  the  train  of  light  following  the  meteor  in  its 
flight  divided,  and  the  remainder  of  its  path  was  continued  at  a 
short  distance  (about  30')  above  the  level — if  I  may  use  such  a 
term— of  the  path  pursued  by  it  at  its  first  appearance,  though 
parallel  to  it.  I  have  on  one  or  two  previous  occasions  noticed 
breaks  in  the  path  of  a  meteor,  but  never  took  any  particular 
notice  of  it,  looking  upon  it  as  merely  an  optical  illusion ;  or 
the  phenomenon  has  been  so  slight  that  I  have  not  been  able  to 
decide  whether  I  had  actually  seen  it,  or  if  it  was  due  to  fancy. 
Such  an  appearance  as  I  have  tried  to  describe  would  be  caused, 
for  instance,  if  at  the  point  of  disappearance  of  a  meteor  another 
made  its  appearance,  and  so  as  it  were  continued  the  path  of  the 
first.  But  in  this  case,  owing  to  the  brightness  and  slow  motion 
of  the  meteor  (it  was  visible  for  two  seconds),  and  to  the  fact 
that  I  was  looking  at  the  part  of  the  heavens  in  which  it  appeared 
at  the  moment  it  did  so,  thus  having  it  in  view  from  first  to  last, 
I  can  most  confidently  affirm  that  it  was  not  an  illusion  due  to 
the  cause  just  mentioned,  or  to  the  imagination. 


Diagram  of  Erratic  and  broken-pathed  Meteor,  1886,  Dec.  4. 

A  suggestion  put  forward,  I  believe,  by  Mr.  Ranyard,  during 
the  discussion  which  followed  the  reading  of  my  former  Paper, 
viz.,  that  the  irregular  shape  of  some  meteors  is  the  reason  of 
their  describing  curved  paths,  will  probably  account  for  the 
slight  curve  I  observed  in  the  path  of  this  meteor.  But  it  is 
not  so  easy  to  explain  the  break  in  the  path.  Mr.  Denning  has 
observed  meteors  with  divided  paths,  and  accounts  for  them  by 
ascribing  the  appearance  as  due  to  variations  in  the  light  of  the 
meteor ;  this  meteor  did  not,  however,  vary  in  brightness,  and 
differed  from  those  observed  by  Mr.  Denning  in  that  the  second 
portion  of  its  path  was  not  in  a  line  with  the  first.  Whatever 
caused  the  meteor  to  change  its  course  seems  also  to  have  been 
the  cause  of  the  momentary  disappearance  of  the  meteor,  and  it 
is  in  hopes  of  some  explanation  of  the  phenomenon  being  forth* 
coming  that  I  venture  to  bring  this  observation  before  the 
notice  of  the  Society. 

Forest  Gate,  E.  : 
1 886,  Decemler  9. 


Dec.  1 886.         Mr.  Marth,  Satellites  of  Uranus. 


15 


Ephemeris  of  the  Satellites  of  Uranus,  1887.     fy  A.  Marth. 

Pt  angle  of  position  of  the  minor  axes  of  the  apparent  orbits. 

«,  6,  major  and  minor  semi-axes  of  the  apparent  orbits. 

«— U,  longitudes  of  the  satellites  in  their  orbits,  reckoned  from  the  points 
which  are  in  superior  conjunction  with  the  planet  or  in  opposition  to  the 
Earth. 

U+ 1800,  planetocentrie  longitude  of  the  Earth  reckoned  in  the  assumed  plane 
of  the  orbits  from  the  ascending  node  on  the  celestial  equator. 

B,  planetocentrie  latitude  of  the  Earth  above  the  plane  of  the  orbits,  the 
ascending  node  N  and  inclination  T  in  reference  to  the  equator  of  18800 
are  assumed  to  have  the  values 


N=i65°77o 


T«75°-2io 


The  corresponding  values  in  reference  to  the  plane  of  the  orbit  of  Uranus  are : 
long,  of  node  1 66°  005,  inclination  o8°-oi7,  the  long,  of  the  node  being 
reckoned  along  the  planet's  orbit  from  the  point  which  precedes  the 
ascending  node  of  the  planet's  orbit  on  the  ecliptic  by  its  ecliptical 
longitude. 


Ariel. 


UmbrieL 


Greenwich 
Noon. 

P 

«i 

», 

ti.-U 

Dill. 

a» 

*, 

«,-U 

Diff. 

1887. 
Jan.    13 

284388 

14-62  +  6^-42 

34606 

0 
1428*49 

"            A' 
20-31  +  8-94 

18978 

0 
86877 

23 

•39« 

1472 

647 

33455 

•46 

20-50 

9*02 

338-55 

m    m 

74 

Feb.      2 

•409 

14-84 

650 

32301 

1 

*43 

2068 

9*06 

127-29 

m     ■ 

•72 

12 

•438 

1496 

651 

3"'44 

•40 

20-84 

907 

276-01 

9 

•70 

22 

Mar.     4 

•477 
.524 

1506 
15-14 

649 
645 

299-84 
288-21 

'37 
'35 

20*98 

2X'IO 

904 
89S 

6471 
21338 

m 

67 

•66 

14 

•575 

1520 

638 

27656 

•32 

2ri8 

889 

204 

•64 

24 
%      3 

•627 
284679 

1524    630 
15-24  +  6-19 

26488 
25317 

w 

•29 
•27 

21-23    8-77 
21*24  +  863 

150-68 
299-30 

•62 

•61 

13 

•729 

1522 

608 

24144 

• 

25 

2I'2I 

848 

8791 

•61 

23 

Hay      3 

774 
•8^3 

15-18 
15" 

597 
586 

22969 
21793 

•24 
•23 

21-15 
2I05 

832 
816 

23652 
251 1 

•59 

•60 

'3 

•844 

1502 

575 

206' 16 

'22 

20*93 

801 

I737I 

*59 

23 

•866 

1492 

565 

194*38 

•22 

2078 

7-87 

322-30 

•60 

Jane     2 

•880 

1480 

557 

182*60 

•22 

20'6l 

776 

110-90 

•60 

12 

•885 

1467 

550 

17082 

I428'23 

20*44 

767 

25950 

86862 

22 

284-881 

14*54 

+  5*4-5 

15905 

■                   %f 

20-25  +  7-60 

48-12 

76  Mr,  Marth,  Ephemeris  of  the  •    xlyii.  2, 

Titania,  Oberon. 


1887. 
Jan.      13 


Feb. 


Mar. 


Apr. 


May 


June 


23 
2 

12 
22 

4 
14 
24 

3 
13 
23 

3 
13 

«3 

2 

12 
22 


// 


6* 


#/. 


M.-U 


33-32+I4-66  155*68 

33'63        1479  20922 

33*92        i486  262'75 

34'19        I4'88  3l6'26 

3442    1483  975 

3460    1473  63'23 

3474     1458  116-69 

3482     14-38  170-14 

34-83+14*15  22359 

3479    1390  27703 

3469    1364  33047 

3453    1338  2391 

3433     1 3- 14  7736 

34-08    12-91  13081 

33*8 1     12*72  184-27 

3352    12*57  23774 

33-22+12*47  291-22 


Diff. 
o 
413*54 
•53 
•51 

•49 
•48 

•46 
•45 

•45 
•44 
•44 
•44 

•45 

•45 

•46 

•47 
41348 


». 


# 


«.-u 


44-56  +  19-61  1 16-88  2483  +  26*109 

44*97     1978  2429  2492    26*098 

4536    1988  29169  2515    25*989 

4572     I9'9°  »99*o7  2552    25797 

46-03    19*84  106-43  2601     25*530 

46-28    1970  13*78  2659    25*199 

46*46    19-50  281*12  2724    24*818 

46-56     19-24  188-45  2792    24-405 

4658  + 18-93  9578  2861  +  23*978 

4652     18*59  310  2927    23557 

46*39    18*24  270-43  2988    23-159 

46*18    17-89  177*76  3-040    22-801 

4590    17*57  8509  3*083    22498 

4558    1727  35244  3*114    22-262 

4522     17*02  25979  3*132    22-103 

44-83     16-81  167*16  3*136    22-027 

4443  + 1667  7453  3*  127  +  22038 


The  values  of  P,  a,  b  and  u-U  are  to  be  interpolated  directly 
for  the  times  for  which  the  apparent  positions  are  required, 
the  equation  of  light  being  already  taken  into  account.  The 
position-angles  p  and  distances  s  are  then  found  by  means  of  the 
equations 

$  sin  (p— P)  —  a  sin  (« — U), 

8  cos  (p  —  P)  =  b  COS  (tf  —  U). 

The  satellites  move  in  the  direction  of  increasing  position- 
angles,  and  will  be  at  their  greatest  elongations  and  at  their 
conjunctions  with  the  centre  of  the  planet  at  the  following  hours, 
Greenwich  mean  time  : — 

Ariel. 


N.  Elong 
P=       P+900 

.  S.  Eloog. 
P-900 

N.  Elong. 
h 

S.  Elong. 
h 

N.  Elong. 
h 

8.  Elong 

1887          h 

h 

Mar. 

IO    4*2 

11  io*4 

April  16  23-5 

18    58 

Feb.    2  21-3 

4     3*6 

12  166 

13  22'9 

19  120 

20  1 8*3 

5    9*8 

6  16' x 

15    5'i 

16  ii'4 

22    0-5 

23    6-8 

7  223 

9    4'6 

17  176 

18  239 

24  13-0 

25  19*3 

10  10-8 

n  17-0 

20    61 

21    I2'4 

27    i"5 

28    78 

12  23*3 

14    55 

22  18-6 

24    0-9 

29  14-0 

30  203 

Dec.  1886.                 Satellite*  of  Uranus,  1887.  77 

,=    ^P+J?*  "J?"                H.Monf.    8.  Hong.  N.Hong.     S.Blong. 

1S87          h                h                               h                 h  h                 h 

Feb.  15  H'8     16  180        Mar. 25    7*1     26  13*4  May    2    2*5      3    87 

18    0-3    19    6-5              27  19-6    29    18  4  15-0      s  21-2 

20  127    21  190              30    8-i    31  143  7    3-5      8    97 

23    i*2    24    7*5      April  1  20*6      3    2-8  9  160    10  22*2 

25  137    26  200                4    91      5  153  12    45    13  107 
28    2*2 M.  1    8*4                 6  2r6      8    3*8  14  17*0    15  232 

Mar.  2  147      3  20*9                 9  10- 1     10  16*3  17    5*5     18  117 

5    3*2      6    9*4                11  126     13    48  19  i8*o    21     02 

7  157      8  21-9               14  ii-o    15  173  22    65    23  127 

Umbriel. 

Feb.    1  137       3  15*4      Mar.  10  20*8     12  22*6  April  17    4*0    19    5*8 

5  17-2      7  189               15    0-3    17    20  21    75    23    93 
9  20-6    11  22-3               19    3-8    21    55  25  1  ro    27  127 

14    01     16    1-8               23    7*2    25    9*o  29  14-5 M.i  162 

18    3-5    20    53               27  107    29  124  May     3  17*9      5  197 

22    7-0    24    87               31  14*2  A.  2  15*9  7  21-4      9  23-1 

26  10-4     28  12*2     April    4  17*6      6  19*4  12    0*9     14    2-6 
Mar.   2  139      4  156                  8  211     10  228  16    4-3     18    61 

6  174      8  191                13    o-6    15    23  20    78    22    95 

-    Titania.         -  • 

Super.  Con  j.                 N.  Hong.                        Infer.  Gonj.  8.  Blong. 

ps           P                                 P+oo°                               P-x8o°  P-oo* 

h                                      h  h                                    7i 

Jan.   26     15*5           Jan.  28     197          Jan.  31  00          Feb.    2      4*2 

Feb.     4      8*4           Feb.    6     127          Feb.    8  16*9                   10    2 1 '2 

13      i*4                   *5      5*6                  *7  99                  19    14*1 

21     18*3                   23    22*6                  26  2*8                  28      7*i 

Mar.     2     1 1*3          Mar.    4    155         Mar.    6  19*8          Mar.    9      00 

11      4*3                  13      8*5                  15  127                  17    17-0 

19    2i*2                   22       15                   24  57                   26    IO'O 

28     14*2                   30    1 8-5         April    1  227         April    4      2-9 

April    6      72         April    8     11*4                   10  157                   12     19-9 

15      0*2                   17      4*4                  19  86                  21     1 2*9 

23     17*1                   25    21*4                  28  i*6                  30      5*9 

May     2    lo-i           May   4    14*4          May    6  i8a6          May   8    22*8 

11      3'i                   13      7*3                  lS  "*6                  17    15*8 

19    20*  I                   22      0*3                  24  4*6                  26      8*8 

28    130                  30    17*3          June    1  21*5          June   4      18 


L_ 


78 

Mr,  Man 

!A,  tf a 

teUtte8  of  U\ 

rami*. 

XLYII.  2 

Oberon. 

Super.  Conj. 
i>=           P 

N.  Elong. 
P+900 

Infer.  Conj. 
P-1800 

S.  Elong. 
P-90f 

1887 
Jan.    22 

h 
2*2 

Jan.  25 

h 
II'O 

Jan.  28 

h 

197 

Feb.    1 

h 
4*5 

Feb.      4 

13*3 

Feb.    7 

22*1 

Feb.  11 

6*9 

14 

157 

18 

0-5 

21 

9*2 

24 

180 

28 

28 

Mar.     3 

1 1*6 

Mar.    6 

20'4 

Mar,  10 

5-2 

Mar.  13 

14*0 

16 

228 

20 

7*6 

23 

1 6*4 

27 

1*2 

30 

10*0 

April  2 

188 

April   6 

3-6 

April  0 

1 2*4 

April  12 

212 

16 

6't> 

19 

14*8 

22 

236 

26 

*4 

29 

I7'2 

May   3 

2*0 

May    6 

108 

May     9 

19-6 

May  13 

4*4 

16 

13*2 

19 

22*0 

23 

68 

26 

156 

30 

04 

June   2 

9*2 

Titania  and  Oberon  will  appear  in  the  same  direction  from 
the  centre  of  the  planet  February  3,  2  3*5  ;  February  28,  I4h*8 ; 
March  25,  6h-i ;  April  18,  2ih,4;  May  13,  I2h  7;  June  7,  4h,i ; 
and  in  opposite  directions  February  16,  7h*2  ;  March  12,  22b*4  ; 
April  6,  I3h7;  May  1,  Sbo;  May  25,  20h4. 


Erratum,  vol.  xlrii.  p.  9,  3rd  line  from  bottom : — 

for  —  sin  *M.  read  ._  sin  2M. 


MONTHLY   NOTICES 

or  THE 

EOYAL   ASTRONOMICAL   SOCIETY. 

Vol.  XLVIL  January  14,  1887.  No.  3 

J.  W.  L.  Glaishbr,  M.A.,  F.R.S.,  President,  in  the  Chair. 

Bey.  W.  Birks,  Wanstead  Villa,  Villiers  Road,  Southsea ; 

Captain  Thomas  Exham,  Officers'  Clnb,  Canute  Road, 
Southampton ; 

Shelley  Fisher,  The  Priory,  Larkhall  Rise,  S.W. ; 

Cuthbert  Hutchinson,  Rock  Lodge,  Roker,  Sunderland ; 

William  Edward  Jackson,  Constantinople ; 

Captain  Thomas  Mackenzie,  Royal  Mail  s.s.  "Moselle," 
Southampton ; 

Horace  Pearce,  F.G.S.,  F.L.S.,  The  Limes,  Stourbridge ;  and 

James  Cruikshank  Roger,  The  Grange,  Walthamstow,  Essex ; 

were  balloted  for  and  duly  elected  Fellows  of  the  Society. 


Observations  of  the  Moon  made  at  theBadcliffe  Observatory,  Oxford, 
during  the  year  1886,  and  a  Comparison  of  the  Results  with  the 
Tabular  Places  from  Hansen's  Lunar  Tables.  By  E.  J.  Stone, 
M.A..,  F.R.S. 

The  present  Paper  contains  the  Right  Ascensions  and  North 
Polar  Distances  of  the  Moon  as  deduced  from  the  observations 
made  at  the  Radcliffe  Observatory  during  the  year  1886.  These 
results  are  here  compared  with  those  deduced  from  Hansen's 
Lunar  Tables  on  two  suppositions : — 

(1)  That  the  mean  times,  found  in  the  usual  way  from  the 

sidereal  times  at  mean  noon  given  in  the  Nautical 
Almanac,  were  not  changed  in  1864. 

(2)  That  the  mean  times  were  changed  in  1864,  in  accord. 

ance  with  the  views  which  I  have  explained  in  Papers 
already  communicated  to  the  Society. 

For  facilities  for  an  accurate  comparison  between  Hansen's 
Lunar  Tables  and  Observations  we  are  again  indebted  to  the 
places  published  in  the  Oonnaissance  des  Temps. 

G 


76 


.Mr.  Martk,  Ephemeris  of  th§  xlvii.  2, 

Titania.  Oberon. 


», 


a,-U 


1887. 
Jan.     13 

• 

33-32  +  14*66 

155*68 

23 

3363 

1479 

20922 

Feb. 

2 

3392 

i486 

262*75 

• 

12 

34*  19 

14*88 

316*26 

22 

34*42 

I483 

975 

Mar. 

4 

34*6o 

1473 

6323 

14 

3474 

I458 

116*69 

24 

34*82 

1438 

170*14 

Apr. 

3 

34*83  H 

■  14*15 

22359 

13 

3479 

13*9° 

277-03 

23 

34*69 

1364 

33047 

May 

3 

34*53 

1338 

23*91 

13 

3433 

I3'i4 

7736 

23 

34o8 

12*91 

130-81 

June 

2 

33'81 

1272 

184-27 

12 

33*52 

1257 

23774 

22 

3T22  H 

h  12*47 

2Q I '22 

Diit. 
o 
413*54 
*53 
•51 
•49 
•48 
46 
•45 

•45 
•44 

•44 
'44 
'45 
•45 
46 

•47 
41348 


ft* 


«4-u 


B 


44*56+19*61  1 1 688  2*483  +  26*109 

44*97     1978  24*29  2-492    26098 

4536    19*88  29169  2515    25989 

4572    19*9°  '99*07  2552    25797 

4603     19*84  10643  2-601     25-530 

46*28    1970  13-78  2659    25199 

46*46    19*50  281*12  2724    24*818 

46-56    19*24  188*45  2792    24*405 

46*58+18-93  9578  2*861+23*978 

4652    1859  310  2927    23557 

4639    18-24  27043  2988    23159 

46*18    17*89  177*76  3-040    22801 

4590    17*57  8509  3083    22498 

4558    17*27  352*44  3* "4    22-262 

45*22    17*02  25979  3*132    22*103 

44-83    16-81  167-16  3-136    22-027 

4443  +  1667  7453  3127  +  22038 


The  values  of  P,  a,  b  and  tt-TT  are  to  be  interpolated  directly 

.for  the  times  for  which   the  apparent  positions  are  required, 

the  equation  of  light  being  already  taken  into  account.     The 

position-angles  p  and  distances  *  are  then  found  by  means  of  the 

equations 

s  sin  (j>— P)  -a  sin  («— U), 

s  cos  (p— P)  =  b  cos  (tt— U). 

The  satellites  move  in  the  direction  of  increasing  position- 
angles,  and  will  be  at  their  greatest  elongations  and  at  their 
conjunctions  with  the  centre  of  the  planet  at  the  following  hours, 
Greenwich  mean  time  : — 

Ariel. 


N.  Elong 
p=       P+900 

.  S.  Elong. 
P-900 

N.  Elong. 
h 

8.  Elong. 
h 

N.  Elong. 
h 

8.  Elong. 
K 

1887          h 

h 

Mar. 

IO    4*2 

11  10*4 

April  16  23*5 

18    58 

Feb.    2  21*3 

4     3'6 

12  166 

13  229 

19  120 

20  183 

5    9*8 

6  16-1 

15  51 

16  1 1-4 

22    0*5 

23    6-8 

7  223 

9    4*6 

17  176 

18  239 

24  13-0 

25  19*3 

10  10-8 

11  17-0 

20     6*1 

21  124 

27     15 

28    78 

12  233 

14    5*5 

22    l8'6 

24    0*9 

29  14-0 

30  203 

Dec.  1 886.                 Satellites  of  Uranus,  1887.  77 

p=      P^*'8?-™?'  N.Htot*.    8.  Elong.  N.  Bong.  &  Elong. 

1887           h                 h  h                 h  h  h 

Feb.  15  1 1 -8    16  180  Mar. 25    7-1     26  134  May    2    2*5  3    87 

18    0-3    19    6-5  27  19*6    29    1*8  4  15*0  5  21*2 

20  127    21  190  30    81    31  14*3  7    3-5  8    97 

23    12    24    75  April  1  206      3    28  9  160  10  22-2 

25  13 7    26  200  4    91      5  153  12    45  13  10 7 
28    22 M.i    8-4  6  2i*6      8    38  14  17-0  15  232 

Mar.   2  147      3  20*9  9  101     10  163  17    5-5  18  117 

5    3*2      6    9*4  11  126     13    4*8  19  18-0  21    0-2 

7  157      8  21-9  14  ii-o    15  173  22    6-5  23  127 

Umbriel. 

Feb.    1  137       3  154  Mar.  10  20*8     12  226  April  17    4*0  19     5*8 

5  172      7  189  15    0-3     17    20  21     75  23    93 
9  20-6    11  223  19    38    21     55  25  no  27  127 

14    01     16    i-8  23    72    25    90  29  14-5 M.i  162 

18    35    20    53  27  107    29  124  May     3  179  5  197 

22    7*0    24    87  31  142  A. 2  159  7  21*4  9  23-1 

26  10-4    28  12*2  April    4  176      6  194  12    0*9  14    26 
Mar.   2  139      4  15*6  8  211     10  22*8  16    4*3  18    61 

6  174      8  19-1  13    06    15    2-3  20    78  22    95 

-    Titania.         ■  • 


Super.  Oonj. 
j>=          P 
h 

Jan.   26     15-5 

N.  Elong. 
P+oo° 
h 

Jan.  28     197 

Infer 
P- 

Jan.  31 

.Oonj. 
x8o° 

h 

o-o 

s. 
p 

Feb.    2 

Elong. 

-? 

42 

Feb.     4 

8'4 

Feb.    6 

127 

Feb.    8 

l6'9 

10 

212 

13 

1*4 

15 

56 

17 

99 

19 

141 

21 

18-3 

23 

22*6 

26 

2-8 

28 

71 

Mar.     2 

n*3 

Mar.    4 

155 

Mar.    6 

198 

Mar.    9 

O'O 

n 

4*3 

13 

*5 

15 

127 

17 

I7'0 

19 

21-2 

22 

i*5 

24 

57 

26 

lO'O 

28 

14*2 

30 

1 8-5 

April    1 

227 

April    4 

29 

April    6 

7*2 

April    8 

1 1-4 

10 

157 

12 

199 

«5 

0*2 

17 

4*4 

19 

8-6 

21 

12-9 

23 

I7"l 

25 

21-4 

28 

16 

30 

5*9 

May     2 

101 

May    4 

14-4 

May    6 

1 8-6 

May    8 

22*8 

11 

3*i 

13 

7*3 

15 

ii*6 

17 

158 

19 

201 

22 

0-3 

24 

4-6 

26 

8-8 

28 

130 

30 

17*3 

June    1 

215 

June   4 

18 

82 


Mr.  Stone,  Observations  of  the  Moon  xlvii,  3, 


Hansen  minus 

Observed. 

Corrected 

for  Error  in  Time. 


2*    *    5 
o    t*»  vo 


vO     l>»   vO     Ov    m 
„o\    «     ro    ^    »*• 

+    +    +    I    +    +   +   +   +    + 


ro    c*      P  vO  ro  00 

-*■    «      N  »o  O  ro 

•  •  ■  •  •  • 

«  «  o  o 

+   +  +  + 


*■ 
c* 
M 


Correction  due  to 
Error  in  Time. 


o    o»  00    ov*^ov^u'vt*.ov^-»"'vo     ^t 
„»o    —     P     N     l*»    »o    ^   00     m    p      *t*    to   00    vO 


i/v    to**     «*     rh    *n    m    ro    ^» 

+     +     +     +     +     +     +     +     + 


is*    is*    m    ro    n 

+     +     +     +     + 


Hansen  minus 
Observed. 

Uncorrected 

for  Error  in  Time. 


Seconds  of 
Hansen's  N.P  J>. 


-^  «*  woo  n  O  o  ^  ^  s  ^  ^  n  \fl 

s»i^  ov  r>»    r^  P  *n  *•*  n  •*  oo  n  t^  oo  w 

*■  ro  P     ■«*  ^  ^  N  «  ^  «  n  tfl  «  « 

I  I  I       I       I  I       I       I  I  I       I  I  I  I 


00     -^    \n    \r\    Th    -*■ 

\0     1^  00     ro    «o   vo 


« 


ro 


10 


r<»    t*.  vo     •* 

«    vo     P    vo 


«%^  ■»  m      ^^*r  *     #         ~ ■  »       ^b^  ^^  •  ^q  %^  *^  ^t^  ^^  ^a^ 

rob     r    n    09    00    00     vt    b     6      <*     P    *©     »n 


O 

NO 


a 
o 


Hansen  min«# 
Observed. 

Corrected 

for  Error  in  Time. 


Correction  due  to 
Error  in  Time. 


N\0*^**>vO  <frvO      OvO  n      **  N  J2>  «*^ 

^w     ^    m    •*     *n  tm     t»vo     »n  **     »o  ^"  00  00 

^00       v     "t    ^      W  roO      N      ^  ">     N  ^"  <^  N 

tt^-^-MNNN^-rorO*-  -*■ 

n      «    «     «  ^     v  ro^-ro^-N 

OQ       M     00      N     C*  N     n     T     «  £>     *">  ~  2*  N 

Ov    00      P      O      Ov  00     00      O      O  On     O^  00  *^  *>. 


_N«0,-,0«-iO*-iOOO«Pro 

00000000000000 


00      rO^O\OSOSN      V     O      N     N     ^     t     <♦> 
OMctM00»*»-«»-iOOi*r)r'> 

I    •  .  •  •  •  •  •  •  •  •  •  •  •  • 

T7T7T7TT7TTT  i  7 


m  oo 
b    b 


u 

n 

a 

§ 

a 
o 

w 

■ 

is 


Hansen  mtatrt 
Observed. 

Uncorrected 

for  Error  in  Time. 


Seconds  of 
Hansen's  BJL 


ro 


t 

£ 


Observer. 


i**   f*  vo    9>  S2     v    o   oo   op    2*53     ;£    EL    ^ 

00N«PPOv~NPOP      Ov     Ov     o 
+     +     +     +     +     +     +      +     +     +      +      +      +     + 


rp     ro 
P      O 


^rooo      Ov    n     is*    Ov   vO     t^^-roO     * 
C*      t^voS      P      *0^"P      t^.00      ro     *>     »- 

^m  ^^ln^n«»nrolnrow, 


t>%    vo 


^       -00      mvOOO      rov5 


ro    »o    r*    ^»     . 
.A   «A    -.  .2    ^   ^ 


i 


^(g 


_  »0     P     vp 

m     vo      ^     P      Ov 

a  ro    Ov    O     *On     €4     wro^i      OvvO 

'*k"~>«»iC<Mro(N 

M      N      «      M 


A  O 


«     ro    Ov   vO     l**     «     vO 
m    «     ^    ro    m    ro    w 

Ov 


*>»    vo 


N         ft       O 


« 
« 


ro    ^. 


«  g  «•  ^  «  «>•  «  «  ^  «  ^'  ^  « 


S> 


! 


« 


a 


3 


c 

0 
t 

O 


I 


Oorreotion  to  be 

subtracted  from  H.T. 

for  change  of  Sidereal 

Time  at  Mean  Noon 

since  1864. 


m    row    «    >o  00    o\«^    «     n    ♦   n    on    o 


•8 
O 


o 


ro    ^    ^o  vo     n    in  vo    \a 
Ov     Ov     Ov     Ov    Ov     P      P      p 


o 

ft 


00  00 

ro  ro  ro  ro  ro  ro  ro  ^^  ^^ 
ro  **>  ro  ro  to  ro  to  co  c^ 


?  ? 


r^  00 

P  P 

^  •«•  V  t*  ^i- 

ro  ro  ro  ro  ro 


Jan.  1887.        made  at  the  Badcliffe  Observatory  etc.  83 

Table  II. 

Badcliffe  Observations  of  the  Moon,  1886. 

Errors  of  the  Moon's  Tabular  Place  in  Longitude  and  Ecliptic  Polar  Distance, 
Uncorrected"  and  "  Corrected"  for  the  change  in  Mean  Time  introduced 


in  1864. 

Day. 

Errors  of  Longitude 
(Hansen  mfata  Observed.) 

Errors  of  E.NJP.D. 
(Hansen  minus  Observed.) 

Uncorrected, 

|  Corrected. 

Uncorrected. 

|  Corrected. 

1886. 
Jan.      13 

+  980 

-  776 

— 0-16 

H 
-1-41 

*4 

+  10*18 

-  7*97 

-0*73 

-1*73 

*5 

+  7-83 

-1095 

-128 

—  I-90 

iS 

+  999 

—  10-71 

—2-46 

-174 

19 

+  13*16 

-  782 

-079 

+  0'37 

Feb. 

11 

+ 10*05 

-  802 

+  057 

— 0'20 

23 

+ 19*66 

+   170 

-179 

-O99 

25 

+ 1832 

+   141 

+  096 

+  0*99 

March 

15 

+  8*35 

—  ii-6i 

—0-69 

+  0'47 

16 

+ 1362 

-  665 

+  o-io 

+  1-62 

17 

+  1286 

-  7*63 

-080 

+  099 

'9 

+ 1344 

-  683 

—0-29 

+  158 

23 

+ 1953 

+   1  36 

-115 

-058. 

April 

15 

+ 13*61 

-  6-27 

—  2-00 

—021 

May 

14 

+ 12*56 

-  6-68 

-032 

+  114 

15 

+ 17*05 

-  1-95 

-I'30 

— o-io 

18 

+  20-18 

+  215 

-1*33 

-125 

Jane 

*5 

+ 1736 

-  °'34 

—0-41 

—064 

July 

12 

+  14-92 

-  275 

+  0-16 

+  003 

14 

+  1567 

-  i*55 

+  0-49 

-033 

15 

+ 18-26 

+   i*35 

+  074 

-0-30 

17 

+  21*14 

+  4*5<> 

+  2-68 

+  1-24 

20 

+  16*00 

-  050 

+  4-11 

+  2-67 

Aug. 

11 

+ 16-87 

+  001 

+  2*07 

+  104 

*3 

+ 16-36 

-  028 

+  189 

+  0-46 

20 

+  15*12 

-  244 

+  i'52 

+074 

Sept 

+ 14-22 

-  289 

+  2-62 

+  r68 

10 

+  16-08 

-  o-53 

+  308 

+  1-60 

11 

+  13*34 

-  3'9 

.    -0-09 

-158 

84 


Mr.  Stone,  Observations  of  the  Moon  etc.  xlvii.  3, 


Day. 


Errors  of  E.N.PJ). 
(HaDBen  minus  Observed) 

Uncorrected.  I  Corrected.    Uncorrected  I  Correeted. 


Errors  of  Longitude 
(Hansen  minus  Observed.) 


1886. 

« 

a 

u 

it 

Sept. 

13 

+  19-80 

+ 

3' 10 

+  4*85 

+  340 

15 

+  17*44 

+ 

0-30 

+  277 

+  1-66 

16 

+  »575 

— 

1 '60 

+  224 

+  141 

17 

+  1790 

+ 

0*17 

+  263 

+  208 

Oct 

4 

+  1573 

— 

179 

+  2'O0 

+  1-17 

8 

+  16*09 

— 

Q'45 

+  2-25 

+  078 

11 

+ 1382 

— 

328 

+  0"99 

-0*36 

13 

+ 1 912 

+ 

151 

+  284 

+  1-91 

Nov. 

1 

+  17*93 

+ 

0-24 

+  1*43 

+  0-39 

2 

+ 1627 

— 

089 

-1-48 

-273 

5 

+  1606 

— 

069 

+  2-06 

+  OS3 

8 

+ 14  77 

— 

250 

+  i'32 

+  013 

9 

+ 163 1 

— 

1-27 

+  3'3» 

+  2*45 

Dec. 

1 

+ 18*40 

+ 

1.44 

+  3*64 

+  2-17 

2 

+  16-34 

— 

043 

+  178 

+  0-30 

3 

+  16-08 

— 

058 

+  3*6o 

+  216 

4 

+  15*31 

— 

1-56 

+  310 

+  172 

7 

+  14-44 

— 

3*47 

+  1-17 

+0-42 

9 

+ 1371 

— 

511 

—  i-oi 

-1-05 

10 

+  14-96 

— 

4*32 

-o*53 

— 0'12 

X  ean  of  Enron,  without 

regard  to  sign        ...  15"*842 


8"-816 


r-666 


1"-1«3 


Mean  Errora  for  Year    + 15"*842 


-2"-531 


Tablb  III. 

Mean  Excess  offer  Observation  of  the  "  Moon's  Tabular  Place  in  Longitude  *  for 
the  Years  1847  to  1 886,  as  computed  from  Hansen's  Tables. 

"  Uncorrected  "  and  "  Corrected  "  on  and  after  1S64  for  the  change  in  Mean 

Tabular  Time  introduced  in  the  year  1884. 


Errors  of  Longitude 
Year.  (Hansen  minus  Observed.) 


Errors  of  Longitude. 
Year.  (Hansen  minu*  Observed.) 


Uncorrected. 

|  Correeted. 

Uncorrected. 

|  Correeted 

1847 

+  1-07 

+  rc7 

1852 

—  092 

M 
—  0*92 

1848 

+  0*20 

+  020 

1853 

-  1*63 

-r63 

1849 

-O47 

-047 

1854 

-  1-68 

-1-68 

1850 

-028 

-028 

1855 

-  0-87 

-0-87 

1851 

—  1-29 

—  1-29 

1856 

—  0-96 

—0-96 

Jan.  i 

887. 

Mr.  Stone, 

Mean  Bight  Ascensions. 

*< 

Tew. 

Brron  of  Longitude 
(Hansen  minus  Observed.) 

Year. 

Brron  of  Longitude 
(Hansen  minus  Observed.) 

1 

Uncorrected, 

|  Corrected. 

Uncorrected. 

|  Corrected 

1857 

-1-86 

-;-86 

1872 

+  7f3* 

* 
+  0*10 

1858 

-198 

-1*98 

1873 

+  8-24 

+  0'20 

1859 

-180 

-r8o 

1874 

+  9*29 

+  0*56 

i860 

—2*90 

—2*90 

I875 

+  9*87 

+  0*36 

l86l 

—  2-19 

—2*19 

1876 

+  9-80 

-05I 

1862 

-283 

-2-83 

1877 

+  923 

—  I*90 

1863 

—  r6i 

~r6i 

1878 

+    8*22 

-3-60 

1864 

+  0*12 

-o-8i 

1879* 

+  9*63 

-3*1* 

1865 

+  1*27 

—0*22 

1880 

+  10*89 

-2*77 

1866 

+  214 

—  0*22 

l88l 

+  10*51 

— 4*o6 

1867 

+  3*48 

+036 

i882f 

+  1268 

-251 

1868 

+  4'I2 

+0*28 

1883 

+  147 1 

-1-50 

1869 

+4*28 

-0-35 

1884 

+ 1465 

— 1*91 

1870 

+483 

-066 

1885 

+  I5'i4 

-187 

1871 

+6-96 

+  o*44 

1886J 

+ 1534 

-253 

Bad  life  Observatory,  Oxford 
1887,  January  4. 

• 
• 

Mean  Bight  Ascensions  of  Polaris,  Oephei  51  (Bet;.),  I  Ursce 
Minoris,  and  X  Ursce  Minoris  for  the  year  1887,  from  the 
Badcliffe  Observations  of  the  years  1880  to  1886.  By  B.  J. 
Stone,  M.A.,  F.R.S. 

From  the  year  1880  to  the  year  1886  the  azimuth  errors  of 
the  Transit  Circle  at  the  RadclifFe  Observatory  have  been  based 
on  the  Nautical  Almanac  places  of  the  stars  Polaris,  Cephei  51 
(ffev.),  0*  Ursce  Minoris,  \  Ursce  Minoris,  after  the  application  of 
corrections  kindly  furnished  by  the  Astronomer  Royal  from  year 
to  year.  The  azimuth  errors  thus  found  agree  well  inter  se, 
except  those  found  from  Polaris  and  Polaris  S.  P.,  which  differ 
more  than  is  desirable  from  each  other  and  from  the  results  found 
from  observations  of  the  other  three  stars.  It  has,  therefore, 
been  thought  necessary  to  collect  the  results.  It  will  be  seen 
that  the  Right  Ascensions  of  the  RadclifFe  Observations  agree 
remarkably  closely  with  the  corrected  Nautical  Almanac  places 

f'ven  by  the  Astronomer  Royal  for  the  three  stars,  Oephei  51, 
TJrsce  Min.,  and  \  Ursce  Min.,  but  that  the  resulting  Right  Ascen- 
sions of  Polaris  agree  much  more  closely  with  the  tabular  Right 
Ascensions  of  the  Berliner  Jahrbuch, 

*  All  to  1879,  Greenwich  Observations. 

t  1880  to  1882,  Mean  of  Greenwich  and  RadclifFe. 

X  1883  and  since,  Hadcliffe  only. 


86 


Mr.  Stone,  Mean  Eight  Ascensions. 


xlyii.  3, 


The  resulting  Bight  Ascensions  for  1887  will  be  employed  in 
the  redactions  of  the  Radcliffe  Observations  during  the  year  1887, 


Year. 


1880 
l88l 
1882 
1883 
1884 
1885 
1886 


1880 
1881 
1882 
1883 

1884 
1885 
1886 


1880 
1881 
1882 
1883 
1884 
1885 
1886 


1880 
1881 
1882 
1883 
1884 
1885 
1886 


Annual  Remits  reduced  to  1887. 

Mean  BJL  from  Number 

Badoliffe  Observations  of 

reduced  to  1887.  Obserrations. 


Polaris. 

h   m      0 

I   17  2084 

15 

2155 

24 

2175 

67 

2118 

62 

21-92 

52 

2168 

83 

2172 

49 

Cephci  51  (Hei 

•■)■ 

6  47  1638 

9 

16-42 

3i 

16-39 

'  24 

1656 

27 

1644 

37 

1643 

21 

1675 

21 

9  Ursa  Minoris. 

18    8  4618 

5 

45*66 

25 

4571 

21 

4575 

20 

46*01 

30 

4593 

17 

45*97 

28 

X  Ursa  Minoris. 

19  3-5  53'24 

3 

47*31 

26 

47-50 

25 

48-38 

19 

47*68 

21 

47*35 

11 

48-53 

4 

Adopted 

Proper 

Motion. 


+  o-i  179 


-OO385 


+  0*0285 


—0-0500 


tjan.  1887.  .P*of'  Pritchard,  Application  of  Pictography  etc.       87 


Comparison  of  Mean  Result*  with  Tabular  Right  Ascensions. 

J!^j!L?i^:         Tabular  RA.  Tabular  B.A.  Tabular  R. A. 

V)mBnfCf„            oilSSK?            from  the  from  Greenwich  from  Ber. 

Name  of  Star.           ObserTatloM      Nautical  Almanac  Clock  star  list  liner  Jahrbuch 

reauoeato                for  1887.  for  x887.  for  1887. 

hms              hms  hms  hms 

Polaris                    1  17  21-60        1  17  1963  1  17  20-00  1  17  2173 

Cephei  51  (Her.)    6  47  1648        6  47  1660  6  47  1657  6  47  1696 

9  Urate  Minoris    18    8  4586      18    8  4600  18    8  4600  18    8  45-98 

A  Ursae  Minoris     19  36  4782       19  36  4688  19  36  47*72  19  36  48*00 

Radcliffe  Observatory,  Oxford  : 
1887,  January  13. 


Note  on  the  Application  of  Photography  to  the  Determination  of 
Stellar  Parallax.     By  the  Rev.  Prof.  Pritchard,  D.D.,  F.R.S. 

At  the  meeting  of  the  Society  in  June  last,  I  communicated 
the  results  of  some  preliminary  trials  with  the  view  of  ascer- 
taining the  applicability  of  photography  to  astronomical  measure- 
ments of  sufficient  delicacy  for  the  accurate  determination  of 
stellar  parallax. 

These  results  proving  eminently  satisfactory,  the  requisite 
operations  for  the  determination  of  parallax  commenced  on 
May  26  of  last  year  by  taking  photographs  of  the  district  round 
61 l  and  6 12  Cygni,  which  sta^r  was  selected  on  account  of  the 
unusually  numerous  examinations  which  had  been  applied  to  it 
by  successive  astronomers  from  the  time  of  Bessel  (1840)  to  the 
present  date;  my  object  being  not  so  much  to  effect  a  re- 
determination of  the  parallax  of  this  historical  star  as  to  obtain 
the  means  of  comparing  the  photographic  method  with  those 
other  methods  of  micrometrical  measurement  heretofore  directly 
applied  to  this  end. 

For  the  purpose  in  view,  four  faint  stars,  viz. : 


D.M.  +  37  No.  4189  .  . 

.  .  (a) 

D.M.  +  38  „  4336  .  . 

.  •  (*) 

D.M.  +  37  „  4175  .  . 

.  .  (c) 

D.M.  +  38  „  4348  .  . 

.    .    {d) 

were  selected  from  others  whose  images  were  impressed  on  the 
photographic  plates.  The  distances  of  each  of  these  four  stars 
(eight  in  all)  were  carefully  measured  from  each  of  the  two 
components  of  61  Cygni,  on  plates  taken  on  fifty  nights,  ending 
on  Dec.  7,  1886.  In  general,  four  plates  were  exposed  each 
night,  so  that  some  200  plates  have  been  measured  in  the  course 


88  Prof.  Pritcliardy  Application  of  Photography  etc.    xlyii.  3* 

of  the  investigation.  All  these  measures  were  strictly  inde- 
pendent of  each  other,  as  were  also  the  ultimate  reductions.  The 
astronomical  importance  and  novelty  of  the  inquiry  seem  to  me 
to  justify  all  this  expenditure  of  time  and  labour. 

In  order  to  meet  the  ever-varying  conditions  of  the  instru- 
ment in  respect  of  focus,  and  other  contingent  elements,  the 
above  measures  were  not  reduced  in  terms  of  the  registered 
scale  of  the  macro-micrometer ;  but  they  were  always  referred 
to  the  presumably  constant  distance  of  the  star  (a)  from  the 
star  (ft),  or  of  (c)  from  (d).  These  fundamental  distances  were 
always  measured  at  the  same  time  as  were  the  other  eight. 

The  proper  motion  of  61  Oygni  has  been  so  exactly  deter- 
mined that  its  effects  could  be  definitively  removed  from  the 
measured  distances,  and  a  temporary  solution  of  the  equations 
on  this  hypothesis  appeared  to  be  desirable  and  legitimate.  The 
results  of  this  preliminary  solution  are  given  as  follows : — 


a 

Star's  Designation. 
D.M.  +  37  No.  4189 

Parallax 

of 
61 x  Cygni. 

0*4412 

Probable 
Brror. 

00154 

Parallax 

of 
61*  Cygni. 

0*4204 

Probable 
Error. 

0*0229 

b 

D.M.  +  38  „    4336 

•4<52Q 

•0330 

•4139 

•0185 

c 

D.M.  +  37  „    4175 

•4433 

•OI97 

•4721 

■02I5 

d 

D.M.  +  38  „    4348 

•4158 

•Ol6l 

•4574 

'O252 

The  provisional  means  for  parallaxes  thus  obtained  for  the 
four  independent  sets  of  measures  of  611  and  6ia  Oygni  respect- 
ively are  as  follows :  — 

For  61»  Oygni    .    .    .    .    Parallax  =»  0488 
61*  Cygni    .    .    .    .    Parallax  «  0-441 

Values  of  the  parallax  of  61  Oygni  have  been  determined  by 
several  astronomers  ;  among  them  are  found 

Bessel  0*348  in  1840 

Auwers  0*564  in  1863 

Ball  0*468  in  1878 

Asaph  Hall  0*261  in  1880 

The  Oxford  determination  is  to  be  regarded  as  provisional 
only  ;  the  research  will  be  continued  to  the  end  of  the  annual 
cycle,  and  full  details  will  be  communicated  at  the  earliest 
opportunity. 

In  the  communication  made  to  the  Society  in  June  last  refer- 
ence was  made  to  the  liability  of  the  photographic  film  to  be 
occasibnally  dislocated.  The  possibility  of  such  an  occurrence 
renders  it  advisable  in  all  cases  where  reliable  accuracy  is  sought 
to  take  photographs  in  duplicate  at  least.  One  of  the  causes  of 
this  liability  has  been  traced  to  its  origin  in  the  mechanical 


Jan.  1887.        Mr.  Roberts,  Photographs  of  Nebula,  89 

action  of  the  impact  of  water  on  the  film ;  which  impact  has 
been  regarded  as  essential  to  the  proper  washing  of  the  plate. 
I  find  that  in  the  entire  series  of  about  200  plates,  seven  have 
exhibited  minute  bat  noticeable  traces  of  this  dislocation ;  these 
have  been  rejected  in  the  above  investigation. 

Univertity  Observatory,  Oxford: 
Jan.  13,  1887. 


Photographs  of  Nebula  in  Orion  and  in  the  Pleiades. 

By  Isaac  Roberts. 

The  accompanying  photograph  of  nebula  in  Orion  is  enlarged 
five  times  from  a  negative  which  I  took  on  November  30  last, 
between  4*  13™  and  5b  20™  sidereal  time  at  Maghull.  The 
exposure  was  intended  to  extend  to  two  hoars,  but  an  accident 
stopped  it  after  ib  7™,  and  clouds  have  prevented  another  photo- 
graph being  taken  since  that  date. 

The  photographic  extensions  of  the  nebulae  may  be  judged  by 
comparing  this  photograph  with  that  taken  by  Mr.  Common, 
and  referring  to  the  included  and  surrounding  stars  in  them 
respectively,  as  places  from  which  to  measure. 

It  will  thus  be  seen  that  the  dark  space  shown  on  Mr. 
Common's  photograph  between  the  small  nebula  (Herschel, 
No.  1 185)  and  the  Great  Nebula,  as  well  as  the  "  fish  mouth,"  are 
filled  with  dense  nebulous  matter,  which  also  can  clearly  be 
traced  between  Declination  —  50  15'  and  —6°  15V  In  Right 
Ascension  it  can  be  traced  between  5h  26™  and  5h  29™ — an  area 
about  seven  times  that  covered  by  Mr.  Common's  photograph. 

There  is  a  large,  dense,  and  characteristically  marked  nebula 
to  the  north  (Herschel,  No.  1180),  and  the  photograph  indicates 
very  faint  nebulosity  stretching  some  distance  between  this  and 
the  Great  Nebula,  but  hitherto,  owing  to  continuous  bad  weather, 
there  has  been  no  opportunity  for  proving  by  a  long  exposure  of 
plates  that  this  nebula  also  forms  a  part  of  the  Great  Nebula. 
If  this  should  be  proved,  and  there  is  now  reasonable  ground  for 
inference,  then  extensions  of  the  nebula  will  be  revealed  to  us  on 
a  scale  still  more'  vast  than  has  hitherto  been  known. 

In  the  accompanying  print  the  central  parts  of  the  nebulae 
are  white,  without  any  shading,  bat  on  the  negatives,  when  they 
are  examined  by  the  eye  or  under  a  microscope,  those  parts  are 
full  of  detail,  and  delicate,  but  dense,  cloud-like,  curdling  masses. 
I  hope  that,  some  time  before  the  close  of  this  session,  I  may  have 
clear  sky  to  enable  me  to  present  to  the  Society  photographic 
analyses  of  this  nebula,  which  will  show  the  appearances  pre- 
sented by  it  with  different  lengths  of  exposure. 

This  method  will  give  a  more  accurate  insight  into  its  con- 
stitution, and  will  furnish  more  reliable  means  for  detecting  any 


90  Mr.  Roberts,  Photographs  of  Nebulas.  xlyu.  3, 

changes  that  may  take  place  within  it  in  future,  than  if  I  were 
to  force  out  the  details  on  a  print  from  one  dense  negative.  I 
already  have  some  of  the  negatives  which  will  be  required  in  the 
demonstrations  here  proposed.* 

Nebula  in  the  Pleiades. 

The  accompanying  photograph  was  taken  on  December  29 
(last  month),  between  sidereal  time  atMaghnll  2h  55™,  and  6h  im. 
The  actual  time  of  the  exposure  of  the  plate  was  three  hours. 

In  bringing  before  the  Society  the  first  and  second  of  the 
series  of  photographs  of  these  nebulae,  I  stated  that  upon  one 
of  them  there  were  traces  of  nebulosity  which  indicated  that  the 
principal  stars  in  the  Pleiades  are  involved,  or  are  in  alignment 
with  one  vast  nebula,  and  this  photograph  seems  to  prove  the 
correctness  of  the  inference. 

The  nebula  (I  now  venture  to  use  the  singular)  is  traceable 
from  the  north  of  Aster  ope,  and  extends  southwards  i°  10'.  It 
includes  Taygeta,  Maia,  Oelcena,  Electra,  Alcyone,  Merope,  and 
numerous  other  small  stars  within  itself. 

On  the  north  side  of  Alcyone  is  a  dense  mass  of  light,  with  a 
dark  space  between  it  and  the  star.  The  negative  shows  that  it 
is  not  due  to  the  contiguous  blister  on  the  glass  plate.  The 
nebulosity  round  Mara  is  characterised  by  broad  streamers 
stretching  in  northerly  and  southerly  directions;  whilst  round 
Merope  somewhat  similar  streamers  have  n.p.  to  s.f.  directions. 

From  Electra  stretches  a  pointed  streamer,  which  can  be 
traced  as  far  as  a  line  drawn  from  Maia  to  Merope,  and  a  little 
distance  further  south  is  another  streamer  resembling  a  detached 
nebulous  straight  lina  These,  and  many  other  points,  will  be 
clearly  seen  on  examination  of  the  photograph,  but  much  more 
clearly  are  they  shown  on  the  negatives.  These  appearances 
are  both  new  and  unexpected,  and  it  is  essential  that  the  evidence 
of  their  reality  should  be  so  clear  that  it  cannot  reasonably  be 
doubted.  To  this  end  I  have  taken  already  six  photographs  on 
different  dates.  The  first  was  on  October  23,  1886,  with  an 
exposure  of  ih  29™,  and  that  showed  all  the  features  which  are 
indicated  on  the  chart  prepared  by  MM.  Henry  at  the  Paris 
Observatory,  and,  in  addition,  large  extensions  of  nebulous 
matter  round  Maia  and  Merope. 

The  second  photograph  was  taken  on  the  following  night, 
October  24,  with  an  exposure  of  three  hours,  and  it  showed  vast 
extensions  of  nebulous  matter  ronnd,  between,  and  beyond 
Alcyone,  Merope,  Electra,  Maia,  Taygeta,  Asterope,  and  other 
smaller  stars. 

These  photographs  were  presented  to  the  Society  in  November. 
On  October  25,  and  December  16  and  24,  I  obtained  one 
negative  each  night,  but  the  sky  was  more  or  less  misty,  and  at 

*  The  short  lines  upon  the  photograph  were  caused  by  an  accidental 
momentary  movement  of  the  instrument  during  the  exposure  of  the  plate. 


Jan.  1887.  Mr.  Williams,  New  Variable  Star.  91 

times  cloudy,  daring  the  exposure  on  each  occasion,  and  conse- 
quently the  nebula  are  not  well  developed,  bat  what  is  shown 
confirms  the  features  on  the  other  negatives. 

On  December  29  I  obtained  the  sixth  negative,  an  enlarge- 
ment of  which  I  now  present  to  the  Society,  and  have  already 
given  in  these  notes  a  brief  description  of  its  general  appearance. 

The  photographs  are  placed  in  the  Library. 


A  New  Variable  Star  in  Puppis.     By  A.  Stanley  Williams. 

The  variability  of  the  star  L.  3105  in  Puppis  does  not  seem  to 
have  attracted  attention  hitherto.  Whilst  in  southern  latitudes 
last  winter,  I  paid  considerable  attention  to  the  magnitudes 
of  the  stars,  and  on  February  17,  1886,  noticed  it  as  being 
exactly  equal  in  brightness  to  the  neighbouring  star  L.  3069. 
Upon  referring  to  some  previous  '  determinations  of  magnitude 
I  found  that  it  had  been  rated  both  brighter  and  fainter 
than  this  star,  and  as  these  two  stars  had  always  been 
observed  for  magnitude  at  the  same  time,  there  seemed  to  be  a 
reasonable  suspicion  that  one  or  other  of  them  was  variable,  and 
they  were  consequently  kept  under  examination.  Further  ob- 
servations soon  snowed  that  this  suspicion  was  correct,  and  that 
L.  3105  is  the  variable  star.  The  following  table  gives  all  the 
determinations  of  magnitude  of  these  two  stars  which  I  was  able 
to  obtain. 

Bem&rks. 


Date. 
1885. 

Estimated  Mag*. 
L.  3069.        L.  3105. 

Not.  14 

505 

5'4 

21 

47 

44 

1886. 
Feb.  12 

47 

455 

17 

4*5 

4*5 

21 

47 

47 

Mar.  16 

47 

49 

21 

48 

5** 

22 

4*9 

47 

30 

5-2 

5*4 

L.  3105  distinctly  a  little  brighter  than 
L.  3069. 

The  two  stars  exactly  equal. 

Equal. 

L.  3069  distinctly  a  little  brighter  than 
L.  3105. 

L.  3069  distinctly  and  considerably 
brighter  than  L.  3105. 

L.  3105  distinctly  brighter  than  L.  3069. 

The  relative  brightness  probably  more 
exactly  estimated  than  the  actual  de- 
terminations of  brightness,  the  stars 
being  very  low.  Two  or  three  days 
previous  L.  3069  was  seen  distinctly 
superior  to  L.  3105,  but  the  date  was 
not  registered. 


92  Dr.  Copeland,  Spectrum  of  y  Cassiopeia.  xlvii.  3, 

The  results  are  clearly  not  sufficiently  numerous  to  indicate 
in  a  satisfactory  manner  the  period  of  variation.  This,  however, 
is  probably  short,  and  if  the  differences  between  the  brightness 
of  the  two  stars  L.  3069  and  L.  3105  are  chiefly  considered,  the 
observations  are  all  well  represented  by  a  period  of  about  4*2 
days ;  the  probable  extent  of  the  variation  being  about  "j  of  a 
magnitude.  The  star  L.  3105  must  have  been  near  a  maximum 
on  November  21,  1885,  and  again  on  March  22,  1886,  but  not 
so  near ;  and  near  a  minimum  on  March.  21,  1886. 

The  colour  of  the  new  variable  was  noted  as  "  orange  yellow  " 
on  February  12,  1886.  The  magnitudes  both  of  this  and  L.  3069 
are  given  as  50  in  the  Uranometria  Argentina;  Lacaille  made 
them  6  mag.,  and  in  the  Brisbane  Catalogue  they  are  also  put 
at  this  figure.  Behrmann's  estimations  are  5^  mag.  for  L.  3069, 
and  5  mag.  for  L.  3105.  The  estimations  of  brightness  given 
above  were  made  by  means  of  an  opera-glass  accurately  focnssed ; 
the  comparison  stars  were  as  under,  the  magnitudes  being 
assumed  from  the  "  Harvard  Photometry  " : — 

1  Canis  Majoris  =4-5  mag. 

17    ,.  „       =59    », 

HP.  1342    „  ,;       -6 1    „ 

The  position  of  L.  3105  for  1887*0  is  R.A.  7h  55m  o8,  Dec. 
S.  480  55''4. 

West  Brighton:  Dee.  28,  1886. 


On  the  Variability  of  the  Spectrum  of  y  Cassiopeia. 
By  Ralph  Copeland,  Ph.D. 

On  page  16  of  the  current  volume  of  the  Monthly  Notices, 
Mr.  0.  T.  Sherman  quotes  a  passage  from  Miss  Gierke's  "  History 
of  Astronomy  during  the  Nineteenth  Century,"  which  says  that 
the  brilliant  rays  indicative  of  hydrogen  in  the  spectrum  of 
y  Gassiopeice  died  out  during  the  nine  years,  1874-1883.  As 
to  the  fading  of  the  rays  there  is  room  for  little  doubt,  but 
the  epochs  of  their  disappearance  and  reappearance  seem  un- 
fortunately quite  indeterminate.  Possibly  the  lines  appear  and 
vanish  at  comparatively  short  intervals,  for  there  are  two  records 
of  their  having  been  seen  here  nearly  in  the  middle  of  the  nine 
years  mentioned  above.  The  most  precise  observation  was  made 
on  Dec.  20,  1879,  when  testing  a  large  experimental  spectroscope 
which  separated  the  D  lines  in  the  Moon's  spectrum,  and  also 
showed  four  lines  in  that  of  the  Great  Nebula  io  Orion  on  the 
same  night.    The  bright  G  line  was  then  noted  as  "  superbly 


Jan.  1887.  Mr.  Seabroke,  Spectroscopic  Observations  etc.  93 

visible "  by  Lord  Crawford  (then  Lord  Lindsay),  Mr.  J.  G. 
Lohse,  and  the  writer.  There  is  also  a  record  of  two  bright 
lines  haviDg  been  seen  by  me  on  October  28,  1877,  one  of  which 
was  "  well  seen  "  about  the  place  of  F,  the  other  being  referred 
to  about  477mmm  of  wave-length,  and  described  as  "another  bright 
line  "  without  farther  remark.  No  mention  is  made  of  C  on  this 
occasion.  At  present,  however,  January  1 1,  1887,  C  is  extremely 
bright ;  and  as  it  was  not  visible  at  Bothkamp  on  June  18,  1872, 
although  the  red  end  of  the  spectrum  was  specially  examined 
and  the  position  of  the  bright  F  determined,  there  cannot  be  the 
slightest  doubt  as  to  the  variability  of  the  spectrum,  as  pointed 
out  by  M.  von  Gothard  several  years  ago. 

It  is  very  remarkable  that  the  0  line  is  obviously  more 
variable  than  F*  in  the  spectrum  of  this  most  interesting  star ; 
this  must  necessarily  involve  a  certain  amount  of  colour  change, 
which  may  partly  explain  the  very  conflicting  evidence  respecting 
the  star's  variability. 

Lord  Crawford?*  Observatory, 
Dun  Echt :  Jan.  12,  1887. 


Spectroscopic  Observations  of  the  Motion  of  Stars  in  the  Line  of 
Sight,  made  at  the  Temple  Observatory,  Eugby.  By  Geo.  M. 
Seabroke. 

In  the  year  1879  I  brought  before  the  notice  of  the  Society 
some,  perhaps  rather  premature,  results  of  my  spectroscopic 
observations  of  the  motions  of  stars  towards  or  away  from  our 
system.  Since  that  time  I  have  been  engaged,  whenever  a 
sufficiently  long  period  without  interruption  could  be  obtained, 
in  continuing  this  line  of  research. 

A  large  number  of  my  observations  have  been  made  with  a 
view  to  perfecting  instrumental  arrangements,  and  being,  of 
course,  otherwise  valueless,  are  not  recorded. 

The  following  arrangement  appears  at  present  to  be  satis- 
factory, and  with  it  the  results  detailed  below  have  been  ob- 
tained. 

The  telescope  is  a  silver-on-glass  Newtonian  Reflector  of 
1 2^  inches  aperture,  and  6  feet  6  inches  in  focal  length,  equatorially 
mounted.  The  spectroscope  has  a  collimator  of  a  focal  length  of 
1 2  inches  and  J-inch  aperture,  and  a  Barlow  lens  in  the  telescope 
elongates  the  cone  of  rays  to  fit  the  same ;  a  cylindrical  lens 
is  also  used  to  give  sufficient  width  of  spectrum.  The  prisms  are 
used  twice,  the  rays  of  light  passing  first  through  the  lower 
portions,  and  back  through  the  upper  portions  to  the  observing 

*  The  variability  of  the  F-line  was,  however,  remarked  at  Greenwich,  on 
September  4,  1884,  and  may  be  generally  inferred  from  its  varying  appearance 
on  several  other  occasions. 


94 


Mr.  Seabroke,  Spectroscopic  Observations.       xlyii.  3, 


telescope  of  1  foot  focal  length,  carrying  an  eyepiece  which  mag- 
nifies the  slit  about  15  times.  The  number  of  prisms  used  is 
equivalent  to  either  3  or  5  of  6o°. 

For  comparison  of  the  positions  of  the  lines  observed,  I  use 
a  spot  of  light,  or  "  ghost/'  produced  by  the  reflection  from  the 
surface  of  the  last  prism  of  the  rays  of  light  proceeding  from  a 
minute  slit  carried  by  a  micrometer,  after  passing  through  a 
collimating  lens.  The  slit  in  question  is  illuminated  by  rays 
from  a  lamp  carried  on  the  large  telescope,  reflected  from  a  silvered 
glass  attached  to  the  micrometer ;  the  light  is  passed  through  a 
glass  of  a  colour  as  near  as  possible  that  of  the  part  of  the  spec- 
trum under  examination,  so  as  to  avoid  want  of  focal  coincidence. 

The  vacuum  tube,  or  magnesium  wire,  is  carried  in  front  of 
the  slit,  and  can  be  moved  to  and  from  that  position  at  pleasure. 

To  compare  the  lines,  the  slit  of  the  spectroscope  is  illuminated 
by  the  star  and  comparison  lights  alternately,  and  a  reading  of 
position  of  each  taken  with  the  ghost.  The  value  of  the  divisions 
of  the  micrometer  screw  are  ascertained  by  measurement  of  known 
lines  on  the  solar  spectrum. 

For  these  observations  the  telescope  at  my  disposal  is  very 
small,  and  therefore  it  is  only  the  spectrum  of  the  brighter  stars 
that  I  am  able  to  attack.  There  is  a  fine  field  in  this  line  of  re- 
search open  to  the  possessors  of  large  telescopes  giving  good 
definition. 

In  the  following  list  of  measures  the  sign  +  means  that  the 
star  is  receding  from,  and  —  approaching,  our  system.  The 
corrected  motion  is  the  apparent  value  corrected  for  the  orbital 
motion  of  the  earth. 


Number  of 
Prisms. 

Line 
Compared. 

Number  of 
Measures. 

a 

Cor.  Motion 

in  Miles  per 

Second. 

AndromecUr. 

Bate 
1800+ 

Remarks. 

5 

F 

6 

-22*5 

85-87 

5 

F 

4 

—29-2 
7  Pegasi. 

•90 

5 

F 

5 

+  136 

8587 

Very  difficult 

5 

F 

4 

-66-8 
a  Auriga. 

•90 

5 

F 

2 

-415 

8627 

Doubtful. 

5 

F 

5 

+  151 

32 

5 

F 

3 

+   80 

33 

5 

F 

3 

y 

+  8'5 
Gcminorum. 

34 

5 

F 

3 

-463 

8519 

Jan.  1887.     of  Motion  of  Stan  in  the  Line  of  Sight.  ^95 

CompuwL    Xmmm*.     ^j^^g"  ,8oo+         »«"»»»*•• 


S  F 

S  F 

S  F 


7  F 

5  F 


7  F. 

7  F 

7  F 

S  F 

5  F 

S  F  • 


S  F 

7  F 

7  F 

S  F 

5  F 

5  F 

5  F 


S  F 

S  F 

5  F 

5  F 


S  F 

5  F 

S  F 


Sirius. 

4 

—3172 

86-12 

9 

-436 

•i« 

7 

-495 
Castor, 

•17 

1 

3 

+  19-6 

8230 

5 

+  I5'8 

8519 

6 

+  75 
Pollux. 

8617 

2 

-344 
a  Leontt. 

5 

+  32*1 

82-30 ' 

3 

+  340 

35 

4 

—  o-i 

8535 

3 

-  3*5 

8633 

4 

+  52*5 
y  Leonis. 

•40 

2 

+  12*2 

7933 

3 

+  23-2 

8235 

2 

-485 

•36. 

4 

+  7-2 

85-35 

2 

+  213 

•41 

2 

-315 

86-34 

2 

-315 

•40 

t 

a  Ursa  Maj. 

• 

3 

-  0"5 

85-42 

4 

—  11*2 

86-42 

2 

+  22 

49 

3 

+  21-5 

7  Ursa  Maj. 

54 

3 

-249 

8542 

4 

-  6-5 

86-40 

4 

-249 

•49 

u 


96 

Mr.  Sedbroke, 

Spectroscopic 

Observations        xlvii.  3, 

Number  of 
Prisms. 

line 
Compared. 

Number  of 
Measures. 

Cor.  Motion 

in  Miles  per 

Second* 

fi  Ursm  Maj. 

Date 

1800+ 

Remarks. 

5 

F 

5 

-587 

8542 

5 

F 

3 

+  II-6 

8649 

5 

F 

3 

-500 

•49 

Very  doubtful. 

5 

F 

4 

+  27*2 
ft  Leonis, 

•54 

Line  wide. 

7 

F 

5 

-42-4 

8236 

7 

F 

5 

+  39-o 

•36 

5 

F 

7 

-445 

8535 

5 

F 

4 

-470 

•41 

5 

F 

3 

+  32'° 

8640 

5 

F 

4 

+  7*o 
€  Leonis. 

•40 

7 

F 

4 

+  21-5 

8236 

7 

F 

8 

+  33'8 

•36 

5 

F 

4 

+  8-2 

85-35 

5 

F 

5 

+  433 

•41 

5 

F 

4 

+  32*5 

8640 

5 

F 

4 

-3i'5 
B  Leonis. 

•40 

5 

F 

4 

+  145 

8535 

5 

F 

5 

+  23-8 

•41 

5 

F 

4 

-53-0 

86-34 

5 

F 

3 

+  5-0 

•40 

5 

F 

3 

-245 
Z  Ursa  Mqj. 

•40 

5 

F 

3 

-31-6 

8542 

5 

F 

2 

— 16'4 

•48 

5 

F 

3 

+  20-4 

8649 

• 

5 

F 

I 

+  36-0 
(  Virginis. 

•54 

5 

F 

i 

-430 
c  Urw  Maj. 

8541 

Doubtful. 

5 

F 

3 

-293 

85-41 

5 

F 

6 

-61-3 

•48 

5 

F 

9 

-52-2 

8649 

5 

F 

6 

-699 

•50 

Jan.  1887.      of  Motion,  of  Stars  in  the  Line  of  Sight 


97 


ber  of 

SUM. 

Line 
Compared. 

Number  of 
lieuureg. 

Id  Miles  per 
Beoond. 

C  Ursa  Maj, 

Date 

180©+ 

5 

F 

3 

-23-5 

85-4I 

5 

F 

3 

-480 

'45 

5 

F 

5 

+  20*1 

■48 

5 

F 

4 

+  H'4 

8650 

5 

F 

4 

—  2-6 

54 

5 

F 

3 

—  10-4 

•64 

5 

F 

3 

+  295 

•66 

5 

F 

5 

+  25*0 

•69 

5 

F 

2 

+  155 
«  Virginis, 

•70 

7 

F 

7 

+  169 

8236 

7 

F 

7 

+  135 

•36 

5 

F 

7 

+   37 

8541 

5 

F 

4 

+  43*2 
11  Bootti* 

•41 

7 

F 

6 

+  59 

8237 

5 

F 

3 

—40*1 

8650 

5 

F 

5 

-  8-5 

i)  Ur$*Maj. 

•54 

5 

F 

5 

+  25-0 

8650 

5 

F 

5 

—in 

•54 

5 

F 

5 

+  10*0 

•64 

5 

F 

4 

+  8-6 

•66 

5 

F 

7 

+  26*5 

•69 

5 

F 

3 

+  24-0 

70 

5 

F 

3 

+  18-9 

Arcturus. 

•70 

7 

F 

4 

+  24-1 

8237 

5 

F 

5 

+  132 

8541 

5 

F 

3 

-76*6 

44 

5 

F 

5 

—  24*1 

45 

5 

F 

3 

-44'i 

48 

5 

F 

4 

-1 8-2 

•48 

5 

F 

3 

+  14*6 

•5i 

5 

F 

4 

—40-1 

•55 

Remarks. 


Difficult. 


H  2 


96 

Mr.  Sedbroke, 

Spectroicopic 

O606rvatiofi«        xlvii.  3, 

Number  of 
Prisms. 

Line 
Compared. 

Number  of 
Measures. 

Coor.  Motion 

in  Miles  per 

Second. 

3  Ursa  Maj. 

Date 
2800+ 

Remarks. 

5 

F 

5 

-S»7 

85-42 

5 

F 

3 

+  11*6 

8649 

5 

F 

3 

-500 

•49 

Very  doubtful 

5 

F 

4 

+  27-2 
ft  Lconis. 

•54 

Line  wide. 

7 

F 

5 

-42-4 

8236 

7 

F 

5 

+  39*o 

•36 

5 

F 

7 

-445 

85-35 

5 

F 

4 

-470 

•41 

5 

F 

3 

+  32*0 

8640 

5 

F 

4 

+  7-0 
4  Ltonii. 

•40 

7 

F 

4 

+  21-5 

8236 

7 

F 

8 

+  33*8 

•36 

5 

F 

4 

-1-  8-2 

8535 

5 

F 

5 

+  433 

•41 

5 

F 

4 

+  32S 

86*40 

5 

F 

4 

-31-5 
jB  Lconti. 

•40 

5 

F 

4 

+  14*5 

85*35 

5 

F 

5 

+  23-8 

•41 

5 

F 

4 

-530 

8634 

5 

F 

3 

+   5*o 

•40 

5 

F 

3 

-245 
ft  Z7rsa  Afq;. 

•40 

5 

F 

3 

-316 

85*42 

5 

F 

2 

— 16-4 

48 

5 

F 

3 

+  20-4 

8649 

• 

5 

F 

l 

+  36-0 
f  Virginia. 

'54 

5 

F 

i 

-430 
e  Z7r«r  Afcy . 

8541 

Doubtful. 

5 

F 

3 

-293 

85*41 

5 

F 

6 

-61-3 

•48 

5 

F 

9 

—  52-2 

86*49 

5 

F 

6 

-699 

•50 

Jan.  1887.      of  Motion  of  Stan  in  the  Line  of  Sight 


97 


Number  of 
Prisms. 

Line 
Compared* 

Number  of 
Measures. 

Cor.  Motion 

la  Miles  per 

Second. 

C  Ursa  Maj, 

Date 

1800+ 

5 

F 

3 

-235 

85-41 

5 

F 

3 

-480 

•45 

5 

F 

5 

+  201 

•48 

5 

F 

4 

+  H4 

8650 

5 

F 

4 

—    2*6 

•54 

5 

F 

3 

—  IC4 

•64 

5 

F 

3 

+  295 

•66 

5 

F 

5 

+  25-0 

•69 

5 

F 

2 

+  15*5 
■a  Virginia. 

•70 

7 

F 

7 

+  16-9 

8236 

7 

F 

7 

+  13*5 

•36 

5 

F 

7 

+  37 

8541 

5 

F 

4 

+  43*2 
ti  Bootti. 

•41 

7 

F 

6 

+   59 

8237 

5 

F 

3 

—40*1 

8650 

5 

F 

5 

-  8-5 
y  UrsmMaj. 

•54 

5 

F 

5 

+  250 

8650 

.  5 

F 

5 

—  in 

•54 

5 

F 

5 

+  iao 

64 

5 

F 

4 

+  8-6 

•66 

5 

F 

7 

*26*5 

■69 

5 

F 

3 

+  240 

•70 

5 

F 

3 

+  18-9 

Arcturus. 

•70 

7 

F 

4 

+  24*1 

8237 

5 

F 

5 

+  13-2 

85*41 

5 

F 

3 

-76-6 

'44 

5 

F 

5 

—  24*1 

•45 

5 

F 

3 

-44-1 

•48 

5 

F 

4 

-l8'2 

•48 

5 

F 

3 

+  14-6 

•5i 

5 

F 

4 

—40-1 

•55 

Remarks. 


Difficult 


H  2 


9» 


Mr.  Sedbroke,  Spectroscopic  Observations        jllyii.  3, 


Number  of 
Prism*. 

Line 
Compared. 

Number  of 
Measures. 

Cor.  Motion 

in  Miles  per 

Second. 

*  Arcttcrus. 

Date 
1800+ 

5 

F 

3 

+   30 

8649 

5 

F 

4 

-43'o 

64 

5 

F 

3 

—  29-0 

•66 

5 

F 

2 

-360 
c  Booth. 

•69 

• 

5 

F 

4 

-167 

8555 

5 

F 

3 

-29*3 

8650 

5 

F 

1 

+  80 

•66 

5 

F 

3 

+    2'0 

•69 

5 

F 

• 

4 

-364 

a  Corona  Bor. 

74 

5 

F 

3 

-36S 

8664 

5 

F 

3 

+  13*9 

•64 

5 

F 

1 

-330 

•66 

5 

F 

3 

-450 

•69 

5 

F 

• 

4 

-275 

70 

• 

%  a  OphiuehL 

5 

F 

4 

-11-3 

8551 

5 

F       • 

4 

-554 

•75 

5 

F  ; 

5 

"-   1*4 

8664 

5 

F 

4 

-231 

•66 

5 

F 

2 

+  7-0 

•69 

5 

F 

2 

-245 
Vega. 

•69 

7 

F 

3 

-65 

81-53 

7 

F 

3 

-459 

73 

5 

F 

2 

-289 

8548 

5 

F 

4 

-592 

•50 

5 

F 

8 

-433 

71 

5 

F 

3 

-49-2 

74 

5 

F 

• 

%    * 

-41'S 

8669 

5 

F  . 

3 

-324 

70 

5 

F 

4 

-32'9 

72 

Remarks. 


Jan.  1887.       of  Motion  of  Stars  in  the  Line  of  Sight.  99 


Kmnber  of 
Prisms. 

Line 
Compared. 

Number  of 
Measures. 

Cor.  Motion 

in  Miles  per 

Second. 

y  Lyra. 

?**^_          Remarks. 
1800+ 

5 

F 

4 

+  !.r5 

8674    Very  faint 

3 

F 

6 

-w6 

75 

3 

F 

4 

-357 

•87 

3 

F 

2 

-660 
(  Aquila. 

•88 

5 

F 

10 

-29-5 

8575 

5 

F 

4 

-1773 

78 

5 

F 

5 

-300 

8672 

3 

F 

5 

+  14*0 
y  Aquiite. 

75 

5 

F 

-3T9 

8672 

3 

F 

+  34'4 

75 

3 

F 

• 

est. 

^300 
I  Cygni. 

•87 

7 

F 

2 

-265 

8174 

7 

F 

3 

.  -55*6 

79 

5 

F 

6 

+  24*6 

8572 

5 

F 

4 

-  5* 

75 

5 

F 

4 

-157 

75 

5 

F 

4 

+  381 

78 

5 

F 

2 

-369 

S7 

3 

F 

5 

-635 

8680 

3 

F 

4 

-507 

•88 

* 

3 

F 

3 

-502 
AUair. 

•91 

5 

F 

3 

+  227 

8470 

5 

F 

4 

-386 

77 

5 

F 

2 

-43*6 

8574 

5 

F 

4 

;    +  60 

75 

5 

F 

7 

-194 

75 

5 

F 

5 

—  251 

78 

5 

F 

3 

—  220 

8664 

• 

5 

F 

7 

-  04 

72 

5 

F 

4 

-  28 

74 

3 

F 

4 

—  700 

•88 

rjo2  Spectroscopic  Results  for  Motions  of  Stars     xlyii.  3, 

t^«.  No.  5rt?*,,  Concluded 

15£f'         Ob*,    of   line.  I„«I<2L      Motion  of  Star.  Remarks. 

l886-  Meaa.  'iSS?      Meat.     Katlmd. 

&  Persei. 
h 

Not.  2920    M     6     F     +3*9     +  4*3     +21  Definition  good. 

Dec    4  22    M     4     F     +   5-4-111-8  —  106-4  Spectrum  faint ;  definition 

poor. 
14  20    M     5     F     +8*3     +12*2     + 13*6  Definition  fair. 

14  20    L     5     F     +  8*3     —  34     + 1 2- 1  Definition  fair. 

a  Persei. 

Jan.  27  20    M     2     F     +15*1     —40-9     —348  Definition  fair. 

Feb.     1  20    M     2     F     +156     —21 '2     —257  Wind  Tery  high;  defini- 
tion poor. 
Not.  29  21    M     2     F     +20     +  6*8     +76  Star-line  faint 

Dec.    423    M     2     F     +3*5     —  io*4     —  76  Definition  good. 

Aldebaran. 

Jan.  27  20  M  2  F  +16*3  +229  +   8-3 

Mar.    3  21  M  2  F  +18*5  +24*8  + 13*4  Definition  poor. 

17  20  M  2  6,  +17*4  +13*6  +  24*9  Definition  poor. 

Not.  17  23  M  4  F  —  4*1  +44*3  +400  Star-line  faint. 

29  22  M  2  F  —  0*2  +l8*9  +18*2  Definition  poor. 

Dec.    423  M  2  F  +1*5  +41*5  +  43*0  Definition  fair. 

CapeUa. 

Jan.  27  22    M     4     F     +12*9     —  40  —  3-9  Star-line  very  well  seen. 

Mar.    3  21     M     2     F     +171     —  54'5  —525  Definition  fair. 

17  20    M     2     0j     +169     +42-3  +  466  Star-line  faint 

23  21    N     2     6,     +166     —20-8     —  1 6*6  Spectrum  tremulous;  star- 
line  faint. 
Apr.    6  22     N     2     F     + 15*1     +   1*5     —  0*4  Spectrum  tremulous. 

Not.'  29  22    M     2     F     —  3-8     +  295     +  302  Star-line  faint. 

*  ■ 

Rigel. 
Jan.  2721    M     2     F     +12*9     +306     + 17-8  Star-line  fairly  well  seen. 

Feb.     1  20    M     2     F     +137     +   5 '5     +  0-3  Wind  very  high;  star-line 

r  seen    with    great    diffi- 

culty. 

Mar.    3  20    M     2     F     +160     +19*4     +  88  Definition  poor ;  measures 

rough. 

Not.  5  23  M  2  F  —  8-4  (  +  58*5)(  +  6i-6)  Spectroscope  out  of  ad- 
justment 

18  o    M     2     F     -  5-4     +  98     +96  Star-line     distinct     and 

well-defined. 
y  Ononis. 

Jan.  27  21     M     2     F     +13-6     +4*9     —  27  Star-line  very  well  seen. 

Feb.     1  20    M     2     F     +  14-6     -   1*3     -  40  Wind Tery  high ;  star-line 

seen   with   great   diffi- 
culty. 


Jan.  1887.    in  the  Line  of  Sight,  obtained  at  Greenwich.  103 

twf-  No«  %*u«  Concloded 

IJ*f-  Ota.   of  Tine.  .rzSSZ      Motion  of  SUr.  Remark*. 

1886.  M  in  miles       M  Estimd. 

MLvmm.  pcr§«C.        «■"*■»       """ 

y.Orkmi$. 
h 
Mar.    3  20    M     2     F     +178     +63     +  06  Star-line  smd  with  great 

difficulty. 
Not.  18    1    M     4     F     —  72     +11*5     + 1 r6  Spectrum    fairly    bright 

and  steady. 
0  Tauri. 

Jan.  27  21    M     2     F     +13*8     —38*0     -379  Star-line  fairly  well  seen. 

Feb.    121    M     2     F     +14*8     —25*4     —  25*3  Wind  very  high.    Defini- 
tion bad. 
Mar.    3  20    M     4     F     +184     -31*5     —35*1  Definition  poor. 

Not.  18    1    M     2     F     -80     r>  8ao    —  8*i  Star-line  well  seen. 

9  Ononis. 

Jan.  27  21    M     2     F     +127     +   7*8     +   3*8  Spectrum  rather  faint  and 

tremulous, 
c  Orumis. 

Jan.  27  21    M     2     F     +12-4     +14*8     +   7-3  Spectrum  rather  faint  and 

tremulous. 
(Ononis. 

Jan.  2721    M     2     F     +121     +13*2     + 14*2  Spectrum  rather  faint  and 

tremulous. 
k  Orients. 

Jan.   2721    M     2     F     +10*9    —21*4     —19*1  Star-line  fairly  well  seen. 

a  Orionis. 
Mar.  17  21    M     2     64     +17*8     +340     +  39-4  Definition  fair. 

0  Awrigm. 

Jan.  2722    M     2     F     +113     —  35*5     —40-9  Spectrum  rather  faint  and 

tremulous. 
Mar.   3  21     M     2      F     +168     -587     -551  Definition  fair. 

7  Geminorum. 

Jan.  27  22    M     6     F     +9*5     —  48- 1     —407  Spectrum     bright     and 

steady,  but  star-line  ex- 
ceedingly broad  and  dif- 
fused and  difficult  to 
bisect. 

Feb.  1  21  M  2  F  +109  —437  —34-2  Wind  Tery  high;  defini- 
tion bad. 

Sinus. 

Jan.  19  22    M     2     F     +  4*4     -137     —13*1  Spectrum  very  tremulous. 

27  22    M     6     F     +  6*3     —32*6     —32-2 

Mar.   3  22    M  F     + 12*6     -38*6     —357  Definition  bad.     Star  in 

light  cloud. 
Not.    5    i    M     4     F     -123  (  +  3i"o)(  +  32'3)  Spectroscope  out  of  ad- 

.     .  justment. 

18    2    M     6     F     - 106     +  8-4     +  8*3  Star-line  well  seen. 


104  Spectroscopic  Results  for  Motions  of  Stars       xlyii.  3, 


Date. 
1886. 

No. 
Obe.  of 
Meat. 

line. 

Earth's 
Motion 
In  miles 
per  sec. 

Concluded 
Motion  of  Star.                  Remarks. 
Meaa.      Estimd. 

h 
27  23 

6  23 

Castor. 

Jan. 
Apr. 

M 

N 

2 

4 

F 
F 

+    6*2 

+  i8*o 

+  292 
-149 

+  32*1  Spectrum  tremulous;  star- 
line  very  ill-defined. 
- 158  Star-line  ill  defined. 

May 

1  22 

M 

2 

F 

+  16-4 

+  247 

+  130  Definition  good. 

Nov. 

18    2 

M 

2 

F 

-147 

+  278 
Procyon. 

+  27*2  Star-line  well  seen. 

Jan. 

18  23 

27  23 

28  22 

N 
M 

N 

3 
6 

1 

F 
F 
F 

+  i'S 

+   44 
+  47 

+  03 
-138 
-  41 

—  I'5  Spectrum  bright;   defini- 

tion fair. 

—  13*5  Spectrum  bright;  defini- 

tion good. 

—  47 

Mar. 

3  22 

M 

4 

F 

+  136 

-388 

-413 

Apr. 

6  22 

N 

2 

F 

+  i7*S 

-21-5 

—  21  "9 

May 
Not. 

1  21 
18    2 

M 
M 

2 
4 

F 
F 

+ 166 
-154 

-579 
+  95 
Pollux. 

—41*3  Definition  bad ;  measures 

very  rough. 
+  9'8  Star-line  well  seen. 

Jan. 

27  23 

M 

2 

F 

+  S3 

-45*1 

—  51*8  Definition  good. 

Mar. 

17  22 

M 

2 

*i 

+  168 

•294 

—390  Star-line  difficult  to  see. 

Apr. 
May 
Nov. 

23  23 
6  23 
1  22 

18    2 

N 
N 
M 
M 

2 
2 
2 
2 

F 
F 
F 

+  17-4 
+  181 

+  16-9 
-i5"5 

-243 
-30*5 
-45* 
-155 

Regxdus. 

—23*8  Measures  rendered  diffi- 
cult by  mist 

—29*9  Spectrum  tremulous ;  star- 
line  faint. 

—45*1  Measures  made  with  great 
difficulty. 

—  12*3  Star-line  fairly  well  seen 
at  times. 

Apr. 

30  22 

N 

2 

F 

+  172 

—  17-2 

-17-2 

May 

3  23 
6  23 

15  21 

M 

N 
M 

2 
2 
2 

F 
F 
F 

+  17*5 
+  17-6 

+  179 

+   18 

-143 
-  5  2 

+  47  Spectrum  bright;  defini- 
tion fair. 

— 13*4  Measures  made  with  diffi- 
culty. 

—  3*4  Star-line  very  ill-defined. 

18  23 

N 

2 

F 

+  17*9 

-  30 

—  2*9  Star-line    diffused     and 
faint. 

0  Ursa  Major  is. 

May 

1  23 

M 

2 

F. 

+  127     +   57 
a  Ursa  Mojo 

—  2*o  Spectrum  faint ;  measures 
rough. 

ris. 

May     1  23    M     2     F     +117     —597     —527  Star-line  very  difficult  to 

see 
June  16    1    N      2     6j     +  87     -57-3     -575 


Jan.  1887.    in  the,  Line  of  Sight,  obtained  at  Greenwich.  105 

*£         fc^IteS       llSSStf&r.  ■««*■• 

1886.  ir^,„  in  miles       ■Umm4,      grtimd. 


per  teo* 

I  Leonis* 
h 
Ms j  15  22    M     2     F     + 1 6-8     —440    —50*1  Definition  fair. 

fi  Leonis. 

Apr.  30  23    N     2     F     +136     -305     -30-3 

May     4     1    M     2     F     +14*2     —109     —10*5  Spectrum  fairly  bright  and 

steady. 

1522    H     2     F     +15*9     —147     —13-8  Definition  fair. 

y  Ursa  Majoris. 

May     1  23    M     2     F     +117     4*1*2     +  o*8  Star-line  very  ill-defined. 

June  16    o    X     2     bx     + 10*9     —  2*9     —  2*8  Spectrum  faint,  but  star- 
line  seen  veil  at  times. 

y  Virginia. 

May    4     1    31     2     F     +10*3     —43*6     —41*1  Spectrum    fairly    bright 

and  steady. 

e  Ursa  Majoris. 
May     1  23    M     2     F     +9*5     —  5'i     —3*0  Star-line  very  ill-defined. 

a  Canum  Venaticorum. 

May  13  22    M     2     F     +11*9     —35*6     —36*8  Spectrum  steady,  but  defi- 
nition poor. 

Spice, 

Apr.  30  23    N     2     F     +57     r'6'5     -157 

May    4    1    M     2     F     +6*6     —  6o*8     —  53*4  Spectrum  rery  tremulous. 

18  23    N      2     F     + 10-5     —  7*4     —  6*4  Definition  poor ;  measures 

rough. 

C  Ursa  Majoris. 
May    2    o    M     2     F     +8-4     +6*5     +  7*0  Definition  fair. 

Arcturus. 

F     ■••  4-8     -2i'o     —21*5 

F     +  5*5     —71*3     —64*6  Spectrum  bright;  defini- 
tion good. 
F     +  6-2     —237     —23*9 

F     +  7*8     -350     —39*4  Spectrum  bright,  but  de- 
finition poor. 
18  23    N     2     F     +  89     -35-0    -33-5 

20  22    N     2     F     +93     —26*5     —27*8  Star-line  very  indistinct. 


Apr. 

30  23 

N 

2 

May 

4    2 

M 

2 

6  23 

N 

2 

13  22 

M 

2 

io6  Spectroscopic  Results  for  Motions  of  Stars     xlyii.  3, 

tw*                 No-             SlSon  Concluded 

I2£T"         Ota.    of    Line.    *otI1?n  Motion  of  Star.                    „       _. 

1886.                 mJm.           In,nile,,  mSST  Brtlmd.                  B*naa*«. 

por  sec. 

h 
Jane    7  22    M     2     6,     +12*5     —49*1     —46*9  Spectrum  and  star-Lines 

rather  faint. 
15  23    N     2     o,     +135     -573    -54-2 

28  23    M     2     o,     +147     —37*8     —387  Definition  poor. 

July     5  23    M     2     F     +15*1     —36*8     —38*9  Star-line  seen  fairly  well 

at  timet. 

c*  Bootis. 
Jane  28  23    M     2     F     +127     —15*0     — 10*4  Definition  bad. 

$  Libra. 

Kay  13  23    M     2     F     +17     —24*8     —23*3  Spectrum     bright,      but 

tremulous. 

a  Corona  Bor talis. 

Hay    4    2    M     4     F     +07     —26*6     —23*8  Star-line  very  difficult  to 

bisect. 
14    o    M     2     F     +2*8     +12*8     +19*6  Spectrum  bright;  defini- 
tion fair. 
20  23    N      2     F     +  4*2     — 16*2     —15*0 

* 

July     5  23    M     2     F     +ii*4     +24*3     +  24*3  Definition  fair. 

a  Serpentis. 

June  29    o    M     2     6,     +117     —  4*0     —   1*5  Star-lines  very  faint ;  de- 
finition poor. 

$  Serpcntis. 
May  14    o    M     2     F     +13     —14*2     -1 6*2  Star-line  well  seen. 

.  7  Herculis. 

May  14    1     M      1     F     —   vi     —36*9     —388  Observation     interrupted 

by  cloud. 

a  Ophiuchi. 

Jnly     5  23    M     2     F     +57     — 197     — 19*6  Definition  fair. 

7  Draconi*. 

June  29     I     M     2     6j     +09+  20-9     +  337  Definition  bad ;  star-lines 

seen  with  great  difficulty. 

Vega. 

July     6    o    M     2     F     +00     -129     —  ii*9  Definition  fair. 

Aug.   10  23    N      2     F     +  4*8     —297     —31*3  Spectrum      bright      and 

steady ;  definition  good. 


Jan.  1887.     tn  ^  ^ne  °f  Sight,  obtained  at  GreenwicJi.  107 

»£■  Ota.    *'  line.  |§£       nSSS?Sf5Lr.  ■~'** 

,886-  Meas.  in  miles       M  Eetimd. 

per  sec 

Tew. 
h 
Oct    13  20    M     2     F     +87     —608     —48*6  Observations   interrupted 

by  cloud. 
22  19    M     2     F     +8*5     —58-6     -448  Spectrum      bright     and 


steady. 


Altair. 


July 

6  1 

M 

2  F 

Aug. 

10  23 

N 

2  F 

Oct. 

18  22 

M 

2  F 

22  20 

M 

1  F 

—  4*3     —237     —215  Definition  fair. 

+  4*9  —31*2  —32*8  Star-line  broad  and  dif- 
fused. 

+  161     —67-6     —  54*4  Spectrum  very  faint  and 

tremulous. 

fi6*2     —42-9     —38*5  Spectrum      bright     and 

fairly  steady. 

y  Cygn*. 
June  29     1     M     2     6,     —  6*9     +   9*9     +12' 2  Definition  very  bad. 

a  Cygni. 

June  29    2    M     2     b{     —  7*4     +  0*5     —  0*6  Definition  bad ;  star-lines 

seen  with  great  difficulty. 
July     6     1    M    "2     F     -  6-8     -22*1     -23-0  Definition  fair. 

Oct.    18  22    M     2     F     +   73     -55*3     -45'6  Definition  fair. 

a  Pegasi. 

+  12*4     —34*4     —261  Measures  made  with  great 

difficulty. 

+  H-2     -35*8     —25-1  Definition  bad ;  measures 

rough. 

—  9*3     +   3*4     +   5'4  Spectrum  faint. 

Mars. 

+  ro-8     +  15*9  Definition  fair ;  calculated 

motion  +20. 

—  6*9     —  90  Planet-line  faint;   calcu- 
lated motion  +  3*3. 

+  2*3     +   1  *5  Calculated  motion  +5 '6. 

+   18         O'O  Calculated  motion  +  7*3. 
+   5*1     +  4*0  Calculated  motion  +7*8. 

—  7*2     —  7 '4  Definition  fair ;  calculated 

motion  +8*o. 

Venus. 

—  6*8     —  77  Computed  motion  —67. 
— 13*6     —  7*6  Computed  motion  —5*4. 


Jan. 

27  19 

M 

4 

F 

Feb. 

1  19 

M 

2 

• 

F 

Aug. 

11  1 

N 

2 

F 

Mar. 

17  22 

M 

• 
4 

*i 

23  23 

N 

4 

*, 

Apr. 

6  23 

N 

2 

F 

22  23 

N 

I 

F 

30  22 

N 

2 

F 

May 

4  0 

M 

4 

F 

Jan. 

16  18 

M 

10 

F 

27  18 

M 

10 

F 

io8 


Greenwich  Spectroscopic  Results  etc. 


xlyii.  3, 


Moon. 


Date.         Ota.  Jj^J*  Line. 


Jan.   18  23  N 

Mar.  17  22  M 

May  13  23  M 

15  23  M 

18  23  N 

20  23  N 

June  15  23  N 

Aug.  10  23  N 

Nov.     5  23  M 

18    3  M 

Dec     422  M 

Jan.  28  12  M 

Feb.    2  12  M 

Mar.    4  12  M 

24  12  N 

May    3  10  M 

June    8  10  M 

29  12  M 

July    6  13  M 

Nov.  30  12  M 


4 
5 
5 
5 
4 
4 
4 
5 
5 

5 
5 


5 

5 
5 

3 
5 
5 
5 
5 
5 


F 

*. 
F 

F 

F 

F 

A, 
F 

F 

F 
F 


F 
F 
F 

F 
F 

F 
F 


Motion 
Measured. 


+  2*5! 

—  O'l 

+  0*2 

—  II 


Remarks. 


\  The  coincidence  of  the  two  spectra  ap- 
_  i-e  /  peared  perfect. 

-4'6 

-5'4 
—  ro/ 

(  +  5*5)    The  comparison  was  not  quite  satis- 
factory. 

+  °"3 1   The  coincidence  of  the  two  spectra  ap- 
peared perfect* 


+  o-3\ 
+  0-9} 


Sly. 


+  I'2\ 
+  3'2j 


—  2'I 


The  coincidence  of  the  two  spectra  ap- 
peared perfect. 

No   want    of    coincidence   could   he 
detected* 


The  coincidence  of  the  two  spectra  ap- 
peared perfect. 


No    want    of    coincidence    could    be 
detected. 


Rotation  of  JupUer. 
Displacement  between  the/)  and /limbs. 


May  15  23    M     5 


+  32*3  Position-angle  of  slit  260.  The  mean 
point  observed  was  about  o"*5  from 
the  limb.    Definition  fair. 


Computed  relative  motion  of  the  limbs  p  —  /  +  30*9  miles  per  second,  the 
equatorial  diameter  of  Jupiter  being  taken  as  88,000  miles,  and  its  period  of 
rotation  as  9*  56°. 


Jan.  1887.      Greenwich  Observations  of  Occtdtations. 


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Jan.  1887.     U&c.  #.  /.  Johnson,  Occultation  ofAldebaran.        115 


Occultation  of  y  Virginia,  1886.     By  F.  C.  Penrose. 

A  few  remarks  on  an  observation  of  an  occultation  of  y  Vir- 
ginis  on  the  18th  inst.  may  be  interesting  to  the  Royal  Astro- 
nomical Society. 

The  morning  was  fine,  bat  there  were  some  slight  clouds,  and 
one  was  over  the  Moon  near  the  time  predicted  for  the  reappear- 
ance, so  that  I  could  not  see  the  grey  Moon,  and,  as  I  was 
dependent  on  the  position-angle  at  the  vertex,  could  not  use  a 
power  high  enough  to  separate  the  star  properly,  but  I  think  the 
observation  was  more  interesting  and  beautiful  in  consequence. 

At  G.M.T.,  +  say  29,  i6h  33™  32s,  a  bright  flash  showed  the 
reappearance  of  ylf  and  exactly  10  seconds  later  was  another 
flash,  which  seemed  to  double  the  brightness  of  the  star. 

The  time  was  corrected  by  altitudes  of  east  and  west  stars 
observed  at  nearly  the  same  altitude  and  azimuth  with  a  theodo- 
lite. 

I  got  several  positions  of  Barnard's  Comet,  particularly 
Nov.  29,  Dec.  4,  and  Dec.  9,  but  they  are  probably  liable  to  errors 
of  two  or  three  minutes  of  arc. 

Approximate  place  of  station,  longitude  ih  34m  58s  E.,  and 
latitude  370  58'  15"  N. 

Athens:  1886,  Dec,  26. 


Occultation  of  Aldebaran,  Jan.  6,  1887.     By  the  Rev, 

S.  J.  Johnson,  M.A. 

The  occultation  of  Aldebaran  on  the  6th  was  observed  here 
very  favourably.  Disappearance  at  i2h  i2m  49s  was  instan- 
taneous ;  not  the  slightest  lingering  or  projection  on  the  limb, 
though  a  portion  of  the  Moon's  dark  limb  was  left,  and  the  sky 
around  was  perfectly  clear.  The  star  seemed  to  lose  its  redness  as 
the  Moon  approached  it ;  the  emersion  at  1311  i4m  5s  not  nearly 
so  sudden.  Star  seemed  to  creep  out  leisurely  from  a  point  just 
north  of  the  Mare  Crisium,  but  some  haze  was  present.  Power  50 
employed,  on  3^-inch.     Time  by  sextant. 

MelpUuh  Vicarage,  Dorset : 
1887,  Jan.  10. 


n6 


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Jan.  1887.   Dr.  Dreyer,  Note  on  Electric  Illumination  etc.         117 

Sextant  Observations  of  Oomsts  Fabry  and  Barnard, 
(Communicated  by  Captain  H.  Toynbee.) 

Comet  Fabry. 

Observations  made  on  board  the  ship  "  Earl  of  Shaftesbury/' 
by  Captain  Wm.  Randall. 

1886,  May  5,   p.m.    (9h  im  3o»  G.M.T.),  Lat.  40   12'  N. 
Long.  22°o'  W. 

o  / 

Nucleus  of  Comet  to  Sirius 13     50 

„  „        BeUatrix  23    54 

1886,  May  7  :  8h  24*  4"  Astronomical  G.M.T.   Lat.  30  36'  N. ; 
Long.  200  o'  W. 

Nucleus  to  Sirius        8    23    20 

„        „  BeUatrix    ...        ...        ...        ...    30    34 

Comet  Barnard. 

Observations  made  on  board  the  s.s.  "  Neto,"  by  Captain 
Wm.  G.  Browne.  Ship's  position,  Lat.  310  54'  N. ;  Long. 
670  S3'  W. 

^  h  m  8  o  t  // 

Dec  4     21    49    25    Nucleus  to  Arcturus        24    21     20 

57     13  »       „Dubhe     ...    66    33      o 

22      6      4         ,,        „  Spica      ...    47    32    20 


Note  on  the  Electric  Illumination  of  the  Armagh  Refractor. 

By  J.  L.  B.  Dreyer,  Ph.D. 

As  inquiries  have  been  made  from  several  sides  about  the 
system  of  electrio  illumination  adapted  to  the  10-inch  Refractor 
at  the  Armagh  Observatory  by  Mr.  Grubb,  it  may  be  of  use  to 
give  a  short  description  of  it. 

The  principal  difficulty  of  connecting  the  eyepiece  and  other 
parts  of  an  Equatorial  with  a  battery  is  the  necessity  of  the  observer 
being  able  to  turn  the  telescope  about,  and  even  to  reverse  the 
instrument,  without  getting  it  entangled  with  the  connecting 
wires.  This  difficulty  Mr.  Grubb  has  obviated  in  a  very  neat 
manner  by  letting  the  current  pass  through  two  insulated  brass 
rings,  one  of  which  is  attached  round  the  upper  end  of  the  polar 
pillar,  and  the  other  round  the  end  of  the  Declination  axis  away 
from  the  telescope.  The  current  passes  from  these  rings  through 


n 8  Dr.  Dreyer,  Note  on  Electric  Ilkmination  etc.      xlyii.  3, 

brass  combs  sliding  on  them,  and  moving  with  the  telescope 
respectively  in  Right  Ascension  and  in  Declination.  The  rings 
are  kept  clean  by  being  from  time  to  time  rubbed  with  sand-paper. 

The  bichromate  battery  is  placed  in  the  porch  to  the  east  of 
the  dome,  and  the  wires  are  carried  under  the  floor.  One  wire 
ends  in  a  binding  screw  on  the  base  casting  of  the  Equatorial ; 
the  other  passes  through  the  base,  along  the  outside  of  the  polar 
pillar  to  the  first  of  the  above-mentioned  rings.  From  the  comb 
sliding  on  this  the  wire  passes  to  the  ring  on  the  Declination 
axiB ;  and  from  the  comb  sliding  on  this  a  wire  runs  along  the 
counterpoise  to  the  end  of  the  Declination  axis,  through  this  and 
out  through  the  "  cradle"  of  the  telescope  down  to  the  eye-end 
of  the  latter.  I  have  here  fixed  a  commutator,  with  four  holes 
in  it ;  by  sticking  a  brass  peg  into  one  of  these  the  current  is 
sent  to  the  lamp  giving  bright  field  illumination,  or  to  the  lamp 
illuminating  the  wires  on  a  dark  field,  or  to  the  lamp  illuminating 
the  Declination  circle,  or  to  a  small  hand-lamp  used  for  throwing 
light  on  the  micrometer  and  the  note-book.  From  each  of  these 
lamps  a  wire  goes  to  some  metallic  part  of  the  telescope.  The 
bright  wire  lamp  is  enclosed  in  a  small  brass  cylinder  on  the 
micrometer,  while  the  bright-field  lamp  is  placed  at  the  side  of 
the  tube  opposite  the  Declination  axis,  the  light  being  reflected 
down  to  the  eyepiece  by  a  very  small  central  mirror  on  an  arm 
which  the  observer,  if  he  wishes,  can  put  out  of  the  way  of  the 
pencil  of  light  from  the  object-glass  by  pushing  a  rod  which  goes 
down  to  the  eye-end.  The  hand-lamp  consists  of  a  short  brass 
tube  with  a  lens  at  one  end,  and  closed  at  the  other  end  by  a 
piece  of  wood,  through  which  pass  the  wires  and  an  ebonite  rod 
carrying  the  lamp  ;  when  not  in  use  it  hangs  on  one  of  the  arms 
to  which  the  finder  is  attached. 

There  is  no  arrangement  for  reading  the  R.A.  circle  from  the 
eye-end :  the  observer  has  to  stand  on  one  of  two  steps  east  and 
west  of  the  pier,  and  reads  the  circle  by  means  of  a  magnifying 
lens  and  an  electric  lamp  placed  in  a  short  tube,  which,  when  not 
required,  hangs  on  a  wire  holder  on  the  south  end  of  the  pier. 
From  this  lamp  an  "  earth  wire"  goes  to  the  base  of  the  telescope 
mounting,  and  contact  is  made  simply  by  resting  the  brass  tube 
against  an  uncovered  portion  of  the  principal  wire  from  the 
battery. 

The  incandescent  lamps  are  from  Laing,  Wharton  &  Down, 
8  and  9  Holborn  Viaduct,  London  ;  the  glass  globes  are  -^  of  an 
inch  in  diameter.  The  bichromate  battery  has  four  cells,  but 
only  three  are  required  for  the  micrometer,  and  one  or  two  would 
be  enough  for  illuminating  the  circles.  The  cells  are  very  large, 
the  glass  jars  being  9  inches  high  and  6  inches  in  diameter.  To  the 
metallic  lids  are  fastened  four  carbons,  6i  by  z\  inches,  and  the 
zinc  plate  is  9  inches  by  3  inches.  By  keeping  the  zinc  plates 
lifted  above  the  acid  when  not  in  use  they  last  a  long  time.  The 
whole  arrangement  has  been  found  extremely  convenient  and 
clean. 


Jan.  1887.      Mr.  Denning,  Meteors  with  Ourved  Paths.  129 


Meteors  with  Carved  Paths.     By  W.  P.  Denning. 

The  term  "  erratic  "  applied  by  Mr.  Hopkins  to  such  meteors 
as  display  carved  paths  appears  to  me  inappropriate.  Erratio 
meteors  are  usually  understood  to  refer  to  such  of  these 
bodies  as  belong  to  unknown  systems,  and  are  therefore 
synonymous  with  sporadic  meteors.  The  title  has  also  been 
employed  to  denote  meteors  which,  though  probably  emanating 
from  known  showers,  exhibit  a  certain  discordance  in  their 
directions,  though  such  discordance  may  have  been  induced  by 
perturbations  exercised  upon  them  far  beyond  oar  atmosphere, 
and  has  nothing  to  do  with  the  curved  paths  they  sometimes 
pursue  when  under  ignition.  The  term  adopted  by  Mr.  Hopkins 
is  not  expressive  of  the  peculiarity  to  which  he  refers  it.  Such 
words  as  devious,  sinuous,  deflected,  or  tortuous  meteors  would 
be  preferable,  as  conveying  a  distinct  idea  of  the  anomalous 
flights  alluded  to. 

As  a  rule,  I  believe  the  alleged  crooked  paths  are  nothing 
more  than  mere  impressions.  The  curious  flickering  in  the  light 
of  individual  meteors  often  giving  rise  to  considerable  alternations 
in  their  apparent  brilliancy,  combined  with  the  fact  that  these 
phenomena  rarely  last  long  enough  to  ensure  a  steady  view, 
occasion  the  idea  of  curved  flights.  The  observer  is  seldom 
looking  towards  the  exact  place  of  a  meteor's  course,  and  the 
glimpse  he  obtains  is  more  or  less  hurried,  imperfect,  and 
erroneous. 

On  December  20,  1886,  i3h  nm,  I  was  watching  for  shooting 
stars  and  looking  towards  the  immediate  region  of  Gemini  and 
Cancer,  when  suddenly  a  brightish  meteor  shone  out  north  of  /3 
Leonis.  Instantly  directing  my  eyes  to  the  spot,  I  caught  the  end- 
course  well,  and  received  a  very  strong  impression  that  the  path 
was  much  crooked  or  curled,  but  about  i£  sec.  later  a  bright  streak 
of  phosphorescence  came  oat  on  the  course  of  the  meteor,  and  I 
saw  it  was  perfectly  straight  along  its  whole  length.  My  idea 
as  to  the  bent  path  was  therefore  quite  illusory,  and  doe  to  the 
scintillations  of  the  meteor  in  its  rapid  flight  which  I  had  seen 
but  imperfectly.  I  may  add,  that  of  some  thousands  of  meteor 
streaks  and  trains  observed  here  at  various  times  very  few  have 
shown  decided  curvature. 

In  1885,  out  of  a  total  of  1,334  meteors  recorded  (omitting 
Andromedes  of  November  27),  I  noticed  four  which  were  con- 
spicuously curved.  In  1886  I  saw  1,431  meteors,  of  which  about 
fifteen  exhibited  the  same  peculiarity  in  a  striking  degree.  One 
of  the  best  examples  of  these  was  recorded  on  December  25, 
1886,  8h  22m.     The  meteor  was  3rd  mag.  and  moved  very  slowly 


i2o  Mr.  Doming,  Meteors  with  Owned  Path*.        xivn.  3. 

from    between    a    and  ft    Gem.lnoru.rn ;    at  the  end    it    curved 
upwards  bo  :  — 


Meteors  are  not  infrequently  broken  during  their  flights  and 
are  observed  to  wax  and  wane  several  times  before  final  dis- 
appearance. The  large  meteor  of  November  17,  1886,  revived 
seven  or  eight  times  daring  its  long  flight  of  63",  which  it  per- 
formed in  seven  seconds.  Fireballs  of  the  finest  typo  are  often 
accompanied  with  a  series  of  outbursts  and  brilliant  flashes 
directly  resulting  from  increased  combustion  at  certain  points  of 
their  courses.  Meteor  streaks  and  trains  are  sometimes  separated 
into  three  or  four  visible  parts,  but  they  are  almost  invariably 
sections  of  a  straight  line  until  they  begin  drifting  nnder  the 
influence  of  atmospheric  currents,  which  occasionally  mould 
them  into  grotesque,  serpentine  forms  before  they  entirely  fade 
from  view. 

As  to  the  meteor  of  December  4,  1886,  quoted  by  Mr. 
Hopkins,  the  phenomenon  he  describes  must  have  been  due,  as 
Colonel  Tnpman  suggested,  to  the  nearly  simultaneous  appear- 
ance of  two  meteors  with  parallel  paths,  and  hence,  presumably, 
belonging  to  the  same  radiant.  Bnt  the  difference  of  30'  is  so 
small  that  it  seems  to  me  quite  inappreciable  when  the  circum- 
stances of  such  observations  are  considered.  Occasionally  the 
beginning  or  end  point  of  a  meteor's  Sight,  when  near  prominent 
stars,  may  be  noted,  very  accurately  ;  bnt  the  details  of  the  slight 
curve  and  secondary  raised  track  of  the  meteor  described  by 
Mr.  Hopkins  would  be  far  too  trivial  to  be  noticed  by  my  eye 
or,  I  venture  to  affirm  by  any  other  eye  not  endowed  with 
extraordinary  powers. 

Brutal:  1S86,  Dee.  31. 


Erratum  (in  some  copies). 


MONTHLY   NOTICES 


or  THE 


ROYAL  ASTRONOMICAL  SOCIETY. 


Vol.  XLVIL 


February  ii,  1887 


No.  4 


J.  W.  L.  Glaishkr,  M.A.,  F.R.S.,  President,  in  the  Chair. 


Report  of  the  Council  to  the  Sixty-seventh  Annual  General 

Meeting  of  the  Society. 


The  following  table  shows  the  progress  and  present  state  of 
the  Society : — 


December  31,  1885 


Since  elected 

Deceased 

Resigned 

Expelled 

Removals 


December  31,  1886 


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224 


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E 

o 

3 

o 
H 


6oi 


599 


s 


48 


+  2 
—  I 


49 


A- 


65O 


649 


122 


Report  of  the  Council  to  the 


xlyii.  4, 


Mr.  Common* 8  Account  as  Treasurer  of  the  Royal 
RECEIPTS. 


£  «.  d. 

Balance  at  Bankers',  Jan.  i,  1 886              395  2  7 

in  hand  of  Assistant  Secretary  on  account 

of  Tumor  and  Horrox  Funjls 22  7  5 


it 


Half-year's  dividend  on  £7,500  Consols     108  15  o 

£5,700    New  3  per   cent. 

Stock 82  13  o 

£7.500  Consols     108  15  o 

£5,700   New  3  per   cent. 

82  13  o 

14  10  o 


»i 


>i 


tt 


if 

ff 


•  •  •        •  •  • 


Stock 
Dividends  on  £500  Metropolitan  Stock 

Received  on  account  of  Subscriptions : 

AJTOSIb    ■••  •••  «••  ••• 

260  Annual  Contributions  for  1886 

4  »  »»  1887 

21  Admission  Fees 

18  First  Contributions ... 


•  «  •  •  •  t 


•  •  •  •  •  • 


•  ••  •  *  • 


•  •  •  •  ■  4 


Composition  Fees  

Sales  of  Publications : 

At  Williams  and  Norgate's,  1885 
At  Society's  Rooms,  1886 


•  •  •  •  •  • 


Audited  and  found  correct,  Jan.  8, 1887. 

Robt.  Bryant. 
Robt.  J.  Lbckt. 
Hubert  Sadlrb. 


161  14    o 

546    o    o 

880 

44    2    o 

31  10    o 


•• •  • • • 


29  15    7 
38    7    9 


£     8.  d. 


417  10    0 


397    6   0 


791  14   0 
105    o   0 


68    3    4 


*i,779  13    4 


Feb.  1887.      Sixty-seventh  Annual  General  Meeting. 


123 


Astronomical  Society,  from  Bee.  31,  1885,  *° 

EXPENDITURE. 

Assistant  Secretary :  Salary  

„  ,,  for     assistance     in     editing 

Society's  Publications 

Income  Tax  and  House  Duty  

Fire  Insurance  

Printing 

Engraving  and  Lithography  

Computation  of  Ephemerides  in  Monthly  Notices  ... 

Tumor  and  Horrox  Funds  :  purchase  of  Books  for 
■Ux Drary  •  •  •         •••         ...         ...         . . . 

Binding  Books  in  Library 

Preparation  of  Library  Oatalogue 

House  Expenses        

*  V  Qp£^*9  «  •  •  •••  •••  •  •  •  •  •  •  1  •  • 

Jt \A9uBUfV|  Ov4*»     ■••  •••  •••  ■•■  •  •  • 

Carriage  of  Parcels,  &c 

Stationery  and  Office  Expenses       

Expenses  of  Meetings  

Coals  and  Gas 
Fittings  and  Repairs... 
Sundries 

Gold  Medals ...        ...        ...        ...        ... 

Portrait  of  Sir  Isaac  Newton  

•uoo  jS Tinci  ...  .  ..  ...  ...  . .,  ... 

Mrs,  Jackson  Gwilt's  Annuity        ...         

Bankers' Commission  on  Cheques 

Cheque  Book ...         ...        ...        ...        ...        ... 

Balance  at  Bankers'.  Dec.  31, 1886 

Cheque  not  Credited  in  Pass  Book 

Balance  in  hand  of  Assistant  Secretary  on  account 

of  Tumor  and  Horrox  Fund    

,,        in  hand  of  Assistant  Secretary  on  Petty 
Cash  Account    ...        ...        ...        ...        ... 

Paid  Balance  due  to  Assistant  Secretary.  Jan.  I, 
1886,  on  Petty  Cash  account 


Dec.  31 

,  1886. 

£     *. 

d. 

£       8. 

d. 

225  0 

0 

50  0 

0 

275  0 

0 

%& 

13  2 

6 

7  16 

6 

577  11 

0 

4  8 

0 

50  0 

0 

631  19 

0 

21  1 

5 

r 

19  16 

9 

25  0 

0 

65  18 

2 

34  13 

5 

31  4 

0 

58  13 

1 

2  6 

6 

6  12 

9 

20  0 

0 

56  7 

9 

12  16 

6 

4  12 

11 

227  6 
52  10 

11 

O 

18  18 

O 

5  0 

O 

8  19 

0 

0  2 

4 

0  8 

4 

0  10 

8 

434  2 

9 

2  2 

0 

21    6    o 


1  18    3 


459    9    o 


13    3    7 


1,779  13    4 


L  2 


124 


Report  of  the  Council  to  the 


xlyii.  4, 


Assets  and  Present  Property  of  the  Society,  Jan.  i,  1887. 


£     s.   d.        £     s.  d. 


Balance  at  Bankers',  including  an  amount  of 
£40  16s.  3<£.,  being  the  accumulated  in- 
terest of  the  Lee  Fund,  Dec  31,  1886    434 

Cheque  not  Credited  in  Pass  Book 2 

in  hand  of  Assistant  Secretary  on  account 

of  Tumor  and  Horrox  Funds 

^in  hand  of  Assistant  Secretary  on  Petty 
Cash  account      


2 
2 


9 
o 


>» 


*t 


21     6    o 


1  18    3 


Due  on  account  of  Subscriptions  : 

4  Contributions  of  4  years'  standing 

14  »  3 

30  »  2 

67  „  1  year's  standing 

3  Admission  Fees  and  First  Contributions 


» 


»» 


Less  4  Contributions  paid  in  advance 


459    9    0 

-      33  12 

0 

...      88    4 

0 

...     126    0 

0 

...     140  14 

0 

9    9 

0 

397  19 

0 

•••        00 

0 

<«Q/\      V  *         A 

•  • .  •  •  . 


Due  from  Messrs.  Williams  and  Norgate  for  sales 
of  Publications  during  1886 

£7,500  Consols,  including  the  Lee  Fund,  the  Tumor  Fund,  and 
the  Horrox  Memorial  Fund. 

£5,700  New  3  per  cent.  Stock,  including  Mrs.  Jackson  Ghrilt's 
gift  (£300). 

£500  Metropolitan  Board  of  Works  Stock. 

Astronomical  and  other  Manuscripts,  Books,    Prints,  Instru- 
ments ;  and  Furniture. 

Unsold  Publications  of  the  Society. 

Three  Gold  Medals. 


37  15  1° 


Feb.  1887.      Sixty-seventh  Annual  General  Meeting,  125 


Beport  of  the  Auditors* 


We,  being  the  duly  appointed  Auditors,  beg  to  lay  before  this 
Annual  General  Meeting  of  the  Royal  Astronomical  Society  the 
following  Beport : — 

We  have  examined  the  Treasurer's  account,  and  have  found 
and  certified  the  same  to  be  correct.  The  receipts  and  expendi- 
ture for  the  past  year  are  as  stated  in  the  Treasurer's  account. 
The  cash  in  hand  on  December  31,  1886,  including  the  balance 
at  the  bankers',  amounted  to  459/.  90. 

The  funded  property  is  the  same  as  at  the  end  of  last  year. 

The  books,  instruments,  and  other  effects  have  been  examined 
and  found  to  be  in  a  satisfactory  condition,  so  far  as  their  safe 
keeping  is  concerned. 

We  have  laid  on  the  table  a  list  of  the  names  of  those 
Fellows  who  are  in  arrear  for  sums  due  at  the  last  Annual 
General  Meeting,  with  the  amount  dne  against  each  Fellow's 
name. 

(Signed)     Robt.  J.  Leckt, 
Root.  Bryant, 
Hbrbirt  Sadler. 


126 


Report  of  the  Council  to  the 


xlvii.  4, 


Stock  in  hand  of  volumes  of  the  Memoirs : — 


VoL 

At  Society's 
Booms 

At  Williams 
fc  Norgate's 

VoL 

At  Society's 
Booms 

At  Williams 
*  Norgate's 

L  Part  I 

7 

•  •  • 

XXIX. 

411 

... 

L  Part  2 

43 

•  •  • 

XXX. 

159 

I 

II.  Part  I 

56 

•  •■ 

XXXI. 

143 

■  t  • 

II.  Part  2 

21 

•  •■ 

XXXII. 

154 

I 

HI.  Part  I 

67 

I 

XXXIIL 

164 

... 

III.  Part  2 

86 

I 

XXXIV. 

164 

4 

IV.  Part  I 

8o 

3 

XXXV. 

108 

6 

IV.  Part  2 

92 

3 

XXXVI. 

198 

10 

V. 

VI. 

106 
125 

4 
3 

xxxvn. 

Parti 

xxxvn. 

339 
287 

8 
8 

VTL 

V1LL 

IX. 

145 
127 

134 

3 
3 
3 

Part  a 

xxx  vm. 

XXXIX. 
Parti 

276 
248 

1 

4 

X. 

XI. 

146 
151 

XXXIX. 

Part  a 

XL. 

253 
268 

4 

2 

xn. 

159 

XLL 

417 

I 

xin. 

163 

XLIL 

239 

4 

XIV. 

370 

* 

I 

XUII. 

243 

I 

XV. 

140 

XLIV. 

224 

I 

XVI. 

165 

XLV. 

260 

I 

xvn. 

147 

] 

1 

XLVI. 

242 

3 

XVITL 

146 

XLVIL 

3 

XIX. 
XX. 

152 
142 

Parti 

xlvh. 

Part  a 

19 

XXI.  Part  I 
XXI.  Part  2 

3H 
99 

XLVII. 
Part3 
XLVLI. 

2 
10 

XXI.  I  &  2 
(together) 

xxn. 
xxin. 

61 

164 
150 

Part  4 

xlvti. 

Part  5 

xlvh. 

Part  6 

10 

10 

XXIV. 

156 

xlvu. 

240 

2 

XXV. 

166 

172 
422 

383 

XLvm. 

Parti 

XLVIIL 
Parts 

Index  to  "\ 
Memoirs  J 

310 
348 

645 

3 

3 

1 

XXVI. 
XXVTI. 

xxvin. 

Feb.  1887.      Sixty-seventh  Annual  General  Meeting. 


127 


Stock  in  hand  of  volumes  of  the  Monthly  Notices  : — 


Vol. 

At  Society's 
Booms 

At  Williams 
*  Norgate's 

Vol. 

At  Society's 
Booms 

At  Williams 
&  Norgate's 

L 

68 

•  •  ■ 

XXV. 

7 

•  •  • 

n. 

69 

>•• 

XXVI. 

10 

•  *  « 

hi. 

... 

p  • 

xxvn. 

3 

■  •  • 

IV. 

... 

•  • 

XXVHI. 

72 

I 

v. 

••• 

t  •  • 

XXIX. 

5i 

■  •  • 

VI. 

37 

► •  • 

XXX. 

68 

2 

vn. 

2 

»•  ■ 

XXXI. 

96 

•  •  • 

vm. 

'39 

2 

XXXII. 

118 

5 

rx. 

*5 

2 

XXXIIL 

100 

2 

X. 

174 

I 

XXXIV. 

79 

2 

XL 

185 

I 

XXXV. 

61 

1 

xn. 

11 

2 

XXXVI. 

32 

1 

xi  n. 

157 

3 

XXXVII. 

39 

3 

XIV. 

109 

3 

XXXVIII. 

103 

2 

XV. 

127 

2 

XXXIX. 

108 

1 

XVI. 

108 

2 

XL. 

113 

3 

XVII. 

137 

1 

XLL 

114 

5 

xvm. 

166 

•  •  • 

XLH. 

122 

2 

XIX. 

56 

•  •  • 

XLIIL 

122 

2 

XX. 

35 

•  •  • 

XUV. 

125 

5 

XXI. 

18 

•  •  • 

XLV. 

130 

3 

xxn. 

33 

•  •  • 

XLVI. 

137 

4 

XXIIL 
XXIV. 

1. 

19 
24 

•  •  • 

•  ■  ■ 

Index  to  "| 
Monthly  V 
Notices   J 

568 

1 

Library  Catalogue 


668 


In  addition  to  the  above  volumes  of  the  Monthly  Notices^  the 
Society  has  a  considerable  stock  of  separate  numbers  of  nearly 
all  the  volumes.  With  the  exception,  however,  of  Vols.  XXXVI. 
to  XLVI.  no  complete  volumes  can  be  formed  from  the  separate 
numbers  in  stock. 


Instruments  belonging  to  the  Society. 

No.  1.  The  Harrison  clock. 
„    2.  The  Owen  portable  circles,  by  Jones. 


91 


3.  The  Beaufoy  circle. 

4.  The  Beaufoy  transit  instrument. 


99 


128  Report  of  the  Council  to  the  xlvii.  4, 

No.  5.  The  Her8chel  7-foot  telescope. 

„  6.  The  Oreig  universal  instrument,  by  Reichenbach  and 
Ertel.  The  transit  telescope,  by  Utzschneider  and 
Frannhofer,  of  Munich. 

„     7.  The  Smeaton  eqnatoreaL 

,,     8.  The  Cavendish  apparatus. 

„     9.  The  7-foot  Gregorian  telescope  (late  Mr.  Shearman's). 

„  10.  The  variation  transit  instrument  (late  Mr.  Shear- 
man's). 

„  11.  The  universal  quadrat,  by  Abraham  Sharp. 

„  12.  The  Fuller  theodolite. 

„  13.  The  standard  scale,  by  Troughton  and  Simms. 

„  14.  The  Beaufoy  clock,  No.  1. 

„  15.  The  Beaufoy  clock,  No.  2. 

„  16.  The  Wollaston  telescope. 

17.  The  Lee  circle. 

18.  The  Sharpe  reflecting  circle. 
„  19.  The  Brisbane  circle. 

„  20.  The  Baker  universal  eqnatoreaL 

„  21.  The  Beade  transit. 

w  22.  The  Matthew  eqnatoreal,  by  Cooke. 

„  23.  The  Matthew  transit  instrument. 

„  24.  The  South  transit  instrument. 

„  25.  A  sextant,  by  Bird  (formerly  belonging  to  Captain 

Cook). 
„  26.  A  globe  showing  the  precession  of  the  equinoxes. 

The  Sheepshanks  collection : — 
„  27.  (1)  30-inch  transit  instrument,  by  Simms,  with  level 

and  two  iron  stands. 
„  28.  (2)    6-inch  transit  theodolite,  with  circles  divided  on 

silver ;  reading  microscopes,  both  for  altitude  and 

azimuth  ;  cross  and  siding  levels ;  magnetic  needle ; 

plumbline ;  portable  clamping  foot  and  tripod  stand. 
„  29.  (3)  Eqnatoreal   stand    and    clock    movement    for 

4^  inch  telescope  (telescope  lost)  ;  double-image 

micrometer;  two  wire  micrometers;  object-glass 

micrometer. 
91  3°-  (4)  3^-inch   achromatic    telescope,   with  eqnatoreal 

stand;  double-image  micrometer;  one  terrestrial 

and  three  astronomical  eyepieces. 
»  31*  (5)  zf-inch  achromatic  telescope,  with  stand;  one 
1  y  _  terrestrial  and  three  astronomical  eyepieces. 

»  33*  (7)  2-foot  navy  telescope. 
19  34*  (8)  Transit  instrument  of  45  inches  focal  length; 

with  iron  stand  and  also  Ys  for  fixing  to  stone 

piers ;  two  axis  levels. 
91  35-  (9)   Repeating    theodolite,    by  Ertel,   with  folding 

tripod  stand. 
„  36.  (10)  8-inoh  pillar  sextant,   by   Troughton,  divided 

on  platinum,  with  counterpoise  stand  and  artificial 

horizon. 


Feb.  1887.      Sixty  seventh  Annual  General  Meeting.  129 

No.  37.  (11)  Portable  zenith  telescope  and  stand,  2  f -inch 
aperture  and  26  inches  focal  length ;  io-inch  hori- 
zontal circle  and  8-inch  vertical  circle,  read  to  10" 
by  two  verniers  to  each  circle. 

„  38.  (12)  18-inch  Borda  repeating  circle,  by  Tronghton, 
2^-inch  aperture  and  24  inches  focal  length ;  the 
circles  divided  on  silver,  the  horizontal  circle  being 
read  by  four  verniers,  and  the  vertical  circle  by 
three  verniers,  each  to  10". 

„  39.  (13)  8-inch  vertical  repeating  circle,  with  diagonal 
telescope,  by  Tronghton  and  Simms ;  circle  divided 
on  silver,  reading  to  10" ;  a  5-inch  circle  at  eye- 
end,  reading  to  single  minutes  ;  horizontal  circle 
9  inches  diameter  in  brass,  reading  to  single 
minutes. 

„  40.  (14)  A  set  of  surveying  instruments,  consisting  of 
a  1 2-inch  theodolite  for  horizontal  angles  only, 
reading  to  10"  ;  two  sets  of  adjusting  plates ;  tripod 
stand  with  enclosed  telescope ;  heavy  stand  for  theo- 
dolite ;  Y  piece  of  level;  two  large  and  three  small 
ground-glass  bubbles  divided ;  level  collimator, 
object-glass  if- inch  diameter  and  16  inches  focal 
length ;  micrometer  eyepiece,  comb,  and  wires ; 
mercury  bottle  and  trough. 

„  41.  (15)  Level  collimator  with  object-glass  i£-inch 
diameter  and  16  inches  focal  length ;  stand,  rider- 
level,  and  fittings. 

„  42.  (16)  10-inch  reflecting  circle  by  Tronghton,  reading 
by  three  verniers  to  20" ;  counterpoise  stand ; 
artificial  horizon,  with  mercury  ;  two  tripod  stands. 
43»  (x7)  Hassler's  reflecting  circle,  by  Tronghton,  with 
counterpoise  stand. 

44.  (18)  6-inch  reflecting  and  repeating  circle,  by 
Tronghton  and  Simms,  contained  in  three  boxes, 
two  of  which  form  stands.   Circle  divided  on  Bilver, 

"  reading  to  single  minntes  ;  two  inside  arcs  divided 
to  single  degrees,  150  degrees  on  each  side;  artificial 
horizon  and  mercury. 

45.  (19)  5 -inch  reflecting  and  repeating  circle,  by  Lenoir, 
of  Paris. 

46.  (20)  Reflecting  circle,  by  Jecker,  of  Paris,  1 1  inches 
in  diameter,  with  one  vernier  reading  to  1 5". 

47.  (21)  Box  sextant;  reflecting  plane  and  level. 

48.  (22)  Prismatic  compass,  by  Tronghton  and  Simms. 

49.  (23)  Mountain  barometer. 

50.  (24)  Prismatic  compass,  by  Thomas  Jones,  mounted 
with  a  cylindrical  lens. 

51.  (25)  Ordinary  4^-inch  compass  with  needle. 
„    52.  (26)  Dipping  needle,  by  Robinson. 

53*  (27)  Compass  needle,  mounted  for  variation. 


» 


i> 


J! 

If 

» 
11 
» 


130  Report  of  the  Oowncil  to  the  xlvii.  4, 

No.  54.  (28)  Magnetic  intensity  needle,  by  Meyerstein,  of 
Gottingen ;  a  strongly  fitted  brass  box  with  heavy 
magnet ;  filar  suspension. 

»    55'  (29)  Box  of  magnetic  apparatus. 

»  5°*  (30)  Hassler's  reflecting  circle,  by  Trooghton;  a 
10^- inch  reflecting  and  repeating  circle,  withstand 
and  counterpoise,  divided  on  platinum  with  two 
movable  and  two  fixed  indices ;  four  verniers  read- 
ing to  10". 

„  57.  (31)  Box  sextant  and  glass  plane  artificial  horizon, 
by  Trough  ton  and  Simms. 

„  58.  (32)  Plane  2  § -inch  speculum,  artificial  horizon,  and 
stand. 

„    59.  (33)  2^ -inch  circular  level  horizon,  by  Dollond. 

n  °o.  (34)  Artificial  horizon,  roof,  and  trough ;  the  trough 
S\  by  4J  inches ;  tripod  stand. 

»  61.  (35)  Set  of  drawing  instruments,  consisting  of 
6-inch  circular  protractor  and  common  protractor, 
T-square ;  one  beam  compass. 

„    62.  (36)  A  pantagraph. 

»    63-  (37)  A  noddy. 

>i  64.  (38)  A  small  Galilean  telescope  with  object-glass  of 
rock  crystal. 

»    65*  (39)  Five  levels. 

„    66.  (40)  18-inch  celestial  globe. 
fq       »    67.  (41)  Varley  stand  for  telescope. 
0  *  -  „    69.  (43)  Telescope,  with  object-glass  of  rock  crystal. 
yO   —  „     71.  Portable  altazimuth  tripod. 
'  „    72.  Four  polarimeters. 

7  3j*  „    74.  Registering  spectroscope,  with  one  large  prism. 
J$  ~  „    76.  Two  five-prism  direct-vision  spectroscopes. 
£jj  -  „    78.  9^-inch     silvered-glass    reflector    and    stand,     by 
//  Browning. 

„    79.  Spectroscope. 

„  80.  A  small  box,  containing  three  square-headed  Nicol's 
prisms ;  two  Babinet  s  compensators ;  two  double- 
image  prisms  ;  three  Savarts ;  one  positive  eyepiece, 
with  Nicol's  prism ;  one  dark  wedge. 

,,    81.  A  back-staff,  or  Davis'  quadrant. 

„    82.  A  nocturnal  or  star  dial. 

„  83.  An  early  non-achromatic  telescope,  of  about  3  feet 
focal  length,  in  oak  tube,  by  Samuel  Scatliffe, 
London. 

„    84.  A  Hollis  observing  chair. 

„    85 .  Double  image  micrometer,  by  Troughton  and  Simms. 

„  86.  4^-inch  Gregorian  reflecting  telescope,  by  Short, 
with  altazimuth  stand  and  6-inch  altitude  and 
azimuth  circles  and  two  eyepieces. 

»  **7 •  3j-inch  Gregorian  reflecting  telescope  with  wooden 
tripod  stand. 


Feb.  1887.     Sixty-seventh  Animal  General  Meeting. 


*3* 


No. 


91 


99 
99 
99 

99 

99 
91 
»9 


99 
99 


19 

99 

99 

99 
99 
99 
19 
19 
19 
11 
19 
91 
9! 
99 
99 
99 

99 
91 
99 
99 
99 


90. 
91. 
92. 

93. 
94. 

95. 
96. 


97. 
98. 


88.  Pendulum  with  5 -foot  brass  suspension  rod,  work- 

ing on  knife  edges,  by  Thomas  Jones. 

89.  A  Bhabdological  Abacus.     A  contrivance  invented 

by  Mr.  H.  Goodwyn,  consisting  of  a  box  filled 
with  compartments,  in  which  are  square  rods 
covered  with  numbers,  which  can  be  arranged  so 
as  to  facilitate  the  labour  of  multiplying  high 
numbers. 

An  Arabic  celestial  globe  of  bronze,  5  J  inches  in 
diameter. 

Astronomical  time  watchcase,  by  Professor  Cheval- 
lier. 

2-foot  protractor,  with  two  moveable  arms,  and 
vernier. 

Beam  compass,  in  box. 

2-foot  navigation  scale. 

Stand  for  testing  measures  of  length. 

Artificial  planet  and  star,  for  testing  the  measure- 
ment of  a  fixed  distance  at  different  position- 
angles. 

1 2- cell  Leclanche'  battery. 

2  feet  6  inch  navy  telescope  with  object-glass  2i 
inches,  by  Cooke,  with  portable  wooden  tripod 
stand. 

12-inch  transit  instrument,  by  Fayrer  &  Son,  with 
level  and  portable  stand. 

9 -inch  transit  instrument,  with  level  and  iron 
stand. 

Small  equatoreal  sight  instrument,  by  G.  Adams, 
London. 

Sun-dial,  by  Troughton. 

Sun-dial,  by  Casella. 

Sun-dial 

Box  sextant,  by  Troughton  and  Simms. 

Prismatic  compass,  by  Schmalcalder,  London. 

Compass,  by  C.  Earle,  Melbourne. 

Prismatic  compass,  by  Negretti  and  Zambra. 

Dipleidoscope,  by  E.  Dent. 

Abney  level,  by  Elliott. 

Pocket  spectroscope,  by  Browning. 

Small  brass  astrolabe. 

Double  sextant,  by  Jones. 

Two  models,  illustrating  the  effects  of  circular 
motions. 

A  cometarium. 

A  pair  of  18-inch  globes. 

Two  old  sun  dials. 


99. 
00. 
01. 

02. 

03- 
04. 

°5- 
06. 

07. 

08. 

09. 

10. 

11. 

12. 

x3- 
14. 

15- 
16. 

17 
18 

19 


} 


Specimens  of  Diffraction  gratings,  by  Prof.  W.  A, 
Rogers. 


132  Report  of  the  Council  to  the  xlvii.  4, 

No.  120.  A  6-prism  spectroscope,  by  Browning. 

„  121.  Spitta's  Improved  maximum  and  minimum  thermo- 
meter. 

,,  122.  A  6-inch  speculum,  with  flat ;  the  speculum  said  to 
be  by  Sir  W.  Herschel,  and  re- figured  by  Sir  J. 
Herschel. 

„  123.  A  6-inch  refracting  telescope,  by  Grubb,  with  3 
eyepieces. 

The  following  instruments  are  lent,  during  the  pleasure  of 
the  Council,  to  the  undermentioned  persons  : — 

No.      4.  The  Beaufoy  transit  instrument,  to  the  Observatory, 
Kingston,  Canada. 

22.  The  Matthew  equatoreal,  to  Mr.  J.  Brett. 

23.  The  Matthew  transit,  to  Captain  W.  Noble. 

29.  (3)  Equatoreal   mounting,    clock  movement,   and 
stand,  to  Mr.  W.  Peck. 

30.  (4)  3^-inch  equatoreal  and  stand,  to  Mr.  H.  Sadler. 
34.  (8)  Transit  instrument,  to  Prof.  C.  Pritchard. 
69*  (43)  Telescope,  with  rock-crystal  object-glass,  to 

Dr.  W.  Huggins. 
„      78.  Two  eyepieces,  to  Mr.  B.  T.  A  Innes. 

The  Oold  Medal. 

The  Council  have  awarded  the  Society's  Gold  Medal  to  Mr. 
G.  W.  Hill  for  his  researches  on  the  Lunar  Theory.  The 
President  will  lay  before  the  Society  the  grounds  upon  which 
the  award  has  been  founded. 


Lunar  Computations. 

The  computations,  made  by  means  of  the  Government  Grant 
of  320L  for  the  purpose  of  comparing  the  Greenwich  lunar  ob- 
servations 1847  to  1 86 1  with  Hansen's  Tables  de  la  Lune,  have 
been  completed,  and  will  shortly  be  published. 


u 


Feb.  1887.      Sixty  seventh  Annual  General  Meeting.  133 


Obituary. 


The  Council  regret  that  they  hare  to  record  the  loss  by  death 
of  the  following  Fellows  and  Associate  daring  the  past  year : — 

Fellows : — ^Major-General  J.  T.  Boilean. 
W.  W.  Boreham. 
D.  T.  Evans. 
W.  S.  Gillett. 
George  Hamilton. 
R.  J.  Mann. 
Rev.  J.  Pearson. 
H.  S.  Redpath. 
Rev.  S.  H.  Saxby. 
Admiral  Sir  G.  F.  A.  Shadwell. 
David  Smith. 
Captain  F.  Smith. 
Edwin  Story. 
Rev.  S.  K.  Swann. 
C.  G.  Talmage. 
William  Tomlinson,  jnn. 

Associate : — Theodor  von  Oppolzer. 


Major-General  John  Theophilus  Boileau,  R.E.,  F.R.S.,  was 
born  on  May  26,  1805,  at  Calcutta,  where  his  father,  Mr.  Thomas 
Boilean,  was  chief  magistrate.  This  family  claim  descent  from 
fitienne  Boilean,  Lord  of  Castelnan  and  St.  Croix,  who  was  left 
by  Louis  IX.  as  Constable  and  Provost  of  France  when  he  went 
crusading ;  and  Jacques  Boileau,  the  poet,  through  Charles, 
Baron  of  Castelnan,  who  was  driven  from  France  at  the  time  of 
the  Revocation  of  the  Edict  of  Nantes. 

Mr.  Boileau  died  in  1806,  and  his  widow,  with  her  two  sods, 
John  and  Henry,  then  came  to  England  and  settled  at  Bury  St. 
Edmunds,  where  the  boys  attended  the  grammar  school,  under 
Mr.  Blomfield,  at  which  John  is  said  to  have  exhibited  great 
capacity  for  languages.  Soon  after  he  was  fourteen  he  received 
a  nomination  to  a  cadetship  at  Addiscombe,  from  which  he 
passed  brilliantly  into  the  Bengal  Engineers  in  December  1820. 
After  the  usual  course  of  training  at  Chatham,  under  Sir  C. 


134  Report  of  the  Council  to  the  xlvii.  4, 

Pasley,  he  sailed  for  India,  and  reached  Calcutta  in  September 
1822,  when  little  more  than  seventeen  years  of  age.  His  energies 
were  soon  employed  on  the  duties  of  the  corps  in  bnilding  and 
repairing  barracks,  churches,  bridges,  and  roads ;  and  he  soon 
acquired  a  reputation  for  the  excellence  of  his  work. 

In  1836  he  published  in  India  (by  lithography)  "  Traverse 
Tables  to  every  Minute  of  the  Quadrant";  and  in  1839,  when  in 
England  on  furlough,  these  were  printed  and  republished  in 
London.  In  this  latter  year  the  Honourable  Court  of  Directors 
of  the  East  India  Company  selected  Lieutenant  Boileau  for  the 
charge  of  one  of  the  three  observatories  which  they  undertook  to 
support  for  magnetic  and  meteorological  research.  Simla  was 
assigned  as  the  charge  of  Lieutenant  Boileau,  and  he  was  also 
directed  to  superintend  the  construction  and  despatch  of  instru- 
ments for  the  three  observatories.  After  instruction  by  Prof. 
Humfrey  Lloyd  at  Dublin,  Lieutenant  Boileau  and  the  other  two 
superintendents  embarked  (with  the  instruments)  for  India  at 
the  end  of  February  1840 ;  and  he  finally  reached  Simla  in 
October  of  that  year,  after  leaving  his  colleagues  and  their 
instruments  at  Madras.  During  the  voyage  a  series  of  meteoro- 
logical observations  was  kept  up,  and  on  the  way  from  Calcutta 
Boileau  made  observations  of  magnetical  data  at  places  at  which 
he  stopped.  Work  was  commenced  soon  after  his  arrival  at 
Simla  in  a  temporary  building,  and  the  erection  of  the  more 
permanent  one  was  begun. 

During  the  period  prescribed  for  observation  it  appears  that 
periodical  abstracts  were  sent  to  Dr.  Lloyd  and  the  Royal  Society, 
and  Colonel  Boileau,  after  the  observatory  was  closed,  was  em- 
ployed, in  addition  to  other  duties,  till  his  retirement  early  in 
1857,  in  reducing  and  printing  his  observations.  On  his  leaving 
India  the  instruments  and  records  were  placed  in  store,  and, 
having  got  mixed  up  with  inflammable  articles,  the  whole  were 
in  1858  destroyed  by  fire.  A  portion  of  the  meteorological 
results  were  published  at  Madras  in  1851,  and  a  further  portion 
were  published  under  General  Boileau's  care  in  1872  by  a  grant 
from  the  India  Office,  procured  by  the  Royal  Society. 

During  his  residence  at  Simla,  General  Boileau  published 
from  the  Observatory  press  a  set  of  astronomical,  magnetic,  and 
meteorological  tables;  some  logarithmic  tables  and  tables  for 
computing  time  from  extra-meridian  observations ;  besides  some 
other  works  of  purely  Indian  interest. 

After  arriving  finally  in  England  in  1857,  General  Boileau's 
energies  were  devoted  to  such  useful  and  charitable  work  as  he 
could  find.  He  soon  became  a  member  of  the  Committee  of  the 
Soldiers'  Daughters'  Home,  and  afterwards  became  Chairman. 
Later  he  joined  that  of  the  Royal  School  for  Officers'  Daughters. 
In  i860  he  became  a  member  of  the  1st  Middlesex  (Victoria) 
Rifles,  and  served  in  that  corps  for  six  years  as  a  private  till  his 
health  prevented  his  longer  attending  regularly  to  drills,  parades, 
Ac.     In  1867  he  became  a  member  of  the  Kensington  Vestry, 


Feb.  1887.      Sixty -seventh  Annual  General  Meeting.  135 

and  served  zealously  for  thirteen  years,  earning  the  respect  of  his 
fellow  vestrymen  by  his  good  sense,  experience,  and  courtesy. 

With  endless  humour  and  perpetually  overflowing  spirits, 
John  Boileau,  during  his  Indian  career,  was  widely  known  for 
his  eccentricities  and  practical  jokes.  Men  would  believe  him 
capable  of  any  joke  that  was  not  unkind.  Bat  he  always  had 
the  confidence  and  regard  of  all  who  came  in  contact  with  him. 
Sir  Henry  Lawrence  was  among  his  companions  at  Addiscombe, 
and  was  his  intimate  friend  to  the  last,  while,  in  a  long  residence 
of  seventeen  years  at  Simla,  he  was  brought  into  close  contact 
with  the  rulers  of  India  during  that  time  without  making  any 
but  friends ;  and  so  it  would  seem  to  have  been  after  his  set- 
tling in  England.  His  fellow  vestrymen,  the  members  of  the 
boards  with  which  he  was  connected,  and  the  staff  and  pupils  of 
the  schools  he  managed  were  all  represented  among  the  mourners 
at  his  funeral. 

General  Boileau  was  elected  a  Fellow  of  the  Royal  Society 
in  January  1840.  He  served  on  the  Council  of  the  Royal  Society, 
and  was  their  representative  on  the  governing  body  of  Christ's 
Hospital.  He  died  on  November  9  last,  after  an  illness  of  about 
six  months. 

He  was  elected  a  Fellow  of  this  Society  January  10,  1840. 

William  Wakeling  Boebham  was  born  at  Haverhill,  in  Essex, 
on  March  3,  1804,  and  received  his  early  education  at  Saffron 
Walden,  where  he  soon  displayed  great  talent  for  mathematics 
and  music. 

Following  his  father's  tastes,  he  at  first  became  a  brewer,  and 
was  in  business  in  London  and  afterwards  in  Manchester ;  he 
subsequently  returned  to  Haverhill,  where  he  erected  an  obser- 
vatory, and  devoted  himself  industriously  to  observations  of 
comets  and  minor  planets.  Many  of  his  observations  were  pub- 
lished in  the  early  volumes  of  the  Monthly  Notices. 

Mr.  Boreham  was  an  ardent  admirer  of  all  science,  and  in  his 
early  life  tried  hard  to  promote  the  higher  education  of  those  in 
his  native  place.  In  later  life  he  devoted  his  energies  to  educa- 
tion in  all  its  branches. 

He  was  for  many  years  a  Fellow  of  the  Anthropological 
Society. 

He  was  elected  a  Fellow  of  this  Society  April  11,  1845. 

George  Hamilton  was  born  in  Belfast  in  18 13.  Removing 
to  Liverpool  at  an  early  age,  he  was  apprenticed  to  Mr.  Bartain 
Haigh,  builder.  Soon  after  completing  his  term  he  was  offered 
an  appointment  as  architect,  which  he  declined,  having  found 
his  vocation  to  be  that  of  a  teacher.  In  1836  he  was  appointed 
master  of  Mount  Pleasant  Schools,  and  amongst  the  children  of 
the  poor  he  worked  out  for  several  years  his  ideal  course  of 
instruction,  which  included,  in  addition  to  the  usual  branches, 
algebra,  as  far  as  quadratic  equations,  geometry,  including  the 


136  Report  of  the  Council  to  the  xlyii.  4, 

first  and  second  books  of  Euclid,  and  weekly  lectures  on  che- 
mistry and  natural  philosophy  to  both  boys  and  girls. 

While  thus  engaged  he  was  appointed  assistant  and  after- 
wards head  master  of  the  mathematical  department  of  the 
evening  school  of  the  Liverpool  Institute.  From  this  class 
sprang  "The  Working  Men's  Science  Association,"  to  which 
Mr.  Hamilton  lectured  nearly  every  week  for  two  years  to  a 
working-class  audience  averaging  400  persons.  In  1844  Mr- 
Hamilton  lectured  in  Liverpool,  Leeds,  Bradford,  and  Ghorley 
on  "  The  Use  of  Science  to  Working  Men,"  his  aim  being  to 
establish  free  public  evening  lectures  in  every  town  in  the 
kingdom,  and  to  organise  science  teaching  in  every  elementary 
school.  But  public  opinion  was  then  against  the  innovation. 
Mr.  Hamilton  was  associated  with  the  Liverpool  Institute  from 
1840  to  1879  (when  a  serious  accident  obliged  him  to  resign  all 
his  professional  duties),  successively  holding  the  appointments 
of  Teacher  of  Architectural  Drawing  and  Building  Construction, 
Teacher  of  Mathematics,  Lecturer  on  Chemistry  and  Natural 
Philosophy  in  both  Blaokbnrne  House  and  the  High  School,  and 
in  1856  Professor  of  Chemistry  in  Queen's  College  (in  connec- 
tion with  the  London  University). 

In  1850  he  was  appointed  first  Lecturer  on  Chemistry  and 
Teacher  of  Practical  Pharmacy  to  the  Liverpool  Chemists' 
Association. 

In  1856  he  was  elected  a  member  of  the  Liverpool  Compass 
Committee,  to  investigate  the  causes  of  deviation  of  the  compass 
in  iron  ships. 

He  designed  a  self-registering  compass,  for  recording  the 
course  of  a  ship  at  sea,  indicating  every  change  of  tack  and  the 
exact  time  of  change  for  the  whole  voyage.  He  also  invented  a 
self-registering  thermometer,  and  a  gas  transferrer,  or  siphon, 
for  transferring  small  quantities  of  gas  for  accurate  measurement. 

Mr.  Hamilton  was  widely  known  as  a  teacher  of  science,  and 
for  many  years  successfully  carried  out  a  scheme  for  delivering 
a  regular  and  systematic  course  of  scientific  instruction  in 
middle-class  schools — a  task  attempted  by  many  before  him, 
and  rendered  arduous  from  the  expense  and  delicacy  of  much  of 
the  apparatus  required,  the  difficulty  of  conveying  it  from  place 
to  place,  the  mental  strain  entailed  by  an  average  of  twelve 
lectures  weekly,  and  by  the  diversity  of  subjects,  the  course 
embracing  astronomy,  chemistry,  geology,  and  natural  philo- 
sophy. Nor,  in  his  zeal  for  science,  were  the  languages  for- 
gotten, each  day  having  its  apportioned  task  of  classics  and 
modern  languages. 

For  several  years,  until  prevented  by  failing  health,  he  con- 
ducted the  examinations  for  the  Science  Department  of  the 
Liverpool  Council  of  Education. 

Mr.  Hamilton  was  a  member  of  the  Chemical  Society  and  of 
the  Society  of  Arts.  He  wrote  "  Glimpses  of  Nature,"  "  Social 
Science,"  "  Gravitation,"   »  Physical  Science,"  "  On  the  Con-. 


Feb.  1887.      Sixty-seventh  Annual  General  Meeting.  137 

gervation  of  Force,"  "On  Iron,"  "The  Chemistry  of  the 
Gases,"  "  On  Dr.  Medlock's  Process  of  Filtering  and  Purifying 
Water,"  "The  Gyroscope  and  Rotary  Motion,"  "Note  on 
Strychnine,"  "  Chemistry  in  its  Relation  to  the  other  Sciences," 
"  Suggestions  for  a  New  System  of  Chemical  Nomenclature," 
"  Gaseous  Exhalations  and  Miasmata  as  Causes  of  Nuisance  and 
Disease,"  "  Progressive  Changes  of  Form  in  Rotating  Spheroids," 
"High  Tides  and  Colliery  Explosions,"  "A  Law  of  Elliptic 
Motion,"  Ac. 

Mr.  Hamilton  had  the  satisfaction,  in  the  closing  years 
of  his  life,  of  witnessing  the  adoption,  in  modified  form,  by  the 
Liverpool  Council  of  Education  and  the  Liverpool  School  Board, 
of  that  system  of  scientific  education  which  he  had  at  the  be- 
ginning of  his  career  as  a  teacher  regarded  as  a  necessary  part 
of  primary  instruction  ;  and  in  the  department  of  higher  educa- 
tion his  later  years  were  cheered  by  the  establishment  of  Uni- 
versity College,  Liverpool. 

From  his  earliest  years  Mr.  Hamilton  had  advanced  views 
on  education,  but  he  was  no  theorist.  In  the  face  of  oppo- 
sition and  many  difficulties,  he  practised  what  he  believed. 
Others  have  now  entered  into  his  labours,  and  the  cause  is 
making  rapid  progress.  Mr.  Hamilton's  courteous  manners, 
his  devotion  to  duty,  and  his  high  intellectual  attainments  won 
for  him  the  affection  and  esteem  of  all  who  knew  him. 

He  was  elected  a  Fellow  of  this  Society  January  12,  1855. 

Robert  James  Mann  was  born  in  Norwich  in  January  181 7. 
At  an  early  age  he  evinced  a  great  love  of,  and  aptitude  for, 
physical  science.  Botany  was  his  first  pursuit,  and,  while  still  a 
student,  he  published  an  excellent  list  of  the  flowering  plants  of 
the  Norfolk  district. 

He  was  educated  for  the  medical  profession,  and  studied  at 
University  College.  He  took  the  M.R.C.S.  and  L.S.A.  degrees 
in  1840,  and  for  some  years  practised  in  Norfolk,  continuing  his 
scientific  pursuits,  and  beginning  to  occupy  himself  with  literary 
undertakings  also.  It  was  during  this  time  that  he  published 
his  first  book,  "  The  Planetary  and  Stellar  Universe." 

In  1853  domestic  circumstances,  connected  with  health, 
caused  him  partially  to  abandon  the  practice  of  his  profession. 
In  1854  he  became  an  M.D.  of  St.  Andrews,  and  about  this  time 
was  employed  in  assisting  his  old  teacher  and  attached  friend, 
Dr.  C.  J.  B.  Williams,  in  the  revision  and  publication  of  his 
"  Principles  of  Medicine,"  assistance,  the  value  of  which  was 
generously  acknowledged  in  the  work  itself,  and  again  in  the 
much  more  recently  published  "Memorials  of  Life  and  Work" 
of  that  eminent  physician. 

In  1857,  on  the  invitation  of  Bishop  Colenso,  Dr.  Mann  left 
England  for  Natal,  where  he  resided  nine  years,  during  seven  of 
which  he  was  Superintendent  of  Education  for  that  colony ;  an 
office  established  by  the  then  Governor,  Mr.  (now  Sir  John) 


138  Report  of  the  Council  to  the  xlvil  4, 

Scott,  to  which  he  received  the  first  appointment.  In  this 
capacity  he  succeeded,  working  against  great  difficulties,  in 
starting  elementary  schools  for  both  the  English  and  Dntch 
inhabitants,  and  ultimately  in  assisting  those  for  the  native 
population  also.  This,  no  doubt,  is  a  noteworthy  achievement 
in  his  life,  and  its  value  and  the  way  in  which  it  was  accom- 
plished have,  since  his  death,  been  borne  testimony  to  in  the 
Natal  Mercury  of  September  14  of  last  year,  in  the  following 
words : — "  For  several  years  he  gave  up  his  time  most  unspar- 
ingly to  a  task  which  to  him  was  a  labour  of  love,  and  the 
measure  of  his  personal  success  may  be  gauged  by  the  extent 
to  which  his  work  suffered  when  his  own  part  in  it  was  with- 
drawn." 

From  his  first  arrival  in  Natal  he  also  carried  out  day  by  day 
and  recorded  meteorological  observations,  the  tabulated  results 
of  which  are  in  the  hands  of  the  Meteorological  Office.  After 
his  return  to  England  he  twice  served  as  President  of  the 
Meteorological  Society.  While  still  in  Natal  he  was,  besides,  the 
referee  of  the  whole  colony  on  all  matters  connected  with  science. 

In  1862  he  was  the  chief  organiser  of  the  exhibits  the  colony 
contributed  to  the  great  exhibition  of  that  year,  and  he  arranged 
and  carried  out  a  preliminary  exhibition  in  Durban. 

He  returned  from  Natal  in  1866,  in  consequence  of  receiving 
a  special  appointment  from  the  Legislative  Council  to  inaugurate 
a  scheme  of  Government  emigration  to  the  colony.  This  he  held 
for  four  years,  during  which,  besides  undertaking  all  the  arduous 
work  of  his  ofnciarposition,  he  took  charge  of  the  arrangements 
of  the  Natal  exhibits  in  the  Paris  Exhibition  of  1867.  He 
laboured  gratuitously  in  promoting  emigration  to  Natal  for  two 
years  after  his  appointment  as  agent  was  withdrawn. 

From  about  that  time  he  ceased  to  have  any  special  connec- 
tion with  the  colony,  and  for  the  rest  of  his  life  devoted  himself 
to  the  scientific  and  literary  pursuits  which  had  ever  been,  con- 
genial and  delightful  to  him. 

Of  all  the  sciences  which  early  engaged  his  attention  and 
became  subjects  of  study  none  excited  so  profound  an  interest 
or  kept  so  permanent  a  hold  upon  his  regard  as  that  of  astro- 
nomy. All  through  his  life  it  was  the  one  which  he  would  have 
desired,  had  circumstances  permitted,  to  make  his  chief  pursuit 
and  occupation.  His  first  work  was  entitled  "  The  Planetary 
and  Stellar  Universe."  He  was  prompted  to  write  it  solely  by 
his  own  profound  sense  and  fervid  appreciation  of  the  grandeur 
and  beauty  of  the  subject  of  which  it  treated.  This  was  followed, 
in  1850,  by  a  smaller  work  on  "The  Achievements  of  Sidereal 
Astronomy  in  the  middle  of  the  Nineteenth  Century."  Later  on 
he  published  "  A  Guide  to  Astronomical  Science."  He  also  fur- 
nished to  Chambers's  Repository  a  "  History  of  the  Moon." 

Dr.  Mann  was  for  many  years  on  the  staff  of  the  Edinburgh 
Review,  and  the  admirable  articles  which  he  contributed  to  it  on 
astronomical  subjects  are  well  known.    His  last  piece  of  literary 


Feb.  1887.     Sixty-seventh  Annual  General  Meeting,  139 

work,  indeed,  was  an  article  on  "  The  Recent  Progress  of  Astro- 
nomy," which  appeared  in  the  number  for  April  of  last  year. 

He  was  a  popular  and  prolific  writer,  and  was  a  frequent 
contributor  to  several  magazines  and  reviews.  The  protection 
of  buildings  from  lightning  was  a  subject  on  which  he  wrote  a 
good  deal,  and  for  which  he  did  much  valuable  work. 

In  1874  he  was  appointed  Secretary  to  the  African  Section  of 
the  Society  of  Arts  ;  a  post  he  only  resigned  in  consequence  of 
failing  health  at  the  completion  of  the  last  session  of  the  society. 

For  four  years  he  served  as  one  of  the  Board  of  Visitors  of 
the  Royal  Institution  of  which  he  became  a  member  in  1876, 
subsequently  being  elected  on  the  Council. 

In  1878  he  was  elected  a  Fellow  of  the  Royal  College  of 
Surgeons.  Dr.  Mann  was  well  known  in  scientific  circles,  and 
for  many  years  he  was  a  member  of  the  Astronomical,  Meteoro- 
logical, Geographical,  and  Photographic  Societies. 

From  first  to  last  he  was  a  most  active  and  indefatigable 
worker,  and  his  end  was  probably  hastened  by  his  being,  during 
the  last  four  months  of  his  life,  when  already  in  failing  health, 
busily  engaged  in  preparing  and  bringing  out  the  catalogue  of 
the  Natal  Court  at  the  Colonial  and  Indian  Exhibition.  He  was 
at  the  Natal  Court  engaged  in  this  last  work  only  three  days 
before  being  suddenly  struck  down  by  paralysis,  which  termi- 
nated fatally  two  days  afterwards,  on  August  4.  He  was  buried 
at  Kensal  Green  Cemetery. 

He  was  elected  a  Fellow  of  the  Society  March  9,  1855. 

James  Pearson,  M.A.,  vicar  of  Fleetwood,  was  born  at 
Preston,  Lancashire,  and  received  his  education  there,  up  to  the 
period  of  becoming  an  undergraduate  of  Cambridge  University, 
first  with  Mr.  Abbott,  a  highly  reputed  private  schoolmaster  of 
fifty  years  since,  and  afterwards  at  the  Grammar  School,  chiefly 
under  the  mastership  of  the  ,Rev.  G.  Nun  Smith,  an  excellent 
teacher  and  proficient  scholar.  Here  the  foundation  was  laid 
for  the  distinguished  college  honours  afterwards  gained  by  the 
pupiL  Whilst  at  the  grammar  school  he  took  the  second  place 
for  several  years,  and  finally  was  bracketed  as  equal  with  the 
first,  the  two  entering  together  upon  their  university  career. 
Mr.  Pearson  came  out  as  a  first  class  in  the  examinations  of  his 
year  at  Trinity  College,  was  subsequently  rewarded  with  a 
scholarship,  and  graduated  in  the  high  position  of  fifteenth 
wrangler  in  1848.  After  two  years  of  further  residence  he 
accepted  the  curacy  of  the  rural  parish  of  Scarisbrick,  near 
Ormskirk,  a  position,  it  may  well  be  allowed,  not  very  congenial 
to  a  man  of  his  antecedents  and  abilities,  and  he  resigned  it  to 
accept  the  dual  appointment  of  rector  of  St.  Edmund's  and 
mathematical  master  of  the  King  Edward  the  Sixth  Grammar 
School  at  Norwich.  After  retaining  this  for  about  four  years 
he  was  chosen  one  of  the  mathematical  professors  in  the  ttoyal 
Military  College,  Sandhurst.    Either  a  longing  to  live  near  the 

M  2 


140  Report  of  the  Council  to  the  xlvii.  4, 

scenes  of  his  childhood  or  a  preference  for  parochial  work,  prob- 
ably both  combined,  led  him  to  forego  this  advantageous  posi- 
tion for  a  second  edition  of  the  life  of  a  coantry  clergyman  at 
Altcar,  near  Liverpool,  a  presentation  of  the  Earl  of  Sefton.  The 
population  was  a  scattered  one  of  three  hundred  souls,  and  the 
care  and  companionship  of  these  was  scarcely  adequate  to  keep 
up  the  mental  calibre  in  a  man  like  Mr.  Pearson,  who  was  always 
full,  even  to  excitement,  of  scientific  instincts.  Here,  however, 
he  found  one  or  two  congenial  spirits  and  kindred  tastes , 
whose  friendship  he  held  dear  to  the  end  of  his  days.  Another 
change  yet  awaited  him,  and  in  1862  he  went  to  Workington  as 
vicar  of  St.  John's  in  that  town,  and  remained  nine  years, 
quitting  it  in  1871  to  go  to  Fleetwood.  At  Workington  he 
was  greatly  appreciated  both  as  a  teacher  and  a  preacher,  and 
this  appreciation  was  manifested  in  a  high  degree  by  a  hand- 
some testimonial  presented  on  his  leaving,  and  more  handsomely 
impressed  by  the  testimony  to  his  worth  in  the  words  which 
accompanied  the  presentation. 

His  scientific  researches,  besides  astronomy,  went  in  the 
direction  of  the  study  of  the  tides,  and  on  this  subject  he  was  a 
very  frequent  and  constant  contributor  to  scientific  papers.  His 
system  of  tide  computation  was  adopted  by  the  Admiralty  for 
this  coast,  and  he  designed  and  had  erected  on  the  pier  at 
Fleetwood  a  novel  and  ingenious  contrivance  for  registering  the 
height  of  the  tides  'and  testing  his  calculations,  which  were 
always  found  to  be  very  accurate.  He  designed  several  novel 
contrivances  in  connection  with  this  subject,  one  of  which  has 
been  for  some  time  erected  on  the  Blackpool  Pier  and  another  at 
Fleetwood.  It  consists  of  a  dial,  which  is  set  each  day  and  points 
to  the  height  of  the  tide  at  all  hours  during  that  day,  both  ebb 
and  flow.  He  also  published  a  Treatise  on  the  Tides  in  1881, 
which  was  hailed  with  much  approval  by  many  astronomers 
of  the  day,  and  very  soon  became  scarce.  Several  works  of  a 
minor  character  on  this  and  kindred  subjects  proceeded  at 
different  periods  from  his  pen,  all  denoting  the  enthusiasm  of 
the  author  for  his  favourite  studies. 

Mr.  Pearson  died  on  April  8,  1886,  after  a  lingering  and 
painful  illness. 

He  was  elected  a  Fellow  of  the  Society  April  10,  1874. 

Admiral  Sir  Charles  Frederick  Alexander  Shadwell, 
K.C.B.,  F.R.S.,  was  born  on  January  31,  1814,  and  was  the 
fourth  son  of  the  late  Right  Hon.  Sir  Lancelot  Shad  well,  Vice- 
chancellor  of  England.  He  entered  the  navy  May  3,  1827, 
from  the  Royal  Naval  College,  and  passed  his  examination  in 
1833.  On  June  28,  1838,  he  obtained  his  lieutenant's  com- 
mission, and  was  appointed  in  the  following  July  to  the  Castor, 
Captain  Edward  Collier,  with  whom  he  served  on  the  coast  of 
Syria  in  1840,  and  assisted  at  the  operations  against  Caiffa, 
Jaffa,  Tsour,  and  St.  Jean  d'Acrc.     His  next  appointment  was 


Feb.  1887.      Sixty- seventh  Annual  General  Meeting.  141 

as  first  lieutenant  of  the  Fly,  in  the  East  Indies,  from  December 
1 84 1  until  June  1846,  when  he  was  promoted  to  be  commander. 
In  February  1 850110  commanded  the  Sphynx,  for  service  in  the 
East  Indies,  and  held  this  command  through  the  Burmese  War 
of  1851-1853,  for  his  services  in  which  he  was  on  February  7, 
2853,  promoted  to  post  rank,  was  gazetted  to  the  Order  of  the 
Bath,  and  received  the  Burmese  war  medal  with  clasp.  His 
next  appointment  was,  in  August  1856,  to  the  Highflyer,  which 
he  commanded  in  the  last  war  with  China,  taking  part  in  the 
operations  in  the  Canton  River  and  in  the  capture  of  Canton, 
And  being  wounded  in  the  attack  on  the  forts  at  the  mouth  of 
the  Peiho  River  in  July  1859.  For  his  services  on  this  occasion 
Captain  Shadwell  was  mentioned  in  despatches  for  "  his  valuable 
assistance."  After  the  China  War  he  was  appointed  to  the 
Aboukir,  which  he  commanded  in  the  Channel  and  North 
America  and  West  Indies  in  1861  and  1862.  His  next  appoint- 
ment was  that  of  flag-captain,  in  the  Hastings,  to  Rear- Admiral 
Sir  Lewis  F.  Jones  at  Queenstown,  which  he  held  till  June  1864, 
when  he  was  made  Captain  Superintendent  of  the  Royal  Haslar 
Hospital  and  of  the  Royal  Clarence  Victualling  Yard.  In  this 
post  he  remained  till  he  became  Rear- Admiral  in  January  1869, 
vacating  at  the  same  time  his  appointment  as  Naval  Aide-de- 
Camp  to  the  Queen,  which  he  had  received  in  March  1866.  He 
was  commander-in-chief  on  the  China  station  from  1 871-1874. 
In  1873  he  was  gazetted  a  Knight  Commander  of  the  Bath,  and 
in  1877  received  the  flag  officers'  pension  for  meritorious  service. 
His  last  appointment  was  that  of  President  of  the  Royal  Naval 
College  at  Greenwich,  which  post  he  held  from  March  1878  till 
March  1881.  He  died  at  Meadowbank,  Melksham,  Wilts,  on 
March  1,  1886. 

In  the  year  1861  Sir  Charles  F.  A.  Shadwell  was  elected  a 
Fellow  of  the  Royal  Society.  He  was  the  author  of  the  following 
works  : — "  Formulas  of  Navigation  and  Nautical  Astronomy  " 
(for  the  use  of  naval  officers  and  students  of  nautical  astro- 
nomy), "Tables  for  Facilitating  the  Approximate  Prediction 
of  Occultations  and  Eclipses/1  "  Tables  for  Facilitating  the 
Determination  of  the  Latitude  and  Time  at  Sea  by  Observations 
of  the  Stars,"  "  Tables  for  Facilitating  the  Reduction  of  Lunar 
Observations,"  "Notes  on  the  Management  of  Chronometers 
and  the  Measurement  of  Meridian  Distances,"  "  Notes  on  Inter, 
polation,  Mathematical  and  Practical "  (intended  to  form  Ch.  VI. 
of  a  work  on  navigation  and  nautical  astronomy,  which  the 
author  left  incomplete  at  his  death). 

He  was  elected  a  Fellow  of  this  Society  on  January  8,  1847. 

David  Smith  was  born  at  Selby,  Yorkshire,  in  September 
1821.  He  left  school  at  the  age  of  fourteen,  and  for  about 
eighteen  months  was  employed  as  a  railway  clerk,  after  which 
he  was  apprenticed  to  a  carpenter  and  builder,  and  also  studied 
for  an  architect  and  surveyor.     In  the  year  1842  he  went  to 


142  Eepart  of  the  Council  to  the  XLVii.  4, 

America,  where  he  remained  two  years,  travelling  through  the 
United  States,  and  also  the  backwoods,  collecting  specimens  of 
natural  history,  and  at  the  same  time  earning  his  living  by 
his  trade  of  a  carpenter,  &c.  Upon  his  return  to  England  he 
went  to  Birmingham,  and  there  spent  the  remainder  of  his  life, 
the  last  twenty  years  of  which  he  practised  as  an  architect  and 
surveyor.  Always  of  a  profoundly  studious  turn  of  mind,  he 
early  became  deeply  interested  in  the  science  of  astronomy,  and 
soon  made  himself  conversant  with  that  and  other  kindred 
physical  sciences. 

His  meteorological  observations  were  daily  recorded,  and 
published  periodically  in  the  local  newspapers.  In  1865  he  was 
elected  a  member  of  the  British  Meteorological  Society,  and  he 
had  the  honour  of  reading  a  paper  before  the  British  Association, 
at  their  meeting  in  Birmingham  in  1865,  on  "  The  Meteorology 
of  Birmingham,"  being  the  results  of  personal  observations 
extending  over  a  period  of  twelve  years,  viz.  from  1853  to  1864 
inclusive. 

He  was  indefatigable  in  his  efforts  to  spread  scientific  and 
useful  knowledge  amongst  those  around  him,  and  by  popular 
lectures,  and  the  formation  of  science  classes,  he  laid  the 
foundation  of  that  well-known  and  valuable  establishment,  the 
Bloomsbury  Institution,  where  educational  work  is  still  carried 
on  in  connection  with  other  useful  agencies.  As  a  public 
lecturer  on  astronomy,  geology,  meteorology,  physiology,  and 
various  other  subjects,  Mr.  Smith  was  deservedly  popular,  and  his 
removal  has  caused  a  gap  which  it  will  be  difficult  to  fill  up. 

His  decease  occurred  after  a  short  illness  on  December  23, 
1885,  ^d  n,s  l°flS  *8  deeply  felt  and  regretted  by  all  who  were 
connected  with  him. 

He  was  elected  a  Fellow  of  this  Society  on  June  13,  1862. 

Edwin  Story  was  educated  at  Shrewsbury  School  and  St. 
John's  College,  Cambridge.  He  was  a  great  lover  of  science, 
and  became  a  member  of  the  Linneean,  Geological,  Historical, 
and  Royal  Geographical  Societies.  His  favourite  recreation  from 
sterner  mental  study  was  the  indulgence  of  poetical  composition, 
particularly  of  classical  poetry,  in  which  he  delighted  and 
excelled. 

-  Mr.  Story  was  essentially  of  a  retiring  disposition  ;  he  led  a 
studious  and  well-spent  life,  which  was  terminated  by  paralysis 
on  February  1,  1886. 

He  was  elected  a  Fellow  of  this  Society  November  8,  1867. 

Charles  George  Talmage  was  born  at  Greenwich  on 
November  12,  1840.  He  was  educated  at  a  proprietary  school 
there,  and  afterwards  studied  mathematics  under  a  private  tutor. 

Mr.  Talmage  commenced  his  astronomical  career  in  the  year 
1856,  at  the  Royal  Observatory,  Greenwich,  where  he  remained 
for  about  four  years.     In  i860  he  joined  Mr.  Hind  as  assistant 


Feb.  1887.      Sixty-seventh  Animal  General  Meeting.  143 

air  Mr.  Bishop's  Observatory  in  the  Regent's  Park.  At  this 
time  Mr.  Talmage  was  in  very  delicate  health,  and  it  was  con- 
sidered necessary  for  him  to  sojourn  in  a  warmer  climate;  he 
therefore  was  compelled  to  leave  Mr.  Bishop's  Observatory,  and 
subsequently  accepted  an  appointment  as 'private  secretary  to  the 
late  Mr.  R.  Coventry,  who  was  then  residing  at  Nice.  There 
Mr.  Talmage  devoted  himself  to  double  star  observations, 
and  undertook  a  re-examination  of  Admiral  Smyth's  Bed- 
ford Catalogue*  Four  years'  residence  in  the  south  of  France 
so  far  restored  him  to  health  as  to  enable  him  to  return  to 
England,  where  he  again  joined  Mr.  Hind  for  a  short  time  at 
the  Observatory,  which  Mr.  Bishop  had  removed  from  the 
Regent's  Park  to  Twickenham. 

In  1865  Mr.  Talmage  was  appointed  Director  of  the  private 
Observatory  of  Mr.  J.  Ournev  Barclay  at  Leyton,  which  appoint- 
ment he  held  up  to  the  time  of  his  death.  Here  he  devoted  the  fine 
1  ©-inch  Cooke  refractor  almost  exclusively  to  double  star  work. 
Most  of  his  excellent  observations  have  been  published  in  the 
volumes  of  the  "  Leyton  Astronomical  Observations,"  and  others 
will  be  found  in  the  volumes  of  the  Monthly  Notices.  (It  is  to  be 
regretted  that  with  Mr.  Talmage's  death  the  work  of  the  Leyton 
Observatory  has  closed,  as  Mr.  Barclay  has  since  then  presented 
the  large  equatoreal  to  the  Radcliffe  Observatory,  Oxford,  and 
the  Transit  circle  to  the  Oxford  University  Observatory.) 

In  1 870  Mr.  Talmage  went  out  in  the  "  Urgent "  to  Gibraltar 
to  observe  the  Total  Solar  Eclipse  of  that  year,  his  duty  being 
to  take  angular  measurements  of  Saturn  if  seen  through  the 
cerona,  but  the  unpropitkros  weather  on  the  day  of  the  eclipse 
prevented  any  observation  being  made.  In  1882  he  was  ap- 
pointed by  the  Government  as  officer  in  charge  of  the  West 
Indian  expedition  for  observing  the  Transit  of  Venus.  He  was 
located  at  Barbadoes,  in  company  with  Lieut.  Thomson,  R.A., 
where  he  was  fortunate  in  securing  good  observations  of  all 
contacts  both  at  ingress  and  egress. 

Mr.  Talmage  was  for  many  years  a  member  of  the  British 
Association,  and  regularly  attended  their  meetings.  Besides 
being  an  able  microscopist,  he  had  no  mean  knowledge  of 
medicine  and  botany. 

In  the  locality  in  which  he  lived  Mr.  Talmage  was  both 
respected  and  beloved.  His  hearty,  genial,  and  kind  disposition 
made  him  numerous  friends  whithersoever  he  went.  Ever  ready 
to  afford  to  others  all  the  help  that  was  in  his  power,  and  with  a 
happy  ungrudging  manner  which  made  him  deeply  esteemed,  it 
is  no  wonder  that  his  untimely  death  has  caused  a  wide-spread 
feeling  of  regret  among  those  who  knew  him.  He  was  taken 
seriously  ill  on  February  23,  1886,  and,  after  much  suffering, 
died  on  March  20. 

A  memorial  to  him  has  been  erected  by  his  many  friends  in 
the  church  of  St.  Michael  and  All  Angels,  Walthamstow. 

He  was  elected  a  Fellow  of  the  Society  Dec.  n,  1863. 


144  Report  of  the  Council  to  tJie  xlvii.  4, 

William  Tomlinson,  Junior,  was  born  at  York  about  forty- 
five  years  ago,  where  be  received  bis  education  at  St.  Peter's 
School,  in  which  bis  father  held  the  position,  of  mathematical 
master.    About  twenty  years  ago  he  went  out  to  New  Zealand 
to  Bishop  Abraham,  of  Wellington,  witb  the  intention  of  taking 
holy  orders.     From  Wellington  be  proceeded  to  Wanganui,  and 
there,  feeling  that  the  teaching  profession  was  the  vocation  of 
bis  life,  be  entered  upon  its  duties  with  all  the  zeal  of  his  enthu- 
siastic nature  as  assistant  master  in  the  school  conducted  by 
Mr.  Goodwin.    While  in  Wanganui  it  may  be  mentioned  that 
the  Maori  War  was  raging,  and  during  that  troublous  time  Mr. 
Tomlinson  belonged  to  a  local  cavalry  corps,  took  part  in  some 
engagements  with  the  natives,  and  was  rewarded  with  a  New 
Zealand  war  medal.     Subsequently  be  was  appointed  to   the 
position  of  assistant  master  at  the  Nelson  College,  where  be 
remained  until  1873,  when  he  received  the  appointment  at  the 
Auckland  College  and  Grammar  School,  which  he  held  at  the 
time  of  his  death.    During  his  residence  at  Nelson  he  married  a 
daughter  of  the  late  Mr.  Samuel  Kingdon.    Mr.  Tomlinson  was 
of  very   scholarly  habits,   and  in    1883,   notwithstanding   the 
demands  upon  his  time  by  bis  professional  duties,  be  succeeded 
in  obtaining  the  B.  A.  degree  in  connection  with  the  New  Zealand 
University.     He  was  a  diligent  student  of  astronomy  himself, 
and  encouraged  the  study  of  it  in  no  small  degree  in  others.    He 
took  a  creditable  degree  in  the  University  of  New  Zealand,  in 
which  astronomy  was  a  subject  of  examination,  and  he  gained 
considerable  repute  by  his  writings  on  educational  matters,  and 
was  also  distinguished  as  a  public  teacher  and  private  coach ; 
but  his  onerous  duties,  and  the  exigencies  of  a  large  family,  did 
not  allow  him  to  carry  out  the  practical  views  which  his  sound 
mathematical  knowledge  would  have  enabled  him  to  do  ;  but  at 
the  time  of  his  death  be  was  looking  forward  with  a  lively  hope 
to  a  time  when  more  leisure,  less  onerous  duties,  and  easier 
circumstances  would  have  enabled  him  to  do  good  service  to 
practical  astronomy. 

His  success  as  a  teacher  must  be  attributed  to  bis  enthu- 
siasm for  his  profession.  He  always  felt  that  the  imparting 
of  knowledge  was  comparatively  a  small  part  of  a  school* 
master's  work,  and  that  the  development  of  a  manly  and 
upright  character  in  each  of  bis  pupils  was  bis  highest  aim. 
In  fact,  he  wished  to  make  them  gentlemen  in  the  true  sense  of 
the  term,  and  bis  own  demeanour  and  bearing  towards  bis  pupils 
were  the  most  powerful  factors  in  producing  this  result.  His 
genial  disposition  and  active  habits  led  him  to  take  the  deepest 
interest  in  the  doings  of  bis  pupils  in  the  playground,  and  be 
naturally  became  a  great  favourite  with  them.  His  interest  in 
his  pupils  did  not  cease  when  they  left  school  to  enter  upon 
business  pursuits,  and  he  always  manifested  a  great  concern  for 
their  welfare,  and  was  ever  ready  to  assist  those  who  desired  to 
further  pursue  their  scholastic  studies. 


Feb.  1887.      Sixty-seventh  Annual  General  Meeting.  145 

Mr.  Tomlinson's  death  took  place  under  exceptionally  lament- 
able circumstances.  On  the  morning  of  January  21,  1886,  he 
went  out  with  a  double-barrelled  gun,  intending  to  shoot  gulls. 
He  was  accompanied  by  bis  eldest  son,  aged  eleven,  and  in 
climbing  up  a  nill  in  the  Wakapuaka  Road,  he  slipped,  when 
the  gun  exploded  and  the  shot  from  the  charge  went  through 
his  heart.  He  has  left  to  mourn  his  loss  a  widow  and  a  family 
of  five  children. 

He  was  elected  a  Fellow  of  the  Society  April  9,  1873. 

Professor  Theodor  yon  Oppolzer,  the  only  son  of  the  cele- 
brated physician  Dr.  Johann  von  Oppolzer,  was  born  at  Prague, 
October  26,  1841.  His  early  years  were  spent  at  Leipzig,  whence, 
while  yet  in  his  childhood,  he  moved  to  Vienna,  as  his  father  had 
been  appointed  professor  at  the  university  of  that  city.  Here  he 
studied  physics,  but  his  abilities  and  great  predilection  for 
mathematics  induced  him  to  devote  all  his  spare  time  to  the  study 
of  natural  philosophy.  In  these  studies  he  was  aided  by  Dr.  E. 
Weiss,  the  present  Director  of  the  Vienna  Observatory,  who  soon 
recognised  his  eminent  talents  for  Astronomy,  and  encouraged 
him  to  devote  his  life  to  that  science.  Oppolzer,  who  was  pos- 
sessed of  independent  means,  sufficient  to  remove  all  necessity 
for  seeking  immediate  employment,  therefore  constructed  a  well- 
appointed  observatory  after  he  had  taken  the  degree  of  a 
Doctor  of  Physics.  At  this  observatory  he  observed  asteroids 
and  comets  during  the  years  1862  to  1872  with  great  zeal,  and  his 
computations  of  the  orbits  of  such  bodies  were  the  first  papers  by 
which  he  introduced  himself  to  the  astronomical  world.  For 
such  work  he  was  especially  qualified  by  the  quickness  and  cer- 
tainty with  which  he  conducted  extended  numerical  computa- 
tions.    He  published  numerous  papers  on  this  subject. 

He  also  published  all  his  valuable  theoretical  researches 
in  this  branch  of  Astronomy  in  an  excellent  "Lehrbuch  zur 
Bahnbestimmung  der  Kometen  und  Planeten,"  of  which  the 
first  volume  appeared  1870 ;  and  in  a  second,  totally  revised  and 
much  enlarged  edition,  1882.  The  second  volume  was  published 
in  1880.  In  this  classic  work  the  author  has  in  fact  recon- 
structed on  a  more  comprehensive  plan  the  Theoria  Motus  of 
Gauss.  The  theories  upon  which  the  calculation  of  the  orbits 
of  comets  and  planets  depend  are  discussed  so  fully  and  ex- 
haustively, that  the  work  forms,  indeed,  a  Treatise  on  Astro- 
nomy, "  not  only  useful  to  the  practical  Astronomer,  but  of  the 
highest  value  to  the  Mathematician  who  desires  to  know  the 
exact  manner  in  which  the  dynamical  formulae  he  is  acquainted 
with  are  actually  applied  in  practice  to  the  calculation  of  orbits." 
This  most  important  work  has  been  recently  translated  into 
French  by  Prof.  Ernest  Pasquier,  of  Louvain. 

In  the  year  1873  Prof.  Oppolzer  was  entrusted  by  the  Austrian 
Government  with  the  astronomical  work  for  the  Europaische 
Oradmessung.     In  this  position,  which  he  held  till  his   death, 


146  Report  of  the  Council  to  the  xlyii.  4, 

being  in  bis  last  years  chairman  of  ibe  Austrian  Commission  of 
the  Europaische  Gradmessung,  be  showed  an  extraordinary 
ability  as  an  organiser,  and  executed  a  long  series  of  telegraphic 
longitude  operations  between  various  cities  of  Austria  amongst 
each  other,  and  with  the  capitals  of  other  countries.  For  many 
weeks  in  the  summer  of  1876  operations  were  undertaken  at 
the  Royal  Observatory,  Greenwich,  by  Professor  Oppolzer's 
assistants  for  the  purpose  of  making  the  time  observations 
and  telegraphic  observations  necessary  for  determining  the 
longitudes  of  Vienna  and  Berlin,  connected  also  in  some 
measure  with  Munich  and  Paris.  All  the  observations  for 
this  very  extensive  work  are  finished,  but  unfortunately  the 
reductions  are  not  very  far  advanced.  In  connection  with  these 
investigations  he  also  conducted  a  series  of  pendulum  experi- 
ments for  determining  the  intensity  of  gravity  at  Vienna,  and 
he  made  a  very  interesting  and  important  study  of  the  vibrations 
of  the  stand  of  the  pendulum  and  their  influence  on  the  time  of 
its  oscillation.  But  here  also  his  very  premature  death  pre- 
vented him  from  discussing  more  than  a  small  part  of  these 
extremely  delicate  researches,  for  which  he  devised  special 
methods  of  observation  and  reduction. 

In  the  year  1881  Oppolzer  published  "  Syzygien-Tafeln  fur 
den  Mond,"  which  were  intended  to  supply  a  simple  and  con- 
venient means  of  finding  very  approximately  the  time  of  New  and 
Full  Moon,  particularly  hi  the  case  of  an  ecliptic  syzygy,  and  of 
calculating  all  the  circumstances  of  an  eclipse  without  the 
necessity  of  having  recourse  to  the  Solar  and  Lunar  Tables. 

But  the  most  important  work  undertaken  by  Oppolzer  is 
his  "Canon  der  Finsternisse"  [Table  of  eclipses],  which  will 
be  found  to  be  an  invaluable  basis  for  all  historical  researches 
connected  with  solar  eclipses,  and  will  form  an  enduring  monu- 
ment of  the  power  of  its  author. 

This  masterly  paper  contains  not  only  the  elements  of 
eclipses  of  the  Sun,  but  also  of  those  of  the  Moon  from  1 207  B.C. 
to  2162  a.d.  The  elements  are  given  for  all  the  eclipses  partial 
and  central  occurring  during  this  period  of  time. 

The  tables  furnish  the  computations  of  8,000  Solar  Eclipses, 
of  which  about  2,220  are  total,  355  annular  and  total,  2,605 
annular,  and  2,820  partial. 

Of  the  Moon,  5,200  eclipses  are  computed;  for  which  the 
tables  give  not  only  the  date,  but  also  the  magnitude,  the  time 
of  the  middle  of  the  eclipse,  and  the  geographical  position  of 
the  point  on  the  earth  where  the  Moon  at  that  moment  is  at  the 
zenith. 

Appended  to  the  work  are  160  charts,  in  which  is  laid  down 
the  central  line*  of  all  Solar  Eclipses  visible  in  the  northern 
hemisphere,  and  as  far  as  30°  south  latitude.  Partial  eclipses 
of  the  Sun,  and  those  which  are  central  only  in  regions  more 
south  than  300  are  not  mapped. 


Feb.  1887.      Sixty-seventh  Annual  General  Meeting.  147 

The  work  forms  vol.  lii.  of  the  Memoirs  of  the  Imperial 
Academy  of  Sciences  at  Vienna. 

This  noble  undertaking  Oppolzer  was  only  jasfc  able  to  bring 
to  a  conclusion,  for  it  was  but  a  few  hours  before  his  death  that 
he  read  the  last  proof-sheets  of  it. 

Besides  all  this,  Oppolzer  was  engaged  daring  the  last  years 
of  his  life  in  researches  on  planetary  disturbances,  especially  on 
the  theory  of  the  motion  of  the  Moon,  on  astronomical  refractions, 
and  on  the  resisting  medium,  Ac. 

From  this  brief  record  of  his  more  important  researches  it  will 
readily  be  understood  that  his  life  was  one  of  constant  work, 
and  that  he  was  enabled  to  perform  all  he  did  only  by  an 
indefatigable  diligence,  a  very  remarkable  power  of  memory, 
quickness  of  perception,  and  intuitive  grasp  of  whatever  he 
studied. 

Von  Oppolzer  was  appointed  in  1876  Professor  of  Astronomy 
at  the  University  of  Vienna,  and  received  besides  this,  various 
other  distinctions  from  the  Austrian  Government  and  several 
foreign  sovereigns.  He  was  also  Member  of  the  Imperial 
Academy  of  Sciences  at  Vienna,  Honorary  Member  of  the  Royal 
Academy  at  Munich,  Correspondent  of  the  Institute  of  France, 
and  Fellow  of  many  other  scientific  bodies.  He  was  elected  an 
Associate  of  the  Royal  Astronomical  Society  on  Jan.  9,  1874. 

In  the  middle  of  November  1886  Oppolzer  returned  to 
Vienna  somewhat  ill,  after  attending  the  Paris  International 
Conference  on  Weights  and  Measures,  and  the  meeting  of 
the  Permanent  Commission  of  the  Europdische  Oradmessung 
at  Berlin.  No  one  would  have  considered,  however,  from  his 
appearance,  that  his  end  was  so  near.  At  first  his  illness  was 
thought  to  be  a  kind  of  malaria,  but  it  very  soon  proved  a 
serious  disease  of  the  heart,  of  which  he  suddenly  died,  on  the 
morning  of  December  26,  at  the  early  age  of  45  years. 

B.  w. 


148  Report  of  the  Gouncil  to  the  •  xlvii.  4, 


Proceedings  of  Observatories. 

The  following  Reports  of  the  proceedings  of  Observatories 
during  the  past  year  have  been  received  by  the  Gonncil  from 
the  Directors  of  the  several  Observatories,  who  are  alone  respon- 
sible for  the  same. 


"Royal  Observatory,  Greenwich. 

During  the  past  year  the  meridian  work  at  this  Observatory 
has  been  sensibly  increased  by  the  efforts  made  to  complete  the 
forthcoming  Ten  Year  Catalogue  of  Stars  (187 7-1886)  as  far  as 
possible,  both  by  securing  places  of  nearly  all  stars  down  to  the 
sixth  magnitude  inclusive,    not  observed  at  Greenwich  since 
i860,  and  by  obtaining  at  least  three  observations  of  each  star. 
Thus  the  total  number  of  meridian  transits  for  1886  is  6,417, 
and  of  meridian  zenith  distances  6,219;  the  numbers  for  the 
mouth  of  December  alone,  when  special  efforts  were  made,  being 
1, 1 33  and  1 ,093  respectively.  The  number  of  stars  observed  during 
1886  is  1,666.      At    the  same  time  the  stellar  work  has    not 
been  allowed  to  interfere  with  the  regular  observations  of  Sun, 
Moon,  and  planets,  and  the  general  work  in  other  respects  has 
been  rather  heavier  than  in  previous  years.     The  proper  motions 
in  use  have  been  carefully  revised  and  compared  with  those  of 
Auwers ;  and,  in  the  case  of  clock  stars,  a  further  comparison 
has  been  made  with  the  last  ten  years  of  Greenwich  observa- 
tions, from  which  it  is  clear  that  Auwers'  proper  motions  may  be 
advantageously  adopted  throughout.     They  will  accordingly  be 
used  regularly  from  January  1,  1887,  and  also  in  the  formation 
of  the  Ten  Year  Catalogue.    As  a  preliminary  to  this,  the  appli- 
cation of  proper  motion  for  fraction  of  the    year  has   been 
thoroughly  examined  for  every  observation  in  the  period  1877- 
1886,  and  corrections  applied  where,  as  occasionally  happened, 
different  proper  motions  had  been  used  in  the  same  year.     Pre- 
parations have  been  made  to  apply  corrections  for  reduction  to 
Auwers'  proper  motions,  and  for  reduction  to  the  same  R— D 
•correction  throughout  in  the  computations  for  the  Ten  Year 
Catalogue. 

A  considerable  amount    of   information  has  been  obtained 
.as  regards  personality  in  observation,   both  as  depending  upon 


Feb.  1887.      Sixty-seventh  Annual  General  Meeting.  149 

direction  of  measurement  or  motion,  and  on  the  differences  between 
the  chronographic  and  the  eye-and-ear  method  of  observing. 
The  reversion  prism  has  been  used  to  observe  about  200 
transits  of  clock  stars  and  200  of  polar  stars  with  the  transit- circle, 
and  about  550  of  the  Moon  and  stars  with  the  altazimuth,  more 
than  200  of  these  latter  being  observed  by  eye  and  ear.  As  & 
general  result,  it  appears  that  there  is  in  no  case  any  sensible 
personality  depending  on  the  direction  of  measurement,  and  that 
the  personality  depending  on  the  direction  of  motion  is  in  every 
instance  very  small  for  clock  stars,  and  insensible  for  slow- 
moving  polar  stars.  For  the  regular  observers  the  eye- and- ear 
personal  equations  differ  but  little  from  the  chronographic, 
except  in  one  instance,  where  the  difference  amounts  to  as  much. 
as  os*6.  From  observations  made  with  the  personal  equation 
machine,  which  has  been  found  to  work  satisfactorily,  and  to 
give  results  in  accordance  with  those  deduced  from  observations 
of  clock  stars,  it  would  appear  that  all  the  observers  observe  too 
late.  Further  observations  are,  however,  required  to  determine 
the  absolute  personal  equations  with  certainty.  With  a  view  to 
obtaining  a  register  of  the  end  as  well  as  the  beginning  of  the 
contacts  made  by  the  personal  equation  machine,  a  small 
chronograph,  by  Krille,  made  many  years  ago  for  mechanical 
registration,  is  being  adapted  by  Messrs.  E.  Dent  &  Co.  to 
electric  registration  of  make-and-break  contacts. 

The  mean  error  in  R.A.  of  Hansen's  Lunar  Tables  with 
Prof.  Newcomb's  corrections  is  +  o8*o29  for  the  year  1886,  as 
deduced  from  ninety-six  observations  with  the  transit-circle ; 
for  the  years  1883,  1884,  1885,  the  corresponding  quantities 
were  respectively  +  o8o32,  +  o802i,  and  +  o8,028. 

Four  determinations  of  flexure  of  the  transit- circle  in  1886 
gave  results  -ro"*i5,  +  o"*42,  —  o"- 16,  and  +  o"*i3. 

The  apparent  correction  to  the  nadir  observation,  deduced 
from  reflexion  observations  of  stars  in  1886,  is  —  o"aoo;,  the  results 
for  individual  months  showing  considerable  fluctuations.  In 
comparing  this  with  results  for  previous  years,  it  is  to  be  re- 
marked that  new  steel  screws  were  applied  to  the  microscope 
micrometers  on  January  1,  1886.  It  is  considered  that  no 
correction  is  now  required  to  the  nadir  observation. 

Experiments  on  the  effect  of  the  limitation  of  aperture  when 
observations  are  taken  through  the  central  cube  of  the  transit- 
circle  having  led  to  the  suspicion  that  the  object-glasses  of  the 
collimators  might  be  defective,  they  have  been  examined  by 
Mr.  Simms,  who  has  reported  that  they  are  excellent. 

The  altazimuth  observations  of  the  Moon  in  the  first  and  last 
quarters  have  been  regularly  continued  as  before. 

Further  additions  have  been  made  to  the  Lassell  Equatorial  r 
with  a  view  to  adapting  it  to  stellar  photography.  With  this 
object  the  Corbett  Refractor  of  6£  inches  aperture  has  been 
mounted  on  the  cradle  of  the  Lassell  telescope,  so  that  the 
position  of  the  compound  instrument  can  be  very  conveniently 


IS©  Report  of  the  Council  to  the  xlvii.  4, 

watched  by  an  observer.  Slow  motion  in  R.A.  with  differential 
wheels,  and  an  improved  clamp  and  slow  motion  in  N.P.D.  are 
being  added.  A  circular  camera  to  carry  plates  of  8£  inches 
diameter  has  been  mounted  at  the  principal  focus,  bat  no  photo- 
graphs hare  jet  been  taken. 

Progress  has  been  made  in  the  construction  of  the  new 
28-inch  refractor.  A  satisfactory  flint-glass  diso  has  been  pro- 
duced by  Messrs.  Chance,  and  M.  Feil  of  Paris  has  undertaken 
to  supply  the  crown  disc.  The  details  of  the  special  tube  have 
been  finally  settled,  and  Mr.  Grubb  is  engaged  on  its  con- 
struction. 

Comet  d  1885  (Fabry)  has  been  observed  on  five  nights  with 
one  or  other  of  the  equatorials ;  Comet  e  1885  (Barnard)  on 
nine  nights  ;  Comet  a  1886  (Brooks)  on  six  nights,  and  Comet/ 
1886  (Barnard)  on  twelve  nights.  Twenty-four  occultations  of 
stars  by  the  Moon  have  been  observed,  in  five  cases  by  two 
observers,  in  one  by  three  observers,  and  in  two  by  four  ob- 
servers ;  and  forty  phenomena  of  Jupiter's  satellites,  with  one  or 
other  of  the  equatorials. 

Owing  to  the  pressure  of  the  San-spot  work  and  the  absence 
of  Mr.  Maunder  in  the  summer  for  observation  of  the  solar 
eclipse  in  Grenada,  the  chromosphere  has  only  been  examined  on 
eight  days.  With  respect  to  measures  of  the  displacements  of 
lines  in  stellar  spectra,  283  comparisons  of  the  F  line,  and  30  of 
the  b  lines  have  been  made,  the  number  of  stars  examined  being 
54.  The  displacements  of  the  b  and  F  lines  in  the  spectra  of 
Venus  and  Mars  have  also  been  measured,  20  observations  having 
been  made  on  Venus  and  19  on  Mars;  while  94  comparisons  of 
the  b  or  F  lines  in  the  spectrum  of  the  Moon  or  of  the  sky  have 
been  made  for  general  check  on  the  accuracy  of  the  results ;  and 
5  measures  have  been  obtained  of  the  relative  motion  of  the 
limbs  of  Jupiter. 

The  spectra  of  Mr.  Gore's  new  star  in  Orion,  of  51  Scbjelle~ 
rup,  and  of  Comets  e  1885  (Barnard)  and  /  1886  (Barnard), 
have  also  been  examined.  Photographs  of  the  Sun,  420  in  all, 
have  been  taken  on  209  days,  and  these  have  been  supplemented 
by  photographs  taken  at  Dehra  Dun,  in  India,  and  at  the  Royal 
Alfred  Observatory,  in  Mauritius ;  so  that  in  the  year  ending  Oct. 
31,  1886,  there  are  only  5  days  on  which  no  photograph  is  as 
yet  available  for  measurement.  A  very  marked  decrease  in  the 
number  of  spots  is  noticeable  in  1886,  especially  in  the  last  six 
months ;  indeed,  since  the  middle  of  September,  the  Sun  has 
been  almost  free  from  spots. 

The  magnetical  and  meteorological  observations  have  been 
carried  on  on  the  same  lines  as  in  previous  years,  and  the  obser- 
vations of  the  principal  meteor-showers  have  been  continued. 

The  arrangements  for  trials  of  chronometers  and  deck  watches 
have  engaged  much  attention  during  the  past  year,  and  the 
business  connected  with  chronometers  generally  has  pressed 
heavily  on  the  Observatory.     One  of  the  clocks  returned  from 


Feb.  1887.      Sixty-seventh  Annual  General  Meeting.  151 

the  Transit  of  Venus  Expedition  (1874),  has  been  fitted  up  at 
Devonport,  under  Oapt.  Wharton's  directions,  to  give  time  signals 
to  the  port.  This  dock  is  adapted  to  give  hourly  signals  (bjthe 
collapsing  of  a  cone  or  drum),  and  is  corrected  daily  by  the  help 
of  a  time  signal  from  Greenwich  at  10  A.M.,  which  automatically 
starts  an  auxiliary  seconds'  pendulum,  suspended  freely  just 
behind  the  clock  pendulum.  The  attendant  then  accelerates  or 
retards  his  clock  pendulum,  by  electro-magnetic  action,  so  as  to 
synchronize  it  with  the  free  pendulum,  indicating  Greenwich 
mean  time.  Preliminary  trials  of  the  clook  were  made  at  Green- 
wich last  summer,  and  it  has  been  in  successful  action  since 
December  1,  a  return-signal  to  Greenwich,  sent  automatically 
by  the  Deyonport  clock  at  ih  o™  39s  p.m.,  giving  evidence  of 
the  accuracy  with  which  the  clock  has  been  corrected. 

The  volume  of  Greenwich  Observations  for  1884,  and  the 
separate  copies  of  results,  were  distributed  last  October,  and  the 
printing  of  the  volume  for  1885  is  nearly  complete.  In  an 
appendix  to  the  Greenwich  Observations,  is  given  a  series  of 
diagrams  representing  the  diurnal  change  in  magnitude  and 
direction  of  the  magnetic  horizontal  force  for  each  month  of  the 
years  1841  to  1876,  by  Sir  G.  B.  Airy,  K.C.B.,  late  Astronomer 
Boyal. 

Two  members  of  the  staff  of  this  Observatory,  Mr.  Turner 
and  Mr.  Maunder,  took  part  in  the  expedition  to  Grenada,  West 
Indies,  to  observe  the  total  solar  eclipse  of  1886,  August  29. 


Armagh  Observatory. 

The  micrometrical  observations  of  nebulae  have  been  continued 
with  the  10-inch  refractor,  but  during  the  greater  part  of  the 
year  the  weather  was  very  unfavourable  for  faint  objects.  The 
nebulae  on  the  working  list  are  chiefly  such  as  have  not  yet  been 
observed  with  wire  micrometers.  A  great  deal  of  time  has  been 
spent  in  reducing  to  the  epoch  of  i860  all  the  positions  of  nebula? 
published  during  the  last  ten  years,  with  a  view  to  the  compila- 
tion of  a  new  General  Catalogue  of  nebulae  and  clusters. 

The  Second  Armagh  Catalogue  of  3,300  stars  was  distributed 
in  August  last. 

Cambridge  Observatory. 

The  zone  stars  are  nearly  all  now  observed,  and  the  reductions 
are  steadily  progressing. 

The  total  number  of  observations  of  stars  made  with  the 
Meridian  Circle  during  the  year  is  2,252 ;  of  these  651  were  of 
clock  stars,  70  of  Polaris  above  the  pole,  involving  152  circle 


152 


Report  of  the  Council  to  the 


xlvii.  4, 


readings,  and  the  same  number  below  tbe  pole  with  169  circle 
readings ;  the  remaining  1,461  observations  were  of  zone  stars.  < 

The  Nadir  point  and  level  were  observed  202  times,  the 
line  of  collimation  200  times. 

The  entire  number  of  observations  of  zone  stars,  since  the 
commencement,  now  amounts  to  43,576. 

The  Mean  Bight  Ascensions  at  the  epoch  (1875*0)  are  de- 
termined up  to  July  12,  1877;  the  Mean  Bight  Ascensions 
January  ro  of  each  year  up  to  the  end  of  1881 ;  and  the  True 
Bight  Ascensions  to  September  30,  1886. 

The  North  Polar  Distances  are  reduced  to  the  epoch  up  to 
March  16, 1878  ;  the  Mean  North  Polar  Distances  for  January  ro 
of  each  year  to  the  end  of  188 1 ;  and  the  True  to  November  25, 
1886. 

511  observations  of  standard  stars  made  by  Mr.  Graham  in 
1885  give  +o"*55  for  the  mean  reduction  to  the  standard  Berlin 
places  in  North  Polar  Distance,  without  making  any  allowance 
for  flexure  or  errors  of  division ;  82  observations  by  Miss  Walker, 
nearly  all  taken  by  daylight,  gave  +i"'i8.  The  North  Polar 
Distance  was,  as  in  former  years,  deduced  from  the  observed 
Nadir  point,  and  the  assumed  colatitude  37 °  47'  8"*4. 

60  observations  of  Polaris  above  pole,  corrected  for  flexure 
and  errors  of  division  give,  for  reduction  to  Berlin  N.P.D., 
+  °"*45;  while  59  observations  below  pole,  similarly  corrected, 
give  —  o"  *33 .  These  give  for  the  reduction  of  Cambridge  to  Berlin 
N.P.D.  for  Polaris  +o"'o6,  and  for  correction  of  assumed  co- 
latitude  +  o"*39. 

It  may  be  interesting  to  compare  the  colatitudes  obtained 
from  Polaris  and  observed  Nadir  Point  for  the  last  eight  years. 


1878 

0 
•      37 

47 

8;86 

1879 

898 

I8S0 

8-815 

i88i 

8'755 

1882 

885 

1883    . 

8-825 

18S4 

896 

18S5     . 

37 

879 

Mean 

47 

8854 

Polaris  was  observed  directly  and  by  reflection  on  April  8  j 
the  coefficient  of  correction  for  level  tbence  deduced  is 
&=  —  o8,337,  the  coefficient  obtained  on  the  same  day  by  means 
of  the  collimators  and  the  reflection  of  the  wires  is  &=  —  os"335  ; 
the  unit  in  each  case  being  15"  of  arc. 

On  May  12,  1886,  we  furnished  Dr.  Gustaf  Ericsson,  of  Upsala, 
with  the  places  for  1875*0  of  four  of  our  zone  stars  which  had 


Feb.  1S87.      Sixty-seventh  Annual  General  Meeting.  153 

been  compared  with  the  Comet  1863  III.,  and  on  November  24 
we  likewise  supplied  Mr.  Bidschof  of  Vienna  with  the  places 
for  1875*0  of  nine  of  the  zone  stars  which  had  been  compared 
with  one  or  other  of  the  Comets  1848  I.  and  1849  HI* 

Dunsink  Observatory. 

Daring  the  early  part  of  the  year  the  Meridian  Circle  was 
employed,  along  with  the  chronograph,  for  observing  stars  with 
large  proper  motion,  taken  chiefly  from  the  sources  mentioned 
in  last  year's  Report.  From  the  middle  of  February,  however, 
up  till  September,  the  observation  of  these  stars  was  frequently 
interrupted  for  the  purpose  of  completing  the  list  of  southern 
stars  referred  to  in  former  Reports.  The  work  of  filling  up  the 
gaps  still  remaining  in  this  list  necessarily  occasioned  long 
delays  at  the  telescope,  so  that  the  number  of  observations  this 
year  will  compare  unfavourably  with  that  in  former  years. 

The  latter  months  of  the  year,  from  September  to  December, 
were  almost  entirely  occupied  with  the  work  of  preparing  for 
the  press  the  Sixth  Part  of  the  Dunsink  Observations,  which 
will  contain  the  observations  of  the  southern  stars  which  were 
commenced  by  Dr.  Dreyer  in  18S2.  This  work  is  now  in  the 
hands  of  the  printer,  and  will  shortly  be  published. 

The  number  of  Right  Ascensions  observed  was  506,  and  of 
Declinations  295,  besides  observations  of  standard  stars  for  the 
time  service  to  Dublin. 

In  addition  to  the  usual  observations  of  Right  Ascension  and 
Declination,  a  large  number  of  measures  were  made  in  January, 
February,  and  December  for  determining  the  periodic  errors  of 
the  microscope  screws.  The  corrections  were  found  to  be  of 
the  same  general  character,  but  smaller  than  at  the  last  deter- 
mination. 

For  the  purpose  of  determining  the  difference  of  the  radii  of 
the  pivots  of  the  Meridian  Circle  a  large  number  of  levellings 
have  been  made  in  both  positions  of  the  instrument.  They  show 
that  the  correction  for  this  irregularity  is  small,  but  its  exact 
value  has  not  been  deduced,  as  the  series  of  observations  is  not 
yet  complete. 

The  results  of  the  observations  of  the  occultation  of  Aldebaran 
on  January  16  which  were  made  at  this  Observatory  have  been 
published  in  the  Monthly  Notices  for  February. 

Records  of  the  velocity  and  direction  of  the  wind  have  been 
taken  as  usual  throughout  the  year. 

Uoyal  Observatory,  Edinburgh. 

Through  the  past  twelve  months,  transit  observations  for 
sidereal  time,  and  electrical  exhibitions  of  mean  solar  time 
computed  for  Greenwich,  and  given  to  the  public  by  means  of 

N 


154  Report  of  the  Council  to  the  xlvii.  4, 

time-ball,  time-gnn,  and  controlled  clocks,  have  been  kept  np 
daily. 

The  bi-diurnal  meteorological  observations  at  55  stations 
of  the  Scottish  Meteorological  Society  have  been  computed, 
condensed,  and  described,  partly  every  month  and  wholly  every 
quarter,  for  the  Registrar- General  of  Births,  Deaths,  <&c.,  in 
Scotland,  in  whose  printed  returns  for  months  and  quarters 
they  have  accordingly  appeared. 

During  the  past  autumn  the  printing  of  the  "Edinburgh 
Catalogue,  Discussion,  and  Ephemeiis  of  Stars  "  was  completed, 
published,  and  distributed  in  the  usual  manner  as  one  thick 
volume,  numbered  XV.  of  the  Observatory  series;  and  MSS. 
chiefly  spectroscopic  are  now  being  prepared  for  a  proposed 
volume  XVI. 

A  paper  has  been  also  written  by  the  Astronomer  descrip- 
tive of  his  proposed  new  method  for  finishing  the  Equatorial  of 
the  Edinburgh  Observatory ;  but  it  is  kept  in  abeyance  until  the 
scheme  of  the  Government  Committee  of  1879  shall  have  been 
either  carried  out  or  given  up  by  those  charged  with  its  execu- 
tion. 


The  Kew  Observatory  of  the  Royal  Society,  Richmond. 

The  Sun-spots  were  delineated  and  numbered  after  Sohwabe's 
method,  as  usual,  on  169  days  during  the  past  year. 

Three  hundred  and  nine  observations  of  solar  and  sixty-one 
of  sidereal  transits  have  been  taken,  for  the  purpose  of  keeping 
correct  local  time  at  the  Observatory,  and  the  clocks  and 
chronometers  have  also  been  compared  daily. 

At  the  request  of  General  Walker,  F.R.S.,  certain  experi- 
ments were  made  with  the  view  of  determining  the  stability  of 
the  Experimental  House  as  a  site  for  pendulum  operations.  These 
having  proved  that  building  unsuitable,  a  wooden  erection  of 
convenient  dimensions  has  been  constructed,  at  the  desire  of  the 
Pendulum  Committee  of  the  Royal  Society,  in  the  lower  South 
Hall  of  the  Observatory,  on  the  spot  occupied  in  1873  by  Captain 
Heaviside,  R.E.,  when  experimenting  with  the  Russian  pendulum. 

In  this  room  the  Indian  Pendulum  Apparatus,  recently 
returned  by  Professor  Pierce  from  the  United  States,  has  been 
erected,  in  order  to  repeat  the  observations  made  by  Colonel 
Herschel,  R.E.,  in  1881,  Captain  Heaviside  in  1873,  and  Captain 
Basevi  in  1865.  Eventually,  it  is  intended  to  convey  the  whole 
to  Greenwich,  and  at  the  Royal  Observatory  another  series  of 
observations  and  experiments  will  be  conducted. 

The  usual  magnetical  and  meteorological  observations  and  re- 
ductions, and  also  the  verification  of  instruments,  operations  to 
which  the  attention  of  the  Observatory  is  mainly  directed,  have 
been  carried  on  as  formerly. 


Feb.  1887.      Sixty-seventh  Annual  General  Meeting.  155 


Liverpool  Observatory,  Bidston,  Birkenhead. 

Careful  attention  has  been  given  to  transit  observations  of 
stars  for  the  determination  of  clock  errors.  The  two  sidereal 
clocks  have  been  compared  daily  with  the  normal  mean-time 
clocks,  and  duplicate  comparisons  of  all  the  chronometers  with 
the  latter  have  been  made  daily  as  heretofore.  Greenwich 
mean  time  has  been  communicated  to  the  Port  daily,  Sundays 
excepted,  by  means  of  the  time-gun  placed  on  the  Morpeth 
Dock  Pier-Head.  No  instance  in  which  the  gun  has  failed  to 
fire  has  occurred  during  the  past  year,  and  the  flash  has  in  each 
case  accurately  indicated  1  p.m.  as  shown  by  the  normal  clock 
in  the  chronometer  room.  Two  hundred  and  twenty-seven 
chronometers  have  been  tested  during  the  past  year.  When  the 
test  certificate  shows  the  performance  to  be  unsatisfactory,  it  is 
the  general  practice  for  the  maker  to  examine  and  adjust  the 
instrument,  and  return  it  to  the  Observatory  to  be  re-tested. 
An  important  service  is  thus  rendered  to  shipowners  and  ship- 
masters by  preventing  defective  and  imperfectly-adjusted 
chronometers  being  taken  to  sea.  The  records  received  during 
the  past  year  of  the  performance  at  sea  of  the  Pacific  Steam 
Navigation  Company's  chronometers  show  that,  using  the  rates 
corrected  for  temperature  supplied  from  this  Observatory,  the 
average  error  of  longitude  by  chronometer  for  an  average  voyage 
of  1 01  days  was  about  four  miles. 

No  alteration  has  been  made  in  the  meteorological  work. 
No  interruption  has  occurred  in  the  records  of  the  self- 
registering  instruments  and  the  daily,  weekly,  fortnightly,  and 
monthly  Reports  have  been  furnished  as  in  previous  years. 


Badcliffe  Observatory,  Oxford. 

The  following  have  been  the  subjects  of  observation  during 
the  year  1886 : — 

With  the  Transit  Circle  :— 

1.  Observations  of  stars  to  the  seventh  magnitude  inclusive 
between  1150  N.P.D.  and  the  Equator. 

2.  Observations  of  the  Moon,  which  are  continued  throughout 
the  lunation,  and  regularly  compared  with  the  Bight  Ascensions 
and  North  Polar  Distances  of  Hansen's  Lunar  Tables.  Sueh 
comparisons  have  been  generally  discontinued  at  other  Observa- 
tories; and  these  results,  therefore,  appear  to  have  a  special 
value  in  keeping  distinctly  before  astronomers  the  extraordinary 

N  2 


156  Report  of  the  Council  to  the  xlyii.  4, 

character  of  the  change  between  the  results  of  observation  and 
theory  which  took  place  about  the  year  1864.  The  mean  error 
in  longitude  of  Hansen's  Tables  has  changed  from  —  i//#6i  in  the 
year  1863*5  *°  +  I5"*34  *n  *ne  vear  i886'5,  being  at  the  average 
rate  of  o""74  per  annum. 

3.  Observations  of  the  Sun. 

4.  Reflexion  observations  of  stars. 

The  following  table  gives  the  number  of  observations  made 
during  the  year  1886  : — 

Transits,  2,812. 

Circle  observations,  2,663. 

These  totals  include — 


Observations  of  the  Moon  on  49  days. 

Observations  of  the  Sun  on  76  days. 

23  Reflexion  observations  of  stars. 

365  Determinations  of  Nadir  point. 

2  Durations  of  passage  of  the  Moon's  diameter. 

2  Vertical  diameters  of  the  Moon. 

With  the  extra-meridional  instruments  : — 

13  observations  of  9  occultations  of  stars  by  the  Moon. 

The  volume  for  1883  has  been  printed  and  distributed. 

The  volume  for  1884  is  being  prepared  for  press. 

The  observations  made  in  1885  and  1886  are  completely 
reduced. 

A  well-mounted  Equatorial  by  Cooke  with  an  exquisite  object- 
glass  of  ten  inches  aperture  has  been  presented  to  the  Observatory 
by  J.  Gurney  Barclay,  Esq.  The  building  for  the  reception  of 
the  instrument  has  been  prepared  from  designs  kindly  furnished 
by  Mr.  Common,  but  the  continuance  of  the  late  severe  frost  has 
delayed  the  arrival  and  mounting  of  the  instrument. 


Oxford  University  Observatory. 

The  work  of  this  Observatory  has  been  necessarily  confined, 
during  the  past  year  to  a  research  as  to  whether  the  new  process 
of  Astronomical  Photography  is  or  is  not  practically  applicable 
to  the  most  delicate  of  astronomical  investigations,  such,  for 
instance,  as  the  determination  of  Stellar  Parallax.  The  reply  is 
unmistakably  in  the  affirmative,  inasmuch  as  the  Parallax  of 
6 11  and  612  Gygni  has  been  obtained  in  reference  to  no  less 
than  four  comparison  stars,  with  singularly  accordant  results. 
The  preliminary  particulars  have  been  communicated  to  the 
Royal  Society  and  the  Royal  Astronomical  Society. 


Feb.  1887.      Sixty-seventh  Annual  Qeneral  Meeting.  157 

The  attention  of  the  Observatory  staff  has  also  been  directed 
to  the  mounting,  renovation,  and  electric  lighting  of  the  excel- 
lent Transit  Circle  presented  to  the  Observatory  by  Mr.  J.  G. 
Barclay. 


Temple  Observatory,  Rugby. 

This  Observatory  has  been  opened  on  seventy-six  evenings 
during  the  year,  on  most  of  which  there  has  been  the  usual 
attendance  of  members  of  the  School,  when  the  usual  instruction 
has  been  given. 

Mr.  Seabroke  has  given  the  whole  of  bis  spare  time  to  the 
measurement  of  the  motion  of  stars  in  the  line  of  sight  with  the 
spectroscope  on  the  Reflector,  and  100  sets  of  measures  have 

been  made. 

The  results  of  the  last  few  years  have  been  reduced  and 
lately  brought  before  the  notice  of  the  Society. 

Mr.  Percy  Smith  has  continued  the  work  of  measuring  the 
position  and  distance  of  double  stars,  and  has  been  doing  clerical 
work  in  connection  therewith.  He  has  also  arranged  all  our  star 
forms  for  future  re-observation. 


SionyhuM  College  Observatory. 

The  solar  work  continues  to  receive  the  same  attention  as  in  ' 
previous  years.     The  Sun  was  observed  on  235  days,  and  224 
drawings  were  made  of  the  whole  disk,  including  spots  and 
faculsB. 

Whenever  the  definition  was  particularly  good  the  general 
surface  of  the  Sun  has  been  studied  in  conjunction  with  Janssen's 
excellent  photographs,  and  continual  change  is  seen  everywhere. 

The  measures  of  the  chromosphere  and  prominences  have 
been  more  successful  than  in  any  other  years,  101  complete  ' 
observations  and  two  partial  ones  being  recorded. 

The  spectra  of  San-spots  were  examined  on  21  days,  and' 
on  six  of  these  occasions  spot  bands  were  visible.     The  lines-2 
most  widened  this  year  were  generally  the  ordinary  solar  lines,- 
which  was  far  from  being  the  case  during  the  maximum  period. 

A  new  class  of  solar  observations  has  been  added  to  the 
routine  work  this  year,  the  direction  of  the  flames  of  the 
chromosphere  being  noted  with  a  wide  tangential  slit.  As 
these  observations  require  a  very  perfect  sky,  and  are  only  made 
when  the  others  are  completed,  they  are  entered  only  on  21  days. 

Positions  of  the  comets  of  Fabry,  Brooks,  Barnard,   and 


158  Report  of  the  Council  to  the  xlyii.  4, 

Finlay  have  been  determined,  and  the  usual  watch  kept  for  the 
phenomena  of  Jupiter's  satellites  and  for  lunar  occupations. 

In  preparation  for  the  total  solar  eclipse  of  August  29,  a 
5^-inch  object-glass  by  Alvan  Clark  and  a  powerful  direct- 
vision  spectroscope  by  Hilger  were  purchased  by  the  college 
authorities. 


Mr.  Common's  Observatory,  Ealing. 

The  last  year  has  been  entirely  devoted  to  the  construction 
of  the  5-foot  reflector.  The  machine  for  grinding  was  com. 
pleted  in  September,  and  great  progress  has  been  made  with  the 
mirror.  Photography  has  been  used  to  obtain  permanent  records 
of  the  state  of  the  surface  by  using  the  reflected  light  from  a 
pinhole  (illuminated  by  a  lamp),  as  in  the  system  of  testing  used 
by  Foucault.  It  is  found  that  so  small  a  quantity  of  light  as 
can  come  through  a  hole  '004  inch  placed  at  the  centre  of  curva- 
ture can  be  photographed  in  a  few  seconds  after  reflection  from 
the  surface. 

A  series  of  photographs  have  been  taken  from  the  first  rough 
polish  to  the  present  state,  and  will  be  continued. 

The  kind  of  mounting  has  been  determined  upon,  and  the 
heavy  work  put  in  hand.  It  is  hoped  that  the  whole  may  now 
be  completed  without  further  delay. 

The  telescope  is  to  be  devoted  to  photography,  and  the  mounting 
has  been  designed  to  give  the  greatest  amount  of  steadiness  and 
perfection  of  movement. 


The  Earl  of  Crawford's  Observatory,  Dunecht. 


Early  in  the  year  Dr.  L.  Becker  concluded  the  determination 
of  the  latitude  by  prime  vertical  observations  begun  in  1885. 
This  involved  an  exact  examination  of  the  pivots  with  the  level, 
which  proved  particularly  interesting,  as  it  could  be  made  in 
both  the  pairs  of  Y's  with  which  the  instrument  is  provided. 
The  maximum  error  is  o"*66,  corresponding  to  0*00006  inch. ; 
but  only  a  small  fraction  of  this  affects  the  telescope  when  near 
the  zenith.  The  general  figure  of  the  axis  comes  out  the  same 
when  rotated  in  the  meridional  bearings,  as  in  those  for  the  prime 
vertical.     The  observations  are  all  reduced. 

In  the  moonless  nights  of  the  autumn  Dr.  Becker  turned  the 
large  aperture  of  the  Transit  Circle  to  account  by  observing' 
nebulae;  in  this  way  ninety-six  places  have  been  secured  in 
•  seventeen  nights.  The  bright  nights  were  devoted  to  comparison 
stars  and  to  a  complete  re-determination  of  the  positions  of  the 


Feb.  1887.      Sixty-seventh  Annual  General  Meeting.  159 

Durchmusterung  stars  within  i°  of  the  pole.  This  latter  work  is 
carried  on  with  bright-field  illumination.  Observing  was  com- 
menced on  eighty-three  nights,  bat  on  only  forty-five  of  these  did 
the  clouds  permit  of  fairly  continuous  work. 

Daring  the  past  year  the  15 -inch  Equatorial  has  been  used 
almost  solely  for  spectroscopic  observations.  A  few  measures  of 
double  stars  or  of  faint  stars  in  the  Great  Nebula  in  Andromeda, 
or  near  Mr.  Gore's  variable  star  in  Orion,  were  taken  when  the 
spectroscope  was  dismounted. 

The  large  star  spectroscope  mentioned  in  former  Reports  was 
punctually  finished  by  Messrs.  T.  Cooke  and  Sons  in  March.  It 
works  well  in  all  respects.  The  single  flint  prism  of  6o°  supplied 
with  the  instrument  defines  so  well,  that,  with  a  dispersion  of 
only  50  7'  from  A  to  H,  it  separates  the  pair  of  lines  488*8inimm 
and  488*84mmm,  and  shows  forty-three  lines  between  B  and  C. 
All  three  lines  in  the  ring  nebula  in  Lyra  can  be  measured  with- 
out difficulty.  A  prism  of  200  refracting  angle,  by  Merz,  promises 
to  be  very  useful  for  faint  stars,  while  a  large  compound  prism 
by  Mr.  Grubb  gives  about  as  much  dispersion  as  even  the 
brighter  stars  will  satisfactorily  bear. 

The  solar  spectrum  was  measured  on  twenty-one  days  to 
obtain  data  for  reducing  observations  of  other  spectra.  A  very 
pliable  formula  with  three  coefficients  devised  by  Dr.  Becker 
represents  the  minimum  deviations  from  A  to  H  for  the  6o°  prism 
to  within  about  20",  leaving  outstanding  errors  that  can  be  dealt 
with  graphically. 

Owing  to  its  unfavourable  position  Brooks'  first  comet  was 
only  observed  once  with  the  large  spectroscope,  but  both  it  and 
Fabry's  comet  were  observed  three  times  with  a  smaller  instru- 
ment. Barnard's  October  comet  was  examined  on  eight  occa- 
sions with  the  new  spectroscope,  and  was  photographed  on  the 
16th,  17th,  and  26th  December  with  a  4-inoh  lens.  The  two 
earlier  photographs  show  the  lateral  tail. 

Twenty-three  circulars  were  issued  in  the  year,  all  dealing 
with  comets,  with  the  addition  of  two  notes  on  Jupiter* s  fourth 
satellite.  Observers  are  again  largely  indebted  to  Dr.  H.  Op- 
penheim  for  elements  and  ephemerides  of  comets. 

Comet  Brooks  (2)  of  1885  could  not  be  found  on  March  9 
and  11  by  Dr.  Becker,  although  the  ephemeris  afforded  some 
hope  that  it  might  be  visible. 

The  weekly  time-gun  and  the  meteorological  observations 
have  been  continued  as  usual. 

The  maximum  and  minimum  thermometers  were  stolen  on 
August  2. 


160  Report  of  the  Council  to  the  xlvii.  4, 


Mr.  Edward  Crossley's  Observatory,  Bermerside,  Halifax. 

The  observations  made  in  1886  were  similar  to  those  in  pre- 
vious years.  Of  the  satellite  phenomena  of  Saturn  thirteen 
observations  were  obtained,  and  ten  of  those  of  Jupiter.  Some 
180  measures  with  the  wedge  photometer  were  made,  and  forty 
stars  observed  with  the  Transit  Circle  for  time.  The  3-ft.  Re- 
flector has  taken  np  a  good  deal  of  time.  The  dome  for  this 
instrument  is  now  complete :  it  can  be  moved  round  once  in 
five  minutes  or  once  in  twenty-four  hours  by  a  water-engine 
with  two  speeds.  The  observing  platform  and  gallery  are 
suspended  from  the  dome,  and  therefore  the  observer  movea 
with  the  dome.  The  opening  is  6  feet  wide  from  top  to  bottom, 
and  extends  from  the  horizon  to  3  feet  beyond  the  zenith.  The 
shutter  is  in  two  pieces,  which  move  horizontally ;  and  one 
handle  opens  and  closes  both  in  about  one  minute.  The  Reflector 
is  now  in  good  working  order,  and  the  clock  drives  well.  The 
mirror  will  soon  need  re-silvering,  as  it  has  been  much  exposed 
to  damp,  Ac.,  during  the  erection  of  the  Observatory. 


Mr.  0.  E.  Peek's  Observatory,  Lyme  Regis. 

The  equatorial  (of  6^  inches  aperture)  has  been  employed 
in  the  systematic  observation  of  variable  stars  from  a  selected 
list :  146  nights  were  suitable  for  observation.  Transit  obser- 
vations for  time  have  been  taken  on  all  available  nights.  Tbe 
most  cloudy  month  was  February ;  the  clearest',  December. 


The  Earl  of  Rosse's  Observatory,  Birr  Castle. 

During  the  year  1886  some  experiments  have  been  carried 
on  at  intervals  with  a  view  of  increasing  the  accuracy  of  the 
apparatus  for  measuring  Lunar  Radiant  Heat,  but  they  are  still 
only  in  progress. 

Some  photographs  of  the  Moon  were  taken  towards  the  close 
of  the  year.  Several  are  of  average  good  quality,  and  show  in 
every  case,  and  especially  with  the  longer  exposures,  a  decided 
advantage  from  the  electric  control  of  the  driving  clock,  which 
had  not  been  applied  at  the  time  when  the  last  photographs 
were  taken.  In  attempts  to  photograph  the  Great  Nebula  in 
Orion,  however,  the  tilting  of  the  speculum  upon  its  supports* 


Feb.  1 887.      Sixty-seventh  Annual  General  Meeting.  161 

during  the  prolonged  exposure  still  causes  serious  difficulty. 
No  band-correction  has  been  as  yet  resorted  to. 

About  eighty  sketches  of  the  planet  Jupiter,  which  have 
accumulated  since  the  last  series  was  published,  are  awaiting 
publication  when  some  decision  as  to  the  best  mode  of  repro- 
ducing them  shall  have  been  arrived  at. 

Dr.  Boeddicker  has,  during  a  considerable  number  of  nights, 
been  engaged  upon  an  eye-sketch  of  all  the  Milky  Way,  so  far 
as  it  can  be  satisfactorily  reached  in  this  latitude,  and  he  hopes 
to  represent  it  in  more  minute  detail  than  has  hitherto  been 
done. 

Meteorological  observations  have  been  carried  on  as  usual* 


Colonel  Tomline's  Observatory. 

The  work  at  this  Observatory  has  suffered  some  interruption 
owing  to  the  illness  of  the  observer,  but  it  is  now  again  fully 
resumed.  The  observation  of  comets  continues,  as  for  some 
years  past,  to  be  the  principal  work  to  which  the  instrumental 
means  are  devoted,  as  it  also  appears  to  be  that  for  which  they 
are  best  fitted.  Progress  has  been  made  in  the  reduction  of 
previous  observations,  and  two  communications  containing 
results  of  observations  have  been  made  to  the  Astronomische 
Nachrichten  within  the  past  year.  They  will  be  found  in 
Nos.  2,723  and  2,754,  and  comprise  observations  of  Comets 
1884  III.  Wolf,  1885  I.  Encke's,  1885  II.  Barnard,  1886  I. 
Fabry,  1886  II.  Barnard,  and  1886  V.  Brooks  I.  At  the  time 
of  the  latter  publication  the  whole  of  the  cometary  work  at  this 
Observatory  had  been  reduced  and  published.  Subsequently 
satisfactory  series  of  observations  have  been  made  of  comets 
Barnard-Hartwig  and  Finlay :  the  former  having  been  observed 
on  twenty  and  the  latter  on  fifteen  occasions,  while  both  series 
are  at  the  end  of  the  year  still  incomplete.  Efforts  will  be  made 
to  publish  these  at  an  early  date,  and  thus  avoid  the  accumu- 
lation of  arrears  in  future. 


Lieutenant*  Colonel  Tupman's  Observatory  y  Harrow. 

The  Meridian  Circle  has  been  employed  in  the  determination  of 
the  places  of  comparison  stars  and  stars  which  have  been  occulted 
by  the  Moon.  Five  hundred  and  fifty  observations  of  both  elements 
have  been  obtained,  about  one-third  of  which  are  of  funda- 
mental stars.  The  errors  of  division  of  the  circle  have  not  been 
investigated ;  and  the  Nadir  observation  being  generally  difficult, 
owing  to  the  vibrations  of  the  soil,  the  Declinations  of  stars  are 
determined  by  comparing  them  with  the  fundamental  stars,  on 


1 62  Report  of  the  Council  to  the  xlvii.  4, 

the  same  principle  as  is  customary  for  Bight  Ascensions.  All 
the  star  observations  are  reduced  to  the  mean  places  for  the 
beginning  of  the  year5.  Seventeen  observations  were  made  of 
the  B.A.  of  the  Moon's  bright  limb,  and  two  of  the  horizontal 
diameter. 

With  the  Equatoreals  twenty-one  occnltations  have  been 
observed.  The  final  equations  in  the  Greenwich  form  have  been 
computed  for  forty-seven  occupations,  observed  between  1884, 
October  4,  and  1887,  February  10. 

Comet  1886  I.  (Fabry)  was  observed  for  place  altogether  on 
nineteen  nights  between  1885,  December  7,  and  1886,  April  1 ; 
Comet  1886  II.  (Barnard),  on  fourteen  nights  between 
1885, December  27,  and  1886,  April  15  ;  Comet  1886  V.  (Brooks  L) 
on  four  nights  between  May  6  and  May  20.  These  observations 
are  completely  reduced,  and  all  the  comparison  of  stars  have  been 
observed  on  the  Meridian  two  or  three  times.  Comet  Barnard- 
Hartwig,  at  present  visible,  has  been  observed  for  place  on 
seven  nights  between  December  19  and  January  5. 

The  18-inch  Reflector  has  been  fitted  with  a  new  decli- 
nation-axis, and  is  now  sufficiently  rigid;  but  the  driving 
movement  is  very  irregular. 

An  instrument  by  Kahler,  of  Washington,  D.C.,  for  deter, 
mining  absolute  personal  equations  in  observing  transits,  has 
been  brought  into  use  with  the  Morse  chronograph.  • 


Mr.  WigglesworOC  8  Observatory,  Scarborough. 

The  building  of  the  observatory  was  commenced  in  the 
summer  of  1884,  and  by  the  end  of  the  year  the  dome  was  ready 
for  the  reception  of  the  instrument.  The  dome  is  30  feet  in 
diameter,  hemispherical  in  shape,  and  covered  with  very  strong 
papier-mache,  £  inch  in  thickness,  which  is  ri  vetted  with  copper 
rivets  to  the  framework  of  T-iron.  The  shutter  is  of  a  con- 
struction  originally  introduced  by  Messrs.  T.  Cooked; Sons.  It  has 
the  form  of  a  semicircle  striding  over  the  dome.  The  tail  end 
terminates  as  a  pivot,  while  the  other  end,  which  is  the  base  of 
the  real  shutter,  rests  on  a  rail.  The  shutter  therefore  turns 
round  the  pivot  in  a  circle  of  more  than  30  feet  radius.  It  moves 
with  great  ease,  and  practically  without  noise.  On  the  top  of 
the  dome  is  another  rail,  to  steady  the  shutter  in  case  of  a  strong 
wind.  The  slit  has  a  width  of  5  feet  10  inches  at  the  bottom, 
and  of  fully  3  feet  at  the  top.  The  dome  is  supported  by  a  brick 
wall  13  feet  in  height  from  the  floor  to  the  top  of  the  flat  rail  on 
which  the  wheels  of  the  dome  are  running.  The  dome  is  turned 
by  a  cogwheel  running  in  a  rack-circle,  and  is  moved  with  great 
ease.  The  rigidity  of  the  dome  is  very  great ;  it  has  never  been 
noticed  to  shake,  even  when  the  wind  was  very  strong. 

The  telescope,  which  was  also  constructed  by  Messrs.  T.  Cooke 


Feb.  1 88  7.     Sixty -seventh  Annual  General  Meeting.  163 

&  Sons,  was  set  up  in  the  dome  in  February  1S85.  The  object- 
glass,  which  is  a  very  fine  one,  has  a  clear  aperture  of  15*5  inches, 
and  a  focal  length  of  231*5  inches.  The  mounting  is  executed  in 
Cooke's  well-known  style.  Both  the  polar  axis  and  the  declina- 
tion axis  are  of  steel.  There  are  no  friction  wheels  to  the  latter, 
but  the  instrument  turns  with  great  ease  in  declination.  The 
hour  circle  reads  to  2  seconds  of  time,  and  the  declination  circle 
to  10  seconds  of  arc.  The  latter  is  read  from  the  eye  end  of  the 
instrument.  The  clamps  and  slow  motions  in  right  ascension 
and  declination  are  worked  from  the  eye  end.  The  driving- 
clock  is  of  the  same  construction  as  that  at  Dunecht,  bat  with- 
out the  electric  control.  There  are  two  finders  of  2*5  inches 
aperture.  In  front  of  the  object-glass  is  an  iris-diaphragm,  by 
which  the  aperture  may  be  reduced  down  to  4  inches.  It  is 
worked  by  a  rod  from  the  eye  end,  and  the  aperture  is  read  off 
on  a  dial.  It  has  been  found  very  convenient  on  many  occa- 
sions; the  full  aperture,  however,  gives  as  a  rale  the  best 
definition. 

The  mean-time  clock  is  believed  to  be  a  unique  specimen.  It 
was  invented  and  made  at  the  beginning  of  this  century  by 
George  Prior,  who  was  a  watchmaker  in  Leeds,  and  who  received 
a  medal  of  the  Society  of  Arts  for  the  escapement  in  this  clock. 
For  a  long  time  it  was  the  standard  clock  of  Leeds ;  after  the 
death  of  George  Prior,  however,  it  came  into  the  possession  of 
Mr.  Wigglesworth.  The  impulse  received  by  the  pendulum  is 
independent  of  the  train  of  the  clock ;  it  is  given  every  alternate 
second  by  a  spring,  which  is  then  pushed  back  to  its  starting- 
point  by  a  tooth  of  the  escapement  wheel.  There  is  a  great 
difference  between  the  two  drops  of  the  escapement  wheel ;  the 
one  is  nearly  three  times  as  large  as  the  other,  and  on  this 
difference  depends  the  impulse  given  by  the  spring  to  the  pen- 
dulum. At  the  long  drop  the  spring  is  pushed  back ;  at  the 
short  drop  it  is  released,  and  gives  impulse  to  "the  pendulum 
until  it  is  arrested  by  the  next  tooth  of  the  escapement  wheel. 
The  length  of  the  drop  is  best  seen  by  the  motion  of  the  seconds 
hand,  which  shows  alternately  long  and  short  seconds ;  the  beat, 
however,  is  perfectly  even — one  second  is  as  long  as  the  other. 
The  locking  is  effected  by  jewelled  detent  springs,  which  are 
independent  of  each  other.  Steel  and  zinc  bars  form  the  com- 
pensation of  the  pendulum,  and  by  the  addition  of  a  very  small 
mechanism  they  have  also  been  made  to  act  as  a  metallic 
thermometer.  The  clock  keeps  very  good  time,  and  has  a  clear, 
sharp  beat. 

There  are  two  spectroscopes  by  Browning,  a  reversion  spec- 
troscope for  observing  the  Sun,  and  a  McClean  star  spectro- 
scope. 

A  micrometer  by  Mens  was  kindly  lent  by  Lord  Crawford  in 
'July  1&85.  It  has  only  one  micrometer  screw,  but  a  fine  move- 
ment can  be  given  to  the  whole  micrometer  by  two  screws  in 


164  Report  of  the  Council  to  the  xlyii.  4, 

the  adapter,  which  is  a  more  convenient  arrangement  than  to 
have  two  micrometer  screws. 

Regular  observations  were  commenced  in  September  1885. 

The  value  of  the  micrometer  screw  was  determined  from 
numerous  transits  of  Polaris. 

The  new  star  in  Andromeda  was  observed  on  fourteen  nights, 
and  the  results  have  been  published  in  the  Monthly  Notices. 

Nova  Cygni  was  examined  on  several  occasions. 

Gore's  new  star  was  examined  with  the  spectroscope  and 
measured  from  neighbouring  stars  on  two  occasions. 

The  dimensions  of  Saturn  were  also  measured  with  the 
micrometer. 

Comet  1885  a  Barnard  was  observed  for  place  on  two 
nights. 

Comets  1885  &  Fabry,  and  1885  e  Barnard,  were  each  ob- 
served on  five  nights. 

In  1886  the  observations  were  of  a  similar  kind. 

The  dimensions  of  Saturn  were  measured  on  one  occasion. 

The  nebula  in  Andromeda  was  examined  on  several  occasions, 
but  no  changes  could  be  detected  in  it.  The  same  was  the  case 
with  Nova  Cygni. 

Gore's  new  star  was  measured  on  three  nights. 

Comet  1885  e  Barnard  was  observed  once  in  this  year. 

Comet  1886 /Barnard-Hart wig  was  observed  on  twenty-one 
nights,  and  some  sketches  of  it  were  also  made. 

Comet  Finlav  was  observed  twice. 

The  minor  planet  Sappho  has  been  observed  six  times  at  the 
request  of  Mr.  R.  Bryant. 

A  want  of  star  places  has  often  made  a  delay  in  the  reduc- 
tions inevitable. 

The  adopted  co-ordinates  of  the  observatory  have  been 
taken  from  the  6-inch  survey  map,  and  are — 

Longitude  of  Observatory  =  im  388,o,  west  of  Greenwich. 

Latitude  „  =  +  54°  16'  30". 

The  height  above  the  level  of  the  sea  is  about  150  feet. 


Royal  Observatory,  Cape  of  Good  Hope. 

The  present  report  includes  the  period  January  1  to  Decem- 
ber 31,  1886. 

Observations  with  the  transit-circle  have  been  continued 
regularly  throughout  the  year,  the  objects  of  observation  being 
the  Sun,  Mercury  and  Venus,  the  stars  on  the  list  of  the  Cape 
Ten  Year  Catalogue  for  1890,  comet  comparison  stars,  stars 
occulted  by  the  Moon,  stars  employed  in  determining  latitudes 
in  connection  with  the  Geodetic  Survey,  and  stars  employed  in 


Feb.  1887.      Sixty-seventh  Annual  General  Meeting.  165 

zones  for  determining  the  scale-value  of  the  heliometer.     The 
work  accomplished  has  been : — 


Number  of  determinations  of  collimation 

„  le?el 

Nadir  Point 


53 
510 

463 

455 

47 

439 


„  „  runs 

„  „  horizontal  flexure 

Observations  of  meridian  mark  (from  April  5) 

Direct.  Reflex. 

Number  of  observations  of  stars  in  R.A.        .    5333  634 

N.P.D.     .    4531  634 

Observations  of  both  limbs  of  the  Sun  in  both 

elements 191 

Observations  of  Mercury  in  both  elements       .       109 

„  Venus        „  „  •      142 

The  errors  of  all  the  new  steel  screws  of  the  circle  micro* 
scopes  have  been  very  thoroughly  determined  ;  and  they  prove, 
though  small,  to  be  appreciable. 

Since  April  5  regular  observations  have  been  made  on  a 
meridian  mark,  placed  in  the  focus  of  a  lens  of  about  200  feet 
focal  length,  situate  to  the  south  of  the  transit- circle.  This 
mark  is  observed)  at  .the  .beginning  and  end  of  each  series  of 
observations,  and  it  appears  that  the  transit- circle  has  a  very 
small  diurnal  motion  in  azimuth,  over  which  observations  of  the 
mark  afford'  an  efficient  control.  During  the  winter*  period, 
April  1  to  September  30,  observations  were  regularly  made  on 
every  available  morning  before  sunrise  as  well  as  in  the  evening; 
thus  a  large  number  of  double  transits  of  ciroumpolars  have 
been  secured. 

A  great  deal  of  time  and  care  have  been  devoted  to  the 
Great  Indian  Theodolite,  the  study  of  its  constants,  and  the 
development  of  the  best  plan  of  working.  The  errors  of  division 
of  the  horizontal  circle  have  been  thoroughly  investigated — a 
work  of  great  labour,  requiring  special  adaptations  in  conse- 
quence of  the  peculiar  form  of  the  instrument,  and  of  which  an 
account  will  be  communicated  to  the  Society.  The  best  arrange- 
ment of  the  azimuth  marks  has  been  a  matter  of  considerable 
experiment.  When  the  space  between  the  marks  and  the  long 
focus  lenses  is  left  open  the  images  of  the  marks  are  generally 
ill-defined,  because  of  ascending  currents  of  air  from  the  soil 
which  has  been  heated  by  a  strong  sun  during  the  day.  The 
experiment  was  tried  of  enclosing  the  space  between  one  long 
focus  lens  and  the  corresponding  mark  by  means  of  a  wooden 
tube  or  tunnel  1  foot  square.  The  effect  was  to  produce  a 
great  apparent  improvement  in  the  steadiness  and  sharpness  of 
definition  of  the  mark ;  but,  unfortunately,  measurements  showed 


1 66  Report  of  the  Council  to  the  xlvh.  4, 

that  this  improvement  was  accompanied  with  a  slow  oscillation 
of  the  mark,  which  seemed  far  more  likely  to  produce  systematic 
error  than  the  rapid  irregular  vibrations  of  the  marks  before 
the  tube  was  used.  It  is  possible  that  by  protecting  the  tube 
from  direct  rays  of  the  Snn,  by  means  of  a  long  narrow  shed, 
with  sides  as  well  as  roo£  this  slow  movement  of  the  mark 
might  be  reduced  or  eliminated;  but  the  experiment  was  not 
carried  out  because  of  its  considerable  cost  and  its  problematical 
success.  Accordingly,  after  much  experiment,  the  wooden  tube 
was  removed,  and  the  observations  were  resumed  with  open-air 
space  between  the  lenses  and  the  marks.  The  stability  of  the 
relative  azimuth  of  the  marks  continues  to  be  very  satisfactory. 
The  illumination  of  the  theodolite  by  small  incandescent  lamps 
and  storage  batteries  has  proved  most  successful,  and  the  system, 
has  been  extended  to  the  azimuth  marks  and  the  zenith  tele- 
scope with  the  most  satisfactory  results.  Indeed,  any  one  who 
has  once  employed  electric  incandescent  lamps  for  illumination 
of  his  instruments,,  especially  in  a  windy  neighbourhood,  will 
never  willingly  return  to  the  flicker,  heat,  and  general  inconve- 
nience of  oil  lamps.  A  proposal  has  been  made,  and  partly 
carried  out,  for  extending  electric  illumination  to  all  the  instru- 
ments of  the  Observatory. 

Tho  following  observations  have  been  made  with  the  Great 
Theodolite : — 

Observations  of  meridian  marks      .        ....    73 
Azimuths  at  greatest  elongation       .        .        .        •  229 

„        of  N.  Stars  for  latitude  by  Kapteyn's  method  •    32  pairs. 

With  the  zenith  telescope  an  investigation  has  been  made  of 
the  value  and  temperature-coefficients  of  the  screw  by  observa- 
tions in  summer  and  winter,  and  104  pairs  of  stars  have  been 
observed  for  difference  of  meridian  zenith  distance. 

The  general  rule  has  been  adhered  to  of  observing  all  comets 
visible  south  of  the  Equator,  or  which  otherwise  cannot  be  con- 
veniently observed  in  the  Northern  Hemisphere.  The  fulfilment 
of  this  programme  has  led  to  a  considerable  amount  of  work  in 
the  past  year. 

Winnecke's  Comet,  which  was  only  seen  during  fourteen 
days  in  1875,  and  not  at  all  at  the  opposition  of  188 1,  was  swept 
for  and  found  by  Mr.  Finlay  on  August  19,  $\°  from  the  pre- 
dicted place  of  Dr.  Lamp's  Ephemeris  (Asbron.  Nach.  2,720,  2,731), 
corresponding  to  a  time  of  perihelion  passage  twelve  days  earlier 
than  predicted. 

On  Sunday,  September  26,  Mr.  Finlay  discovered  another 
periodic  comet,  which,  if  identical  with  the  comet  of  De  Vico, 
has  not  been  observed  since  the  year  of  its  discovery  in  1844. 

The  following  is  a  list  of  the  observations  of  comets  made 
during  the  year : — 


Feb.  1887.      Sixty-seventh  Annual  General  Meeting.  167 

Fabry  was  observed  on  31  nights  between  May    1  and  July  30. 
$  Barnard  „  18      „  „        May  29    „    July  26. 

tf  Brooks  L  „  13      „  „        July    5    „    July  30. 

jf  Winnecke  „  32      ,.  „       Aug.  19    „    Not.  29. 

<#  Knlay  „  34      „  „       Sept.  26    „    Dec.  28. 

A  paper  containing  the  results  of  these  observations  -will  be 
communicated  to  the  Society  at  the  March  meeting. 

Occupations  of  thirty-two  stars  and  three  planets  by  the  Moon 
have  been  observed  during  the  year. 

The  result  of  observations  of  stars  with  the  transit-circle 
for  1882,  83,  84,  and  till  1885,  February  7,  are  reduced,  and  will 
be  passed  through  press  by  H.M.  Astronomer  when  in  England. 
The  Catalogue  for  1885,  from  the  meridian  observations  1879-85, 
is  in  progress. 

Aided  by  the  vote  of  300Z.  from  the  Government  Grant  Fund 
of  the  Royal  Society,  the  services  of  Mr.  C.  Bay  Woods  have 
been  continued  as  photographic  assistant. 

The  extension  of  the  Photographic  Durchmusterung  has  been 
pushed  forward  as  rapidly  as  possible.  Pictures  for  the  whole 
sky  from  declination  —  570  to  —  900  have  now  been  obtained  in 
duplicate,  and  considerable  progress  has  been  made  in  further 
zones  towards  the  Equator.  The  following  amount  of  work  has 
been  secured  during  the  year : — 

Perfectly  successful  Durchmusterung  plates,  exposed  one  hour 
in  clear  sky  • 263 

Plates  for  special  purposes       .......      37 

Plates  exposed  for  more  than  an  hour,  snch  as  comets,  star 
clusters,  &c.         .        . 11 

Failures  •        *,..•••        ,        •      16 

327* 

The  new  photographic  objective  of  9  inches  aperture  and 
9  feet  focus,  presented  by  Mr.  Nasmy  th,  has  been  received  from 
Mr.  Grubb,  and  also  a  new  6-inch  Dallmeyer  rapid  rectilinear 
lens  (bought  by  a  grant  from  the  Government  Grant  Fund  of 
the  Royal  Society).  These,  together  with  a  guiding  telescope 
of  5  inches  aperture  and  9%  feet  focal  length,  have  been 
mounted  after  a  design  by  H.M.  Astronomer  on  a  single  powerful 
stand  at  his  private  expense,  and  the  work  has  been  continued 
since  September  30  with  the  new  apparatus.  This  apparatus  is 
fitted  with  refined  means  for  centring,  and  with  fine  scales  for 
focussing,  and  also  with  means  for  giviDg  definite  orientation, 

*  The  dismounting  of  the  old  apparatus,  and  the  erection  of  the  Nasmyth 
telescope,  &c,  in  a  more  convenient  observatory,  caused  some  interruption  of 
regular  work* 


1 68  Report  of  the  Council  to  the  xlvii.  4, 

defined  by  a  ground  edge  on  the  sensitive  plate,  which  edge  rests 
by  spring  pressure  upon  two  cylinders  that  have  rigid  relation 
to  the  declination  axis.  The  dark  slides  are  of  metal.  The  whole 
apparatus  was  made  by  Mr.  Grubb,  and  is  found  to  give  very 
satisfactory  resnlts. 

Each  picture  of  the  Durchmusterung  photographs  taken  with 
the  Dallmeyer  lens  has  now  a  corresponding  picture  for  the 
central  position  of  its  area  (perfect  over  four  square  degrees), 
taken  simultaneously  by  means  of  the  Nasmyth  lens,  and  show, 
ing  stars  to  a  higher  order  of  magnitude.  The  enumeration  of 
the  stars  in  the  corresponding  areas  of  the  two  pictures  will 
furnish  very  valuable  data  for  discussing  the  distribution  of 
stars  of  different  orders  of  magnitude,  after  the  comparative 
light-factor  for  the  two  lenses  has  been  accurately  determined. 
Some  pictures  of  remarkable  star  dusters,  Ac,  have  been 
obtained  with  the  Nasmyth  lens. 

For  the  reduction  of  the    Durchmusterung    pictures,  H.AL 
Astronomer  has  received  a  noble  offer  of  co-operation  from  Prof. 
J.  G.  Kapteyn,  of  Groeningen.     Appreciating  the  importance  of 
the  work,  and  the  suitability  of  the  means  to  the  end,  Prof. 
Kapteyn  proposed  to  devote  his  own  time  and  that  of  three 
assistants  during  the  next  seven  years  to    measurement  and 
reduction  of  the  Durchmusterung  photographs,  and  the  prepara- 
tion of  a  catalogue  somewhat  resembling  that  of  Argelander. 
Such  an  offer  from  one  so  capable  and  so  devoted  could  not  but 
be  gratefully  and  cordially  accepted.     Accordingly  the  pictures 
from  S.P.D.  o°  to   130  were  forwarded  to  him,  together  with 
duplicate  plates  of  an  area  in  the  neighbourhood  of  the  Equator 
for  comparison  with  Argelander.     This  comparison  showed  that 
whilst  with  a  very  few  exceptions  (probably  red  stars)  all  the 
stars  of  the  Durchmusterung 9  including. those  of  the  9*5  magni- 
tude, are  shown  on  the  plate,  there  are  about  30  per  cent,  more 
stars  on*  the  plates  tnan  are  contained  in"  Argelander's  work. 
After  much  discussion  by  correspondence,  a  method  of  observa- 
tion was  arranged  by  which  the  Right  Ascensions  and  Declina- 
tions of  the  stars,  reduced  to  the  equinox  of  the  Catalogue,  are 
obtained   directly  from    the    instrumental  measurement;    the 
instrumental  results  require  only  small   final    corrections   for 
index    errors,  orientation,  <fcc.,  which  can  be  easily  tabulated 
from  comparison  of   the  instrumental  and  tabular  R.A.  and 
Declin.  of  the  known  stars.    A  rough  temporary  apparatus  was 
arranged  by  Prof.  Kapteyn,  which  it  was  resolved  to  employ  for 
obtaining  preliminary  plates  of  the  stars  within   io°  of  the 
South  Pole,  and  with  the  working  catalogue  so  formed,  it  will 
be  then  easy  to  observe  all  these  stars  in  zones  with  the  Cape 
transit-circle.      Thus  the  first  portion  of  the  Durchmusterung 
would  be  published  with  places  exact  to  1"  of  arc.     With  the 
preliminary  apparatus  Prof.   Kapteyn    had   already  measured 
in  duplicate  all  the  stars  within  io°  of  the  South  Pole  from 
R.A.   23h  iom  to  9h  5om.      The  accuracy  obtained  with  the. 


Feb.  1887.       Sixty-seventh  Annual  General  Meeting.  169 

Ttragh  apparatus  has  exceeded  expectations,  as  will  be  shown 
by  the  following  comparison  of  the  instrumental  R.A.  and 
Declin.  with  corresponding  tabular  places  of  the  Cape  1880 
Catalogue : — 


By 

Deduced  Decln.  of 
tero  of  Male. 

Index  error 
In  B.A. 

Zone  IX.    Stone  2948 

80  295 

n 
+     16 

3290 

295 

+  *5 

338o 

295 

+  10 

3457 

296 

+   18 

3680 

295 

+  18 

4084 

297 

+  18 

4486 

295 

+  20 

The  Declinations  are  read  off  by  estimation  to  o'*r,  from  a 
glass  scale,  graduated  to  1'  of  arc,  placed  in  focus  of  the  small 
telescope  by  which  the  photograph  is  viewed ;  and  the  R.A. 
is  read  off  by  estimation  to  28  of  time,  by  a  small  circle 
graduated  to  20*  attached  to  and  rotating  with  the  axis, 
which  serves  as  the  polar  axis  of  the  arrangement.  There 
seems  to  be  little  doubt  that,  with  a  more  refined  measuring 
apparatus  the  places  of  stars  can  be  determined  from  the  photo- 
graphs to  a  single  second  of  arc,  without  much  additional 
trouble  on  the  part  of  the  observer.  An  apparatus  amply  provid- 
ing for  this  accuracy  has  been  devised  by  H.M.  Astronomer,  and 
he  hopes  to  be  able  to  have  it  executed  during  his  approaching 
visit  to  Europe. 

A  very  laborious  attempt  has  been  made  since  July  20,  1885, 
to  photograph  the  Corona  by  Dr.  Huggins's  method.  From 
time  to  time  some  of  the  pictures  obtained  showed  persistent 
similarity,  under  conditions  which  appeared  to  preclude  the  possi- 
bility of  instrumental  error,  but  no  gradual  change  could  be 
traced  in  these  appearances,  such  as  one  might  expect  in  the 
representation  of  successive  features  of  the  true  Corona. 

With  every  confidence  in  the  method,  and  with  laborious 
care,  some  hundreds  of  these  pictures  have  been  taken  and 
examined  in  different  ways  and  in  different  lights,  and  the 
appearances  have  also  been  discussed  in  relation  to  the  elonga- 
tions of  Mercury  and  Venus,  as  suggested  by  Dr.  Hugging.  The 
most  hopeful  series  have  been  independently  drawn  by  Mr. 
Wesley,  with  results  as  to  the  general  features  of  the  pictures  of 
the  same  day  coinciding  with  those  remarked  at  the  Cape,  but 
the  results,  while  sometimes  leading  to  hope  of  success,  have 
never  brought  the  conviction  that  the  true  Corona  had  been 
really  photographed.  The  crucial  test  as  to  whether  the  dark 
body  of  the  Moon  could  be  photographed  against  the  back- 
ground of  the  Corona  was  tried  under  favourable  atmospheric 

0 


170  Report  of  the  Council  to  the  xt,vii.  4, 

conditions  on  the  occasion  of  the  partial  eclipse  of  August  29. 
No  trace  whatever  of  the  dark  body  of  the  Moon  outside  the 
Snn's  limb  conld  be  discovered  on  the  pictures,  and  it  appears 
that  further  experiments  in  this  direction,  to  be  successful,  must 
be  made  at  a  higher  altitude,  or  at  a  time  when  the  Sun's 
Corona  is  brighter  than  the  recent  eclipse  observations  show  it 
to  be  at  present. 

The  new  observatory  for  the  heliometer  is  completed. 
Messrs.  Bepsold  report  that  the  new  heliometer  will  be  finished 
in  the  end  of  February,  and  H.M.  Astronomer  has  received 
instructions  from  the  Admiralty  to  visit  Europe  for  the  purpose 
of  inspecting  it  before  it  is  sent  to  the  Gape. 

The  Geodetic  Survey  continues  to  make  considerable  pro- 
gress, notwithstanding  somewhat  disheartening  conditions — viz. 
reduction  of  the  vote  by  one- third  of  its  amount,  on  account  of 
the  depressed  financial  condition  of  the  Colony.  In  consequence 
of  this  reduction  the  services  of  Lieut.  Laffan,  R.E.,  have  been 
transferred  to  the  Survey  of  British  Bechuanaland,  the  staff 
otherwise  reduced,  and  the  equipment  and  transport  reorganised. 
Captain  Morris,  R.E.,  has  carried  on  the  field  work  in  these 
new  and  more  trying  conditions  with  the  same  energy  and 
ability  as  formerly.  The  triangulation  has  been  carried  from 
Natal  through  Griqualand  East  to  King  William's  Town  in  the 
Cape  Colony,  and  the  stations  have  been  selected  and  beaconed 
from  King  William's  Town  to  Port  Elizabeth. 

H.M.  Astronomer  has  taken  part  in  measurement  of  a  base 
line  at  Port  Elizabeth,  of  which  an  account  will  be  communi- 
cated to  the  Society.  The  extension  of  this  base  to  the  first 
great  side  is  now  in  progress.  The  subsequent  measure  of 
the  angles  of  the  triangles  already  selected  and  beaconed 
between  Port  Elizabeth  and  King  William's  Town  will  be  com- 
pleted in  June,  when  Baily's  existing  triangles  between  Sir  T. 
Maclear's  southern  stations  and  Port  Elizabeth  will  complete  a 
chain  of  triangles  about  1,300  miles  in  length,  checked  by  three 
base  lines  and  with  numerous  astronomical  stations,  which 
should  afford  some  valuable  geodetic  data. 

Lieut.  Laffan,  B.E.,  has  compared  his  personal  equation  with 
Mr.  Pett  at  the  Observatory  on  four  nights,  not  by  the  usual 
methods,  but  by  actual  determination  of  the  longitude  of  a  hut 
on  the  Observatory  grounds  by  telegraphic  exchange  of  signals, 
as  in  the  ordinary  process  of  a  longitude  operation ;  the  results, 
therefore,  include  the  relative  personal  equation  of  the  observers 
in  giving  and  receiving  signals  as  well  as  in  determination  of 
time. 

The  longitude  of  the  following  points  on  the  Geodetic 
Survey  have  been  determined  by  telegraphic  exchange  of 
signals  with  Captain  Morris : — 

Umtata,  by  exchange  on  6  nights. 
Berlin,        „  „         4     „ 


Feb.  1887.      Sixty-seventh  Annual  General  Meeting.  171 

and  the  longitude  of  Dryhartz,  in  British  Bechnanaland,  by 
exchange  of  signals  with  Lieut.  Laffan,  R.E.,  on  five  nights. 

The  heavy  pressure  of  a  great  variety  of  work  requiring  the 
close  personal  attention  of  H.M.  Astronomer  has  rendered  it 
impossible  to  complete  the  reduction  of  the  observations  of 
Victoria  and  Sappho  in  1882,  but  it  is  expected  that  the  work 
will  be  pushed  to  completion  before  the  end  of  the  year. 

The  Meteorological  Observations  made  in  the  year  1885  at 
the  Observatory,  together  with  those  taken  in  different  parts  of 
the  Colony,  have  been  printed  in  the  Reports  of  the  Cape 
Meteorological  Commission. 


Hong  Kong  Observatory. 

The  second  annual  volume  was  published  early  in  the 
summer,  and  the  third  volume  will  probably  be  ready  for  distri- 
bution within  a  few  months.  The  meteorological  observations 
and  researches  have  been  extended,  and  kept  up  to  date  since 
the  appointment  of  an  additional  clerk.  Absolute  magnetic 
observations  were  made  monthly,  and  Sir  W.  Thomson's  auto- 
matic tide-gauge  was  erected  and  worked  since  the  end  of 
October. 

The  electric  time-ball  was  dropped  as  usual  at  1  p.m.,  and 
the  sidereal  standard  clock  was  kept  going  without  being 
touched  throughout  the  year.  As  soon  as  two  years'  ten-day 
rates  are  available,  it  is  intended  to  re-examine  the  co- 
efficients. 

Micrometric  measures  of  Jupiter  and  Saturn  occasionally 
made  since  1879  have  been  reduced,  and  will  be  published  in 
the  astronomical  Report. 


0  2 


172 


Report  of  the  Council  to  the 


xlvii.  4, 


Notes  on  some  Points  connected  with  the  Progress  of 
Astronomy  during  the  past  Year. 

Discovery  of  Minor  Planets. 

The  following  eleven  minor  planets  were  discovered  in  the 
year  1886: — 


No. 

Name  of 
Planet. 

Date  of 
Discovery,  1886. 

Discoverer. 

Place  of 
Discovery. 

254 

Augusta 

Mar.  31 

Palisa 

Vienna 

255 

Oppavia 

3* 

>» 

• 
»» 

256 

Walpurga 

Apr.    3 

ti 

M 

257 

Silesia 

5 

t» 

»f 

258 

Tyche 

May    7 

Lather 

Dosseldorf 

259 

Aletheia 

June  28 

Peters 

Clinton 

260 

Huberta 

Oct.     3 

Palisa 

Vienna 

261 

Prymno 

3* 

Peters 

Clinton 

262 

Not.    3 

Palisa 

Vienna 

263 

3 

it 

tt 

264 

Libussa 

Dec.  22 

Peters 

Clinton 

Minor    planet    No.  253,    discovered    by    Herr    Palisa    on 
November  12,  1885,  has  been  named  Mathilde. 


The  Comets  of  1886. 


Including  the  periodic  comet  of  Winnecke,  six  comets  have* 
been  discovered  during  the  year.  It  will  be  more  convenient  to 
describe  these  in  the  order  of  their  discovery,  than  according  to 
their  several  dates  of  perihelion  passage  or  catalogue  order. 

The  first  (known  as  1886,  Comet  V.)  was  discovered  by  Mr. 
Brooks,  of  Phelps,  New  York,  on  April  27,  in  the  constellation 
Cassiopeia,  and  moving  south  and  east.  At  the  time  of  dis- 
covery it  was  round,  tolerably  bright,  and  about  one  minute  in 
diameter.     The  comet  was  approaching  both  the  Sun  and  the 


Feb.  1887.       Sixty-seventh  Annual  General  Meeting.  173 

Earth,  and  the  brilliancy  consequently  increasing.  The  maximum 
brilliancy  was  attained  about  June  9,  near  the  date  of  perihelion 
passage,  when  it  had  twenty  times  the  intensity  that  it  possessed 
when  first  seen,  but  was  too  near  the  San  to  permit  of  observation. 
After  perihelion,  the  comet  was  not  well  situated  for  observation, 
and  does  not  seem  to  have  been  seen.  The  observations  are  well 
represented  by  a  parabola. 

Four  days  later,  on  May  1,  Mr.  Brooks  discovered  another 
comet  in  the  constellation  Pegasus  (designated  1886,  Comet  III.). 
This  comet  was  fairly  bright,  and  had  on  May  3  a  short  tail, 
eight  minutes  in  length.  Owing  to  the  morning  twilight  the 
comet  soon  became  a  difficult  object  to  observe,  and  was  ap- 
parently lost  sight  of  in  the  third  week  of  May,  but  the  change 
of  form  in  the  comet  was  interesting.  On  May  20,  Col.  Tupman 
could  see  no  trace  of  a  bead,  and  the  two  ends  of  the  tail  were 
so  similar,  it  was  impossible  to  say  by  mere  inspection,  which 
was  the  head.  On  May  22  Dr.  Tempel  gave  a  very  similar  de- 
scription, but  suspected  two  very  slight  condensations  in  a 
spindle-shaped  nebulous  mass,  about  twelve  minutes  long. 

As  in  the  previous  case  the  orbit  is  apparently  parabolic,  but 
sdme  interest  attaches  to  the  elements,  since  at  the  ascending 
node  which  the  comet  passed  on  July  9,  its  distance  from  the 
Earth  was  only  0*075,  and  therefore  might  have  originated  a 
meteor-radiant,  visible  in  the  southern  hemisphere,  the  co- 
ordinates being  approximately  a  =  190  and  8  =  —  42°. 

On  May  22,  Mr.  Brooks  discovered  a  third  comet  (1886,  IV.), 
which  does  not  appear  to  have  been  observed  very  frequently,  the 
more  to  be  regretted,  as  the  comet's  orbit  will  probably  prove 
to  be  elliptic.  Dr.  Oppenheim,  failing  to  represent  the  path 
with  sufficient  accuracy  by  means  of  a  parabola,  has  computed 
an  elliptic  orbit  of  nine  years'  period,  which  fairly  well  repre- 
sents the  few  observations  at  his  command. 

Comet  1886  VI.  is  the  periodic  comet  of  Winnecke,  detected 
by  Mr.  Finlay  at  the  Royal  Observatory,  Cape  of  Good  Hope,  on 
Aug.  19,  the  possibility  of  the  comet  being  found  in  the  northern 
hemisphere  during  the  summer  months  not  having  been  realised. 
The  last  return  of  this  comet  was  in  1880,  when,  owing  to  its 
proximity  to  the  Sun,  it  passed  unobserved.  In  the  interval, 
1880-1886,  the  comet  underwent  very  considerable  perturbations 
from  Jupiter,  to  which  planet,  in  heliocentric  longitude  no°,  it 
can  approach  within  0*06.  No  accurate  calculations  of  the  per- 
turbations were  undertaken,  but  Dr.  Palisa  gave  sweeping 
Ephemerides  from  elements  approximately  corrected.  These 
elements  show  that  the  chief  effect  of  the  perturbation  has  been 
still  further  to  diminish  the  mean  motion,  which  had  been 
steadily  decreasing  since  the  re-discovery  in  1858.  The  passage 
through  the  perihelion  was,  however,  twelve  days  earlier  than 
was  predicted  by  Dr.  Palisa.  It  cannot  be  doubted  but  that 
rigorous  calculations  will  be  made  in  order  to  connect  the  ob- 
servations of  this  year  with  those  of  the  earlier  apparitions, 


1 74  Report  of  the  Council  to  the  xlvii.  4, 

since,  according  to  the  late  Dr.  Oppolzer,  the  theory  of  the  comet 
cannot  be  satisfactorily  reconciled  with  observation  on  the 
purely  gravitational  theory,  but  that  the  mean  motion  and 
eccentricity  require  the  correction  of  small  terms,  depending  on 
a  supposed  resisting  medium. 

On  September  26,  Mr.  Finlay  discovered  another  comet,  in 
the  constellation  Scorpio,  having  small  south-easterly  motion. 
The  comet  was  round,  one  minute  in  diameter,  and  without  tail. 
As  soon  as  the  elements  were  computed,  it  was  seen  that  they 
strongly  resembled  those  of  De  Vico's  comet  of  short  period, 
which  had  not  been  seen  since  1844.  There  are,  however, 
some  difficulties  in  accepting  the  suggestion  that  the  two  comets 
are  identical,  and  the  doubt  cannot  be  cleared  up  till  the  mean 
motion  of  the  comet  is  sufficiently  well  determined  to  permit  the 
rigorous  calculation  of  the  perturbations  of  the  comet  by  Jupiter 
(and  possibly  Mars)  in  the  interval. 

The  period  assigned  by  Dr.  Brunnow  was  5*466  years,  and 
if  we  assume  that  either  eight  or  seven  returns  of  the  comet 
had  occurred  between  1844  and  the  present  time,  we  must  admit 
either  the  action  of  very  considerable  perturbation,  which  is  not 
likely,  or  that  Brunnow's  period  was  more  in  error  than  seemed 
possible,  though  it  is  admitted  that  the  change  of  form  in  the 
comet  during  visibility  in  1844  may  explain  the  existence  of 
a  larger  error  than  has  hitherto  been  suspected.  The  more 
accurate  elements  that  have  been  computed  from  a  more  extended 
series  of  observations,  and  in  which  no  assumption  of  the  axis 
major  has  been  made,  agree  in  giving  a  period  considerably 
longer  than  that  found  by  Dr.  Brunnow,  bo  that  it  is  not  im- 
possible that  the  two  comets  may  not  be  identical,  but  two 
moving  in  a  similar  orbit,  an  example  of  which  was  seen  in  the 
case  of  Comets  1843  I.,  1880  1.,  and  1882  II. 

The  sixth  comet  of  the  year  was  discovered  on  October  4  by 
Mr.  Barnard,  and  independently  by  Dr.  Hartwig  on  the  following 
day.  The  comet  at  discovery  was  round  and  tolerably  bright, 
and  was  increasing  in  brilliancy.  By  October  29  a  short  broad 
tail  was  visible,  and  early  in  December  this  tail  had  increased  to 
several  degrees  in  length,  and  a  shorter  tail  of  15'  in  length,  and 
distant  400  of  position  angle  had  been  developed.  These  details 
have  been  satisfactorily  photographed  by  Von  Gothard,  of  the 
Physical  Observatory  of  Her6ny.  It  was  seen  with  the  naked 
eye  in  Turin' on  November  21,  but  was  too  near  the  morning 
twilight  to  become  a  conspicuous  object.  The  orbit  is  apparently 
parabolic. 

In  addition  to  these  comets,  it  is  well  to  remark  that  Olbers* 
Comet,  to  which  reference  was  made  in  the  last  Annual  Report, 
has  not  yet  been  detected,  and  that  as  the  most  probable  time  of 
perihelion  passage  has  now  been  reached  the  search  should  be 
severely  maintained.  A  comet,  which  was  discovered  by  Tern  pel 
on  November  27,  1869,  and  re-discovered  by  Swift  on  October  1 1, 
1880,  has  probably  passed  this  year  through  perihelion  unde- 


Feb.  1887.      Sixty-seventh  Annual  General  Meeting.  175 

tected.  The  orbit  has  been  rigorously  computed  by  M.  Bossert 
of  the  Paris  Observatory,  who  gave  an  ephemeris  to  assist  the 
search.  It  is  a  peculiarity  of  the  comet  that  it  is  well  situated  for 
observation  at  alternate  returns,  and  this  approach  was  unfor- 
tunate, the  theoretical  brilliancy  never  attaining  one-tenth  of  that 
possessed  by  the  comet  at  the  last  recorded  observation. 

w.  E.  p. 


The  Total  Solar  Eclipse  of  1886,  August  28-29. 

The  expedition  sent  out  to  Grenada,  West  Indies,  to  observe 
this  eclipse,  consisted  of  the  following  persons :  Captain  Darwin, 
Mr.  Lockyer,  Mr.  Maunder,  Father  Perry,  Dr.  Schuster,  Pro- 
fessor Thorpe,  and  Mr.  Turner.  Professor  Tacchini  also  accom- 
panied the  expedition  on  behalf  of  the  Italian  Government.  The 
observers  divided  into  several  parties  on  reaching  Grenada,  as  a 
precaution  against  purely  local  masses  of  cloud,  or  bad  weather ; 
it  being  also  arranged  that  observations  should  be  made  as  far  as 
possible  in  duplicate.  Although  the  weather  at  the  time  of  the 
eclipse  was  not  all  that  could  be  desired,  successful  observations 
were  secured  at  three  stations ;  at  the  fourth  the  Sun  was  ob- 
scured by  heavy  clouds. 

The  following  is  a  brief  account  of  the  results  obtained, 
taking  the  stations  in  order  from  the  south : — 

Station  I.— Prickly  Point,  lat.  120  o'  N.,  long.  6i°  46'  W. 
Captain  Darwin  with  the  coronograph  exposed  six  plates  during 
totality,  one  for  five  seconds,  one  for  ten  seconds,  and  four 
instantaneous.  During  the  partial  phases  he  obtained  more  than 
twenty  satisfactory  photographs,  and  on  the  day  before  the 
eclipse,  fifteen.  These  were  all  taken  with  the  object  of  testing 
Dr.  Huggins's  method  for  photographing  the  Corona  without  an 
eclipse,  and  the  result,  as  far  as  is  yet  known,  is  unfavourable  to 
that  method,  under  such  conditions  of  hazy  sky  and  low  sun  as 
were  obtained. 

Captain  Darwin  also  took  one  photograph  with  the  prismatic 
camera. 

Dr.  Schuster  obtained  four  photographs  of  the  Corona  with  a 
5-foot  camera,  and  two  of  the  coronal  spectrum,  with  slits 
radial  and  tangential  respectively. 

Station  II. — Hog  Island,  lat.  120  o'  N.,  long.  6i°  44'  W.  Pro- 
fessor Thorpe,  assisted  by  Mr.  Lawrance,  obtained  a  satisfactory 
series  of  photometric  measures  of  the  intensity  of  the  Corona. 
He  made  in  all  fifteen  separate  and  independent  comparisons  of 
the  coronal  and  diffused  light  beyond  the  visible  edge  with  a 
Swan  electric  lamp  of  known  photometric  value,  by  a  method 
arranged  by  Captain  Abney.     During  the  latter  part  of  totality 


1 76  Report  of  the  Council  to  the  xlyii.  4, 

the  coronal  light  was  dimmed  by  haze,  bat  he  sees  no  reason  for 
thinking  the  measures  made  in  the  first  hundred  seconds  other 
than  perfectly  trustworthy.  Belying  on  these  seven  only,  the 
final  photometric  values  obtained  are  not  very  different  from 
those  found  by  Professor  Harkness  in  the  1878  eclipse. 

Station  III. — Boulogne,  near  QrenviUe,  lat.  120  9'  N.,  long. 
6i°  38'  W.  Professor  Tacchini  made  a  careful  comparison  of 
the  prominences  detected  by  the  spectroscope  before  and  after 
totality  with  those  seen  during  totality,  and  found  important 
differences  between  them,  viz. :  all  prominences  showed  them- 
selves larger  and  taller  during  an  eclipse,  the  upper  portions 
being  white  when  the  prominence  exceeds  1'  of  arc  in  height, 
while  some  very  fine  prominences  seen  during  totality  were  not 
discernible  in  full  sunshine  at  all ;  these  latter  were  almost  entirely 
white,  and  their  luminous  intensity  was  small,  so  that  they  were 
not  visible  to  the  naked  eye  unless  they  extended  beyond  the 
brightest  part  of  the  Corona.  He  also  observed  the  spectrum 
of  the  "  flash  "  noticed  by  Professor  Young  in  1870,  and  traced 
it  to  a  much  greater  height  than  before. 

Mr.  Turner  obtained  a  qualified  confirmation  of  Mr.  Lockyer's 
Egyptian  observations  with  regard  to  the  order  of  appearance  of 
the  bright  lines  near  F  in  the  spectrum  of  the  inner  Corona. 
During  totality  he  looked  for  currents  in  the  Corona,  but 
obtained  no  satisfactory  results. 

Station  IV. — Green  Island,  lat.  120  14'  N.,  long.  6i°  35'  W. 
Cloudy  during  totality.  Mr.  Lockyer  considers,  however,  that 
important  information  was  obtained  by  preliminary  drills  as  to 
the  number  of  photographs  which  could  be  taken  during  totality 
by  careful  management. 

Station  V.-  -Hermitage,  Oarriacou,  lat.  120  27'  N.,  long. 
6i°  29'  W.  Father  Perry  made  observations  of  the  order  of 
appearance  of  lines  in  the  coronal  spectrum  near  E.,  and 
observed  1474  K  and  other  short  bright  lines  two  minutes  before 
totality.  During  totality  he  looked  for  the  carbon  flutings  seen 
by  Professor  Tacchini,  but  with  a  negative  result. 

Mr.  Maunder  obtained  seven  photographs  of  the  Corona  with 
a  5 -foot  camera,  exposures  varying  from  0**2  to  40s,  and  two  pho- 
tographs of  the  coronal  spectrum  with  slits  radial  and  tangential. 

Almost  at  the  last  moment  another  observer  arrived  on  the 
scene.  Mr.  W.  H.  Pickering,  from  Boston,  Mass.,  took  up  his 
position  in  Fort  George,  lat.  120  3'  N.,  long.  61  °  45'  W.,  armed 
with  a  photoheliograph  of  38  feet  focal  length.  He  exposed  a 
number  of  plates  during  totality,  and  also  organised  a  series  of 
observations  of  the  shadow  bands. 

The  observers  owe  a  very  large  debt  of  gratitude  to  the 
Governor  of  Grenada,  who  helped  them  in  every  way,  and  they 
received  invaluable  assistance  from  the  leading  officials,  and  from 
the  officers  and  crews  of  H.M.S.  Fantume,  H.M.S.  Bullfrog,  and 


Feb.  1887.      Sixty- seventh  Annual  General  Meeting.  177 

H.M.S.  Sparrowhawk,  both  in  transport  and  preparations  for 
observing,  and  in  the  actual  observations.  A  number  of  discs 
had  been  taken  oat  with  the  view  of  repeating  Professor  New- 
comb's  observation  of  1878  on  the  coronal  extension,  and  fairly 
accordant  results  were  obtained  by  the  following  observers  at 
the  different  stations : — 

I.  Captain  Maling,  Colonial  Secretary. 
II.  Captain  Archer,  of  H.M.S.  Fantdme. 

III.  Lient.  Smith,  of  H.M.S.  Sparrowhawk. 

IV.  Captain   Hughes,    Protector  of   Immigrants,  and  Mr. 

Bel  ton. 
V.  Captain  Masterman  and  Mr.  Osburn,  of  H.M.S.  Bullfrog. 

At  Station  II.  also  Lieuts.  Douglas  and  Bairnsfather,  of 
H.M.S.  Fantdme,  made  a  series  of  photometric  measures  with  an 
integrating  apparatus,  which  agree  with  Professor  Thorpe's 
general  results.  The  Governor  of  Grenada,  the  Chief  of  Police, 
fiie  Clerk  of  the  Council,  Dr.  Boyd,  Mr.  Elliott  (Government 
Botanist),  and  Captain  Oldham,  of  H.M.S.  Sparrowhawk,  were 
all  busily  engaged  at  Station  IV.,  and  were  prepared  to  assist  in 
the  photographic  operations. 

On  the  whole,  the  expedition  may  be  considered  a  very  suc- 
cessful one,  and  the  passing  clouds  which  obscured  part  of  the 
phenomenon  at  the  more  fortunate  stations  served  perhaps  to 
remind  the  observers  how  nearly  they  had  escaped  complete 
failure.  h.  h.  t. 


Professor  Hall's  Researches  on  the  Orbits  of  the  Six  Inner 

Satellites  of  Saturn* 

In  Appendix  I.  of  the  Washington  Observations  for  1883 
Prof.  Asaph  Hall  communicates  the  positions  of  the  six  inner 
satellites  of  Saturn,  observed  with  the  26-inch  refractor,  and  the 
results  of  the  computations  to  which  they  have  been  subjected. 

The  observations  of  Titan,  which  extend  over  nearly  ten 
years,  from  August  1874  to  February  1884,  consist  partly  of 
measurements  of  differences  of  Right  Ascension  and  Declination 
between  the  satellite  and  the  centre  of  the  planet,  and  partly  of 
measurements  of  position-angle  and  distance.  The  observed 
positions  are  compared  with  the  corresponding  places  computed 
with  the  values  of  Bessel's  tables  in  vol.  9  of  the  Astron. 
Nachrichten.  Bessel's  determination  of  the  elements  of  the  orbit 
there  given  is  founded  upon  the  first  series  of  his  own  helio- 
metrical  measurements  of  Titan,  taken  in  1830,  the  mean  motion 
of  the  satellite  in  its  orbit  and  the  motion  of  the  line  of  apses 
being  deduced  from  a  careful  discussion  of  the  scanty  observa- 
tions of  conjunctions  of  the  satellite  with  the  centre  of  the 
planet  made  by  Halley,  Cassini,  Herschel,  and  Kohler.     The 


178  Report  of  the  Council  to  the  xlvii.  4, 

Washington  computations  boow  that  only  small  corrections  of  the 
tabular  values  are  demanded  by  the  Washington  observations. 
Indeed,  the  correction  of  the  motion  of  the  apses  is  left  doubtful ; 
for,  while  the  earlier  series  of  observations  made  from  1874  to 
1882  indicate  a  slight  augmentation,  only  the  last  series  made 
1883-84  show  a  diminution,  and  it  will  have  to  be  decided  by 
further  evidence  what  is  the  true  motion. 

From  his  computations  of  the  micrometrical  measurements 
of  Rhea,  Dione,  and  Tethys,  which  were  made  in  the  years  1874 
and  1875,  Prof.  Hall  draws  the  conclusion  that  the  eccentricities 
of  the  orbits  are  left  practically  undetermined,  and  also  that  the 
planes  of  the  orbits  probably  coincide  very  nearly  with  the 
plane  of  the  ring.  For  the  determination  of  the  mean  motions 
of  the  satellites  he  assumes  that  the  mean  longitudes  for  the 
epoch  1858,  which  Jacob  has  deduced  from  his  Madras  observa- 
tions, are  free  from  error,  and  the  values  of  the  daily  motion 
resulting  from  the  positions  of  1858  and  1875  are  then  partly 
corrected  with  the  help  of  the  conjunctions  observed  at  Wash, 
ington  in  the  years  1882  to  1886.  In  the  case  of  Mimas,  the 
mean  motion  is  simply  deduced  from  seven  conjunctions,  ob- 
served within  three  years  and  a  quarter.  But,  as  the  adopted 
motion  leaves  an  error  of  about  half  an  hour  in  HerscheTs 
trustworthy  observation  of  October  18,  1789,  the  value  cannot 
be  accepted  as  sufficiently  correct.  JL  M. 


The  Argentine  General  Catalogue  of  Stars. 

It  was  only  in  the  middle  of  the  year  1872  that  observations 
with  the  Cordoba  Meridian  Circle  were  commenced,  and  by  the 
end  of  1880  no  less  than  145,000  observations  had  been  made, 
suitable  for  the  General  Catalogue,  and  more  than  105,000  zone 
observations.  It  is  probable  that  the  whole  of  the  meridian 
work  of  all  the  other  observatories  in  the  world  put  together 
during  the  same  interval  would  fall  short  of  these  numbers. 
Only  seven  years  ago  the  state  of  our  knowledge  of  the  southern 
heavens  was  deplorable.  The  publication,  in  1 88 1 ,  of  Mr.  Stone's 
great  work  at  the  Cape  and  of  the  present  truly  wonderful  work 
of  Dr.  Gould  and  his  able  assistants,  during  the  last  few  months, 
has  suddenly  turned  the  scale  so  completely  that  the  southern 
heavens  are  now  more  thoroughly  surveyed  than  the  northern, 
and  must  remain  so  until  all  the  zones  of  the  Astronomische 
Gesellschafb  have  been  united  into  a  complete  catalogue.  The 
rapidity  with  which  the  reductions  have  been  effected  and 
published  is  no  less  amazing  than  the  observations  themselves. 
Nothing  like  it  has  been  known  in  the  history  of  astronomy. 

The  instrument  is  described  in  the  introduction  to  the  ob- 
servations in  1872.  Several  volumes  of  the  observations  and 
the  Zone  Catalogue  have  already  been  published.     The  present 


Feb.  1887.      Sixty  seventh  Annual  General  Meeting.  179 

volume  forms  No.  XIV.  of  the  series.  It  contains  the  places  of 
32,448  stars  Bonth  of  the  parallel  of  N.P.D.  1130  in  the  body  of 
the  Catalogue,  and  of  11 26  stars  in  remarkable  clusters  arranged 
as  separate  small  catalogue*.  The  epooh  is  1875*0.  The  arrange- 
ment of  the  Catalogue  exhibits  separately  each  year's  results  for 
each  star.  The  annual  precessions  and  secular  variations,  the 
epoch  of  observation,  the  number  of  observations  and  references 
to  other  catalogues  are  given.  Most  of  the  stars  have  been 
observed  at  least  three  times.  The  adopted  mean  places  of  the 
time  and  circnmpolar  stars,  nsed  for  the  determination  of  the 
instrumental  corrections  in  each  year,  are  given  in  the  corre- 
sponding volumes  of  observations. 

The  Right  Ascensions  of  the  Catalogue  depend  exclusively 
upon  75  time  stars  of  the  American  Nautical  Almanac.  The 
declinations  are  independent. 

The  stereotype  plates  of  the  Catalogue  have  been  presented 
to  the  Royal  Astronomical  Society  by  Dr.  Gould,  with  the 
consent  of  the  Government  of  the  Argentine  Republic. 


The  Harvard  Catalogue  of  1213  Stars  for  i875'o. 


This  work,  which  represents  a  large  part  of  the  labours  of 
Prof.  W.  A.  Rogers  for  the  last  fifteen  or  sixteen  years,  forms 
Part  I.  of  vol.  xv.  of  "  Annals  of  Harvard  College  Observatory." 
The  observations  on  which  it  depends  were  made  with  the  large 
Meridian  Circle,  described  in  vol.  viii.,  between  1870  November 
and  1879  January.  The  stars  are  of  two  classes ;  492  being 
fundamental  stars  from  Dr.  Auwers'  Catalogue  in  "  Publication 
der  Astronomischen  Gesellschaft,"  XIV.,  the  remainder,  termed 
secondary  stars,  being  miscellaneous  stars  observed  for  various 
purposes.  The  observations  were  concurrent  with  those  of  the 
«me  +5o°to  +  550,  A.G. 

The  observations  of  the  fundamental  stars  have  been  printed 
in  vol.  xvi.  with  an  elaborate  and  masterly  Introduction  by  Prof. 
Rogers,  giving  the  method  of  reduction  in  great  detail.  The 
Introduction  to  the  present  Catalogue  contains  the  mean  places 
of  these  fundamental  stars  separately  for  each  year,  and  the  star 
ledgers  of  such  of  the  other  stars  as  are  not  given  in  vol.  x.  or  xii. 

Instead  of  the  usual  spider-lines,  a  reticule  ruled  upon  glass 
was  employed.  The  Declinations  were  measured  by  recording  on 
the  chronograph  transits  over  very  oblique  lines.  For  a  number 
of  years  only  two  microscopes  were  used  for  reading  the  circle ; 
hut  Prof.  Rogers  has  elaborately  investigated  the  reduction  of 
the  mean  of  two  to  the  mean  of  four  from  the  observations  of 
subsequent  years. 

The  Right  Ascensions  of  Publication  XIV.  were  used  in 
determining  clock  error;  hence,  for  the  fundamental  stars  the 


i8o  Report  of  the  Council  to  the  xlyji.  4, 

Bight  Ascensions  of  the  Catalogue  are  almost  exactly  repro- 
ductions of  Auwers9.  The  same  applies  to  the  Declinations* 
The  errors  of  the  circle  and  accumulated  errors  of  the  micro- 
scopes were  determined  by  and  expressed  in  terms  of  Auwers* 
system  of  Declinations.  The  discussion  of  the  observations  of 
the  fundamental  stars  (which  are  very  numerous  and  of  a  high 
degree  of  accuracy)  demonstrates  the  homogeneity  of  Auwers9 
systems.  The  places  of  the  remaining  720  stars  have  a  corre- 
sponding degree  of  accuracy.  For  Bradley's  stars,  Dr.  Auwers9 
original  proper  motions  are  given  in  the  Catalogue,  and  were 
nsed  for  reduction  to  mean  epoch. 


The  Pulkowa  Catalogue  0/3542  Stars  for  185  5*0. 

This  Catalogue,  which  forms  a  portion  of  vol.  viii.  of  the 
"  Pulkowa  Observations,9'  has  been  formed  from  the  observations 
published  in  vols.  vi.  and  vii.  It  contains  all  Bradley 9s  stars  from 
the  Pole  to  105  °  N.P.D.,  except  the  Pulkowa  fundamental  stars, 
all  other  stars  down  to  the  6th  magnitude  inclusive  in  Arge- 
lander's  Uranometria  Nova  in  the  same  portion  of  the  heavens, 
and  some  other  stars  which  have  been  added  to  the  observing 
list  from  time  to  time  for  special  purposes.  The  observations 
were  made  with  the  Bepsold  Meridian  Circle,  described  in  the 
introductory  volume,  between  the  years  1840  and  1869,  by  MM. 
Sabler,  Dollen,  Lindhagen,  Winnecke,  and  Gromadski.  The 
reductions  were  conducted  throughout  by  M.  von  Asten. 

Each  star  was  observed  four  times  ;  once  in  each  of  the  four 
positions  of  the  instrument  obtained  by  reversing  the  axis  and 
interchanging  the  object-glass  and  eyepiece.  The  Bight  Ascen- 
sions depend  upon  those  of  the  Pulkowa  Fundamental  Catalogue, 
the  Sun  not  having  been  observed  with  this  instrument.  The 
Declinations  are  independent,  having  been  determined  from 
observations  of  the  horizontal  collimators  combined  with  the 
known  colatitude.  The  large  number  of  stars  and  the  com- 
pleteness with  which  the  plan  of  observation  was  carried  oat 
make  this  one  of  the  most  valuable  catalogues  in  existence.  The 
delay  in  the  publication  has  enabled  Dr.  Auwers9  new  proper 
motions  to  be  inserted  in  the  work,  and  to  be  used  in  the  re- 
duction to  mean  epoch. 


Professor  Schanf eld's  Extension  of  the  "  Durchmu&terung." 

An  important  work  has  been  issued  within  the  last  few 
months  from  the  Boyal  Observatory  of  Bonn.  Argelander's 
Durchmusterung,  or  survey  of  the  northern  heavens  from 
the  Pole  to  20  of  South  Declination,  has  been  carried  down   by 


Feb.  1887.       Sixty -seventh  Annual  General  Meeting.  181 

Lis  successor,  Professor  Schonfeld  (who  in  conjunction  with 
Professor  Krneger  was  associated  with  the  late  Professor  Arge- 
lander  in  the  former  part  of  the  work),  to  230  South  Declination, 
and  the  results  are  now  in  the  hands  of  astronomers. 

Professor  Schonfeld  commenced  observing  on  January  6, 
1876,  and  at  first  proposed  to  carry  his  survey  down  to  240  or 
25°  South  Declination,  so  as  to  overlap  by  a  degree  or  so  the 
northern  limit  of  the  Cordoba  zones.  It  was  found,  however, 
that  —  23°  was  the  extreme  limit  for  satisfactory  observation. 
In  view  of  the  lower  altitude  of  the  stars  to  be  observed,  it  was 
decided  to  substitute  for  the  small  comet-seeker  of  34  lines 
aperture,  employed  in  the  earlier  work,  a  telescope  by  Schroder 
of  6  inches  aperture  and  6  feet  focal  length — a  change  which 
was  further  recommended  by  the  fact  that  for  several  years 
Professor  Schonfeld  had  been  engaged  in  magnitude  comparisons 
with  a  telescope  of  the  same  aperture  at  the  Mannheim  Obser- 
vatory. With  this  instrument,  fitted  with  an  eyepiece  of 
26  mag.  power,  having  a  field  of  i°  44',  the  survey  was 
worked  in  zones;  and  the  stars  thus  observed  number  133,659 
between  —  20  and  —  230,  with  an  additional  11 73  stars  falling 
beyond  these  limits.  At  the  same  time,  with  a  view  to  the  more 
satisfactory  designation  of  the  fainter  stars,  the  magnitude  limit 
was  extended  to  io'o.  The  resulting  catalogue  is  arranged  in 
zones  of  i°  of  Declination  on  the  same  plan,  and  calculated  for 
the  same  epoch  (1855*0)  as  the  sections  of  the  earlier  work,  and 
forms  Vol.  VIII.  of  the  "Astronomische  Beobachtungen  auf  der 
Sternwarte  zu  Bonn." 

The  catalogue  is  accompanied  by  an  Atlas,  in  which  the 
charts  are  arranged  in  sheets  of  one  hour  of  Eight  Ascension 
each,  with  an  overlap  of  four  minutes  on  either  side,  and  extend 
in  Declination  from  — 1°  to  —  230.  The  Atlas  will  be  completed 
in  four  parts,  of  which  two  only  have  as  yet  appeared.  These 
contain  Hours  o  to  xi.  (with  the  exception  of  Hour  vii.),  and 
Hour  xxiii. 

This  valuable  work,  completing  the  survey  of  the  heavens  on 
a  uniform  plan  within  the  limits  effectively  practicable  at  an 
Observatory  in  central  Europe,  is  appropriately  inscribed  by 
Professor  Schonfeld  to  Argelander's  memory. 


The  Second  Armagh  Catalogue  of  Stars. 

• 

This  Catalogue  embodies  the  whole  of  the  meridian  work 
done  at  the  Armagh  Observatory  since  the  publication  of  the 
first  Armagh  Catalogue.  It  contains  the  places  of  3300  of 
Lalande's  stars,  from  observations  between  1859  and  1883 
inclusive,  reduced  to  the  epoch  1875*0. 

The  Right  Ascensions  depend  on  the  standard  stars  of  the 
Nautical  Almanacs  of  the  period,  four  or  five  of  which  were 


182  Report  of  tlie  Council  to  the  xlvii.  4, 

observed  on  each  night.  These  stars  were  not  observed  in  Polar 
Distance.  The  Declinations  of  the  Catalogue  depend  upon  the 
Nadir  observation  which  was  made  every  night,  the  assumed 
colatitude,  and  the  division  errors  determined  by  Dr.  Robin- 
son many  years  ago.  The  refractions  employed  were  Dr.  Robin- 
son's. The  precessions  are  given  to  three  places  and  two  places 
of  decimals  in  B*.A.  and  N.P.D.  respectively,  bnt  not  the  secular 
variations.  The  references  to  other  catalogues  are  copious,  and 
are  apparently  complete.  The  observations  upon  which  Dr 
Robinson's  Catalogue  of  1000  Lalande's  stars  depend  are  in- 
cluded in  the  present  volume. 

It  was  only  in  February  1882  that  Dr.  Dreyer  was  appointed 
to  the  directorship  of  the  Observatory,  at  which  time  most  of  the 
work  was  unreduced. 


Dr.  Kams  Catalogue  0^5455  Small  Stars. 

Scattered  through  the  volumes  of  the  Astronomische  Nach- 
richten  are  a  great  number  of  determinations  of  the  places  of 
small  stars,  generally  comparison  stars,  not  to  be  found  elsewhere. 
Prof.  Schjellerup  formed  a  most  useful  index  to  all  these  stars  in 
the  first  sixty- six  volumes,  by  reducing  all  their  places  ap- 
proximately to  1855*0,  and  giving  a  reference  to  the  volume  and 
page  where  the  accurate  place  could  be  found  ("  Publication  der 
Astron.  Gesell."  VIII.) .  That  work  still  remains  useful  for  all 
stars  determined  by  equatorial  comparison  with  others.  Dr.  M. 
Hoek,  late  Director  of  the  Utrecht  Observatory,  commenced  the 
task  of  forming  a  proper  catalogue  of  all  such  stars  as  had  been 
observed  with  meridian  instruments,  and  his  successor,  Dr.  Kara, 
has  completed  it.  The  body  of  the  work  is  a  catalogue  of  4890 
meridian  observations  of  4350  stars,  reduced  to  the  epoch  1855*0 
by  the  application  of  precession.  The  precessions,  secular 
variations,  and  third  terms  are  given  for  the  same  epoch,  a 
reference  to  the  volume  and  page  of  the  Ast.  Nach.,  and  the  name 
of  the  observer  and  observatory.  This  is  accompanied  by  copious 
notes  and  a  comparison  of  every  star  with  its  place  in  the 
Bonn  Durchmu8terung — the  whole  involving  an  immense  amount 
of  labour  which  will  be  duly  appreciated  by  all  who  are  engaged 
in  equatorial  comparison  work,  and  will  ultimately  assist  in 
determining  the  proper  motion  of  these  small  stars. 


The  Great  Comet,  1882.    XT. 

Dr.  Gill  has  recently  published  a  complete  account  of  the 
observations  of  this  comet,  which  were  made  at  the  Royal 
Observatory,  Cape  of  Good  Hope. 


Feb.  1887.       Sixty-seventh  Annual  General  Meeting.  183 

Utilising  all  the  means  at  his  disposal,  Dr.  Gill  succeeded  in 
securing  a  fairly  continuous  scries  of  positions  of  the  comet  from 
1882,  September  7,  to  1883,  May  12,  to  accomplish  which, 
observations  were  made  with  the  Indian  Theodolite,  the  Transit 
Circle,  the  Heliometer,  and  the  6-inch  and  7 -inch  Eqaatorials. 

In  Table  I.  is  given  the  daylight  observations  made  with  the 
Indian  theodolite  on  September  16,  17,  and  18,  before  and  after 
the  comet  passed  on  to  the  Snn's  disc ;  and  the  resulting  R.A. 
and  declination  are  computed  for  the  times  of  observation. 

Table  II.  gives  the  meridian  observations  with  the  Transit 
Circle.  These  consist  of  three  observations  by  Dr.  Gill  in 
September  17,  18,  and  22,  and  a  series  between  January  9  and  30, 
made  by  Mr.  Maclear,  who  endeavoured  to  observe  the  brightest 
part  of  the  nucleus. 

Table  III.  gives  the  apparent  places  of  the  comet  in  R.A.  and 
N.P.D.  from  a  long  series  of  observations,  with  comparison  stars 
made  with  the  Equatorials  from  1882,  September  7,  to  1883, 
May  12.  In  the  majority  of  these  observations,  the  centre  of 
the  nucleus,  or  patch  of  light,  was  supposed  to  be  observed,  but 
towards  the  end  of  the  series  it  was  found  that  one  of  the 
observers  always  observed  a  more  condensed  part  which  slightly 
followed  this  centre. 

The  results  of  Dr.  Elkin's  observations  with  the  Heliometer 
are  given  in  Table  IV.  In  these  observations,  as  in  those  made 
with  the  Equatorials,  the  same  portion  of  the  nucleus  was  not 
always  observed.  Tho  complex  character  of  the  nucleus  of  this 
comet,  and  the  uncertainty  that  must  exist  as  to  which  portion 
of  it  the  observations  refer,  will  present  serious  difficulties  to  the 
computer. 

The  memoir  is  illustrated  by  several  interesting  sketches  of 
the  head  and  nucleus  of  the  comet,  and  by  copies  of  the  unique 
series  of  photographs  so  happily  secured  by  Dr.  Gill. 


Professor  Hall's  Determinations  of  Stellar  Parallax. 

Professor  Asaph  Hall  has  published  in  an  Appendix  to  the 
Washington  Observations  for  1883,  a  further  series  of  observa- 
tions for  stellar  parallax. 

The  method  adopted  was  the  same  as  that  employed  for  the 
earlier  observations,  viz.  to  observe  the  differences  of  Declination 
of  the  principal  stars  with  respect  to  small  stars  near  them  which 
are  supposed  to  have  no  physical  connection  with  the  large  stars. 
The  method  of  measuring  differences  of  Declination  was  chosen 
because  the  measurement  of  distances  with  the  filar  micrometer 
of  the  Naval  Observatory  has  been  found  more  accurate  than 
that  of  angles  of  position ;  and  also  because  observations  had 
shown  that  there  was  no  sensible  term  depending  on  the  temper, 
ature  in  the  value  of  a  revolution  of  the  micrometer  screw. 


184  Report  of  the  Council  to  the  xLViL  4, 

Professor  Hall's  results  for  the  four  stars  observed  give  the 
following  values  of  the  parallax  : — 


n  u 


40 (©*)  Eridani  »-  +  0223 ± 0*0202 
6  B  Cygni  » -  —0021  ± 0*0077 
a  Lyra  t- +0-134  ±0*0055 

61  Cygni  »  -  +  0270  ±  o  0101 

The  parallax  of  40  (o9)  Eridani  was  obtained  by  measures  of 
the  difference  of  Bight  Ascension  of  a  star  of  the  eleventh  magni- 
tude 32s  following  and  48"  south  of  the  principal  star.  The 
distance  was  so  great  that,  with  the  power  of  383  employed,  it 
was  necessary  to  move  the  eyepiece  in  order  to  bring  the  stars 
successively  into  the  field,  which  introduced  an  element  of  con- 
siderable difficulty.  Dr.  Gill's  value  of  the  parallax  of  this  star 
is  o"*i66 +o"*oi8. 

The  negative  value  of  the  parallax  obtained  for  6  B  Cygni  is 
suggested  by  Professor  Hall  as  indicating  a  parallax  of  the  star 
of  comparison  or  some  systematic  error  in  the  observations  of  the 
summer  and  winter  months.  The  result  is  strikingly  different 
from  Sir  R.  S.  Ball's  provisional  determination — 

»«o"-482±o"-o54 

An  error  having  been  detected  in  the  reduction  of  the  obser- 
vations for  determining  the  parallax  of  a  Lyrce  and  61  Cygni, 
made  in  1880  and  1881  (noticed  in  the  Beport  for  1882),  the 
result  now  given  for  a  Lyres  is  from  a  re-reduction  of  the  original 
observations.  In  the  case  of  61  Cygni  two  additional  series 
of  observations,  near  the  times  of  the  maximum  positive  and 
negative  coefficients  of  parallax,  were  made  in  1885  and  1886  and 
combined  with  the  earlier  series  re-reduced.  Professor  Hall's 
concluded  value  of  the  parallax  is  much  smaller  than  what  has 
been  determined  by  other  observers.  The  author  calls  attention 
to  the  discrepancy,  but  considers  that  the  results  appear  to  be 
the  best  that  can  be  derived  from  the  observations. 


Stellar  Photography. 

The  most  notable  records  in  relation  to  stellar  photography 
during  the  past  year  are  embodied  in — 

I. — A  remarkable  article  entitled  *•  An  investigation  in  Stellar 
Photography,"  forming  part  of  vol.  xi.  of  the  Memoirs  of  the 
American  Academy,  by  Professor  Pickering. 

II. — A  Monograph  on  Astronomical  Photography,  by  Admiral 
Mouchez,  in  the  Annuaire  du  Bureau  des  Longitudes,  Paris, 
1887. 


Feb.  1887.      Sixty-seventh  Annual  General  Meeting.  185 

III. — The  article  on  Stellar  Photography  contained  in  the 
February  number  of  the  Nineteenth  Century  %  by  Mr.  Common. 

IV. — The  Successful  Application  of  Photography  to  the 
Determination  of  Stellar  Parallax,  by  Professor  Pritchard,  in  the 
January  number  of  the  Monthly  Notices  of  the  Royal  Astronomical 
Society. 

V. — A  paper  in  the  Astronomische  Nar.hrichten,  No.  2737, 
on  the  photographic  work  executed  in  the  Imperial  Observatory 
of  Potsdam. 

Of  some  of  these  records  it  is  proposed  to  give  a  very  rapid 
outline,  referring  the  Fellows  of  the  Society  to  the  original 
documents  for  the  various  details  connected  with  each.  It  may 
be  remarked,  in  limine,  that  in  the  publications  enumerated,  there 
is  prefigured  nothing  short  of  an  entire  revolution  in  the  applica- 
tion of  instrumental  methods  to  astronomical  research.  The 
superb  instruments  now  existing,  monuments  as  they  are  and 
ever  must  be  of  the  genius  of  a  long  line  of  highly  gifted  men, 
will  not  indeed  be  wholly  superseded,  bat  will  be  mainly  valuable 
as  instruments  of  verification  of  labours  and  results  obtained, 
not  in  painful  driblets,  but  in  groups  and  masses  by  shorter 
processes.  Astronomers'  attention  will,  in  the  near  future,  not 
be  confined  to  the  direct  scrutiny  of  the  heavens  alone,  but  to 
the  study  of  the  faithful  pictures  thereof,  taken  at  will  in  rapidly 
occurring  successive  periods.  The  consideration  of  these  pic- 
torial views  will  take  the  place  of  laborious  catalogues. 
Potentially  they  will  be  such  in  themselves. 

I.  The  Harvard  Memoir. — In  this  memoir  Professor  Picker- 
ing describes  a  modification  of  existing  forms  of  camera,  consist- 
ing mainly  of  an  adjusted  compound  photographic  lens  of  about 
eight  inches  diameter  and  forty-five  inches  focal  length  and  con- 
trolled by  a  standard  clock,  by  means  of  which  he  can,  among 
other  adaptations  to  be  presently  described,  take  pictures  of  the 
heavens  with  considerable  facility  and  sufficiently  accurate  for 
maps.  With  one  hour's  exposure,  stars  of  a  brightness  such  as 
those  in  Peters'  and  Chacornac's  charts  can  be  photographed, 
and  when  conveniently  enlarged,  copies  can  be  printed  in 
permanent  ink  by  some  of  the  many  processes  known  at  present. 
Such  maps  will  be  sufficient  as  charts,  but  unavailable  for  the 
determination  of  small  changes  in  position.  Perhaps  these 
pictorial  charts  might  be  supplemented  by  smaller  and  more 
accurate  pictures  of  selected  portions  of  the  heavens  for  pur- 
poses of  great  precision.  He  entertains  the  thought  that  in  two 
observatories,  respectively  north  and  south  of  the  Equator,  the 
whole  heavens  might  be  charted  (to  mag.  13  ?)  in  less  than 
twelve  months.  Whether  a  much  wider  division  of  labour  and 
a  somewhat  extended  scale  in  the  order  of  faintness  might  not 
be  more  desirable  will  probably  be  best  discussed  in  the  proposed 
.  convention  at  Paris  in  April  next. 

Of  greater  originality,  and  possibly  of  even  greater  value,  i? 

p 


186  Report  of  the  Council  to  the  xlvii,  4, 

the  proposition  of  Professor  Pickering  to  determine  the  relative 
brightness  of  stars,  by  availing  himself  of  the  traces  made  by 
stars  on  the  photographic  plate  while  passing,  either  by  unaltered 
diurnal  motion,  or  instrnmentally  retarded,  across  the  field  of 
view.    In  his  hands  the  method  assumes  a  scientific  value  entirely 
different  from  the  haphazard  estimates  of  magnitude  hitherto  put 
into  practice.     For  the  brighter  stars  (that  is,  brighter  than  the 
eighth  magnitude),  even  when  near  the  Equator,  a  trace  is  formed 
when  the  camera  is  stationary ;  for  others  less  bright  the  dura- 
tion of  the  transit  can  be  regulated  as  need  requires.      It  is 
obvious  that  as  the  stars  approach  the  Pole,  the  traces  made 
during  a  given  exposure  of  the  plate  become  shorter  and  therefore 
necessarily  are  actinised  to  a  greater  extent,  depending  on  their 
length.    When  the  camera  has  been  pointed  to  the  Pole,  traces 
of  stars,  even  of  the  thirteenth  and  fourteenth  magnitudes,  have 
been  photographed  with   a  stationary  telescope.    A  scientific 
method  of  estimating  relative  brightness  thus  becomes  available, 
it  being  always  premised  that  a  scale  of  magnitudes,  depending 
on  the  breadth  and  length  of  the  traces,  has  been  carefully  pre- 
pared beforehand.     The  details  of  the  process  must  be  gathered 
from  the  original  memoir,  and  will  amply  repay  the  attention  of 
the  reader.    It  should  be  added  that  Professor  Pickering  has 
successfully  applied  his  method  numerically  to  stars  in  the 
Pleiades,  and  to  others  near  the  Pole. 

The    most    remarkable    and    valuable    part   of    Professor 
Pickering's  memoir  is  that  in  which  he  applies  the  method  of 
trails  or  traces  to  the  photography  of  stellar  spectra.     Hitherto 
the  method  of  using  a  narrow  slit,  supplemented  or  not  by  a 
cylindrical  lens,  and  requiring  extreme  accuracy  in  the  driving 
clock,  and  even  then  a  continued  personal  vigilance  for  the 
manual  correction  of  its  irregularities,  has  proved  a  most  serious 
drawback  in  the  register  of  stellar  spectra  by  the  aid  of  photo- 
graphy.   By  the  method  of  traces  the  slit,  the  cylindrical  lens, 
and  the  painful  watching  are  dispensed  with.     A  prism  (of  150, 
as  used  by  Professor  Pickering)  is  placed  in  front  of  the  ob- 
jective, with  its  refracting  edges  horizontal  when  the  star  is  on 
the  meridian.     In  this  way  the  star  impresses  its  own  spectrum, 
with  the  lines  thereto  peculiar,  on  the  sensitised  plate.     In  the 
case  of  the  brighter  stars  the  telescope  itself  remains  stationary 
during  the  time  of  exposure ;  in  the  case  of  fainter  stars,  which 
require  a  longer  time  to  impress  their  traces  on  the  plate,  the 
instrument  is  driven  at  any  convenient  rate,  so  as  to  produce  in 
a  given  time  a  line  of  the  necessary  length.     In  point  of  fact, 
the  light  of  the  star  itself,  by  diurnal  motion,  becomes  virtually 
a  line  of  light,  or  illuminated  slit,  which  is  dispersed  into  its 
spectrum  by  the  refracting  prism.     Professor  Pickering,  in  his 
memoir,  gives  an  enlarged  photographic  picture,  containing  ex- 
amples of  this  method  applied  to  the  Pleiades  and  some  of  the 
brighter  stars.     The  process  gives  the  promise  of  great  facility, 
and  probably  great  accuracy,  amply  sufficient  for  the  determi- 


Feb.  1887.       Sixty-seventh  Annual  General  Meeting.  187 

nation  of  the  class  of  a  star's  spectrum,  even  in  the  case  of  stars 
of  the  eighth  magnitude.  This  part  of  the  Harvard  labours 
should  not  be  dismissed  without  reference  to  the  remarkable 
coup  cTonl  of.  the  spectra  of  stars  in  the  Pleiades.  It  is  impossible 
to  look  at  it  without  the  suggestion  of  a  community  of  origin  in 
the  material  and  formation  of  this  historic  group.  And  the 
deduction  of  this  cosmical  fact  is  the  result  of  the  intelligent 
labour  of  a  single  hour !  Altogether  this  valuable  memoir 
indicates  a  very  distinct  advance  of  the  application  of  photo- 
graphy to  astronomical  research. 

"  Annuaire  du  Bureau  des  Longitudes." — Admiral  Monchez  has 
herein  given  an  interesting  account  of  celestial  photography  from 
the  time  of  the  well -aimed  but  unsuccessful  attempts  of  Niepce 
and  Dagnerre,  in  1839,  to  the  superb  results  now  being  achieved 
at  Paris  by  the  brothers  Henry.  The  labours  of  these  latter 
savants  are  now  happily  so  well  known  to  the  astronomical 
world  that  an  account  of  them  here  would  be  superfluous.  One 
of  the  most  striking  features  in  the  photographic  enlargements  of 
the  plates  is  the  definite  roundness  and  general  neatness  of  the 
impressions  of  the  stars  ;  features  which  indicate  the  remarkable 
perseverance,  or  it  may  be  termed  the  endurance,  of  the  observer 
in  the  manual  control  of  the  driving  clock  during  the  usual 
exposure  of  an  hour.  For  any  purpose  of  exact  measures  this 
definiteness  of  outline  is  indispensable.  On  some  of  these  plates 
there  are  traces  of  impressions  of  stars  which  may  probably  be 
regarded  as  of  the  sixteenth  magnitude.  In  submitting  these 
photographs  to  enlargements,  and  subsequent  printing  in  some 
permanent  material,  such  as  a  modification  of  printer's  ink,  there 
is  at  present  an  unavoidable  loss  of  the  faintest  stars,  amounting 
in  general  to  about  a  magnitude  and  a  half ;  this  will  apparently 
limit  printed  copies  to  about  the  fourteenth  magnitude  on 
Pogson's  scale,  and  requires  an  exposure  at  present  exceeding 
an  hour.  We  believe  it  is  the  present  proposition  of  the  Paris 
astronomers  to  effect  arrangements  for  the  photography  of  the 
entire  stellar  regions  to  this  extent  of  brightness.  This  scheme 
is  much  more  extensive,  and  perhaps  more  ambitious,  than  that 
proposed  by  the  American  astronomer,  and  instead  of  its  com- 
pletion at  two  observatories,  in  less  than  a  twelvemonth,  will 
require  the  co-operation  of  eight  or  ten  at  least,  extending  the 
labour  through  four  or  five  years.  Indeed,  if  there  be  a  dupli- 
cation of  the  photographic  plates — and  this  seems  to  be  indis- 
pensable for  securing  reliable  results — the  time  occupied  in  the 
work  and  the  number  of  the  observers  employed  must  be 
further  extended.  But  these  are  points,  as  already  suggested, 
which  must  be  submitted  to  the  consideration  of  the  convention 
at  Paris,  summoned  by  Admiral  Mouchez,  in  April  next. 

In  the  Annuaire  (page  785)  there  is  a  very  interesting  and 
instructive  plate  of  highly  magnified  images  of  stars  impressed 
on  a  photographic  film.  But  impressions  of  this  nature,  and 
thus  highly  magnified,  would  be  far  too  loose  and  scattered  in 

p  2 


1 88  Report  of  the  Council  to  the  xlvii.  4, 

form  to  admit  of  micrometric  measurement ;  they  greatly  differ 
in  appearance  from  the  round  and  definite  and  solid-looking 
formations  submitted  to  measurement  at  Oxford ;  nevertheless 
they  do  afford  a  good  idea  of  the  mode  in  which  the  sensitised 
material  is  blackened  and  deposited.  But  it  should  be  remem- 
bered that  this  form  of  actinised  deposit  was  distinctly  noticed 
and  described  by  Bond  some  thirty  yeara  ago.  . 

The  direction  of  the  valuable  work  so  ably  accomplished  at 
the  Paris  Observatory  will  be  seen  from  the  following  catalogue, 
taken  from  the  last  annual  report  of  that  institution.  It  includes 
forty-two  large  plates  of  the  Milky  Way  and  of  other  regions, 
viz.  the  neighbourhood  of  £  Lyres  and  of  Vega,  showing  after 
two  hours'  exposure,  stars  much  feebler  than  the  debilissima  of 
Sir  J.  Herschel,  and  feebler  than  the  sixteenth  magnitude,  some 
of  which  have  probably  not  been  seen  before.  Clusters  in 
Hercules  (two  plates),  in  Ophiuchns,  in  Perseus,  and  more  than 
six  hundred  double  or  multiple  stars ;  short  exposures  of  groups 
intended  for  micrometrical  measurement,  such  as  the  Pleiades, 
Prcesepe,  and  M.  23  OphiucM. 

Mr.  Common's  Article  in  the li  Nineteenth  Century." — It  is  quite 
unnecessary  to  refer  to  the  highly  interesting  particulars  dis- 
cussed in  this  paper  with  all  the  authority  of  a  master  in  the 
art ;  it  will  be  in  the  hands  of  ail  astronomers  interested  in  the 
progress  of  their  science. 

In  even  this  condensed  reference  to  the  advances  in  Celestial 
Photography,  certainly  established  by  Mr.  Common,  it  is  right  to 
add  that  Mr.  Roberts'  photographs,  which  are  in  the  possession 
of  the  Society,  seem  in  some  respects  to  have  surpassed  the 
Orion  Nebula  of  that  gentleman,  as  well  as  the  Pleiades  Group 
of  MM.  Henry.* 

The  Parallax  of  61  Cygni. — So  far,  the  foregoing  records  refer 
in  the  main  to  what  may,  without  derogation  or  offence,  be 
termed  the  pictorial  or  delineation- side  of  astronomical  photo- 
graphy. We  have  already  stated  what  the  brothers  Henry  have 
been  able  to  achieve  in  the  way  of  celestial  charts ;  possibly  even, 
more  remarkable  results  have  been  accomplished  by  Mr. 
Common,  who  has  produced  a  representation  of  the  Orion 
Nebula  surpassing,  it  may  be,  in  accuracy  and  in  minuteness  of 
detail  the  united  labours  of  Herschel  and  Bosse  in  England,  and 
of  Bond  and  Holden  in  the  United  States.  One  potential  only 
of  the  new  art  remained  still  to  be  examined  ;  can  it  be  relied  on 
as  presenting  an  amount  of  accuracy  in  delicate  micrometrical 
measurement  equal  to  that  derived  from  the  use  of  the  Equa- 
toreal  Telescope  and  the  Heliometer  ?  Jn  the  hands  of  Bond 
thirty  years  ago  it  did  indeed  furnish  the  means  of  measuring 
the  relative  positions  of  the  components  of  such  double  stars  as 
be  could  then  photograph  ;  but  the  important  question  remains, 
can  it  now,  in  its  more  important  modern  development,  vie  with 

*  See  Monthly  Roticea  for  January  1887  and  Admiral  Mouches's  note  on 
p.  813  of  the  Paris  Annuaire  for  1887. 


Feb.  1887.      Sixty-seventh  Annual  General  Meeting,  189 

tho  Heliometer  in  the  determination  of  such  minute  quantities 
as  are  discussed  in  problems  connected  with  Stellar  Parallax  ? 
In  a  word,  can  it  be  relied  on  in  the  conduct  of  varying  measures 
when  they  are  extended  through  a  series  of  many  months  and 
over  hundreds  of  sensitised  plates  P  There  is  reason  to  believe 
that  a  reply  in  the  affirmative  has  been  given  to  this  crucial  ques- 
tion by  the  very  recent  and  successful  determination  of  the 
Parallax  of  61  Cygni  at  the  University  Observatory  in  Oxford. 
No  less  than  eight  independent  determinations  of  the  relative 
parallax  of  the  two  components  of  this  star,  in  relation  to  four 
faint  stars  in  their  neighbourhood,  present  an  accordance  that 
was  scarcely  to  be  hoped  for  anterior  to  the  result.  A  collateral 
advantage  presented  by  this  method  consists  in  this,  that  the 
relative  parallax  is  obtainable  not  merely  in  respect  of  four 
stars,  but  in  respect  of  all  the  other  stars  upon  the  photographic 
plate.  In  this  way  the  resulting  mean  becomes  not  merely 
relative  parallax,  but  approaches  the  absolute.  In  the  case  of 
this  particular  star,  the  result  of  the  computations  is  a  parallax 
lying  as  a  mean  between  those  determined  by  Bessel,  Auwers, 
and  Ball. 

Dr.  Lohse,  at  Potsdam,  ha9  successfully  applied  the  ordinary 
refracting  telescope  to  the  subject  of  Stellar  Photography,  and 
this  he  has  done  without  separating  the  lenses  of  the  object  glass 
or  the  introduction  of  a  subsidiary  lens.  It  is  stated  that  after- 
one  hour's  exposure  of  the  plate  in  the  proper  focal  position,  the 
faintest  stars  visible  in  the  telescope  to  the  eye  are  distinctly 
impressed  on  the  photograph. 

For  information  on  the  valuable  and  interesting  work  in 
Stellar  Photography,  now  in  process  of  execution  under  the 
direction  of  Dr.  Gill,  the  reader  is  referred  to  the  Report  from 
the  Royal  Observatory  at  the  Cape  of  Good  Hope,  printed  in 
the  present  number  of  the  Monthly  Notices. 

On  taking  a  general  survey  of  the  foregoing  records  of  the 
potency  and  astonishing  progress  of  this  new  application  of  a 
recent  art,  placing  the  whole  starry  heavens  as  a  picture  in 
our  hands,  one's  thoughts  irresistibly  turn  to  the  existence 
of  considerable  groups  and  sections  of  learned  men,  who  per- 
suade themselves  that  astronomy,  as  a  science,  culminated  in 
the  researches  of  Lagrange  and  Laplace,  and,  as  an  art  was 
worn  out  in  the  hands  of  Bessel  and  the  Herschels.  It  has  been 
still  further  affirmed  that,  amidst  the  modern  developments  and 
activities  of  other  branches  of  knowledge,  astronomy,  whether  as 
a  science  or  an  art,  has  ceased  to  possess  human  interest.  An 
unprejudiced  perusal  of  the  above  and  similar  records  is  sufficient 
to  indicate  the  utter  unreasonableness  of  the  latter  thought.  It 
would  be  far  nearer  to  the  truth  to  affirm  that  at  the  present 
hour,  both  as  an  art  and  a  science,  astronomy  possesses  the  elasti- 
city and  the  hopeful  enterprise  of  robust  youth.  It  would  be  a 
still  securer  belief  to  rest  assured  that  as  long  as  the  human  mind 
retains  its  experience  of  the  past,  and  its  incentives  to  curiosity 


190  Report  of  the  Council  to  the  xlvii.  4, 

in  respect  of  the  future,  no  true  art  can  ever  culminate,  and  no 
true  science  can  become  effete.  c.  p. 


The  Velocity  of  Light. 

Professor  Newcomb  has  published  in  the  second  volume  of 
the  important  series  of  astronomical  papers  prepared  for  the  use 
of  the  American  Ephemeris  and  Nautical  Almanac  his  measures 
of  the  velocity  of  light  made  during  the  years  1880-82. 
Chapter  I.  is  devoted  to  an  interesting  historical  account  of 
previous  researches  on  the  subject.  The  method  adopted  in  the 
present  investigation  was  that  of  Foucault,  with  certain  modi- 
fications, principally  in  the  optical  arrangements.  The  form  of 
the  apparatus  and  the  conditions  of  the  problem  are  fully  de- 
scribed in  Chapters  II.  and  III. 

The  revolving  mirror  consisted  of  a  rectangular  prism  of 
polished  steel,  the  vertical  faces  of  which  were  nickel-plated, 
and  thus  formed  the  surface  from  which  the  light  was 
reflected.  At  each  end  of  the  prism  a  fan -wheel  was  fixed,  and 
the  mirror  was  driven  by  an  air  blast  playing  upon  the  opposite 
side  of  each  wheel.  For  the  fixed  mirror,  two  concave  mirrors, 
each  about  40  cm.  in  diameter,  were  used  side  by  side,  so  as 
to  obviate  any  slight  displacements  from  a  single  mirror,  and 
in  order  to  strengthen  the  return  image.  The  radius  of  the 
curvature  of  the  mirror  was  about  3000  metres. 

In  1880  the  locations  of  the  mirrors  were  at  a  distance  apart 
of  2550*95  metres,  but  in  1881  and  1882  the  longer  distance  of 
3721*21  metres  was  employed. 

All  the  observations  are  given  in  detail,  and  the  results  are 
very  fully  discussed  on  the  hypotheses  (1)  that  the  motion  of 
the  revolving  mirror  is  uniform  in  running ;  (2)  that  the  figure 
of  the  mirror  remains  invariable ;  and  (3)  that  the  changes  in 
direction  of  the  reflected  ray  are  correctly  measured  by  the 
angular  motion  of  the  receiving  telescope  around  the  axis  of  the 
revolving  mirror.  This  discussion  shows  certain  systematic 
differences  in  the  results  obtained  for  each  year,  the  final  result 
depending  entirely  upon  the  measures  of  1882. 

Professor  Newcomb  gives  the  concluded  velocity  of  light  in 
vacuo  as  299860  kilometres,  with  a  probable  error  of  dt3o  kilo- 
metres. Combining  this  result  with  Nyren's  value  of  the  con- 
stant of  aberration,  the  corresponding  solar  parallax  is  8"' 794. 

To  this  very  important  investigation  are  appended  some 
interesting  researches  by  Mr.  Michelson  on  the  velocities  of  white 
and  coloured  light  in  air,  water,  and  carbon  disulphide.  The 
conclusions  (which  the  author  advances  with  great  diffidence),  are 
that  the  velocity  of  light  in  carbon  disulphide  is  to  that  in  air 
as  1 '00  to  176,  with  an  uncertainty  of  two  units  in  the  second 
place  of  decimals ;  and  that  orange-red  light  travels  in  carbon 
disulphide  from  1  to  2  per  cent,  faster  than  greenish-blue  light. 


Feb.  1887.       Sixty-seventh  Annual  General  Meeting.  191 


The  Visual  Solar  Spectrum  in  1884. 


The  Royal  Society  of  Edinburgh  has  published  during  the  year 
{Transactions,  vol.  xxxii.  Part  III.)  a  remarkable  study  of  the 
solar  spectrum  by  the  Astronomer  Royal  for  Scotland.     The 
work  was  undertaken  by  him  with  the  leading  idea  of  ascertain- 
ing whether  the  spectroscope  would  offer  any  evidence  as  to 
changes  in  the  absorption  of  our  atmosphere  resulting  from  the 
great  volcanic  outbursts  of  1883,  and  especially  from  that  of 
Krakatoa.     The  conditions  at  Edinburgh  being  unfavourable  for 
work  of  the  kind,  Professor  Smyth  selected  as  his  observing 
station  a  country-house  called  "  Kurn  Hattin,"  about  two  miles 
to  the  north  of  Winchester,  and  proceeded  thither  early  in  June 
1884.     He  was  provided  with  a  fine  Rowland  grating  of  14438 
lines  to  the  inch,   and  had  attached  a  recording  apparatus  of 
special  form  to  his  spectroscope,  which  enabled  him  to  record  with 
great  rapidity  the  positions  of  the  lines  observed.     It  was  his  in- 
tention to  form  three  complete  and  independent  charts  of  the 
entire  spectrum,  and  this  design  he  was  enabled  to  carry  out  in 
its  entirety,  despite  very  unpropitious  weather,  by  the  assistance  of 
Colonel  Knight.     The  results  of  his  observations  are  given  in 
sixty  plates,  giving  five  views  of  the  spectrum,  the  first  two 
being  reproductions  of  the  work  of  some  standard  observer  for 
the  sake  of  comparison,  the  maps  of  Angstrom  and  Fievez  being 
nsed  for  the  most  part,  and  the  last  three  the  three  successive 
"Winchester"   spectra.     All  are  reduced   to  the  same  scale, 
which  is  not  the  usual  one  of  wave  length,  but  of  wave  fre- 
quency to  the  British  inch ;    the  wave  length  expressed  in 
tenth-metres  is  however  added.     The    part    of  the  spectrum 
shown  in  any  plate  is  clearly  and  agreeably  indicated  by  tinting 
it  of  one  homogeneous  colour,  approximately  the  average  colour  of 
the  region ;  whilst  the  relative  intensities  of  the  dark  lines  are 
indicated  by  variations  in  tbeir  heights.     The  wave  lengths  are 
not  absolute  determinations,  bat   differential  only,  Angstrom's 
values  for  the  principal  lines  being  assumed  throughout.     Even 
so,  however,  there  are  occasionally,  as  Professor  Smyth  him- 
self points  out,  some  striking  discrepancies  between  the  posi- 
tions of  lines  as  recorded  in  the  three  chartings  ;  but  when  the 
unfavourable   conditions,  under  which  the   greater  part  of  the 
work  was  carried  out,  are  remembered,  and  the  great  rapidity 
with  which  the  observations  were  made — nearly  the  whole  of  the 
second  spectra  m,  extending  from  A  to  h,  and  embracing  about 
7000  lines,  having  been  mapped  in  three  mornings,  1865  lines 
being  laid    down  in     three    hoars — the    general    accord   be- 
tween   the  three  independent  maps  is  very  remarkable.     Per- 
haps not  the  least  important  result  of  the  work  will  have  been  to 


jgz  B-eport  of  the  Council,  etc.  xlvii.  4, 

show  how  rapidly  a  detailed  chart  of  the  entire  visible  spectrum 
can  be  formed  when  a  suitable  recording  apparatus  is  employed. 

With  regard  to  the  immediate  purpose  of  the  charts,  the 
principal  result  Professor  Smyth  deduces  from  them  is,  that  the 
visual  solar  spectrum  in  1884  showed  a  marked  general  dulling 
at  the  two  ends,  the  red  and  violet,  "  such  as  should  arise  from 
the  upper  air,  being  at  that  time  overcharged  with  opaque 
dusty  particles.'1  The  evidence  for  the  existence  of  fresh  atmo- 
spheric lines  was  much  less  satisfactory,  although  a  strong  line, 
wave  length  4733  tenth-metres,  was  repeatedly  observed  at 
Winchester,  which  is  not  shown  on  Fievez's  chart.  The  repetition 
of  such  a  survey  of  the  spectrum  as  Professor  Smyth  has  here 
carried  out,  at  intervals  of  two  or  three  years  apart,  would  prob- 
ably lead  to  the  detection  of  changes  in  it  which  could  scarcely 
fail  to  be  instructive.  In  the  meantime,  Professor  Smyth 
has  supplied  a  valuable  record  of  its  appearance  in  the  summer 
of  1884. 

£.  W.  M* 


*  -*  * 


Feb.  1887.  /        193  r  ,     rx 


{    UN/vri 


Tapers  read  before  the  Society  from  February  1886 

to  February  1887. 

1886.  . 
Mar.  12.  Phenomena  of  the  satellites  of  Jupiter  and  Saturn,  and 
occnltations  of  stars  by  the  Moon,  observed  at  Mr. 
Edward  Crossley's  Observatory,  Bermerside,  Halifax, 
in  the  year  1885,  with  the  a4-inch  Cooke  Refractor. 
J.  Gledhill. 

Occultation  of  Aldebaran,  1886,  Jan.  16.  Professor 
R.  S.  Ball. 

Occnltations  observed  atBeloit,  Wisconsin,  in  1884-85. 
J.  Tatlock. 

On  the  orbit  of  40  (o2)  Eridani.     J.  E.  Gore. 

The  great  shower  of  Andromedes,  1885.  T.  W.  Back- 
house. 

Some  new  red  and  orange-red  stars.  Rev.  T.  E. 
Espin. 

Observation  of  the  conjunction  of  Saturn  and  /n  Gemi- 
norum.     J.  Tebbntt. 

Additional  remarks  on  the  periodic  time  of  a  Centauri. 
E.  B.  Powell. 

Occnltations  of  stars  by  the  Moon  and  phenomena  of 
Jupiter's  satellites  observed  at  Stonyhnrst  in  the  year 
1885.     Rev.  S.  J.  Perry. 

The  new  star  in  Orion,  photometrically  and  spectrosco- 
pically  observed  at  the  Oxford  University  Observa- 
tory.    Professor  C.  Pritchard. 

Observations  of  comets  d  1885  (Fabry),  and  e  1885 
(Barnard),  made  at  the  RoyaJ  Observatory,  Green- 
wich. Communicated  by  the  Astronomer  Royal. 

Note  on  some  recently  published  spectroscopic  observa- 
tions.   E.  W.  Maunder. 

Observations  of  the  new  star  in  Andromeda,  made  at 
Mr.  Wigglesworth's  Observatory  with  15'5-inch  Cooke 
Refractor.    J.  G.  Lohse. 
April  9.  Note  on  the  radiation  of  meteors.     W.  F.  Denning. 

On  some  suggested  improvements  in  the  practical 
working  of  M.  Loewy's  new  method  of  determining 
the  elements  of  astronomical  refraction.     David  Gill. 

On  the  orbit  of  a  Centauri.    E.  B.  Powell. 


194  Papers  read  before  the  Society.  xlyil  '4> 

April  9.  Observations  of  the  phenomena  of  Jupiter's  satellites, 
made  at  the  Adelaide  Observatory  with  the  8-inch 
Cooke  Equatorial  in  the  year  1885.  Communicated 
by  C.  Todd. 

The  magnitude  of  17  Argus  in  March  1886.  W.  H. 
Finlay. 

On  the  protuberances  visible  in  the  spectrum  with  a 
narrow  slit.     E.  L.  Trouvelot. 

Observations  of  occupations  of  the  stars  by  the  Moon, 
1884-85,  and  of  the  IVth  satellite  of  Jupiter,  1885, 
made  at  the  Radcliffe  Observatory,  Oxford.  Com- 
municated by  E.  J.  Stone. 

On  the  semi-diameter  of  Venus.     W.  G.  Thackeray. 

The  nebulae  in  the  Pleiades,     A.  A.  Common. 

Note  on  the  observations  for  coincidence  of  the  colli- 
mators through  the  cube  of  the  Transit  Circle  at  the 
Royal  Observatory,  Greenwich.     H.  H.  Turner. 

Observations  of  Comets  d  1885  (Fabry),  and  e  1885 
(Barnard),  made  at  the  Royal  Observatory,  Green- 
wich.    Communicated  by  the  Astronomer  Royal. 
May  14.  Note  on  M.  Trouvelot's  paper  on  protuberances  visible 
in  the  spectrum  with  a  narrow  slit.   E.  W.  Maunder. 

Introduction  to  a  catalogue  of  the  colours  of  1730 
stars.     W.  S.  Franks. 

Observations  of  the  companion  of  Sirius  made  at  the 
Dearborn  Observatory,  Chicago.  Prof.  G.  W.  Hough. 

Jupiter9 s  third  satellite  in  transit,  April  11,  1886. 
W.  F.  Denning. 

Observations  of  the  new  star  in  Orion.     J.  E.  Gore. 

The  meteor  shower  of  Halley's  Comet.  W.  F.  Denning. 

On  the  proper  motion  of  twenty-nine  telescopic  stars. 
J.  L.  E.  Dreyer. 

Note  on  a  remarkable  sun  spot.     B.  J.  Hopkins. 

Observations  of  Comets  d  1885  (Fabry),  e  1885  (Bar- 
nard), and  a  1886  (Brooks),  made  at  the  Royal 
Observatory,  Greenwich.  Communicated  by  the 
Astronomer  Royal. 

The  fourth  satellite  of  Jupiter  during  superior  conjunc- 
tion on  the  night  of  April  5,  1886.     E.  J.  Spitta. 

Comparisons    of   certain     southern    star    catalogues. 
A.  M.  W.  Downing. 
June  11.  Micrometric  observations  of  Nova  Andromeda,  made 
at  the  Dunsink  Observatory.     Sir  R.  S.  BalL 

Observations  of  the  satellites  of  Saturn  and  Mars,  and 
of  the  companion  of  Sirius,  made  at  the  U.S.  Naval 
Observatory,  Washington.     Professor  Asaph  Hall. 

On  the  orbit  of  £  Sagittarii.     J.  E.  Gore. 

On  Delaunay's  method  of  calculating  the  terms  of  long 
period  in  the  motion  of  the  Moon.     E.  Neison. 


Feb.  1887.  Papers  read  before  the  Society.  195 

June  11.  Observations    of   Comet    Fabry    (d  1885),  made  at 

Grabamstown,  Cape  of  Good  Hope.    L.  A.  Eddie. 
On  Kepler's  problem.    B.  Bryant. 
Observations  of  comet  a  1886  (Brooks),  made  at  tbe 

Boyal  Observatory,  Greenwich.     Communicated  by 

tbe  Astronomer  Boyal. 
On  the  asserted  foreshortening  of  the  inner  side  of  the 

penumbra  of  spots  when  near  the  Son's  limb.     Bev. 

F.  Howlett. 
On  the -superiority  of  zinc  and  steel  pendulums.     T. 

Buckney. 
Ephemeris  of  the  satellites  of  Saturn,  1886-87.     A. 

Marth. 
The  northern  hemisphere  of  Mars.    N.  E.  Green. 
On  a  remarkable  instance  of  the  detection  of  distortion 

in  a  photographic  film,  measured  for  the  purpose  of 

stellar  parallax.     Professor  C.  Pritchard. 
Supplementary  measures  of  the  magnitudes  of  a  zone 

of  stars  near  the  equator  for  reference  as  standards  of 

magnitude  in  lieu  of  Polaris.  Professor  C.  Pritchard. 
Note  with  respect  to  the  invention  of  the  achromatic 

telescope.     A.  C.  Banyard. 
Not.  12.  Observations  of  the  variable  star  B  Oarince  from  Sept. 

1883  to  April  1886.     J.  Tebbutt. 
Observations  of  Comets  d  1885  (Fabry),  e  1885  (Bar- 
nard), c  1886,  and  L    1886  (Brooks),  made  at  the 

Sydney  Observatory.  Communicated  by  H.  C.  Russell. 
Observations  of  Comets  1877,  I.,  II.,  III.,  VI. ;  1880, 

III.  ;  1882,  III. ;  and  1884,  III.,  made  at  the  Dun 

Echt  Observatory  with  the  15-inch  Refractor.     Dr. 

B.  Copeland. 
Sextant    observations  of  Fabry's   Comet.      Capt.   J. 

Campbell,  and  Capt.  D.  S.  Cromarty. 
Observation  of  Calliope,    made    at   the    Observatory, 

Diisseldorf.     [Extract  from  a  letter  to  Mr.  Stone.] 

Dr.  B.  Luther. 
Ephemeris  of  the  satellite  of  Neptune,   1886-87.     A. 

Marth. 
On  the  orbit  of  2  1757.     J.  E.  Gore. 
A  reply  to  Mr.    Neison's     strictures    on  Delaunay's 

method  of  determining  the  planetary  perturbations  of 

the  Moon.     G.  W.  Hill. 
On  the  orbit  of  Comet  II.,  1883,  discovered  by  Mr. 

Boss.     Lieut.-Gen.  J.  F.  Tennant. 
On  the  determination  of  the  Badius  Vector  in  the  abso- 
lute orbit  of  the  planets.     Dr.  H.  Gylden. 
Observations  of  the  phenomena  of  Jupiter's  Satellites 

made  at  Windsor,  New  South  Wales,  in  the  year 

1886.     J.  Tebbutt. 
1 
1 


196  Tapers  read  before  the  Society.  .    xlyu.  4> 

Nov.  12.  NewalTs  occultor.    R.  S.  Newall. 

Distribution  of  Meteor  Streams.    W.  F.  Denning. 

Note  on  the  star  y  Equulei.     G.  Knott. 

Reply  to  certain  questions  raised  before  the  Royal  Astro- 
nomical Society  at  the  meeting  on  1886,  March  12, 
concerning  the  matter  detailed  in  a  paper  entitled 
"  Bright  lines  in  stellar  spectra."     0.  T.  Sherman. 

Note  on  Photographs  of  Stars  in  Cygnw,  taken  in 
August  1886.     Isaac  Roberts. 

Note  on  two  photographs  of  the  Nebulae  in  the  Pleiades, 
taken  in  October  1886.     Isaac  Roberts. 

Ephemeris  for  physical  observations  of  Jupiter,  1887. 
A.  Marth. 

On  evidence  with  respect  to  the  form  of  the  area  of  the 
heavens  from  which  the  meteors  of  November  27, 
1885,  appeared  to  radiate.     A.  C.  Ranyard. 

Observations  of  Comet  /  1886  (Barnard),  made  at 
the  Royal  Observatory,  Greenwich.  Communicated 
by  the  Astronomer  Royal. 

Bands  observed  in  the  spectra  of  sun  spots  at  Stony- 
hurst  Observatory.     Rev.  A.  Cortie. 

Observations  of  Comets  made  at  Mr.  Wigglesworth's 
Observatory  with  the    15*5 -inch    Cooke    Refractor. 
J.  G.  Lohse. 
Dec.  10.  Formulae  for  binary  stars.     J.  E.  Gore. 

Observations  of  Comets  Winnecke  and  Finlay,  1886, 
made  with  the  1  i^-inch  equatorial  and  filar  micro- 
meter at  the  Sydney  Observatory,  Communicated 
by  H.  C.  Russell. 

Ephemeris  of  the  satellites  of  Uranus,  1887.    A.  Marth. 

Second  supplement  to  Sir  J.  Herschel's  general  cata- 
logue of  nebulae  and  clusters  of  stars.   J.  L.  E.  Dreyer, 

Note  on  an  erratic  meteor.     B.  J.  Hopkins. 

On  Hartwig's  Nova  Andromeda.     Dr.  R.  Copeland. 

Mr.  Sherman's  observations  of  bright  lines  in  stellar 
spectra.     E.  W.  Maunder. 

Observations  of  Comet  /  1886  (Barnard),  made  at  the 
Royal  Observatory,  Greenwich.  Communicated  by 
the  Astronomer  Royal. 
Jan.  14.  Spectroscopic  observations  of  the  motion  of  stars  in  the 
line  of  sight  made  at  the  Temple  Observatory,  Rugby* 
G.  M.  Seabroke. 

On  the  best  device  for  revolving  a  dome.     D.  P.  Todd^ 

Meteors  with  curved  paths.     W.  F.  Denning. 

A  new  variable  star  in  Puppis.     A.  S.  Williams. 

On  the  orbit  of  14  (t)  Orionis  (OS  98).     J.  E.  Gore. 

Occultation  of  y  Virginis,  1886,  Dec.  18.     F.  C.  Penrose* 

Photographs  of  nebulae  in  Orion  and  in  the  Pleiades. 
Isaac  Roberts. 


Jeb.  1887.  Papers  read  before  the  Society.  197 

Jan.  14.  Note  on  tbe  electric  illumination  of  the  Armagh 
Refractor.     J.  L.  E.  Dreyer. 

Occultation  of  Aldebaran,  1887,  Jan.  6.  Rev.  S.  J. 
Johnson. 

Observations  of  Comet/  1886  (Barnard),  made  at  the 
Royal  Observatory,  Greenwich.  Communicated  by 
the  Astronomer  Royal. 

Sextant  observations  of  Comets  Fabry  and  Barnard, 
1886.     Capt.  W.  G.  Browne  and  Capt.  W.  RandalL 

On  the  variability  of  the  spectrum  of  y  Gassiopeice. 
Dr.  R.  Copeland. 

Note  on  an  application  of  photography  to  the  deter- 
mination of  stellar  parallax.     Professor  C.  Pritchard. 

Observations  of  the  Moon  made  at  the  Radcliffe  Ob- 
servatory, Oxford,  daring  the  year  1886,  and  a  com- 
parison of  the  results  with  the  tabular  places  from 
Hansen's  Lunar  Tables.     E.  J.  Stone. 

Mean  Right  Ascensions  of  Polaris,  Cephei  51  (He v.), 
&  Ursoe  Minoris  and  X  Ursce  Minoris  for  the  year  1887, 
from  the  Radcliffe  Observations  of  the  years  1880  to 
1886.     E.  J.  Stone. 

Spectroscopic  results  for  the  motions  of  stars  in  the 
line  of  sight  obtained  at  the  Royal  Observatory, 
Greenwich,  in  the  year  1 886.  No.  X.  Communicated 
by  the  Astronomer  Royal. 

Observations  of  occnltations  of  stars  by  the  Moon,  and 
of  phenomena  of  Jupiter's  Satellites,  made  at  the 
Royal  .Observatory,  Greenwich,  in  the  year  1886. 
Communicated  by  the  Astronomer  Royal. 


198  XLYII.  4, 


List  of  Public  Institutions,  and  of  Persons  who  have  contributed  to 
the  Library,  8fc.  since  the  last  Anniversary. 


Her  Majesty's  Government. 

Her  Majesty's  Government  in  Australia. 

Her  Majesty's  Government  in  India. 

The  Lords  Commissioners  of  the  Admiralty. 

The  Norwegian  Government. 

British  Association  for  the  Advancement  of  Science. 

British  Horologies!  Institute. 

Geological  Society  of  London. 

Institute  of  Civil  Engineers. 

Meteorological  Office. 

Photographic  Society  of  Great  Britain. 

Physical  Society  of  London. 

Royal  Asiatic  Society  of  Great  Britain. 

Royal  Geographical  Society. 

Royal  Institution  of  Great  Britain. 

Royal  Meteorological  Society. 

Royal  Observatory,  Greenwich. 

Royal  Society  of  London. 

Royal  United  Service  Institution. 

Society  of  Arts. 

University  College,  London. 

Zoological  Society  of  London. 

Armagh  Observatory. 

Belfast  Natural  History  and  Philosophical  Society. 

Birmingham  Philosophical  Society. 

Bristol  Museum  and  Library. 

Cambridge  Philosophical  Society. 

Camera  Club. 

Edinburgh,  Royal  Observatory. 

Kew  Observatory. 

Leeds  Philosophical  and  Literary  Society. 

Liverpool  Astronomical  Society. 

Oxford,  Radclifife  Observatory. 

Rugby  School  Natural  History  Society. 

Stonyhurst  College  Observatory. 


i 


Feb.  1887.  List  of  Public  Institutions  etc.  199 

Adelaide,  Royal  Society  of  South  Australia. 

Amsterdam,  Royal  Academy  of  Sciences. 

Baltimore,  Joans  Hopkins  University. 

Bafcavia,  Royal  Society  of  Natural  History. 

Berlin,  Royal  Academy  of  Sciences. 

Berlin,  Royal  Observatory. 

Berlin,  Royal  Prussian  Geodetic  Institute. 

Berne  University. 

Bombay  Branch  of  the  Royal  Asiatic  Society. 

Bombay,  Government  Observatory. 

Bordeaux  Observatory. 

Bordeaux,  Society  of  Physical  and  Natural  Sciences. 

Boston,  American  Academy  of  Arts  and  Sciences. 

Boston  Scientific  Society. 

Brisbane,  Queensland  Branch  of  the  Geographical  Society 

of  Australasia. 
Brussels,  Royal  Observatory. 
Buda-Pesth,  Hungarian  Academy  of  Sciences. 
Calcutta,  Asiatic  Society  of  Bengal. 
Gape  of  Good  Hope,  Royal  Observatory. 
Gape  Town,  South  African  Philosophical  Society. 
Chicago  Public  Library. 

Christiania,  Norwegian  Meteorological  Institute. 
Copenhagen,  Royal  Academy  of  Sciences. 
Cordoba,  Argentine  National  Observatory. 
Delft,  £cole  Polytechnique. 
Dijon,  Academy  of  Sciences. 
Geneva,  Society  of  Physios  and  Natural  History. 
Georgetown  College. 
Gottingen,  Royal  Society  of  Sciences. 
Haarlem,  Mnsee  Teyler. 
Halle,  Imperial  Leopold-Caroline  Academy. 
Harvard  College  Astronomical  Observatory. 
Helsingfors,  Society  of  Sciences  of  Finland. 
Hong  Kong  Observatory. 
Kalocsa,  Haynald  Observatory. 
Kasan,  Imperial  University. 
Leipzig,  Astronomische  Gesellschaft. 
Leipzig,  Royal  Society  of  Sciences  of  Saxony. 
Madison,  Washburn   Observatory  of  the  University  of 

Wisconsin. 
Madras  Observatory. 
Madrid  Educational  Institute. 
Madrid,  Royal  Academy  of  Sciences. 
Mannheim  Observatory. 
Melbourne  Observatory. 
Melbourne,  Patent  Office. 
Mexico,  Scientific  Society. 
Moncalieri  Observatory. 
Montreal,  Royal  Society  of  Canada. 


aoo  List  of  Public  Institutions  etc.  xlvii.  4, 

Moscow,  Imperial  Society  of  Naturalists* 

Moscow  Observatory. 

Munich,  Royal  Bavarian  Academy  of  Sciences. 

Munich,  Royal  Observatory. 

Naples,  Academy  of  Sciences. 

Natal  Observatory. 

New  York,  Columbia  College. 

Paris,  Academy  of  Sciences. 

Paris,  Bureau  des  Longitudes. 

Paris,  Dep6t  G&ie'ral  de  la  Marine. 

Paris,  Ecole  Polytechnique. 

Paris,  International  Committee  of  Weights  and  Measures. 

Paris,  Mathematical  Society  of  France. 

Paris  Observatory. 

Paris,  Philomatbic  Society  of  France. 

Philadelphia,  American  Philosophical  Society. 

Philadelphia,  Franklin  Institute. 

Potsdam,  Astrophysics!  Society. 

Praguo  Observatory. 

Pulkowa  Observatory. 

Bio  de  Janeiro  Observatory. 

Rome,  Central  Meteorological  Office* 

Rome,  Italian  Spectroscopic  Society. 

Rome,  National  Library. 

Rome,  Accademia  Pontificia  dei  Linoei. 

Rome,  Reale  Accademia  dei  Lincei. 

St.  Petersburg,  Imperial  Academy  of  Sciences. 

San  Fernando  Observatory. 

Santiago  Observatory,  Chile. 

Sydney,  Government  Observatory. 

Tacubaya  Observatory,  Mexico. 

Taschkend  Observatory. 

Tasmania,  Royal  Society. 

Tokio  University.  * 

Toronto,  Canadian  Institute. 

Toulouse,  Academy  of  Sciences. 

Turin,  Italian  Meteorological  Society. 

Turin,  Observatory  of  the  Royal  University. 

Turin,  Royal  Academy  of  Sciences. 

Upsala,  Royal  Society  of  Sciences. 

Vienna,  Imperial  Academy  of  Sciences. 

Vienna,  Imperial  Observatory. 

Virginia,  Leander  MoCormick  Observatory. 

Washington,  Office  of  the  American  Ephemeris. 

Washington,  Philosophical  Society. 

Washington,  Smithsonian  Institution. 

Washington,  United  States  Chief  Signal  Office. 

Washington,  United  States  Coast  and  Geodetic  Survey, 

Washington,  United  States  Naval  Observatory. 

Yale  College  Observatory. 


Feb.  -1887. 


List  of  Public  Institutions  etc. 


20 


Yokohama,  Seismological  Society  of  Japan. 

Zurich,  Central  Meteorological  Institute. 

Zurich,  Society  of  Natural  History. 

Editors  of  the  American  Journal  of  Science. 

Editors  of  the  American  Journal  of  Mathematics. 

Editor  of  the  Astronomical  Register. 

Editor  of  the  Astronomische  Nachrichten. 

Editor  of  the  Athenaeum. 

Editors  of  the  Bulletin  des  Sciences  Mathematiques. 

Editor  of  the  English  Mechanic. 

Editor  of  Die  Naturforscher. 

Editor  of  Die  Naturwissenschaf  tliche  Rundschau. 

Editor  of  the  Observatory. 

Editor  of  the  Sidereal  Messenger. 

Editor  of  Sirius. 


Signor  A.  Abetti. 
Capt.  W.  deW.  Abney. 
Prof.  J.  J.  Astrand. 
A.  B.  Biggs,  Esq. 
.Dr.  J.  Bischof. 
Prof.  Th.  Bredichin. 
J.  Rand  Gapron,  Esq. 
S.  C.  Chandler,  Esq. 
H.  J.  Chaney,  Esq. 
Latimer  Clark,  Esq. 
Rev.  H.  Collins. 
A.  A.  Common,  Esq. 
M.  A.  Cornu. 
The  Earl  of  Crawford. 
E.  Crossley,  Esq. 
M.  Delauney. 
Padre  F.  Denza. 
E.  Dunkin,  Esq. 
W.  Ellis,  Esq. 
Padre  G.  S.  Ferrari. 
M.  Ch.  Fievez. 
M.  Camille  Flammarion. 
W.  S.  Franks,  Esq. 
Dr.  J.  Franz. 
Dr.  D.  Gill. 
Dr.  B.  A.  Gould. 
J.  E.  Gore,  Esq. 
Herr  E.  von  Gothard. 
N.  E.  Green,  Esq. 
H.  Grubb,  Esq. 
Prof.  A.  Hall. 
J.  Hampden,  Esq. 


Prof.  W.  Harkness. 

H.  Hennessy,  Esq. 

MM.  Paul  and  Prosper  Henry, 

G.  W.  Hill,  Esq. 

Prof.  E.  S.  Holden. 

B.  J.  Hopkins,  Esq. 
E.  Howarth,  Esq. 
R.  Inwards,  Esq. 
Dr.  N.  M.  Kam. 
M.  A.  Lancaster. 
Prof.  S.  P.  Langley. 
E  Lawrence,  Esq. 
Prof.  A.  Liversidge. 
M.  M.  Loewy. 

W.  T.  Lynn,  Esq. 
A.  Marth,  Esq. 
Prof.  R.  Meldola. 
Signor  E.  Millosevich. 
Herr  C.  Monnichmeyer. 
A.  Makhopadhyay,  Esq. 
E.  Neison,  Esq. 
M.  V.  Nielsen. 
Signor  A.  Nobile. 
Capt.  W.  Noble. 
A.  V.  Nursingrow,  Esq. 
J.  M.  Offord,  Esq. 
O.  T.  Olsen,  Esq. 
Prof.  Th.  von  Oppolzer. 
Wm.  Peck,  Esq. 

C.  E.  Peek,  Esq. 
Prof.  C.  F.  W.  Peters. 
Prof.  C.  H.  F.  Peters. 


202 


List  of  Public  Institutions,  etc. 


xlyji.  4, 


Prof.  E.  C.  Pickering. 
G.  L.  Prince,  Esq. 
R.  B.  Prosser,  Esq. 
Dr.  W.  T.  Radford. 
A.  C.  Ranyard,  Esq. 
Signor  A.  Ricco. 
Rev.  W.  J.  B.  Richards. 
Herr  A.  Riggenbach. 
Isaac  Roberts,  Esq. 
H.  C.  Russell,  Esq. 
Herbert  Sadler,  Esq. 
Prof.  H.  Schulfcz. 
Prof.  H.  Seeliger. 
J.  A.  Smith,  Esq. 
Prof.  C.  Piazzi  Smyth. 


Prof.  P.  Tacchini. 
K.  G.  Tarrant,  Esq. 
John  Tebbutt,  Esq. 
Signor  W.  Tern  pel. 
Dr.  F.  Terby. 
G.  Thwaites,  Esq. 
Herr  A.  Tischner. 
J.  Tripplin,  Esq. 
T.  F.  Tyerman,  Esq. 
W.  H.  Wesley,  Esq. 
T.  A.  Wise,  Esq. 
Dr.  R.  Wolf. 
Prof.  C.  A.  Young. 
Prof.  C.  V.  Zenger. 


Feb.  1887.  203 


ADDRESS 


Delivered  by  the  President,  Mr.  J.  W.  L.  Glaisher,  on  presenting 
the  Gold  Medal  of  the  Society  to  Mr.  O.  W.  HtU. 


The  Council  have  awarded  the  Gold  Medal  to  Mr.  George 
William  Hill  for  his  researches  upon  the  Lnnar  Theory ;  and  it 
now  becomes  my  duty  to  lay  before  you  the  grounds  of  this 
award. 

The  investigations  of  Mr.  Hill's  which  the  Council  have 
had  principally  in  view  are  contained  in  the  memoir  "  On  the 
Part  of  the  Motion  of  the  Lunar  Perigee,  which  is  a  Function  of 
the  Mean  Motions  of  the  San  and  Moon,"  which  was  published 
by  him  ten  years  ago  at  Cambridge,  Mass.  The  merits  of  Mr. 
Hill's  treatment  of  this  question  are  such,  that,  even  if  this 
memoir  stood  by  itself  as  his  sole  contribution  to  physical 
astronomy,  the  Council  would  have  felt  themselves  justified  in 
recognising  its  value  by  the  highest  mark  of  appreciation  which 
it  is  in  their  power  to  confer.  Mr.  Hill's  object  in  this  memoir 
is  to  determine  with  absolute  accuracy  the  motion  of  the  Moon's 
perigee,  on  the  assumption  that  the  Sun's  orbit  has  no  eccen- 
tricity, that  the  Moon's  motion  takes  place  in  the  plane  of  the 
ecliptic,  and  that  the  eccentricity  of  the  Moon's  orbit  is  indefi- 
nitely small :  in  other  words,  to  determine  an  absolutely  accurate 
value  of  that  part  of  c  which  depends  upon  m  alone. 

It  will  be  remembered  that  this  quantity  c,  which  expresses 
the  mean  motion  of  the  Moon's  perigee,  has  played  an  important 
part  in  the  early  history  of  the  theory  of  gravitation.  Newton 
proved  a  general  proposition  from  which  it  follows  that  the  dis- 
turbing action  of  the  Sun  necessarily  produces  a  continual 
advance  of  the  Moon's  perigee;  and  he  gave  a  numerical 
example  which  has  been  generally  regarded  as  his  calculation 
of  the  theoretical  amount  of  this  advance  in  the  case  of  the 
Moon.*     The  mean  monthly  progression  obtained  in  this  example 

*  Lib.  L,  Sect,  ix.,  Prop,  xlv.,  Cor.  2.  The  concluding  words  "  Apsis  lunae 
est  duplo  velocior  circiter  "  have  been  quoted  in  support  of  the  view  that  the 
motion  of  the  lunar  apsides  is  the  question  considered  in  this  corollary.  These 
words  were,  however,  intended  to  have  exactly  the  opposite  meaning.  This  can 
be  shown  by  comparing  the  three  editions  of  the  Prineipia ;  further  confirma- 
tion is  also  afforded  by  certain  papers  lately  found  by  Professor  Adams  in  the 
Portsmouth  collection  of  Newton  manuscripts. 

Q2 


204  The  President's  Address.  xlyil  4, 

is  i°  31'  28",  whereas  the  observed  monthly  progression  of  the 
Moon  is  about  doable  this  amount.  This  discrepancy  formed  one 
of  the  chief  impediments  to  the  acceptance  of  the  Newtonian 
system,  and  an  interval  of  sixty  years  elapsed  before  theory 
and  observation  were  brought  into  agreement.  This  was  effected 
by  Clairaat,  who  was  on  the  point  of  publishing  a  new  hypo- 
thesis with  respect  to  the  law  of  gravitation,  when  it  occurred 
to  him  to  extend  the  approximation  to  the  third  order.  He  found 
that  the  numerical  value  of  the  new  term  was  nearly  as  great  as  that 
of  the  term  of  the  second  order.  The  supposed  Newtonian  value 
of  1—6  was  Jw2,  and  Clairaut's  additional  term  was  V^m* » 
amounting  to  about  th  of  the  previous  term.  Thus  the  circum- 
stance which  had  for  some  time  seemed  almost  fatal  to  the 
Newtonian  theory  became  one  of  its  strongest  confirmations. 

The  series  of  which  the  first  two  terms  were  calculated  by 
Newton  and  Clairaut  has  been  continued  by  Delaunay  as  far  as 
the  term  involving  m9.  The  progression  of  the  terms  is  such  as 
we  might  anticipate  from  the  first  two  ;  the  coefficients  increase 
rapidly ;  and,  though  the  smallness  of  m  causes  the  terms  to 
diminish,  their  rate  of  convergence  is  very  slow. 

The  problem  which  Mr.  Hill  set  before  himself  for  solution 
was  the  exact  determination  of  the  numerical  value  of  the 
quantity  represented  by  this  series.  The  development  in  powers 
of  m,  besides  being  extremely  difficult  and  laborious  to  obtain, 
was  from  its  nature  ill  adapted  for  the  calculation  of  c  with  all 
the  precision  that  could  be  desired.  Mr.  Hill  accordingly  had 
recourse  to  an  entirely  different  method  of  obtaining  the  nume- 
rical value  of  this  quantity. 

Starting  with  the  general  equations  of  motion,  he  finds  the 
differential  equations  which  -determine  the  inequalities  having 
the  first  power  of  the  lunar  eccentricity  as  a  factor.  By  a  re- 
markable series  of  analytical  transformations,  the  solution  of 
these  differential  equations  is  made  to  depend  upon  that  of  a 
single  differential  equation  of  the  peculiarly  simple  and  elegant 
form 

where  r  denotes  the  mean  angular  distance  between  the  Sun 

and  Moon,  and  6  can  be  developed  in  a  periodic  series  of  the 

form 

e0+e,co8  2r+e,cos4T+  &c. 

If  ®,,  ®3,  &c.  are  to  a  considerable  degree  smaller  than  ®0,  an 
approximate  solution  of  the  equation  is 


where  i  denotes  v'  —  1,  K  and  K'  are  arbitrary  constants,  and  c 
denotes  the  square  root  of  0O.     When  the  additional  terms  are 


Feb.  1887.  The  Presidents  Address.  205 

taken  into  account,  the  effect  is  to  modify  this  value  of  c,  and 
also  to  add  to  w  new  terms  of  the  form 

We  may,  therefore,  take  as  a  particular  integral 

and  by  substituting  this  value  of  w  in  the  differential  equation, 
we  obtain  an  infinite  system  of  algebraical  equations,  each  con- 
sisting of  an  infinite  number  of  terms.  This  system  of  equations 
suffices  to  determine  the  ratios  of  all  the  coefficients  bly  bt,  Ac., 
to  one  of  them,  as  6©,  and  also  the  value  of  c,  the  ratio  of  the 
synodic  to  the  anomalistic  month. 

If  from  these  equations  we  eliminate  all  the  5'*,  we  obtain  a 
symmetrical  determinant  of  an  infinite  order  involving  c,  which, 
when  equated  to  zero,  determines  this  quantity.     This  equation 

Mr.  Hill  writes 

B(c)«o. 

A  first  approximation  to  the  value  of  c  is  ^60  ;  a  second  and 
much  more  accurate  approximation  is  given  by 


This  very  simple  expression  for  an  approximate  value  of  the 
motion  of  the  Moon's  perigee  is  obtained  by  neglecting  quantities 
of  the  order  m*  in  the  determinantal  equation  13(c)  =  o.  The 
numerical  values  of  O0  and  Bx  are 

©,=     1-1588439 
®i=  -0-0570440, 

and  by  substituting  these  values  in  the  above  expression  for  c  we 
find 

0  =  10715632 

whence 

1 -c=  1— c(i—m)  =  0-008591. 

This  is  about  ^  in  excess  of  the  value  0*008452  given  by  obser- 
vation ;  the  difference  being  mainly  due  to  the  neglect  of  the 
inclination  of  the  lunar  orbit.* 

*  Mr.  Hill  has  also  given  the  following  curious  formula,  which  is  obtained 
by  neglecting  quantities  of  the  order  m1 :    1 

tan*  = ^ , 

4^e,(e0-i) 

then  c  is  given  by  the  equation 

008  0 

This  formula,  though  it  involves  the  same  coefficients  ©0  and  ©,  as  the 
approximate  formula  given  in  the  text,  is  much  more  exact.  It  gives  i—e 
n  0*00857210,  which  is  correct  to  the  sixth  decimal.  See  the  reprint  of  Mr. 
Hill's  paper  in  the  Acta  Mathematical  vol.  viii.  (1886),  p.  28. 


206  The  President's  Address.  xlvii.  4, 

In  order  to  deduce  a  perfectly  accurate  value  of  c  from  the 
equation  23  (c)  =  o,  Mr.  Hill  proceeds  to  consider  the  nature  of 
the  roots  of  this  equation.  He  points  out  that  if  it  is  satisfied  by 
c  =  c0  it  must  necessarily  be  satisfied  also  by  all  quantities  of  the 
form  ±  (c0  +  2jj),  p  being  an  integer ;  and  he  is  thus  led  to  put 

2B  (c)  «-  A  [cos(irc) — 00s  (»c0) } 

The  constant  A  is  next  determined,  and  the  determinant  29  (o) 
is  replaced  by  a  new  determinant  v  (c),  derived  from  it  by  the 
equation 

V(c)-i»(e) 

so  that 

V  (c)  ■  cos  («c) — cos  (»e0) . 

This  equation  is  true  identically.  Putting  c  =  o,  and  subtract- 
ing, we  thus  find 

cos(*c)«i  —  v(o), 

as  the  subscript  zero  may  now  be  omitted.  This  very  remarkable 
equation  is  equivalent  to  ©  (c)  =  o,  and  gives  by  its  solution 
the  value  of  c,  which  we  are  seeking  ;  the  particular  root  to  be 

chosen  being  that  to  which  >/  ®0  is  a  first  approximation. 

Mr.  Hill  makes  still  one  further  change  in  order  to  replace 

V  (o)  by  a  determinant  in  which  all  the  terms  in  the  principal 

diagonal  shall   be  unity.     Denoting  this  new  determinant  by 

(o),  the  final  form  of  the  equation  giving  c  is  expressed  in  the 

form : 

sin*(iwc) 

«r^werD(0)' 

where  a  (o)  denotes  the  very  elegant  determinant 


•••1 

I   , 

4*  -©„' 

4*-e/ 

4*-<V 

_         ®4 

4* -So' 

®1 

®i 

©.. 

®3 

•••? 

2--©0' 

1    t 

*2*-e0' 

2*-©/ 

2*-©0> 

©2 

©1 

©1 

e.. 

•••» 

o2-©0' 

o—e0' 

I    • 

Oa-©o' 

O*-0o 

®s 

e„ 

®1 

©. 

•••» 

2'-©o' 

2s- e; 

2*-©; 

I    1 

— -- f          ••  * 

22-©o 

®4 

©» 

e« 

e, 

•••> 

42-<V 

4J-©.' 

4*-*.' 

42-®o' 

I      ,     ... 

•                         •                         • 

In  the  lunar  theory  the  quantity  ®p  is  of  the  2pth  order.       Mr. 
Hill,  with  great  analytical  skill  developes  this  determinant  as 


Feb.  1887.  The  President's  Address.  207 

far  as  terms  of  the  twelfth  order.  It  is  with  reluctance  that  I 
abstain  from  reproducing  the  remarkable  expression  which  he 
obtains.  It  occupies  eight  lines,  and  consists  of  terms  of  the 
fourth  order,  the  eighth  order,  and  the  twelfth  order.  It  is 
exactly  the  same  result  as  would  be  obtained  if,  starting  with  the 
equation  23(c)  =  o,  and  assuming  c  =  ^@0  as  a  first  approxi- 
mation, we  expanded  the  function  sin9(^irc)  in  ascending 
powers  and  products  of  the  coefficients  ®„  ®s,  &c. 
Passing  now  to  numbers,  Mr.  Hill  puts 

«=»73*5594"<*o85 
«'-   I295977"'4i5i6 

and  deduces  the  value  of  90,  ©j, ...  ©7  to  15  places  of  decimals,  and 
by  substituting  these  values  in  his  expression  for  0(0)  he 
obtains  finally 

0=1*07158  32774  16012, 
whence 

I -c- 000857  25730  04864. 

By  a  process  of  substitution  in  the  original  equations  a  verifica- 
tion of  this  value  of  e  is  afforded. 

It  is  interesting  to  compare  Mr.  Hill's  value  with  the  value 
given  by  Delaunay's  expression  in  powers  of  m,  viz. : 

3  1 .  225  a .  4071    1  .  265493   & .  12822631   B 

4  32     128     2048      24576 


+  1273925965^7  +  71028685589^  +  32145882707741 
589824       7077888        679477248 


m9. 


Using  the  values  of  n  and  n'  given  above,  the  numerical  values 
of  the  terms  of  this  series  are 


m* 

0*00419  6429 

m* 

0*00009  1395 

m* 

0*00294  2798 

m' 

000002  8300 

m4 

000099  5700 

m* 

000000  9836 

»i5 

000030  3577 

?n* 

000000  3468 

giving  0*00857  1503  as  the  value  of  1  — c. 

By  comparing  this  value  with  Mr.  Hill's  it  appears  that  the 
sum  of  the  remainder  of  Delaunay's  series  is  o'oooo  1070,  which 
is  rather  less  than  might  be  inferred  by  induction  from  the  terms 
of  the  series  itself.  In  spite  of  the  labour  expended  by  Delaunay 
in  computing  eight  terms  of  this  series,  the  result  does  not  suffice 
to  give  correctly  the  first  four  significant  figures  of  1— c.  On 
the  other  hand,  in  Mr.  Hill's  process,  the  highest  terms  included 
in  the  calculation  of  the  expression  for  a  (o)  are  only  of  the 
twelfth  order,  and  yet  they  suffice  to  give  c  correctly  to  the 
fifteenth  decimal.     As  well  as  can  be  judged  by  induction,  it 


208  The  President's  Address.  xlvii.  4, 

would  be  necessary,  Mr.  Hill  thinks,  to  prolong  Delaunay's  series 
as  far  as  m27  in  order  to  obtain  an  equally  precise  result. 

I  am  sensible  that  a  presidential  address  does  not  in  general 
afford  a  suitable  opportunity  for  mathematical  exposition ;  but  I 
have  felt  that  on  the  present  occasion  the  novelty  and  intrinsic 
interest  of  the  mathematical  methods  employed  justify  me  in  the 
attempt  I  have  made  to  give  a  brief  sketch  of  the  remarkable 
investigation  by  which  Mr.  Hill  has  arrived  at  his  numerical  value 
of  c.  It  will  be  observed  that  the  problem  of  the  determination  of 
this  quantity  is  attacked  entirely  de  novo,  from  first  principles,  by 
a  peculiar  analytical  method  devised  for  this  especial  purpose. 
The  object  is  to  obtain  the  numerical  value  of  that  part  of  c 
which  depends  upon  m  only ;  and  this  object  is  attained  with  a 
degree  of  precision  that  sets  the  problem  at  rest  for  ever. 

The  mathematical  process  is  very  peculiar.  Not  only  is  it 
quite  different  from  any  of  the  methods  with  which  the  lunar 
theory  is  associated,  but  it  even  displays  novelty  from  the  point 
of  view  of  the  pure  mathematician.  I  am  not  aware  that  actual 
use  has  ever  been  previously  made  of  an  infinite  determinant 
in  any  of  the  applications  of  mathematics,  or  that  the  develop- 
ment of  such  a  determinant  (by  proceeding  outwards  from  its 
central  constituent,  as  it  were)  has  ever  been  the  subject  of 
mathematical  investigation.  One  cannot  admire  too  highly  the 
courage  and  skill  with  which  Mr.  Hill  has  dealt  with  the  new 
mathematical  questions  to  which  his  methods  have  led  him.  Not 
only  has  he  availed  himself  of  the  modern  instruments  which  the 
advance  of  mathematics  had  placed  within  his  reach,  but  he  has 
successfully  grappled  with  the  novel  mathematical  difficulties 
which  have  accompanied  their  use.  The  calculation  of  the 
determinants  formed  from  the  3s,  52,  7',  &c.  constituents  sym- 
metrically disposed  with  respect  to  the  central  constituent  of  an 
infinite  determinant,  and  the  consideration  of  the  convergency  of 
these  determinants,  are  questions  of  mathematical  interest  which 
are  well  deserving  of  Btudy  on  their  own  account,  apart  from  the 
practical  applications  in  which,  as  Mr.  Hill  has  shown,  the  results 
of  such  investigations  are  required. 

Although  the  memoir  of  Mr.  Hill's  to  which  I  have  so  far 
confined  myself  was  the  first  in  order  of  publication  of  his 
papers  on  the  Lunar  Theory,  its  true  chronological  place  is 
subsequent  to  his  "  Researches  on  the  Lunar  Theory,"  which 
appeared  in  the  first  volume  of  the  "  American  Journal  of  Mathe- 
matics "  (1878).  In  the  calculation  of  the  quantities  ®0>  ®u  ®2> 
<fec.  (which  depend  only  upon  the  case  of  no  eccentricities), 
Mr.  Hill  derived  his  numerical  data  from  an  investigation  of  his 
own  to  be  subsequently  published.  This  investigation  is  con- 
tained  in  the  "  Researches,"  which  may  be  regarded  as  introduc- 
tory to  the  memoir  relating  to  the  motion  of  the  perigee. 

At  the  beginning  of  the  "  Researches  "  Mr.  Hill  divides  the 
periodic  developments  of  the  lunar  co-ordinates  into  classes  of 


Feb.  1887.  The  President9 8  Address.  209 

terms,    and    proposes    to  treat  the    following  five  classes   of 
inequalities : 

1.  Those   which   depend  only  on  the  ratio  of    the  mean 

motions  of  the  Sun  and  Moon. 

2.  Those  which  are  proportional  to  the  lunar  eccentricity. 

3.  Those  which  are  proportional  to  the  sine  of  the  lunar 

inclination. 

4.  Those  which  are  proportional  to  the  solar  eccentricity. 

5.  Those  whicji  are  proportional  to  the  solar  parallax. 

He  also  promises  a  general  method  by  which  these  investiga- 
tions may  be  extended  so  as  to  cover  the  whole  ground  of  the 
Lunar  Theory. 

Only  two  chapters  of  the  "  Researches "  were  published : 
the  first  relates  to  the  general  differential  equations  of  motion, 
and  the  second  to  the  first  of  the  five  classes  of  inequalities 
mentioned  above.  The  memoir  on  the  motion  of  the  perigee 
belongs  to  the  second  class ;  so  that  we  are  in  possession  of  Mr. 
Hill's  general  methods  and  their  application  to  two  out  of  the 
five  classes  of  inequalities. 

Passing  over  Mr.  Hill's  able  discussion  of  the  general  equa- 
tions of  motion,  I  proceed  to  give  a  brief  sketch  of  the  analytical 
method  by  which  he  treats  the  first  two  classes  of  inequalities. 

If  the  axis  of  x  rotate  with  uniform  angular  velocity  »', 
so  as  always  to  pass  through  the  Sun,  the  differential  equations 
of  motion  in  the  ordinary  form  are 


dP  dt     \r*      °     J 

dt*  dt     T** 


Mr.  Hill  transforms  these  equations  as  follows 
Denoting  n/(  —  i)  by  %  let 


also  let 


and  put 


v  =  n  —  »', 

V  V2 


■=<<-«•).      c=« 


tT, 


bo  that 


«  =  or  +  iy,        s  =  x-it/t 

t^         .  d       /■  d 
dr.       d( 


Dfp=^fP; 


210  The  President's  Address.  xlvh.  4, 

then  u  and  s  satisfy  the  differential  equations  : 

{  D2  +  2mD  +  |m2 — *-  }  u  +  fm2«  =  o, 
*  (t»)*' 

each  of  which  may  of  course  be  derived  from  the  other  by 
changing  the  sign  of  i. 

These  equations  determine  rigorously  all  the  parts  of  the  lunar 
co-ordinates  which  depend  only  on  the  ratio  of  the  mean  motions 
of  the  Son  and  Moon  and  the  lunar  eccentricity. 

Now  let 

p  having  all  integral  values  from  +  00  to  —  00. 

The  most  simple  method  of  obtaining  the  coefficients  a,,  is  by 
substituting  these  values  of  u  and  s  in  the  differential  equations 

and  equating  coefficients.     The  presence  of  the  factor  — r„  is   a 

great  additional  source  of  complication  in  carrying  out  this  pro- 
cess, and  it  is  therefore  desirable  to  eliminate  it.  This  Mr.  Hill 
effects  by  means  of  a  first  integral  of  the  differential  equations, 
and  he  at  length  obtains,  as  the  final  form  of  the  equations  to 
be  employed, 

D\us)-I>u .  D«-2m(td)*-«Dtt)  +  fm*(«  +  *)*-  C, 
D(«D* — sDu — 2mt«)  +  |m\«2  -  «*)  -  o. 

By  substituting  the  values  of  u  and  s  in  these  differential  equa- 
tions, a  system  of  algebraical  equations  connecting  the  a's  is  ob- 
tained from  which  they  may  be  determined  either  numerically 
or  algebraically  in  terms  of  m. 

It  will  be  noticed  that  tne  differential  equations  in  this  final 
form  are  such  that  in  no  case  is  it  necessary  to  multiply  together 
more  than  two  infinite  series. 

The  system  of  algebraical  equations  obtained  by  equating 
coefficients  is  infinite  in  number,  and  each  equation  contains  an 
infinite  number  of  terms  involving  the  products  of  two  a's. 

It  is  found  that  ap  is  of  the  2pth  order  with  respect  to  m  ;  and, 
in  solving  the  equations,  only  the  terms  of  lowest  order  are  in  the 
first  instance  retained.  The  equations  thus  curtailed  give  the 
first  four  terms  of  the  expansions  in  powers  of  m  of  at,  a.lf  as, 
a_2>  Ao.  Thus  at  and  a_(  are  affected  with  errors  of  the  sixth 
order ;  a2  and  a_2  with  errors  of  the  eighth  order,  and  so  on. 

One  of  the  great  advantages  of  the  method  consists  in  the 
ease  and  rapidity  with  which  the  approximations  can  be  extended ; 
for  we  have  only  to  return  to  the  original  curtailed  equations 
and  augment  each  of  them  by  the  terms  necessary  to  carry  the 


Fob.  1887.  The  President's  Address.  211 

approximation  four  orders  higher ;  we  then  substitute  in  the  new 
terms  the  values  obtained  from  the  first  approximation,  and  in 
the  old  we  determine  what  changes  are  produced  by  employing 
the  more  exact  values  instead  of  the  first  approximations.  A 
repetition  of  this  process  carries  the  approximation  four  orders 
higher  still,  and  so  on. 

Mr.  Hill  gives  in  full  the  equations  which  determine  the  a's 
correctly  to  quantities  of  the  thirteenth  order  inclusive ;  *  and 
he  deduces  from  them  the  expansions  of 


>  • 


»0 


in  powers  of  m  as  far  as  m9. 

From  these  expansions  the  values  of  r  cos  v  and  r  sin  v,  as 
series  proceeding  by  cosines  and  sines  of  multiples  of  21-,  are 
easily  deduced  by  means  of  the  equations 

r  cos  t;  =  2&p  cos  2pr 
r  sin  v  *  2ap  sin  2pr, 

the  summations  extending  to  infinity  both  ways.  The  coeffi- 
cients in  these  series  are  given  as  far  as  the  ninth  order  inclusive 
in  powers  of  m,  where 

m 


m  = 


m  —  £m* 


Not  only  does  Mr.  Hill  give  these  coefficients  in  a  literal  form, 
which  he  afterwards  reduces  to  numbers,  but  he  gives  also  the 
direct  numerical  calculation,  employing  numerical  values  from  the 
outset  in  the  equations  of  condition.  This  latter  method  is  found 
to  be,  as  we  should  suppose,  far  less  laborious  than  the  literal 
development  of  the  coefficients  in  powers  of  a  parameter. 

The  series  given  by  previous  mathematicians  are  unsuitable 
for  the  determination  of  the  motion  of  satellites  having  long 
periods  of  revolution  about  their  primaries;  and  Mr.  Hill  is 
accordingly  led  to  apply  his  method,  which  is  available  in  such 
cases,  to  the  exact  determination  of  the  expressions  for  r  cos  v 
and  r  sin  v  in  terms  of  r  when  m  =  y^,  ^,  J, .  .  .  \.  For  moons 
of  much  longer  lunations  the  method  is  not  practicable,  and  it  is 
necessary  to  resort  to  mechanical  quadratures.     The  motion  is 

*  The  final  differential  equations  only  suffice  to  determine  the  ratios  of 
the  a's  to  any  one  of  themselves,  as  a0.  For  the  actual  determination  of  a0  in 
terms  of  /i  and  »  recourse  must  be  had  to  one  of  the  original  differential 
equations,  and  in  this  way  the  value  of  a0,  viz. 

R,"(£)i[,"im,+ira,+^'im4~&c'  ] 

is  determined  as  far  as  the  term  involving  m9  inclusive.  It  is  from  the  values 
of  the  coefficients  a^,  which  depeod  upon  m  alone,  that  the  values  of  ©0,  ©,,  02, 
&c,  which  were  required  in  finding  the  motion  of  the  perigee,  were  derived  by 
Mr.  Hill. 


212  The  Presidents  Address.  xlvii.  4, 

determined  in  this  manner  in  the  cases  of  m  =  2  and 
m  =  1*78265.  The  latter  value  of  m  corresponds  to  a  lunar 
orbit  (relative  to  the  moving  axes)  having  cnsps  at  the  points  of 
quadratures. 

Brief  as  has  necessarily  been  the  preceding  account  of  the 
mathematical  processes  employed  by  Mr.  Hill,  I  hope  that  it  has 
been  sufficient  to  give  an  idea  of  their  character.  It  is  not  often 
that  the  points  of  novelty  in  an  application  of  mathematics  to  a 
well-known  problem  in  one  of  the  older  sciences  are  so  dis- 
tinctive as  to  admit  of  explanation  within  a  moderate  compass. 
The  present  investigation  is  so  exceptional  in  this  respect  that  I 
have  ventured  to  reproduce  the  main  lines  of  the  mathematical 
procedure. 

Two  obvious  deviations  from  established  custom  at  once 
attract  attention  :  first,  the  use  of  rectangular  instead  of  polar 
coordinates;  and  secondly,  the  introduction  of  the  imaginary 
quantity  i. 

With  regard  to  the  choice  of  coordinates,  it  is  known  that  in 
the  elliptic  theory  the  rectangular  coordinates  of  a  planet  relative 
to  a  central  body  can  be  developed  in  series  of  sines  and  cosines, 
in  which  the  coefficients  are  Besselian  functions,  although  the 
longitude  and  latitude  are  far  from  having  such  simple  expres- 
sions, and  in  fact  are  not  even  finitely  expressible  in  terms  of 
Besselian  functions.  If  this  be  true  in  the  elliptic  theory,  how 
much  more  likely,  Mr.  Hill  asks,  is  a  similar  result  to  be  true 
when  the  complexity  of  the  problem  is  increased  by  the  consider- 
ation of  the  disturbing  forces  ?  Thus  there  is  reason  to  believe 
that  the  coefficients  of  the  periodic  terms  in  the  developments  of  the 
rectangular  coordinates  are  less  complex  functions  of  their  para- 
meters than  in  the  case  of  polar  coordinates.  Another  important 
advantage  is  afforded  by  the  fact  that  when  expressed  in  rect- 
angular coordinates  the  differential  equations  assume  purely 
algebraic  forms,  while  in  polar  coordinates  they  involve  circular 
functions. 

The  quantity  i  is  used  in  order  to  avoid  the  multiplications 
of  series  of  sines  and  cosines,  and  to  reduce  all  the  quantities  to 
an  algebraic  form.  It  is  at  once  apparent  that  the  choice  of 
eH  or  (  as  independent  variable  greatly  simplifies  the  expression 
of  the  series  and  the  analysis  in  general.  Having  had  occasion 
myself,  in  a  very  different  branch  of  mathematics,  to  multiply 
together  infinite  series  of  sines  and  cosines,  I  have  found  the  ad- 
vantage of  making  a  similar  substitution,  and  I  can  bear  testimony 
to  the  analytical  simplicity  and  regularity  produced  in  such  pro- 
cesses by  the  substitution  of 

2r»  AptP  and    -  2™WB^ 

for 

Ao  +  221<"AJI,co8  2p0    and    22Ia°£J)sin2p0 

A_p  and  B_„  being  supposed  equal  to  A„  and  —  Bp  respectively. 


Feb.  1887.  The  President's  Address.  213 

It  may  be  remarked  that  the  vector  u  or  x+iy  is  a  symbol  to 
which  a  clear  conception  is  now  attached,  and  also  that  in  the 
equation 

the  quantities  a*,  at,  a.„  Ac.  are  the  radii  of  actual  epicycles. 
The  geometrical  picture  which  this  equation  represents  is  that 
of  a  pure  epicyclic  system. 


Mr.  Hill  employs  the  parameter  m,  which  is  equal  to 


m 


1—  m 

in  place  of  m.  Although  m  is  slightly  larger  than  m  it  is  found 
that  in  the  series  proceeding  by  powers  of  m  the  coefficients  are 
much  smaller  than  in  the  case  of  those  proceeding  by  powers  of 
m.  and  that  the  series  converge  more  rapidly.  The  quantity  m, 
which  has  been  mentioned  above,  was  specially  determined  in 
order  to  render  the  series  giving  the  a's  as  convergent  as 
possible. 

The  superiority  of  the  expansions  in  powers  of  m,  both  in 
convergence  and  simplicity  of  coefficients,  is  evident  by  comparing 

the  values  of    !       "!  and     ]~  "\    which   when  expressed    in 

a0  ao 

powers  of  m  assume  the  forms 

-{m2+im»-fm4+^m5-&c.{ 
and 

V  m2 + |m8  +  &m4  -si1"8  +  &c. 

respectively ;  the  corresponding  series,  as  given  by  Plana  and 
Delaunay,  being 

-  {wt2  +  \f m'+  lfjm*  +  ^m*  +  &c.} 

and 

V  m*  +  fS  w*  +  rSf  »4  +  res fflS  +  &c- 

With  regard  to  the  general  question  of  parameters,  it  is 
pointed  out  that  the  large  numerical  coefficients  which  occur  in 
Delaunay's  expansions  are  probably  due  to  the  choice  of  m  as 
parameter,  and  that  they  might  be  very  much  diminished  if  a 
more  suitable  parameter  were  employed.  Further,  it  is  not 
necessary  to  use  the  same  parameter  throughout,  and  it  may  well 
happen  that  different  parameters  may  be  advantageously  em- 
ployed in  the  investigation  of  different  classes  of  inequalities. 
Examples  of  the  extraordinary  increase  of  convergence  which 
can  be  affected  by  a  change  of  parameter  are  afforded  by  log- 
arithmic series,  and,  in  a  much  more  striking  form,  by  the 
various  expansions  of  the  elliptic  functions.  Mr.  Hill,  however, 
gives  it  as  the  result  of  his  experience  that  no  useful  results  are 
obtained  by  experimenting  with  the  present  known  developments, 
and  that  in  every  case  the  proper  parameter  must  be  derived 
from  a  priori  considerations  suggested  by  the  course  of  the 
integration. 


214  The  President's  Address.  xlvii.  4, 

Passing  now  to  general  considerations,  it  will  be  noticed  that 
Mr.  Hill  obtains  the  integrals  of  his  differential  equations  by  the 
method  of  indeterminate  coefficients.  This  is  the  method  which 
would  seem  to  offer  the  best  chance  of  discovering  the  law  of 
the  series.  A  farther  advantage  of  this  method,  which  is  not 
possessed  by  Delaunay's,  is  that  it  affords  either  the  numerical 
values  of  the  coefficients  or  the  literal  development  in  powers  of 
a  parameter. 

Of  all  the  general  methods  of  treating  the  Lunar  Theory  as  a 
whole,  Delaunay's  is  by  far  the  most  elegant  and  complete, 
and  is  likely  to  become  the  classic  method  in  this  subject. 
When,  however,  the  object  is  to  investigate  only  a  certain 
class  of  inequalities,  it  is  not  without  its  disadvantages;  for 
example,  even  if  we  only  desire  to  obtain  the  inequalities  whose 
coefficients  depend  solely  upon  m,  we  are  nevertheless  obliged 
to  develop  the  disturbing  function  R  to  all  powers  of  e.  Again, 
in  Delaunay's  method,  the  number  of  variables  is  doubled  in 
order  that  all  the  differential  equations  may  be  of  the  first  order  ; 
but  when  the  coefficients  are  determined  by  direct  substitution 
in  the  differential  equations  their  order  is  immaterial.  The  two 
main  characteristics  which  distinguish  Mr.  Hill's  general  ana- 
lytical treatment  of  the  lunar  theory  are  the  expression  of  the 
equations  in  terms  of  the  coordinates  instead  of  m  terms  of  the 
elements,  and  the  diminution  of  the  number  of  variables  and 
differential  equations  at  the  expense  of  increasing  the  order  of 
the  latter. 

Immediately  after  the  publication  of  Mr.  Hill's  first  memoir 
(on  the  motion  of  the  Moon's  perigee),  Professor  Adams  com- 
municated a  paper  to  the  Monthly  Notices  (vol.  xxxviii.,  p.  43), 
in  which,  after  bearing  testimony  to  the  high  merits  of  Mr. 
Hill's  investigation,  he  mentions  mat  he  has  been  led  to  dwell 
thus  particularly  on  this  subject  because  his  own  researches 
in  the  lunar  theory  have  followed  in  some  respects  a  parallel 
course.    Professor  Adams  states  that  he  has  long  been  convinced 
that  the  most  advantageous  way  of  treating  the  lunar  theory  is, 
first,  to  determine  with  all  desirable  accuracy  the  inequalities 
which  are  independent  of  e,  ef  and  y,  and  then  in  succession  to 
find  the  inequalities  which  are  of  one  dimension,  two  dimensions, 
and  so  on  with  respect  to  those  quantities.     Thus,  the  coefficient 
of  any  inequality  in  the  Moon's  coordinates  would  be  represented 
by  a  series  arranged  in  powers  and  products  of  e,  e'  and  y  ;  and 
each  term  in  this  series  would  involve  a  numerical  coefficient  which 
is  a  function  of  m  alone,  and  which  admits  of  calculation  for  any 
given  value  of  m  without  the  necessity  of  developing  it  in  powers 
of  m.     This  method  is  particularly  advantageous  when  we  wish 
to  compare  our  results  with  those  of  an  analytical  lunar  theory 
such  as  Delaunay's,  in  which  the  eccentricities  and  the  inclination 
are  left  indeterminate,  since  each  numerical  coefficient  could  be 
compared  separately  with  its  analytical  development  in  powers 
of  771.     As  it  is  only  the  series  proceeding  by  powers  of  m  in 


Feb.  1 887 .  The  President's  Address.  2 1 5 

Delaunay's  theory  which  have  a  slow  rate  of  convergence,  it 
is  probable  that  all  the  sensible  corrections  required  by  Delaunay's 
coefficients  would  be  found  among  the  terms  of  low  order  in  e,  e' 
and  y. 

Professor  Adams  proceeds :  "  The  differential  equations  which 
would  require  solution  in  these  successive  operations  after  the 
determination  of  the  inequalities  independent  of  eccentricities 
and  inclination  would  be  all  linear  and  of  the  same  form. 

"  It  is  many  years  since  I  obtained  the  values  of  these  last- 
named  inequalities  to  a  great  degree  of  approximation,  the 
coefficients  of  the  longitude  expressed  in  circular  measure,  and 
those  of  the  reciprocal  of  the  radius  vector,  or  of  the  logarithm 
of  the  radius  vector,  being  found  to  ten  or  eleven  places  of 
decimals. 

"  In  the  next  place,  I  proceeded  to  consider  the  inequalities 
of  latitude,  or  rather  the  disturbed  value  of  the  Moon's  co- 
ordinate perpendicular  to  the  ecliptic,  omitting  the  eccentricities 
as  before,  and  taking  account  only  of  the  first  power  of  y. 

"  In  this  case  the  differential  equation  for  finding  z  pre- 
sents itself  naturally  in  the  form  to  which  Mr.  Hill  reduces,  with 
so  much  skill,  the  equations  depending  on  the  first  power  of  the 
eccentricity  of  the  Moon's  orbit. 

"  In  solving  this  equation  I  fell  upon  the  same  infinite  deter- 
minant as  that  considered  by  Mr.  Hill,  and  I  developed  it  in  a 
similar  manner  in  a  series  of  powers  and  products  of  small 
quantities,  the  coefficient  of  each  such  term  being  given  in  a 
finite  form. 

"The  terms  of  the  fourth  order  in  the  determinant  were 
thus  obtained  by  me  on  December  26,  1868.  I  then  laid  aside 
the  further  investigation  of  this  subject  for  a  considerable  time, 
but  resumed  it  in  1874  and  1875 ;  and  on  December  2  in  the 
latter  year  I  carried  the  approximation  to  the  value  of  the 
determinant  as  far  as  terms  of  the  twelfth  order,  or  to  the  same 
extent  as  that  which  has  been  attained  by  Mr.  Hill.  I  have  also 
succeeded  in  reducing  the  determination  of  the  inequalities  of 
longitude  and  radius  vector  which  involve  the  first  power  of  the 
lunar  eccentricity  to  the  solution  of  a  differential  equation  of  the 
second  order ;  but  my  method  is  much  less  elegant  than  that  of 
Mr.  Hill. 

"  Immediately  after  Mr.  Hill's  paper  reached  me  I  wrote  to 
him  expressing  my  opinion  of  its  merits,  and  telling  him  what  I 
had  done  in  the  same  direction ;  and  I  received  from  him  a  very 
cordial  and  friendly  letter  in  reply. 

"  The  equation  which  I  had  obtained  by  equating  the  above- 
mentioned  determinant  to  zero  differed  in  form  from  Mr.  Hill's  ; 
and  on  making  the  reductions  required  to  make  the  two  results 
immediately  comparable,  I  found  that  there  was  an  agreement 
between  them  except  in  one  term  of  the  twelfth  order.  On 
examining  my  work  I  found  that  this  arose  from  a  simple  error 
of  transcription  in  a  portion  of  my  work,  and  that  when  this  had 


216  The  President's  Address.  ilyii.  4, 

been  rectified  my  result  was  in  entire  accordance  with  Mr. 
Hill's.  The  calculations  by  which  I  have  found  the  value  of  the 
determinant  are  very  different  in  detail  from  those  required 
by  Mr.  Hill's  method,  and  appear  to  be  considerably  more 
laborious." 

The  differential  equation  which  determines  z,  the  Moon's 
coordinate  perpendicular  to  the  equator,  is 

&z    /fi    m'\ 
dP    \r*    r>) 

This  equation  thus  presents  itself  originally  (as  mentioned  by 
Professor  Adams)  in  the  same  form, 

_+ew=o, 

as  that  to  which  Mr.  Hill  succeeds  in  reducing  the  equations 
upon  which  the   inequalities  involving  the  first  power  of  the 
lunar  eccentricity  depend. 
Professor  Adams  puts 

*t  +  ^  =  (»  -»')2  { q-  +  22iCB?pcos2X»  -»')* } 
and  Mr.  Hill  puts 

0  =  SQ  +  ©,C08  2T  +  e2COS4T  +  &C. 

The  same  determinant  is,  therefore,  reached  in  both  cases,  and 
there  is  no  great  difference  in  the  notation.  Professor  Adams's 
form  of  the  developed  value  of  the  determinant  is  given  on 
p.  47  of  volume  of  the  Monthly  Notices  referred  to.  By  means 
of  this  developed  expression,  the  value  of  g,  which  stands  to  the 
node  in  the  same  relation  that  c  does  to  the  perigee,  is  found  to 
fifteen  places  of  decimals.  I  may  mention  that  in  this  paper 
Professor  Adams  also  gives  the  numerical  values  of  the  terms  in 
the  expansions  ofg—i  and  c  —  1  both  in  powers  of  m  and  of  m.  In 
each  case  the  development  in  powers  of  m  is  much  the  more 
advantageous ;  and  he  states  that  he  has  found  that  a  similar 
advantage  results  from  the  employment  of  m  instead  of  ra  in  the 
development  of  the  Moon's  periodic  inequalities. 

Before  considering  in  a  more  general  light  the  inferences 
that  we  may  draw  from  the  similarity  of  the  researches  of 
Professor  Adams  and  Mr.  Hill,  I  should  like  to  draw  attention 
to  the  fundamental  character  of  Mr.  Hill's  infinite  determinant 
in  the  lunar  theory,  and  possibly  also  in  other  applications  of 
mathematics. 

The  differential  equation 

_rf-  +  ew=o. 

may  be  regarded  as  a  canonical  form.*    Mr.  Hill  was  led  to  it  by 

*  Riccati's  equation  and  several  other  well-known  equations  are  reducible 
to  this  form,  which  has  been  much  studied ;  but,  so  far  as  I  know,  the  case  in 
which  ©  is  a  periodic  series  has  not  been  considered. 


Feb.  1 88  7.  The  Presidents  Address.  217 

considering  the  motion  of  the  perigee,  Professor  Adams  by  con- 
sidering the  motion  of  the  node.  It  is  probable  that  many  other 
inequalities  can  be  made  to  depend  upon  the  solution  of  an 
equation  of  this  form.    The  form  of  ®,  viz., 

where  0P  is  of  the  2j?th  order,  is  very  general ;  and  so  also  is  the 
method  of  solution  by  indeterminate  coefficients. 

The  determinant  in  question,  therefore,  possesses  consider, 
able  mathematical  interest  of  its  own,  and  its  properties  and 
development  seem  likely  to  admit  of  a  wide  application  in  mathe- 
matical researches  in  which  periodic  functions  are  involved. 

The  fact  that  the  work  carried  out  independently  by  Professor 
Adams  and  Mr.  Hill  should  have  run  so  much  upon  the  same 
lines,  and  have  so  much  actually  in  common,  affords  strong 
evidence  that  it  is  in  this  direction  that  we  must  look,  in  the 
present  condition  of  the  lunar  theory,  for  any  further  important 
advances.  It  is  almost  impossible  to  study  the  writings  to  which  I 
have  referred  without  becoming  impressed  by  this  feeling.  Mr.  Hill 
puts  the  matter  very  clearly  when  he  points  out  that  the  great 
majority  of  the  mathematicians  who  have  worked  at  the  lunar 
theory  have  had  before  them,  as  their  ultimate  aim,  the  con- 
struction of  tables ;  that  is  to  say,  they  have  viewed  the  problem 
from  the  standpoint  of  practical  astronomy  rather  than  of 
mathematics.  This  accounts  for  the  restricted  choice  of  variables 
and  parameters.  "  Again,"  proceeds  Mr.  Hill,  "  their  object 
compelling  them  to  go  over  the  whole  field,  they  have  neglected 
to  notice  many  minor  points  of  great  interest  to  the  mathe- 
matician, simply  because  the  knowledge  of  them  was  unnecessary 
for  the  formation  of  tables.  But  the  developments  having  now 
been  carried  extremely  far,  without  completely  satisfying  all 
desires,  one  is  led  to  ask  whether  such  modifications  cannot  be 
made  in  the  processes  of  integration,  and  such  coordinates  and 
parameters  adopted,  that  a  much  nearer  approach  may  be  had  to 
the  law  of  the  series,  and  at  the  same  time  their  convergence 
augmented/' 

In  recent  years  it  has  come  to  be  generally  believed  that  a 
worker  had  but  little  chance  of  performing  useful  service  in  the 
lunar  theory  unless  he  was  prepared  to  make  it  the  study  of  his 
life.  The  belief  also  has  been  prevalent  that  the  mathematical 
portion  of  the  treatment  of  the  subject  has  been  worked  out,  and 
that  there  was  no  scope  for  the  display  of  mathematical  skill  or 
the  employment  of  modern  mathematical  methods.  Until  some 
great  discovery  should  change  the  face  of  the  whole  subject,  it 
has  seemed  likely  that  patience  and  diligence  in  traversing  with 
greater  care  the  old  lines,  and  extending  still  further  de- 
velopments already  carried  to  a  wonderful  extent,  would  be  all 
that  was  required  to  perfect  the  theory.  Considering,  on  the 
other  hand,  the  attractiveness  of  the  new  and  rapidly  progressing 

R 


2 1 8  The  President's  Address.  xlvii.  4, 

branches  of  pure  mathematics,  and  of  many  recent  applications 
of  mathematics  to  physical  science,  it  is  scarcely  to  be  wondered 
at  that  so  few  of  the  younger  generation  of  mathematicians  should 
have  included  the  lunar  theory  within  their  subjects  of  research. 
The  papers  of  Mr.  Hill's  which  I  have  described,  and  certain 
recent  papers  of  Professor  Adams's,  have  invested  the  lunar 
theory  with  a  new  mathematical  interest,  and  have  shown  that 
in  the  treatment  of  the  special  problems  included  in  the  subject 
there  is  an  ample  opportunity  not  only  for  the  application  of 
existing  mathematical  methods,  but  even  for  the  discovery  of 
new  ones.  These  papers  show  also  that  it  is  possible  for  the 
mathematician  to  confine  himself  to  these  special  problems 
without  attempting  to  cover  the  whole  ground  of  the  lunar 
theory.  I  hope  that  this  is  the  dawn  of  a  new  day  in  the  history 
of  the  lunar  problem,  and  that,  now  that  the  whole  territory  has 
been  mapped  out  by  Plana  and  Delaunay,  it  will  be  found  that 
the  special  investigations  offer  a  tempting  field  to  the  mathe- 
matician. So  far  from  the  subject  having  been  exhausted  by 
the  general  methods  which  have  been  applied  to  it  as  a  whole,  I 
believe  that  the  future  will  show  that  they  have  but  cleared  the 
ground  and  disclosed  to  view  the  objects  to  which  mathematical 
investigation  may  with  the  greatest  advantage  be  directed. 

I  have  now  described,  though  necessarily  in  a  very  imperfect 
manner,  Mr.  Hill's  mathematical  researches  upon  special  pro- 
blems in  the  lunar  theory,  the  originality  and  peculiar  value  of 
which  the  Council  have  been  especially  desirous  of  recognising 
by  the  award  of  their  medal.  I  can  refer  but  briefly  to  Mr. 
Hill's  other  important  contributions  to  physical  astronomy,  most 
of  which,  however,  have  been  already  noticed  in  our  Annual 
Reports. 

The  American  Journal  contains  two  other  papers  of  his.  The 
first  of  these,  in  the  fourth  volume,  is  a  short  note  on  "  Hansen's 
General  Formulae  for  Perturbations,"  in  which  an  equation  of 
Hansen's  is  expressed  in  a  form  which  is  not  only  more  simple, 
but  also  more  convenient  for  computation.  The  second,  in  the 
sixth  volume,  is  entitled  "  On  Certain  Possible  Abbreviations  in 
the  Computation  of  the  Long-Period  Inequalities  of  the  Moon's 
Motion,  due  to  the  Direct  Action  of  the  Planets."  Hansen  has 
characterised  the  calculation  of  the  coefficients  of  these  inequali- 
ties as  extremely  difficult ;  but  Mr.  Hill  finds  that  if  the  shortest 
methods  are  followed  this  is  no  longer  the  case.  In  this  character- 
istic paper,  Mr.  Hill,  following  the  principles  which,  as  we  have 
seen,  have  guided  him  in  all  his  work,  attacks  the  question  from 
the  very  beginning  by  a  direct  analytical  investigation.  He 
thus  obtains  finally,  not  only  a  new  method  for  the  actual  com- 
putation of  the  inequalities,  but  also  some  results  of  more 
purely  mathematical  interest. 

Three  elaborate  memoirs  have  been  published  by  Mr.  Hill 
among  the  astronomical  papers  prepared  for  the  use  of  the 
American  Ephemeris  and  Nautical  Almanac  (i)  "  On   Gauss's 


Feb.  1887.  The  President's  Address.  219 

Method  of  Computing  Secular  Perturbations,  with  au  Applica- 
tion to  the  Action  of  Venus  on  Mercury  "  (1881)  ;  (ii)  "  Deter- 
mination of  the  Inequalities  of  the  Moon's  Motion,  which  are 
produced  by  the  Figure  of  the  Earth :  a  Supplement  to 
Delaunay's  Lunar  Theory"  (1884);  (iii)  "On  Certain  Lunar 
Inequalities,  due  to  the  Action  of  Jupiter,  and  discovered  by 
Mr.  E.  Neison"  (1885). 

The  'object  of  the  first  of  these  papers  is  to  reproduce  in  a 
form  practically  useful  for  astronomers  the  results  given  by 
Gauss  in  his  celebrated  memoir,  "  Deter minatio  Attractions 
&c."  In  the  original  memoir  the  method  is  not  presented  in 
such  a  manner  that  it  admits  of  easy  application  to  an  actual 
case.  In  this  paper  Mr.  Hill  places  Gauss's  process  within  the 
reach  of  any  computer  possessed  of  ordinary  mathematical 
knowledge.  Gauss's  investigation  is  reproduced  in  full,  with 
the  addition  of  the  details  necessary  for  its  application ;  and, 
finally,  the  formulas  themselves,  in  the  shape  in  which  they  are 
required  by  the  practical  calculator,  as  well  as  the  necessary 
tables  of  elliptic  integrals,  are  given.  As  an  example,  the  com- 
putation of  the  secular  perturbations  of  Mercury,  produced  by 
the  action  of  Venus,  are  worked  out ;  the  final  results  agreeing 
very  closely  with  those  of  Leverrier.  It  is  to  be  hoped  that  this 
paper  may  have  the  effect  of  bringing  into  more  general  prac- 
tical use  Gauss's  very  beautiful  and  perfect  method. 

The  second  memoir  is  described  by  the  author  in  its  title  as 
a  supplement  to  Delannay's  Lunar  Theory      At  the   time  ot 
Delaunay's  death  the  inequalities   caused  by   the    disturbing 
action  of  the  Sun  were  complete ;  but  the  small  effects  produced 
by  the  spheroidal  figure  of  the  Earth,  and  other  minor  portions 
of  the  subject,   were  untouched.      Mr.    Hill's   object  in  this 
memoir  is  to  supplement  Delaunay's  great  work  by  determining, 
in  a  literal  form,  all  the  inequalities  of  the  Moon  which  arise 
from  the  figure  of  the  Earth  to  the  same  degree  of  algebraical 
approximation  as  that  adopted  by  Delaunay  in  determining  the 
solar  perturbations — that  is,  to  terms  of  the  seventh  order  inclu- 
sive.    The  value  of  a  constant  which  enters  into  the  coefficients 
and  depends  upon  the  figure  of  the  Earth  is  determined  by  an 
elaborate  discussion  of  numerous  pendulum  experiments;  and 
by  the  substitution  of  the  values  of  m,  e,  e',  y  and  this  constant, 
the  numerical  values  of  the  coefficients  are  deduced.    The  whole  of 
this  elaborate  investigation  seems  to  have  been  carried  out  with 
great  skill  and  care.  I  should  mention  that,  in  his  treatment  of  the 
subject,  Mr.  Hill  adopts  in  principle  the  usual  method  of  applying 
Delaunay's  theory  to  the  determination  of  the  lunar  inequalities 
which  are  due  to  causes  other  than  the  Sun's  action,  and  that 
there  is  possibly  a  slight  imperfection  in  this  method.     It    is 
probable,  however,  that  the  differences  due   to  this  cause  are 
insensible. 

In  the  third  of  the  memoirs  referred   to   Mr.  Hill   effects 
the  determination  of  the  coefficients  of  two  lunar  inequalities, 


220  The  President's  Address.  xlvii.  4, 

due  to  the  action  of  Jupiter,  to  which  Mr.  Neison  drew  attention 
in  vol.  xxxvii.  of  the  Monthly  Notices.  Mr.  Hill's  values  of  these 
coefficients  do  not  agree  with  those  assigned  to  them  by  Mr. 
Neison.  In  the  case  of  the  second  inequality  Mr.  Hill's  value 
amounts  to  only  about  one-tenth  of  Mr.  Neison's. 

It  is  nine  years  since  Mr.  Hill  undertook  for  the  office  of  the 
American  Ephemeris  and  Nautical  Almanac  an  investigation 
of  the  motions  of  Jupiter  and  Saturn,  with  the  view  of  construct- 
ing  tables  of  these  two  planets.  From  its  commencement  this 
great  work  has  occupied  nearly  the  whole  of  his  time ;  and,  even 
if  no  hindrance  occurs,  it  must  continue  to  do  so  for  the  next 
three  or  four  years.  It  is  well  known  that  the  theory  of  Saturn 
is  in  an  unsatisfactory  state,  Leverrier's  tables  failing  to  represent 
adequately  the  observations.  A  special  interest  therefore  attaches 
to  these  new  investigations  which  have  been  carried  out  by 
means  of  Hansen's  very  refined  methods.  The  work  has  so  far 
progressed  very  satisfactorily.  The  final  expressions  for  the  co- 
ordinates of  the  two  bodies,  together  with  the  details  of  a  pre- 
liminary comparison  of  them  with  observations  made  for  the 
purpose  of  ascertaining  what  corrections  the  perturbations  might 
need  on  account  of  errors  in  the  provisionally  assumed  elements, 
were  published  last  year  in  the  "  Astronomische  Nachrichten  " 
(Nos.  2,705-2,706).  When  these  investigations,  in  which  the 
approximations  are  carried  to  a  much  greater  extent  than  in  any 
previous  treatment  of  the  subject,  are  completed,  the  whole  will 
form  by  far  the  largest  and  most  complete  investigation  of  the 
kind  that  has  yet  been  performed  on  the  American  continent. 

It  is  doubtless  due  to  the  engrossing  character  of  this  work 
that  only  two  chapters  of  the  "  Researches  on  the  Lunar 
Theory  "  were  published.  There  is  abundant  evidence  that  Mr. 
Hill's  researches  must  have  been  extended  far  beyond  those 
given  in  these  two  chapters  at  the  time  when  his  new  labours 
deprived  him  of  the  leisure  necessary  for  completing  and  pre- 
paring them  for  press ;  and  I  trust  that  when  the  Theory  and 
Tables  of  Jupiter  and  Saturn  shall  have  been  published,  Mr.  Hill 
may  be  enabled  to  resume  his  mathematical  researches  at  the 
point  at  which  their  publication  ceased,  and  to  carry  out  his 
original  intention  to  its  full  extent. 

The  President  then,  delivering  the  Medal  to  the  Foreign  Secretary, 
addressed  hvmvn  the  following  terms : 

Dr.  Huggins, — May  I  ask  you  in  transmitting  this  medal 
to  Mr.  Hill  to  assure  him  of  our  high  appreciation  of  the  value  of 
his  contributions  to  physical  astronomy,  and  to  express  to  him 
our  earnest  hope  that  his  life  may  long  be  spared,  and  that  he 
may  have  health  and  strength  to  complete  the  splendid  work 
upon  which  he  is  now  engaged,  and  to  enrich  our  science  still 
further  by  his  mathematical  researches. 


Feb.  1887.  22r 


The  meeting  then  proceeded  to  the  election  of  the  Officers 
and  Conncil  for  the  ensuing  year,  when  the  following  Fellows 
were  elected : — 

President. 
J.  W.  L.  Glaishrr,  Esq.,  M.A.,  F.B.S. 

Vice-Presidents. 

Arthur  Catley,  Esq.,  M.A.,  LL.D.,  D.C.L.,  F.B.S.,  Sadlerian 

Professor  of  Pare  Mathematics,  Cambridge. 
W.  H.  M.  Christie,  Esq.,  M.A.,  F.B.S.,  Astronomer  Royal. 
The  Earl  of  Crawford  and  Balcarres,  F.B.S. 
Edwin  Dunkin,  Esq.,  F.B.S. 

Treasurer. 
A.  A.  Common,  Esq.,  F.B.S. 

Secretaries. 
E.  B.  Kkobel,  Esq. 
Lieut-Col.  G.  L.  Tupman,  B.M.A. 

Foreign  Secretary. 
Willum  Huggins,  Esq.,  LL.D.,  D.C.L.,  F.B.S. 

Council. 

Capt.  W.  de  W.  Abney,  B.E.,  F.B.S. 

J.  C.  Adams,  Esq.,  M.A.,  LL.D.,  D.C.L.,  F.B.S.,  Lowndean 

Professor  of  Astronomy,  Cambridge. 
J.  Band  Capron,  Esq. 
G.  F.  Chambers,  Esq. 
J.  B.  Hind,  Esq.,   LL.D.,    F.B.S.,    Superintendent   of  the 

Nautical  Almanac. 
E.  W.  Maunder,  Esq. 
Capt.  William  Noble. 
Be  v.  S.  J.  Perry,  F.BS. 
A.  Cowper  Banyard,  Esq.,  M.A. 
E.  J.  Stone,  Esq.,  M.A.,  F.B.S.,  Badcliffe  Observer. 
Lieut-Gen.  J.  F.  Tennant,  B.E.,  F.B.S. 
H.  H.  Turner,  Esq.,  B.A.,  B.Sc. 


MONTHLY   NOTICES 

OF  THE 

EOYAL    ASTEONOMICAL    SOCIETY. 

Vol.  XLVIL  March  ii,  1887.  No.  5 

J.  W.  L.  Glaisheb,  M.A.,  F.B.S.,  President,  in  the  Chair. 


On  the  Determination  of  the  Radius  Vector  in  the  Absolute  Orbit 
of  the  Planets.  By  Prof.  Hugo  Gylden,  Director  of  the  Ob- 
servatory, Stockholm. 

The  method  of  variation  of  constants,  given  by  Lagrange, 
forms  the  theoretical  foundation  of  astronomy  at  the  present 
time.  In  cases  where  the  mathematical  problem  cannot  be 
rigorously  solved  we  have,  by  its  help,  not  only  been  enabled  to 
compute  the  movements  of  the  heavenly  bodies  by  successive 
approximations,  but  have  also  succeeded  in  stating  the  nature  of 
the  motions  in  an  intelligible  manner.  We  seem  also  to  have 
attained  to  something  more  precise  than  a  mere  rule  for  the  com- 
putation of  the  effect  of  mutual  attraction  within  definite  intervals 
of  time.  The  way  in  which  this  method  has  been  hitherto  applied 
in  investigations  on  the  theory  of  the  movements  of  the  heavenly 
bodies  was  not,  however,  in  all  respects  the  most  appropriate  for 
giving  that  general  view  of  the  laws  of  movement  which  should 
not  be  absent  from  a  comprehensive  scientific  solution  of  the 
problem  in  question.  The  slight  amount  of  success  which  re- 
sults from  the  application  of  this  method  is  explained  by  the  fact 
that,  if  the  approximations  are  carried  out  in  a  straightforward 
manner,  they  lead  to  developments  in  series  according  to  powers 
of  the  time,  and  these  series  do  not  converge  for  any  arbitrary 
magnitude  of  the  variable ;  so  that  it  is  difficult  to  judge  of  the 
convergence  of  the  approximations  even  when  the  development 
in  powers  of  the  time  has  been  avoided  by  certain  artifices. 

s 


224  Prof.  QyldSn,  On  the  Determination  xlvii.  5, 

It  is  well  known  that  the  method  of  variation  of  constants 
allows  as  a  certain  discretion;  for  a  number  of  the  equations 
from  which  the  variations  of  the  elements  are  to  be  computed  can 
be  fixed  on  at  pleasure,  and  an  arbitrary  number  of  solutions  can 
be  found  for  the  differential  equations  which,  from  a  formal  point 
of  view,  are  distinct  from  one  another,  and  which  together  con- 
tain a  sufficient  number  of  arbitrary  constants  to  give  us  the 
place  and  velocity  of  a  heavenly  body  at  a  given  moment  of 
time.  In  the  application  of  this  method  to  the  planetary  theory 
it  has,  until  recently,  been  attempted  to  satisfy  this  condition  as 
to  the  place  and  velocity  of  the  planet  by  giving  to  the  co- 
ordinates and  to  their  first  differentials  with  respect  to  the  time, 
the  same  form  in  the  later  approximations  as  in  the  first. 

The  values,  which  in  the  first  approximation  appear  as  con- 
stants of  integration,  become  in  the  later  stage  functions  of  the 
time,  whioh  must  be  evaluated  step  by  step.  Under  these  cir- 
cumstances the  orbits  of  the  planets  are  regarded  as  Keplerian 
ellipses,  whose  elements,  however,  vary  from  instant  to  instant. 
But  the  variations  of  the  elements  cannot  be  regarded  from  so 
simple  a  point  of  view ;  little  more  can  be  said  in  description  of 
them  than  that  they  are  small  in  small  intervals  of  time,  but  that 
if  the  time  be  taken  sufficiently  great  they  may  become  so  con- 
siderable that  the  original  ellipse  is  quite  unrecognisable.  The 
motion,  the  nature  of  which  is  thus  intelligibly  described,  holds 
good  strictly  for  a  very  short  time ;  it  can,  however,  be  retained 
without  actual  practical  inconvenience  during  several  decades  of 
years — perhaps  for  several  centuries.  However,  the  representa- 
tion of  the  motion  of  the  heavenly  bodies,  indicated  above,  is  not 
sufficient  from  a  scientific  point  of  view,  where  it  is  desired  to 
regard  the  phenomenon  as  independent  of  shortness  or  length  of 
time;  for  the  condition,  that  the  co-ordinates  and  their  dif- 
ferentials shall  have  the  same  form  as  in  Kepler's  theory  of 
planetary  motion,  does  not  repose  on  a  circumstance  which 
should  a  priori  give  it  the  preference  over  all  other  methods. 
If  actual  analytical  difficulties  did  not  stand  in  the  way,  that 
condition  ought  to  be  replaced  by  another  which  would  be  ap- 
propriate to  represent  the  nature  of  the  planetary  movements 
more  completely  than  has  hitherto  been  the  case.  A  result  of 
this  would  certainly  be  that  a  number  of  conceptions  appropriate 
to  Keplerian  astronomy  would  be  replaced  by  others.  As  may 
be  however  conjectured  without  analysis,  the  practical  rules 
for  computing  the  places  of  the  planets  would  undergo  very  little 
alteration. 

For  many  years  then  I  have  been  convinced  of  the  neces- 
sity of  replacing  the  present  point  of  view  of  the  planetary  theory 
by  another  which  shall  correspond  in  its  actual  features  with  the 
phenomenon  of  planetary  motion  during  any  arbitrary  period. 
The  conception  of  an  absolute  orbit  and  of  absolute  elements 
has  now  been  established  in  consequence  of  the  labour  which  I 
have  devoted  to  this  subject.     The  absolute  orbit  gives  the  path 


March  1887.  of  the  Radius  Vector.  225 

of  the  actual  motion  very  closely,  so  that  the  departure  from  exact, 
ness  of  the  place  computed  in  this  orbit  always  remains  of  the 
order  of  the  disturbing  forces,  and  never  assumes  the  character 
of  a  secular  variation.  In  contrast  with  the  elements  of  the 
oscnlatory  or  mean  ellipse,  which  undergoes  considerable  variation 
under  the  influence  of  the  secular  disturbances,  the  elements  of 
the  absolute  orbit  are  absolute  constants,  which  are  not  subject 
to  secular  variations,  otherwise  than  that  the  longitude  is 
changed  by  the  motion  of  the  planet,  of  the  apses,  and  of  the 
nodes  of  its  orbit. 

Henee,  the  longitude  must  be  given  for  a  definite  epoch. 
The  three  modular  elements  on  which  the  mean  distance,  the 
excentricity,  and  the  inclination  depend,  are,  on  the  other  hand, 
absolutely  invariable,  and  serve  for  any  moment  of  time  what- 
ever. For  the  representation  of  the  co-ordinates  in  the  absolute 
orbit  I  make  use  of  certain  functions  which  depend  on  the  dis- 
turbing masses,  but  which  do  not  vanish  with  them,  but  become 
constants  corresponding  to  elliptic  elements.  For  this  reason  I 
call  these  the  elementary  functions,  and  the  individual  terms,  out 
of  which  these  are  formed,  are  the  elementary  terms. 

The  elementary  terms  have  a  form  which  is  easily  to  be 
recognised ;  they  are  periodic,  and  their  periods  are  either 
very  long  compared  with  the  periodic  time,  form  (A),  or  differ 
very  little  from  that  period,  form  (6).  In  the  course  of  the 
developments,  however,  terms  make  their  appearance  which 
have  the  same  form  as  the  elementary  terms,  but  differ  from 
them  in  that  they  vanish  with  the  disturbing  masses.  Such 
terms  I  call  svbeUmeniary  terms,  and  I  say  that  they  are  of  the 
first  order  when  they  involve,  as  a  factor,  the  first  power  of  a 
disturbing  mass,  and  of  the  second  order  when  they  involve  the 
square  of  a  disturbing  mass,  or  the  product  of  two  masses,  &c. 
With  reference  to  the  excentricity,  or  to  the  constants  which 
determine  its  magnitude,  the  elementary  terms  are  of  various 
orders,  and  the  same  holds  with  respect  to  the  inclination.  I 
reckon  as  of  the  first  class  an  elementary  term  which  contains 
the  first  power  of  a  modulus  of  the  excentricity ;  and  of  the 
second  class  terms  which  contain  the  squares  or  products  in  two 
dimensions  of  these  moduluses,  and  so  on. 

It  may  be  here  pointed  out  that  the  terms  of  the  form  (A), 
whose  periods  are  very  long,  belong  to  an  even  class,  and  the 
terms  of  the  form  (6)  to  an  uneven  class.  If  the  succession  of 
approximations  is  not  appropriately  arranged,  terms  may  make 
their  appearance  in  which  the  disturbing  masses  appear  as 
divisors.  Such  terms  must,  of  course,  vanish  from  the  result  if 
the  approximations  are  in  general  to  converge  and  to  lead  to  a 
real  result.  The  appearance  of  terms  of  this  kind  always  shows 
that  the  method  in  application,  or  the  fundamental  system  of 
differential  equations,  was  not  the  most  appropriate;  for  the 
operations  which  lead  to  the  vanishing  of  these  terms  are  usually 
very  troublesome,  and  the  numerical  results  are  always  inexact, 

s  2 


226  Prof.  Qylden,  On  the  Determination  xlvii.  5, 

because  they  arise  from  the  differences  of  larger  quantities. 
Terms  which  involve  the  disturbing  masses  as  divisors  I  call 
hyperelementary  terms.  It  would  have  been  desirable  that  this 
name  should  not  be  required ;  but  as  such  terms  may  appear, 
and  as  it  would  be  easy  to  give  equations  of  perturbation  which 
necessarily  lead  to  this  complication  of  the  problem,  it  is  neces- 
sary to  arm  each  method  against  the  appearance  of  such  terms. 
If  no  care  is  taken  that  the  hyperelementary  terms  should  not 
appear,  or  should  not  be  made  to  vanish  easily,  the  method  in 
use,  and  the  differential  equations  on  which  it  is  based,  are 
certainly  inappropriate.  Also,  if  it  cannot  be  proved  that  the 
hyperelementary  terms  must  disappear,  the  conclusions  derived 
from  the  method  are  of  course  untenable. 

I  have  already  published  in  several  places  investigations  on 
the  theory  of  the  absolute  orbit,  or  sketches  of  such  investiga- 
tions ;  in  the  following  paper  I  shall  show  the  connection  of  this 
theory  with  that  of  the  variation  of  constants.  This  will  afford 
the  best  means  of  finding  points  of  comparison  with  the  former 
theory  of  the  motion  of  the  heavenly  bodies,  the  basis  of  which 
is  furnished  by  the  laws  of  Kepler.  In  place,  however,  of  a 
complete  comparison  it  must  suffice  to  submit  only  the  equation 
of  the  radius  vector  to  an  examination  from  this  point  of  view ; 
for  this  equation  is  especially  characteristic  of  the  new  method 
of  considering  the  subject. 

At  the  time  t9  let  r  be  the  true  radius  vector,  and  v  the  true 
longitude  in  the  orbit. 

In  the  complete  development  of  the  theory  of  the  absolute 
orbit,  I  do  not  usually  make  r  dependent  on  v,  but  on  an  argu- 
ment vQ,  which  differs  from  v  by  a  magnitude  of  the  order  of 
the  disturbing  force.  For  the  present  purpose,  however,  this 
difference  is  altogether  unimportant,  and  we  shall,  therefore, 
always  write  v  instead  of  v0.  In  place  of  r  I  now  introduce  a 
new  function  p,  defined  by 


r-i, 


i  +  p 

where,  however,  p  must  not  be  regarded  as  constant,  but  has 
the  signification  of  an  elementary  function.  It  is  easy  to  see 
that,  in  the  elliptic  theory,  p  and  p  have  the  following  meanings, 
viz. : — 

/>  =  a(i—  «*);  p  —  «coe  (0  —  w), 

where  a  is  the  mean  distance,  e  the  excentricity,  and  «■  the 
longitude  of  perihelion. 

I  denote  the  radius  vector  in  the  absolute  orbit  by  (r),  and 
put 

finally  I  write 


March  1887.  of  the  Radius  Vector,  227 

So  that 

For  the  determination  of  p  a  differential  equation  of  the 
second  6rder  may  be  found,  which  may  be  written  as  follows : — 

g  +  (i-*+;r),«2?. 

In  this  equation  ft  denotes  a  constant  of  the  order  of  the  per- 
turbing forces,  X  and  B  functions  of  the  same  order  of  mag- 
nitude, which,  however,  for  the  present  are  not  fully  known. 
They  contain,  in  fact,  besides  other  unknown  magnitudes,  the 
function  p. 

If,  however,  we  confine  ourselves  in  the  first  approximation 
to  the  determination  of  the  elementary  terms  of  the  first  class, 
we  may  regard  the  functions  X  and  B  as  known.  After  the 
determination  of  p  corresponding  to  there  values  of  X  and  2£, 
we  obtain  more  exact  values  of  X  and  22,  and  repeat  therewith 
the  determination  of  p.  Thus  these  functions  are  obtained  by 
successive  approximations.  We  here  remark  that  X  may  in  a 
certain  sense  be  considered  as  arbitrary,  for  only  those  terms 
need  be  retained  in  X  which,  on  multiplication  by  p,  produce 
eubelementary  and  elementary  terms  in  the  subsequent  approx- 
imation. 

We  may  further  remark  that,  if  all  terms  which  contain 
uneven  powers  of  p  as  factors  are  regarded  as  being  collected  in 
Xp,  both  X  and  B  (of  course  only  in  so  far  as  they  contain  sub- 
elementary  terms,  or  give  rise  to  such)  may  be  regarded  as 
even  functions  of  p. 

In  the  above  differential  equation  let  us  now  substitute  for  p 
the  value 

a 

and,  further,  let  us  divide  B  into  two  parts,  M  and  N,  such  that 

R-M+N, 
and  that 

g>  +  <i-*+2r)M-JT 


£G0+<'-M>£«-* 


dv' 

Since  the  functions  M  and  N  are  still  quite  arbitrary,  we  can, 
in  choosing  them,  satisfy  a  certain  condition.  The  object  of 
this  condition  is  generally  that  one  of  the  functions  shall  only 
contain  terms  of  a  certain  form,  whilst  the  other  either  does 
not  contain  such  terms  at  all,  or  only  in  such  a  way  as  to 
annihilate  terms  of  the  same  form  which  arise  in  the  function  to 
be  determined. 


228  Prof.  Gylden,  On  the  Determination  xlyti.  5, 

Before  going  farther  we  shall  adduce  some  general  con- 
siderations on  the  form  of  the  integrals  of  a  linear  equation  of 
the  second  order.     Let  the  equation  be 

g+A>=* <«) 

We  assume  that  the  particular  integrals  of  the  equation 

g+Xjr-o. (2) 

are  known.  If  these  integrals  are  denoted  by  yx  and  y^  and 
the  constants  of  integration  by  g  and  h,  we  have 

y-^yi+ty* (3) 

The  functions  yx  and  y%  may  now  be  multiplied  by  arbitrary 
constant  factors,  concerning  which  we  say  that  they  must  be 
chosen  so  as  to  fulfil  the  equation 

As  is  well  known,  the  solution  (3)  may  be  extended  so  as  to 
apply  to  the  equation  (1),  if  we  regard  the  quantities  g  and  h  as 
functions  of  v  instead  of  as  constants.  These  functions,  however, 
fulfil  their  object  if  they  satisfy  only  a  single  equation  of  con- 
dition, which  we  shall  give  immediately ;  hence  they  may  be 
chosen  in  any  infinite  number  of  different  ways,  without  causing 
equation  (3)  to  cease  to  give  the  integral  of  equation  (1).  By 
differentiation  of  (3)  we  obtain 

whence 

If  we  add  this  to  equation  (3),  after  it  has  been  multiplied 
by  X,  we  obtain,  by  help  of  (1)  and  (2),  the  following : — 

-  Aq  .  ~.  Ah  .  d  /    da  .      dh\     tj  f  M\ 

and  this  is  the  single  equation  of  condition,  which  must  neces- 
sarily be  satisfied,  in  order  that  the  value  (3)  of  y  may  give  us 
the  complete  integral  of  (1).  The  second  condition,  which  must 
be  assumed  in  order  to  obtain  an  actual  determination  of  g  and  hf 
may  remain  entirely  arbitrary. 

If  we  take  as  this  second  condition— 

da  .      dh    _ 
dv        av 

we  obtain — 


March  1887.  of  the  Radius  Vector.  229 

In  this  case  not  only  has  the  integral  of  equation  (1)  the 
same  form  as  that  of  equation  (2),  but  the  same  is  also  true  of 
the  first  differential  coefficients.  We  may  understand  the  results 
of  this  determination  by  a  very  simple  example. 

Let  us  take — 

JT-i;  £-?eos[(l-*)f-J]f 

where  y  and  a  are  small  quantities  of  the  order  of  the  disturbing 
forces,  where  y  further  involves  the  eccentricity  as  a  factor,  and 
where  the  quantity  B  denotes  an  arbitrary  constant. 
Then  it  easily  follows  that — 

When  these  values  are  substituted  in  the  formed®— 
they  lead  to  the  following  expressions : — 


\y[aa{<rv  +  B)  +  sin  [(2  -•>-  B]\ 
dv 


dv 

d)=     $7{coe  (jv+B)  +  cos  [(2-o>-  B]} 
dv 

m 

It  may  be  remarked  that  g  and  h  contain  terms  of  two  kinds ; 
the  first  is  an  elementary  term  of  the  form  (A),  the  second,  on  the 
other  hand,  does  not  belong  either  to  the  form  (A)  or  to  the  form 
(6).  This  circumstance  involves  an  unnecessary  complication 
of  the  functions  g  and  h,  which  may  become  extremely  trouble- 
some when  we  have  to  deal  with  continued  approximations.  The 
complication  may,  however,  be  avoided  if  we  do  not  make  the 
condition  at  our  disposal  as  before,  but  make  it  so  as  to  simplify 
the  functions  g  and  h.  I  remark  that  by  such  a  simplification  the 
meaning  of  the  function  y  is  unaltered,  and  only  the  meaning  of  the 
differential  of  y  is  affected.  The  loss  of  simplicity  in  the  meaning 
of  this  differential  is,  however,  in  many  cases  (for  example,  in 
the  planetary  theory)  a  very  slight  evil  in*  comparison  with  the 
advantage  which  is  gained  by  the  simplification  of  the  functions 
g  and  h.  Besides,  the  adoption  of  the  above  condition  depends 
actually  on  the  fact  that  this  choice  appears  obvious,  and  that 
there  is  no  other  before  us;  it  depends  also  on  the  circum- 
stance that  the  Keplerian  representation  of  the  planetary  motions 
can  be  retained  unchanged,  so  that  the  disturbances  may  be 
regarded  as  small  corrections  which  will  exercise  no  charac- 
teristic influence  on  the  representation  of  the  motion. 

We  will  now,  however,  set  aside  the  condition  chosen  above, 
and  will  replace  it  by  a  more  general  one. 

We  write  then — 

»***S"W « 


1 


230  Prof.  Gylden,  On  the  Determination  xlvii.  5, 

so  that  (X)  is  an  arbitrary  function  of  v.    From  equation  (4)  we 
then  find — 

dv        dv  dv ' 

whence  there  results — 

y,(*+^>)+y/(*) y (6) 

Before  going  further  we  will  prove  directly  that  the  func- 
tion y  may  be  made  independent  of  the  function  (X)  by  the  sub- 
stitution of  the  values  of  g  and  h,  which  result  from  the  equations 
just  found,  in  the  equation  (1). 

For  since — 


dh 
dv 


we  obtain — 


d 
dv 


A-*©+yiM+[yi#<**» 


where  g0  and  h0  are  constants  of  integration. 
Hence,  from  equation  (3)  we  obtain — 


y-yi(*t- Jy*8**)  +y*(Ao + JyiJW*Y 


This  is  a  value  which  is  completely  independent  of  the  func- 
tion (X),  and  hence  it  is  the  same  which  we  should  have  found  if 
we  had  made  (X)=o. 

As  we  have  full  disposal  over  the  function  (X),  we  can  choose 
it  so  that  the  functions  g  and  h  may  be  as  simple  as  possible ;  for 
example,  they  may  be  made  to  contain  only  elementary  terms  of 
the  form  (A),  and  this  is  especially  advantageous  in  the  planetary 
theory.  In  every  such  definition  the  equation  of  condition  (4) 
must,  of  course,  be  satisfied,  so  that  it  is  not  possible  completely 
to  attain  the  intended  object  for  every  value  of  B.  As  already 
remarked,  the  differential  equation  must,  for  this  reason,  be 
divided  into  two,  and  the  intended  object,  that  the  functions 
(7  and  h  may  have  the  forms  referred  to,  must  be  kept  in  view.  And, 
further,  certain  terms  of  the  function  B  must  be  retained  whilst  the 
others  are  carried  over  to  the  second  equation.  In  the  simple 
example  considered  above  the  matter  is  as  follows : — the  function 
B  has  already  the  form  corresponding  to  our  intention,  for  we 
may  write — 

if— Y  cob  v  +  *8in  t; 
where — 


March  1887.  of  the  Eadius  Vector.  231 

If  now  the  values  y1=cos  t>,  ys=sin  v  are  substituted  in  the 
equation  of  condition  (4),  that  equation  can  be  satisfied  by 
equating  to  zero  the  coefficients  of  cos  v  and  sin  v  separately. 

Hence,  there  result  the  equations — 

dv%      do 
dv*      dv 

This  system  can  be  integrated  very  easily.  For  if,  after 
multiplying  the  second  by  i  =>/  —  1,  we  add  the  two  equations 
together,  we  obtain  the  following  linear  differential  equation  of 
the  second  order : — 

whence  it  follows  that 

From  this  formula  we  may  compute  -^  and  -    ,  whence  g 

and  h  may  be  found  by  a  simple  quadrature. 

We  remark  that  the  process  remains  unaltered  when  the 
functions  *¥  and  $  retain  any  number  of  terms  of  the  same  form 
as  those  written  above. 

We  now  assume  a  somewhat  more  general  form  for  the  par- 
ticular integrals  yx  and  y2,  writing 

yi  -/(*)  cob  v ;  y,=/(tO  sin  v, 

where  /  denotes  an  elementary  function  of  the  form  (A).  If 
now  the  form  of  the  function  B  be  assumed  to  be  the  same  as  in 
the  preceding  case,  and  if  the  coefficients  of  cos  v  and  sin  v  be 
separately  equated  to  zero,  we  find  from  equation  (4) 

Whence 

From  the  integration  of  this  equation  we  obtain 


dv 


With  this  result  our  problem  may  be  regarded  as  solved,  for 
when /(-»),  ¥,  and  $  are  given,  there  is  no  formal  difficulty  in 

obtaining  the  expressions  for  -/  and  -,-,   and   hence   also   for 

dv  dv 

g  and  h. 


232  Prof.  Gyldeu,  0»  ike  Ddermtmatio*  xiVtt.  5, 

We  will  now  make  a  third  assumption  as  to  y,  and  y*  the 
basis  of  an  mvestigaiion  similar  to  thai  carried  out  above. 
We  shall  now,  however,  go  somewhat  further,  and  take  into 
consideration  the  function  which  was  previoa&l y  regarded  as 
indeterminate.  This  function  has  an  actual  application  in  the 
planetary  theory. 

Suppose,  then,  thai 

y, -fir;  <»•(*  +  #);  y,-/(v)  on  (•  +  •), 

where/  has  the  same  meaning  as  before,  and  0  denotes  a  function 
of  v  which,  besides  one  term  multiplied  by  v,  only  contains 
elementary  terms  ci  the  form  (A). 

On  assuming  for  B  the  same  form  as  above  we  obtain,  by 
comparison  of  the  coefficients  of  cos  v  and  sin  v  in  the  equa- 
tion of  condition  (4),  the  results 

'W  "■•J^/M**  2  +  a[«#/W+(i+ J)/M  «*  •]  ~ 

-/W  «n  #g+/(i;)  cot #J^+ 2[co8#/(r)-(i +^/(p)  .in  #]^ 

- 2[«n  •/(*)  +  (l  +  g)/ («)  cos  •]  £-# 
Whence  we  easily  obtain 

If  the  second  of  these  equations  be  multiplied  by  t,  it  follows 
that 

or 

The  integration  of  the  first  of  these  equations  leads  to  the 
result 

and  a  similar  result  is  obtained  from  the  second.     If,  now,  0  is 

a  known  function,  -/-  and  —  may  be  immediately  computed, 

dv  dv 

and  afterwards  g  and  h.     In  the  case,  however,  which  now  for 

a  time  demands  our  attention,  this  assumption  is  not  suitable. 

We  shall,  on  the  contrary,  assume  that  the  function  0  depends 


March  1887.  of  the  Radius  Vector.  233 

directly  on  the  quantities  g  and  h  to  be  determined,  and  that 
the  relation  between  the  three  quantities  is  as  follows — 


0 


-AifrtZv ($) 


where  /32  denotes  a  small  constant  of  the  order  of  the  disturbing 
masses,  and  where  we  have  put  g*  +  fc2  =  17s. 

We  suppose  that  g  and  h  are  small  quantities  of  the  order  of 
excentricities ;  and,  with  respect  to  the  functions  ¥  and  0,  we 
retain  the  previous  assumption,  namely— 

Y-ycos(0t>+B),  +  =  7  sin  («v  +  2?); 

whence  it  follows  that 

▼  cos  0-*  sin  9-y  coa(<rv+6  +  B), 
V  sin  0++  cos  9=y  sin  (<rt>  +  0+ B). 

Since,  now,  g  and  h  must  be  determined  as  elementary 

functions  of  the  form  (A),  we  must  assume  that   —£  and  -~  6 

chr  dv* 

belong  to  a  higher  order  of  magnitude  than  -J?  and  — . 

If  we  neglect  in  a  first  approximation  the  former  as  well  as 

the  products  of  -^  and  —  with  — ,  we  obtain 

r  dv  dv  dv 

g**gt—±V  I  sin  (av+e  +  B)dv  ] 

t  w 

A-A»  +  |7  \CQ*(cv  +  0+B)dv  J 

where  go  and  h0  denote  constants  of  integration,  and  the  function 
/  is  put  equal  to  unity. 

In  many  cases  the  expressions  for  the  functions  g  and  h  may 
be  freed  from  the  integral  sign  by  the  application  of  the  process 
of  partial  integration.  We  cannot,  however,  always  obtain  con- 
vergent developments  by  these  means ;  and  where  we  have  to 
deal  with  terms  which  undergo  so  great  an  increase  by  integra- 
tion that  they  may  imperil  the  stability  of  the  system,  we  have 
to  strike  out  a  new  path. 

We  obtain  a  method  more  appropriate  for  our  object  if  we 
form  the  sum  of  the  squares  of  the  equation  (y),  multiply  this 
sum  by  /3g,  and,  finally,  differentiate  the  result.  By  referring  to 
the  equation  (/?)  we  then  have 

-r-i~-0j7y*6in  (<rv+e  +  B)  +  0tyhtCoa(<rv+$  +  B) 
dtr 

+  ift7*  sin  {irv  +  0  +  B)  I  sin  (<tp  +  0+  B)  dv 

+  ii8j7*cos  (cr»+  0  +  B)  j  cos  (ov  +  0+  B)  dv     .     .     .     .    (8) 


234  Prof.  Qylden,  On  the  Determination  xlvti.  5, 

If  we  regard  the  coefficient  y  as  sufficiently  small,  we  have 
the  right  to  neglect  in  the  first  approximation  the  sum  of  the 
last  two  terms  in  the  above  equation.     There  then  remains 

jjjiT  -0iW»  «n  (*»  +  e+  B) -^fitjKo  cos  (<r«  +  »+ B). 

We  here  put 

g%~e9  cos  w0,  4#**«#  sin  w0 
and,  further 

so  that  we  obtain 

d  .  -  —  ftr»0  8"1  ^coa  r. 

This  equation  may  be  integrated  at  once.     The  result  is 

where  we  denote  the  constant  of  integration  by  y0*. 
We  write  farther 


V 


and  setting  aside  the  constant  which  arises  in  the  integration  in 
hand,  we  finally  obtain 

V**amy%vtmod.k. 

From  this  there  results  therefore 

0v  +  $  +  B  =  2amy9v  +  w9. 

The  second  approximation  is  to  be  computed  from  this,  the 
process  being  easily  carried  out  by  means  of  Lame's  differential 
equation.  It  may  be  remarked  that  a  term  here  makes  its 
appearance  which  contains  v  as  a  factor ;  it  arises  because  we 
have  neglected  certain  quantities  in  the  original  differential 
equations.  In  a  rigorous  treatment  of  these  equations  terms  of 
this  kind  may  always  be  avoided  if  they  are  not  necessarily 
involved  in  the  original  differential  equations. 

The  method  explained  above  is  also  worthy  of  notice,  because 
it  is  applicable  when  the  quantities  y  cos  B  and  y  sin  B  are 
not  constant,  but  are  subelementary  functions  of  the  form  (A). 

In  these  cases  the  result  is  expressed  by  means  of  elliptic 
functions,  with  a  variable  modulus,  which  is  in  fact  an  ele- 
mentary function  of  the  form  (A).  The  investigation  of  the 
differential  equation  which  appears  here  I  have  treated  in  a 
memoir  as  yet  unpublished.  Dr.  Harzer  has,  however,  already 
made  use  of  the  most  important  part  of  it  in  his  investigation 
of  the  absolute  orbit  of  Hecuba. 

In  the  application  of  the  above  method  of  investigation  to 
the  planetary  theory  y0  is  a  quantity  of  the  order  of  the  disturb- 
ing forces,  and  therefore  of  the  same  order  as  fi%  »  the  constant 


March  1887.  of  the  Radius  Vector.  235 

7  is  of  the  same  order  as  &&$.  Henoe  it  follows  that  the 
modulus  is  of  the  same  order  as  e0 — that  is  to  say,  of  the  order  of 
the  excentricities. 

After  this  preface  we  resume  the  equation, 

*(p\  +  (i-0-X)(p)  =  M     ../....    (7) 

where  we  assume,  as  to  the  functions  X  and  M,  that  they  give 
rise  only  to  elementary  or  subelementary  terms  of  the  form  (B) 
in(p). 

As  in  the  following  investigations  we  need  not  revert  again 
to  the  function  £,  we  may  for  brevity  write  p  instead  of  (j>).  In 
consequence  of  the  assumption  that  the  result  shall  only  contain 
terms  of  the  form  (B),  we  have  also  an  equation  of  the  form — 

p»jc  cos[(i— 1)»— r] 
+  K,coe[(i  —  0"i)t>— J?,]+ic2co6[(i— <r,)«— 2?J+  .... 

where  k  and  r  denote  the  two  constants  of  integration.  The 
remaining  coefficients  and  angular  constants  depend  partly  on  the 
elements  of  the  orbits  of  the  disturbing  bodies,  and,  if  they 
belong  to  terms  of  the  higher  class,  partly  also  on  *  and  r,  as 
well  as  on  the  elements  which  determine  the  position  of  the  orbit. 
We  now  write 

g — 1?  cos  (w — r)  -  k + «,  cos  [(<r,  —  1  )v  +  2?,  —  r] 

+  k,  cob  [(cr,  -  s)v  +  B2 -  T] 
1    •  .  .  . 

A  =  *sin(w—  r)»       *,  Bin  [(<»•,  —  s)v  +  Bl  —  t] 

+  k,  sin  [(oj — s)v  +  Bt — T] 

T      •    •    •    • 

and  thence  obtain  the  following  expression  for  p. 

p=i|cos[(i-s)t;-w] 
If  now  we  put 

*--ism[(i-i)t,-w]-<A) 

we  have 

-(x)-fi,sm[(i-f)t;-W]  +  cw[(i-5>-r]g+Bin[(i-,)«-r]^. 

In  accordance  with  previous  assumption,  the  functions  X  and 
M  depend  on  p2 ;  they  may  besides  contain  terms  multiplied  by 
i)2  and  its  powers,  without  affecting  the  intended  form  of  the 
function  p.  We  now  conceive  these  functions  separated  into 
two  in  the  following  way  • — 


236  Prof.  GyldSn,  On  the  Determination  xlvii.  5, 

The  functions  X0,  Xi9  Mx  and  Mt  are  as  follows — 

X9~20fcoB(<r.v  +  Bv>) 
A>:W{«>cot[(2-,,)*-2?}»>] 

Mt »  XyP>  cos  [(I  -<r,)t>-3W] 
where 

denote  constant  coefficients  of  the  order  of  the  disturbing 
forces  depending  on  the  elements  and  on  the  indexes  *  and  j. 

It  is  hardly  necessary  to  remark  that  the  J?*s  are  angular 
constants  and  the  a  a  small  quantities  of  the  order  of  the  dis- 
turbing force.  The  function  M  has  obviously  been  added  in 
order  to  annihilate  non-elementary  terms  which  may  arise. 

In  the  following  operations  the  last  term  in  X  would  exercise 
a  yery  detrimental  influence,  because,  in  a  later  integration,  it 
would  contain  the  variable  v  as  a  factor.  The  term  in  question 
may,  however,  be  at  once  easily  eliminated.  Let  us  write  the 
above  expression  for  X  as  follows — 

We  remark  that  the  last  term  may  in  general  be  omitted  or 
joined  to  If,  because  on  multiplication  by  p=iy  00s  [(i—s)t?— «r], 
it  can  only  give  rise  to  non-elementary  terms.  Terms  of 
the  same  nature  which  make  their  appearance  later  may  be  set 
aside  in  a  similar  manner,  and  usually  by  only  a  small  alteration 
of  the  constant. 

We  shall  now  endeavour  to  liberate  the  already  simplified 
differential  equation  from  the  function  X%  ;  this  may  be  done  by 
replacing  p  by  a  new  function,  p„  and  v  by  anew  variable,  u;  px 
and  u  being  defined  by 


P 


-_*_,  *.      du 


i  +  f        (i++)f 

Let  us  further  choose  the,  as  yet,  indeterminate  function  vp  so 
as  to  satisfy  the  equation 

*(l+«  +  (l+«{l-*-*+^  +  A*}-l=J=f.       .     .     (8) 

By  equation  (7)  we  then  obtain  the  following  result : — 

jJ+{»-*-<fc  +  *M*'-*+*Jto-jiJty    ...    (9) 

We  shall  be  able  to  dispose  later  of  the  function  AX,  in  such  a 
way  that  \p  may  contain  no  terms  of  the  form  (A). 

In  passing  on  to  the  integration  of  equation  (9),  we  write  for 
brevity 


March  1887.  of  the  Radius  Vector.  237 

and  put 

El 

p,"V(i-ft) 

in  the  equation 
Thus,  we  obtain 


And  if  we  define  Qx  by  the  equation 


as  may  be  very  easily  carried  out  by  successive  approximations, 
we  have 

g..i!(S«<.-«p-$t#» ....  co, 

The  integral  of  this  equation  is  known.  When  Af=0,  whilst 
cx  and  c2  are  constants  of  integration,  the  solution  is 

The  particular  integrals  of  the  equation  (9),  except  as  regards 
a  constant  factor,  always  involve  the  supposition  that 

cosff  V(i  -  C,y»l  Bin  ff  </(i  -  Q{)du] 

One  sees  by  the  light  of  the  preceding  indications  how  the 
complete  integral  of  this  equation  must  be  developed.  The 
steps  which  are  still  necessary  for  the  solution  of  the  differen- 
tial equation  for  the  function 

9-sArfdv 

involve  too  many  details  to  be  here  entered  on. 

If  we  look  back  at  the  expressions  for  the  functions  g  and  ht 
we  easily  perceive  that  the  constant  part  of  q2  (which  will  be 
denoted  by  *0*)  is  made  up  in  the  following  manner — 

By  light  of  the  preceding  expressions  we  now  easily  perceive 
that  the  coefficient  denoted  by  9,  which  represents  the  ratio  of 
the  mean  motion  of  the  apses  to  that  of  the  body,  is  given  approx- 
imately by  the  formula 


\ 


238  Prof.  GyldSn,  On  the  Determination  xlvii.  5, 

If  now  the  quantity  e0  is  of  the  order  of  the  excentricities — 
and  that  this  is  the  case  may  be  seen  from,  the  known  motion  of 
the  apses  in  the  principal  planets — none  of  the  coefficients  icl9  #ca, 
&c.,  can  become  so  large  as  to  get  out  of  their  class.  The  number 
of  the  coefficients  which  belong  to  this  class  cannot  be  very  great, 
because  otherwise  the  quantity  e0  would  increase  beyond  its 
indicated  limit.  These  circumstances  show,  of  course,  that  the 
series  which  we  have  obtained  for  g  and  h,  and  also  for  the 
function  p,  converge ;  but  the  evidence  is  not  complete,  and  we 
can  merely  say  that  this  convergence  is  highly  probable.  The 
series,  in  fact,  arise  from  series  proceeding  by  successive  powers, 
and  in  these  series  single  individual  terms  may  be  increased  by 
very  small  divisors  of  integration.  Hence,  if  we  set  aside  those 
individual  terms,  they  will  either  converge  or  diverge,  like  series 
proceeding  by  successive  powers.  But  there  is  another  circum- 
stance, which  seems  to  put  the  convergence  beyond  all  doubt, 
namely,  that  the  convergence  of  the  series  for  the  differential 
coefficients  of  the  function  p,  with  reference  to  the  variables  v  or 
u,  is  as  good  as  that  of  the  development  of  the  function  itself. 

The  integration  of  equation  (8)  still  remains,  and  for  this  we 
pursue  the  following  method.  We  somewhat  transform  the 
equation,  and  write  it  as  follows : — 

-(I+^)j(iB2  +  iiB4)(,*-0  +  ^.-^} 

-(T^J0*«+i*«)  (*-*■)+*.+*.}. 

On  the  supposition  that  \p  is  a  small  quantity,  we  develop 
part  of  the  last  term  of  the  right-hand  side  in  ascending  powers 
of  v//.     Then  putting 

we  have 

+  4v|(i82  +  £i84)  (u*-o  +  ^) 

Now  this  equation  can  be  integrated  by  continued  approxima- 
tions.    For  this  end  I  write, 

♦  -♦•  +  ♦1. 

and  define  \p0  by  the  equation 

»(I+w+(,-'>l,+*-(»Tgi}-(.+Vr-  *  '  (,,) 

where  T  denotes  (unction  which  is  intended  to  transfer  certain 


March  1887.  of  the  Radius  Vector*.  239 

terms  to  the  equation  next  below,  from  which  i//v  is  determined. 
If  we  only  write  down  the  most  important  terms,  this  equation 
becomes 

^  +  (i-i»){4  +  30+.,}^1  =  T-A^+4^{(/82+JiBj(^-0  +  ^.}+  ...  (12) 

If  the  funotions  X%  and  T  vanish  the  integral  of  equation 
(11)  may  be  given  in  a  simple  form ;  for  we  then  have 

.       vti-5coB(2tt^(i-y)-n)] 

I+*- V(J=&) 

where  $  and  II  denote  the  two  constants  of  integration. 

In  the  following  developments  I  shall  permit  myself  some 
abbreviations  which,  however,  are  quite  unimportant  in  the  final 
result.  In  the  first  place  I  simply  equate  the  factor  <S(i  -p)  to 
unity,  whenever  it  is  not  seen  to  be  multiplied  by  u. 

The  above  value  of  1  +  v//0  must  now  be  substituted  in  equa- 
tion (11)  ;  the  quantities  £  and  II  must,  however,  no  longer  be 
regarded  as  constant,  but  must  be  so  defined  that  the  functions 

dcosn=(r;  dsinllafi; 

may  only  contain  elementary  terms  of  the  form  (A).  In  order 
to  fulfil  this  definition  the  function  T  must  be  chosen  in  a 
corresponding  manner. 

In  consequence  of  our  supposition  with  regard  to  the  func- 
tions Q,  H,  and  3*  we  shall  neglect  their  second  differentials,  and 
then  obtain  from  equation  (11) — 

dG  dH 


[  sin  to .  G — cos  to .  #V  cos  to—  +  sin  w-J-\ 
+  3   \      J\         du duj 


2^(1  -*i)<i/^i-»  cos  (to-n)j     4*  ^(i-&*){i-&cos(«;-n)}! 

•          sin  to.  (r— cos  to.  H  dh2 

+  1  7 .-r 

{i-32}!V(i-&cos(to--n)J*f' 

__,      (i-*8)         X_T 

{I-3cos(to-^)}^,       ' 

where  w  is  written  instead  of  2Us/(i-j>). 

The  functions  O  and  H  must  now  be  so  defined  as  only  to 
contain  terms  of  the  form  (A).  This  condition  is  fulfilled  if  in 
the  above  equation  the  coefficients  of  cos  w  and  sin  w  are  made 
to  vanish  separately,  and  if  at  the  same  time  all  terms  which 
do  not  satisfy  the  above  condition  are,  by  means  of  T,  made  to 
vanish. 
1  If  now  we  put  \  • 

-Y2=,lrcosto  +  *8in  to,  •-,    :     • 

where  ¥  and  *  only  involve  subelementary  terms  of  tifce.  second 


240  Prof.  OyldSn,  On  the  Determination     Tf    xlvii*  5, 


clam  of  the  form  (A),  we  obtain,  as  applicable  to  the  first 
approximation,  the  equations 


de     *" 


whence 


also 


1^  +  }  du  (?a-(i^ 
1  -a* 

dff      ** 

iS+|   du   tf-(i-3«)V 

g-  -§^(1  -*«)  f(i  -**)!*** 

rsinit^-casio^lrcoeiD.  <?  +  gin  w .  #1 

*  [i-dco6(t0-n)]i 

[cos  w  —  +  sin  «>--—  |  Isintt.  6r-cosw.iM 

•  [sin  w .  G— 006 id .  H]  [con to .  (r+sin  tc/7] 

*  (f~y){i-dcos(w-n)}t 

=  y(i-3»).r. 

It  may,  Jiowever,  be  easily  perceived  that,  in  the  development 
of  this  expression  for  T,  terms  arise  of  a  high  class — at  least  of 
the  sixth — which  may  be  retained  in  0  and  H.  There  is  no 
obstacle,  however,  to  taking  account  of  them  in  equation  (12). 
It  is  indeed  advantageous  to  take  account,  in  the  definition  of  i//,. 
of  terms  of  higher  classes,  which  may  become  very  large  in  O 
and  H  by  integration,  and  to  incorporate  them  in  that  function. 
That  such  a  term  in  \pY  cannot  become  of  any  arbitrary  magni- 
tude may  be  shown  in  the  following  manner. 

For  the  sake  of  simplicity,  we  assume  that  in  the  value 

a  and  A.  denote  constants.  According  to  the  preceding  explana- 
tion a  is  an  elementary  coefficient  of  the  second  class,  and  conse- 
quently of  the  second  order  of  excentricities,  but  is  not  multiplied 
by  a  factor  of  the  order  of  the  disturbing  forces ;  <r,  on  the  other 
hand,  is,  as  before,  of  that  order  of  magnitude. 

If  now  this  expression  be  substituted  in  equation  (12)  we 
obtain 

^+{i+*+*e»Mi^)»-a4]ta-*r  ....   (I3) 
eiur  z 

For  the  integral  of  the  equation  found  by  putting  T  equal  to 
zero,  an  approximate  value  may  be  given,  which  is  not  only 
quite  sufficient  for  our  purpose,  but  even  corresponds  better  than 
the  complete  value,  because  it  is  possible  to  judge  more  directly 


March  1887.  of  the  Radius  Vector.  241 

of  the  magnitude  of  the  constants  which  enter  in  the  approxi- 
mate than  in  the  exact  form.     The  approximate  solution  is 

4  -ccoe[(I~fW~ftcwf2(I~<r)t0~"2'<*~~(|~~,)tg] 

'  i  +  rcos[2(i— *)«T— 2A] 

sin  [( 1  —  f  )tp]  +  /u  sin  [3(  I  -  gptp  -  2  A  -  ( 1  —  s)w] 
*  I +rcos  [2(1—^)10-2^] 

The  constants  of  integration  are  here  denoted  by  c{  and  c% ;  p  is 
a  coefficient  which  is  very  nearly  equal  to  unity ;  and  v%  being  £a2, 
is  a  very  small  coefficient ;  and  finally  s  is  given  by  the  formula 

whence  it  is  obvious  that  s  is  a  quantity  of  the  fourth  order  with 
respect  to  the  exoentricities. 

From  the  above  expression,  and  from  the  magnitude  of  the 
quantity  s,  we  must  conclude  that  a  subelementary  term  of  the 
sixth  class  in  T  will  appear  as  a  subelementary  term  of  the  second 
class  in  the  function  i£,. 

It  would  carry  us  too  far  into  details  to  extend  this  investi- 
gation to  the  more  general  case,  where  acos-4  and  asm^l  are 
elementary  functions  of  the  form  (A),  and  we  must  therefore 
pass  this  over. 

It  is  often  possible,  by  a  very  simple  transformation,  to  rednce 
within  the  proper  limits,  terms  which  seem  at  first  as  though 
they  would  become  very  large  in  integration.  It  follows  thence 
that  we  almost  always  carry  out  the  integrations,  after  having 
partially  developed  the  function  to  be  integrated.  Correspond- 
ing to  this  development  there  is  also  a  certain  development  of 
the  divisors  of  integration,  which  is  not  always  convergent,  even 
when  the  development  of  the  function  to  be  treated  was,  before 
integration,  very  highly  convergent.  These  obstacles  may  be 
avoided  by  carrying  over  terms  which  occur  in  the  wrong  place 
in  one  equation,  to  another  where  the  divisor  of  integration  may 
be  determined  more  correctly. 

It  would,  however,  lead  to  no  useful  result  if,  for  example, 
we  should  propose  to  treat  all  the.  terms  of  X2  in  this  function 
4>u  for  the  utility  of  equation  (12)  depends  on  the  fact  that  the 
quantities  G  and  H,  and  also  i//0,  were  found  as  elementary 
functions  of  the  second  class. 

If  now  a  term  should  exist  in  M  which  would  be  very  largely 
increased  in  pl9  the  result  must  be  regarded  as  inappropriate ; 
but  by  carrying  over  this  term  to  equation  (12)  we  again  obtain 
an  appropriate  result.  The  following  steps  are  necessary  for  this 
end : — 

Let  the  term  in  question  be 

yew  [(1  -*)i;— B). 
Since  now 

(i_*)0_U.(2-<r-j)r-B-r-[(i-<r)0-r], 

T  2 


242  Prof.  Qylden,  On  the  Determination  xlv-u.  5, 

we  have 

700s  [( I—  a-)*— 2*]= 7  cos  2  W  cos  K— 7  sin  2  FT  sin  J  \ 
where  for  brevity  we  write 

r«[(i-»)«-r) 

2fF=(2-*-s)&-5-r. 
But 

p=y  cos  V+h  sin  F 

^--^sinr+*cosr-(x). 
dv 

From  which  equations  we  easily  deduce  the  following  values  : — 

H»cos  V=gP  +  k^  +  h(\) 

dv 

H*  sin  V=hp-g(£-g(\)\ 

whence 

:  1«ub  «  rr  Lyp  -r  #f 
1? 


7C08[(l-<r)u-5]=.^{cos2lf[^p  +  ^+A(X)3 


+  8in2fT[V-^-^)]}. 

1 

From  these  results  it  is  already  obvious,  without  repeating 
the  development,  that  the  term  in  question  will  be  carried  over 

to  the  function  AX ;    for  the  term  multiplied  by  -^   may  easily 

dv 

be  eliminated.     The  term  which  is  carried  over  will  now  appear 

in  equation  (12),  and  will  be  treated  like  the  others.     The  result 

of  this  transposition  depends  actually  both  on  the  fact  that  the 

factor  —  may  be  developed,  and  on  the  magnitude  of  the  co- 
efficient y«  The  latter  must  belong  at  least  to  the  third  class, 
and  must  of  course  contain  a  factor  of  the  order  of  the  disturb- 
ing force. 

We  have  above  found  expressions  in  which  the  variable  c  is 
replaced  by  the  new  variable  u.  Since,  then,  the  functions  Xand 
M  were  originally  expressed  in  terms  of  the  variable  r,  it  is 
necessary  to  reduce  the  arguments  which  depend  on  v  to  the 
variable  u,  and  vice  versa. 

The  equation 

,  du 

(l+*)2 

serves  as  the  basis  for  this  operation. 
We  develop  it  as  follows : — 


dv 


du 


Since  the  even  powers  of  \px  contain  constant  terms,  the  non- 
periodic  part  of  v  has  the  form 


March  1 887.  of  the  Radius  Vector*  243 

where gig  a  very  small  quantify,  at  least  of  the  second  order  of 
the  disturbing  forces. 

Bat  the  appearance  of  this  constant  would  have  been  easily 
avoided  if  we  had  originally  put 

and  had  then  determined  g  in  such  a  way  that  the  non-periodic 
part  of  the  coefficient  of  du  was  equal  to  unity. 

All  of  the  terms,  with  the  exception  of  the  first  by  which  dv 
.is  represented  above,  are  multiplied  by  a  factor  of  the  order  of 
the  disturbing  forces ;  they  can,  after  both  integrations,  at  most 
become  elementary.  For  since  i//0  is  not  itself  multiplied,  by  a 
factor  of  the  order  of  the  disturbing  forces,  we  might  opnj/eotare 

that  in  the  integration  of  the  term  ~  —  hyperelementary 

terms  would  make  their  appearance.  This  is,  however,  not  the 
case,  as  we  may  easily  convince  ourselves  by  substitution  of  the 
value 

2ft 

If,  in  fact,  we  put  $=. • ,  we  have 

Jt-'= (I -«*)*» =[i.+,2aco8(w-n)  +  2a»co8  2(«;-n}  +  '.  .  ]<*«. 

(i+W     l~2acoi(to-n)  +  a«     L.     •  V         7  *       >    J 

An  inspection  of  this  expression  suffices  to  convince  us  of  the 
absence  of  hyperelementary  terms. 

In  the  preceding  pages  a  method  of  computing  the  radius 
vector  in  the  absolute  orbit  has  been  laid  down,  which  does  not, 
indeed,  appear  at  present  entirely  free  from  objection  in  every 
point,  but  is,  at  any  rate,  characterised  by  the  advantage  that 
by  it  difficulties  may  be  avoided  which  previous  methods  (for 
example,  that  of  Leverrier)  were  not  in  a  position  to  overcome. 

I  cannot  close  this  explanation  without  making  a  remark 
which  bears  on  the  conception  of  the  absolute  orbit,  in  contrast 
with  the  conception  of  the  so-called  mean  ellipse — assuming 
this  latter  conception  to  be  in  general  possible.  If  we  substi- 
tute for  the  elements  in  the  formula  of  elliptic  motion  those 
functions  which  represent  the  secular  variations  by  trigono- 
metrioal  functions,  we  obtain  the  expressions  for  the  motion  in 
the  absolute  orbit.  This  orbit  is,  however,  not  an  ellipse,  nor  in 
this  formula  of  motion  is  Lagrange's  condition,*  (X)=  o,  satisfied. 
An  ellipse  of  which  the  elements  are  subjected  only  to  secular 
inequalities,  and  which  at  the  same  time  satisfies  the  above 
conditions,  does  not  give  what  is  required.  The  nomenclature 
*  mean  ellipse '  simply  contains  in  itself  a  •  contradictio  in  adjecto.' 
The  ellipse  whose  elements  are  subject  to  secular  inequalities 

,*  In  the  variation?  of  the  planetary  element  the  corresponding  .equation  is. 
written  somewhat  differently.  • 


244  Lieut-Gem.  Tennant,  Note*  on  XLYII.  5, 

may  indeed  be  employed  as  a  means  of  construction  for  indi- 
cating the  absolute  orbit ;  but  it  intersects  the  latter  at  an  angle 
nf  the  order  of  the  product  of  the  exeentrioity  and  of  the  dis- 
turbing force,  and  this  angle  only  vanishes  when  the  radian 
vector  coincides  with  an  apse. 


.Vote*  on  Reflecting  Telescope*,  hy  Lieut-Gen.  J.  F.  Tennant, 
B.E.,  P.R.S. 

In  the  coarse  of  discussions  as  to  making  Reflecting  Tele-- 
scopes,  I  have  been  led  to  investigate  some  formulae  which  have 
not,  so  far  as  I  know,  been  published,  and  which  seem  likely 
to  be  of  nse. 

It  has  been  usual  in  designing  a  reflector  for  astronomical 
purposes  to  determine  the  size  of  the  small  mirror  by  a  formula 
which  only  gires  it  large  enough  to  receive  and  reflect  all  the 
rays  which  come  from  an  object  in  the  axis  of  the  great  specu- 
lum ;  and  the  tnbe  is  only  so  maoh  larger  than  the  speculum  as 
is  necessary  to  allow  the  space  for  the  cell.  When,  however,  it 
is  desired  to  use  the  telescope  fur  photographic  purposes,  and  a 
field  of  some  diameter  is  sought,  this  plan  no  longer  suffices. 
I  propose  in  the  first  place  to  consider  the  necessary  dimensions 
of  the  small  mirror  and  tube.  M.  Ltewy  has  given  an  approxi- 
mate formula  in  a  paper  on  "  A  New  Form  of  Reflector  "  in 
the  Bulletin  Attronomique. 


In  Fig.  I.  let  AB  be  a  section  of  the  parabolic  speculum,  with 
its  geometrical  focus  at  F„  which  will  also  be  the  focus  of  rays 


March  1887.  Beflecting  Telescopes.  245 

parallel  to  the  axis  after  reflection  at  the  surface*  So  long  as 
we  only  consider  such  rays,  the  month  of  the  telescope  need  not 
be  wider  than  cd>  except  by  such  amount  as  will  suffice  to  make 
the  rays  quite  clear  of  the  edge,  and  a  flat  of  the  size  gh  in  the 
position  shown  will  reflect  ail  the  light  to  a  focus  at  /9  outside 
the  tube.  Denoting  AB  by  2t  and  the  focal  length  by  a,  then 
it  will  only  be  necessary  that  <5,  the  perpendicular  distance  of  f2 
from  the  axis  of  the  parabola,  should:  be  a  little  greater  than  half 
the  diameter  of  the  tube,  and  we  shall  have  the  following 
formula  to  determine  the  size  of  gh : — 

tan  ^  =  - ;  m  the  minor  axis  of  gh  =  c  tan  24  and  I  the  major  axis  -=  m  4/2. 
a 

If,  however,  the  field  subtends  an  angle  R,  AR8  =  L,  AI^  =  2a, 
we  shall  have  to  modify  the  design  as  follows : — 

ist.  The  mouth  of  the  telescope  must  have  an  enlarged 
diameter  CD. 

2nd.  The  image  formed  by  the  great  speculum  alone  will  now 
be  enough  to  fill  the  space  F,F3,  and  we  want  to  place  it  outside 
the  tube  in/]/89  we  must  place  the  small  mirror  (or  flat)  nearer 
the  great  one  and  enlarge  its  dimensions :  it  will  now  be  repre- 
sented by  GH.    Using  the  same  symbols  as  before,  we  now  have 

CD  >  2  (r  +  Ac  tan  a)  where  Ae  is  the  length  of  the  tubo  ; 

b^r  cot  ($— a)  ;  m=*(b—a  +  c)  tan  (2^— a)  and  Uffl^/2. 

If  a = O  & = r,  and  the  formula  is  reduced  to  that  before  giren. 

In  order  to  show  how  much  provision  is  necessary  for  a  field 
of  some  diameter,  I  will  take  the  case  of  a  telescope  of  30  feet 
focus  and  60  inches  aperture,  in  which 

tan  4>=  — , 

T      12* 

and 

*~4°'45'49". 

If  only  the  image  of  a  central  object  were  required,  we  might 
assume  c  =  36  inches,  and  we  should  have 

tti-604  in. ;  ^=8*55  in. 

If  a  field  of  i°  diameter  be  required,  c  might  be  taken  =  37 
inches,  and  we  should  have 

m»  1 170 in. ;  J=  16*55  in. 

If  the  field  were  20  in  diameter,  we  might  retain  37  inches 
for  c,  but  we  should  have 

■  m-  17*58  in. ;  /- 24*86  in. 


3*6 


Lieut. *Gen.  Tetmant}  Nates  on 


xlvii.  5, 


For  a  field  of  40  diameter  we  make  e  =  39  inches  and  thus 

should  have 

m  - 29*08  in.,  and  /*=  42*08  in. 

It  is  seen,  that  to  obtain  a  field  doable  the  size  of  the  San  or 
Moon,  it  is  necessary  to  nearly  doable  the  sise  of  the  small  mirror, 
and  to  stop  nearly  four  times  the  light  which  need  be  obstructed 
in  order  to  define  a  star,  and  in  all  cases  the  centre  of  the  fiat 
will  be  out  of  the  axis  of  the  tube. 

In  the  Cassegrain  form  of  telescope,  where  the  secondary 
speculum  is  placed  between  the  great  speculum  and  its  focus, 
and  an  image  is  formed  behind  the  great  speculum,  c  of  our 
formula  would  represent  the  distance  from  the  principal  focus  to 
the  face  of  the  secondary  mirror  measured  along  the  axis  of  the 
tube,  and  our  formulas  would  be 


tan  A-   , 
a 

and  '  • 

6  =  r  cot  (f — a)  as  before ; 

and  then 

•  *  »    » 

d  the  diameter  of  the  secondary  mirror =2(6— a  +  c)  tan  (<*>—«). 

« 

The  value  to  be  assigned  to  c  will  depend  upon  the  desired  size 
of  the  image  behind  the  speculum.  If  that  is  to  be  m  times 
larger  than  what  is  due  to  the  great  speculum  alone,  and  8  be 
the  distance  which  this  image  is  behind  the  face  of  the  speculum, 
then  we  should  have 

Applying  this  to  the  case  of  a  great  speculum  of  the  same 
dimensions  as  before,  we  shall  find  that  when  m=i  and  the 
image  is  12  inches  behind  the  reflecting  surface,  c=  186  inches; 
if  m  =  2,  then  c  =  1 24 ;  if  m  =  5,  then  c  =  62. 


for  mmt. 


for  m  —  2. 


I 


I 


The  image  of  a  point  requires 
a  field  of  i°  diameter 


»» 


i» 


n 


»» 


>» 


ft 


»t 


The  image  of  a  point  requires 
a  field  of  i°  diameter 


>t 


»> 


»» 


ff 


ft 


!• 


ft 


for  m  =»  5.     - 


The  image  of  a  point  requires 
a  field  of  i°  diameter 


it 


ff 


V* 


>t 


»» 


^=3100 
<f«  34*00 
d-3711 
d  ■  44-20. 
d— 20-67 
<?  3*2476 
<*=  28-95 
^  =  3721. 

<f  =10*00 

(£=15-27 

d=  19*22 
rf- 30*07. 


March  1887.  Reflecting  Telescopes.  247 

Clearly,  then,  the  size  of  the  mirror  obstructing  the  light  would 
be  very  large,  unless  the  focal-  image  of  the  great  speculum  were 
considerably  magnified,  and  the  field  very  restricted  ;  so  that  this 
form  of  telescope,  however  well  adapted  for  the  examination  of 
small  objects,  is  not  suitable  for  photography. 

The  Gregorian  form  of  telescope  requires  larger  secondary 
mirrors  than  the  Cassegrain  for  small  objects,  and  in  all  cases 
a  longer  tube,  which  is  a  serious  evil.  Probably  it  will  not  be 
selected  for  use  in  any  case,  unless  it  should  be  found  that  the 
concave  form  of  the  small  mirror  is  easier  to  produce  than  the 
convex  one  required  for  the  Cassegrain.  The  appropriate  formulae 
in  this  case  will  be 

b  -  r  cot  (^  +  a), 


m  —  I 
rf-(a  +  c— b)  tan  (*  +  «). 

On  the  whole  it  would  seem  that  for  photographic  purposes 
a  large  telescope  would  probably  be  best  designed  for  a  front 
view,  with  the  sensitive  surface  facing  the  speculum,  and  no 
second  reflection.  In  such  a  telescope  as  I  have  spoken  of  before, 
a  field  of  40  would  be  about  25  inches  in  diameter,  whereas  the 
small  mirror  even  for  a  Newtonian  would  have  29  inches  for  its 
minor  axis,  and  the  difference  (if  a  round  plate  were  used)  would 
be  ample  for  the  holder  and  exposing  arrangements.  If,  for  con- 
venience, a  plate  of  the  usual  form  were  used,  then  the  Newtonian 
form  of  telescope  would  have  a  slight  advantage  if  the  field  were 
very  large;  but  not  with  a  small  field.  Thus  a  field  of  i° 
diameter  would  be  6*5  inches  across,  and  the  diagonal  of  a 
square  plate  which  would  include  this  field  would  be  9*2  inches, 
which  is  less  than  11*7  inches  required  for  the  minor  axis  of  the 
small  mirror. 

When  the  flat  or  small  mirror  is  insufficiently  large  it  will 
produce  a  field  whose  brightness  diminishes  rapidly  in  passing 
away  from  the  proper  limit;  and,  moreover,  when  either  the 
small  speculum  or  the  mouth  of  the  tube  is  too  small,  the  portion 
of  the  great  speculum  used  to  produce  the  image  of  an  object 
near  the  margin  of  the  field  will  not  be  circular,  and  we  may 
expect  some  falling  off  in  definition. 

I  next  proceed  to  examine  the  image  formed  by  a  parabolic 
speculum.  Let  Fig.  II.  be  a  section  through  the  axis  AX  of 
the  parabola,  whose  revolution  round  it  generates  the  surface 
of  the  speculum,  PA  being  the  curve,  of  which  A  is  the  vertex 
and  S  the  focus.  Take  the  axis  of  the  parabola  for  the  axis  of  X, 
and  A  as  the  origin  of  rectangular  co-ordinates. 

Suppose  three  rays,  L^P^  LPl9  and  L2P,,  to  be  incident  on 
a  point  P,  whose  co-ordinates  are  x'  and  y'.  Then  the  reflected 
ray  corresponding  to  LP}  will  pass  through  S.  Let  PjQ  and 
Pi<?  be  the  directions  of  the  other  two  rays  respectively.  Call  a 
the  angle  between  P,L  and  each  of  the  other  incident  rays ;  then 


246  TAeui.-Oen.  Tennanf,  Notes  on  XLTTI.  5, 

it  will  also  be  the  angle  between  PS,  and  either  P|Q  orPjj.  Make 


Let  S;  be  the  Focub  for  rajs  incident  on  Pt  and  in  the  direction 
L,P1t  and  let  its  co-ordinates  hexuy,.      Write  v   for  y-,  then 

apeclivelj. 


*.'=  "1.    AW 

4 

Then 

write  k  and  h  for  '-,  ■    r* 

UnP.SA-    "    , 

and  the  angle 

therefore 

P,QA  =  P,sA-b; 

and  the  equation  to  I^S,  will  be 


»-•'-— r,* 


-,>-t) 


Now  differentiating  with  respect  to  v,  k  will  disappear,  and 
the  value  of  h  deduced  from  the  result  will  be  hu  the  value  of 


March  1887,  Reflecting  Tels$eop6$.  049 

ft  at  S,.     Performing  this  operation  and  changing  the  signs  we 
get 

A-2»4C~c^~41f  4.  (a*     r^(4  +  agp)(4-.yt-h4CP)4-(4g~20)(4c-cP*~4t;) 
4    *   4- >+4Mr  * V4^        '  (4-t»+4<»)« 


whence 


,  „fg .  32  +  48cg+i4>cpt  +  8cp,+  2(2c*— Qt?4-gt* 
4  '» "  2(i+c*)(4  +  v*/ 


and 

A» — 8(ir^r — • 

or 

*,.»  *  coe2«  {8  +  (i2-v*)t>  tana +Gv*  tan2  «} 

Evidently,  if  »j  be  the  co-ordinate  for  a  similar  ray  incident 
on  P2  opposite  Pi,  we  shall  hare 

jra-~cos*a{8-(i2— «*)i;tan  o+do*  tan' a} 

by  changing  the  sign  of  v. 

Substituting  the  value  of  fc,  in  the  value  found  for  4%  we 
shall  get  &i,  the  value  of  k  at  Slf 

*.=  — c—  {8+i2cw-6ff8-c»»}f 
1     8(14-0 

or 

y,  =     sin  a  cos  a  {8  +  (12  —  v~)  v  tan  a  —  6t>*} 
o 

and  we  shall  have 


also 


and 


y,  *  *  sin  a  cos  a  {8  -(12  +  v*)  v  tan  o—  60*} 
o 


or,— or,«  —  cos  a  810  a  (12— v1), 
4 


y\-yt~—  "n* « (12- »2)- 
4 


When  an  oblique  ray  is  incident  at  the  centre  of  the  specu- 
lum, we  shall  have 

and 

x,axf«eco8%,    y,  =ys  =  acoflosin  a. 

Hence  the  locus  of  the  foci  of  such  rays  will  be  a  spherical 
surface  touching   the  paraboloid  at  its  vertex,  and    pasting 


250  Lieut.-Q*n.  Tewnant,  Notes  on  ,\      xbyu.  5, 

through  the  focus;    its  radius  will  be  -,*  and  there  will  be  no 

aberration. 

In  the  case  of  a  telescope  of  the  dimensions  I  have  spoken  of 
we  shall  have 


Field  40  diameter  ■) 

I  y  + 


Field  20  diameter 


t  y- 


f=+A 

r=o 

*«=-* 

In. 

in. 

In. 

361-1325 

3595615 

357*9953 

"•54S5 

125562 

12-4360 

3603735 

3599981 

3595885 

31449 

3'"4"4 

3-1380 

The  above  applies  to  rays  oblique  to  the  axis  of  the  telescope, 
and  incident  on  small  surfaces  at  any  part  of  the  speculum  in  the 
plane  containing  the  axis  and  the  incident  ray.  I  now-  proceed 
to  consider  the  case  of  a  ray  falling  at  a  point  out  of  this  plane, 
and  at  a  distance  r  from  the  axis.  Calling  the  plane  I  have 
used  the  principal  plane,  let  the  line  r  make  an  angle  with  it  =  <f>. 

Let  0,  y,  *  be  co-ordinates  whose  origin  is  the  vertex,  and 
whose  directions  are :  of  x  in  the  axis,  of  y  perpendicular  to  it 
in  the  principal  plane,  and  of  z  perpendicular  both  to  the  axis 
and  principal  plane ;  and  let  x0,  y0f  *0  be  the  corresponding  co- 
ordinates when  the  plane  containing  r  and  the  axis  is  substituted 
for  the  principal  plane.  In  this  case  the  projection  (on  the 
plane  XY0)  of  the  ray  incident  at  the  vertex  will  be  inclined  to 
the  axis  of  X  at  an  angle  whose  tangent  is  e  =  tan  a  cos  <f>. 

Hence  (making  t;= -j  the  equations  of  the  reflected  ray 
will  be ;  in  the  plane  X0 


4  + 4*0-1;*  \        4/ 


or 


bc(4- t^)— 40       16  ■*•  I2cv  +  C0*    av 
4— v*  +  4cv  4— tP  +  ^cv    *  4 

and  in  the  plane  XZ0 

z%  -  f — — x  jtan  a  sin  p. 

*  I  am  indebted  to  the  Astronomer  Royal  for  a  very  elegant  geometrical 
demonstration  of  this  property. 

Through  A  draw  A<r  parallel  to  AL,,  and  cutting  P.Q  in  <r.  Then  A<r 
will  be  the  reflected  direction  of  the  ray  incident  at  A  and  parallel  to  L,  P„ 
and  the  two  angles  SP,<r  and  SA<r  will,  each  »«.  Hence  a  circle  can  be 
described  through  A,  P.,  <r,  and  S.  If  P  move  towards  A,  <r  will  gradually  more 
towards  S„  and  when  P  is  at  A  will  coincide  with  it,  and  in  this  limiting 
position  the  circle  will  touch  the  vertex  of  the  parabola  at  A,  and  pass 
through  S,  and  S. 


March  1887.  Effecting  Telescopes.  251 

Also  since 

y  -y§  cos^ — 19  sin  9 
and 

z— y9  sin  <f>  +  ?0  cos  ^ 

we  have 

=  (*-^tan«+i;co8*{«+(W-4^ LLton2aC0-8^-__  I 

\        4  /  l        \  /  4  —  v*  +  40  tan  a  cob  f 


and 


s  =  ar  | ^*     p  ^  -^-sin^  —  tan a  sin <*>co8<£ \ 
{  4— t;*  +  4ct;  ' 

av  ( 16+  ncv  +  ev*  .    ^       .  •    ^        .  » 

+  ^Zi_       .-."..   sin*  +  i>tanasin*cosAV 

4  1    4-u*+3cy  > 

„  .    .     (2+  u  tan  o  cos  6)z       M     .     .        t>(i +tan2acos2<>) 
=  at?  sm$.  -- ^ —  4r8TD^.  - — V r? 

4  —  v2  +  40  tan  a  cos  £  4  —  er  +  411  tan  a  cos  <£ 

■ 

.     .  .     . ,     ,         %       I  +  tan2  o  cos2  <p 

.    .  =*  av  sin  <p  +  vsinwa©2— 4r)    -  •   — ,  — -   -    ; 

4—  v2  +  41;  tan  a  cos  ^ 

and  if  we  make 

x»  r .         ,.a\       *  +  tan2«  COB2* 

4—  v*  +  4#  tan  a  cos  <^> 

we  shall  have 

y— {:?— —  itana  +  Rcos^ 
*  =  Rsin  <p. 

,  If  v  =  o  we  have  y  as  »  tan  a,  3  =  0.  This  is  the  case  of  inci- 
dence at  the  vertex,  and  the  reflected  ray  passes  as  it  should 
through  the  focus  in  this  case  as  before  found. 

If  sin  ^  =  o  then  z  will  always  be  o.  In  this  case,  of  course, 
the  incident  and  reflected  rays  lie  in  the  principal  plane. 

We  see  that — 

1st.  If  we  write  —  <f>  for  <p,  z  will  only  change  in  sign,  not  in 
magnitude,  while  y  will  be  unchanged.  Therefore  for  any 
value  of  y  there  will  be  two  equal  values  of  2,  with  opposite 
signs,  and  the  trace  of  the  principal  plane  will  divide  the  curve 
into  two  similar  parts.  1/ v.1        ' 

2nd.  If  sin  0  =  0,  then  z  =*  o ;  but  from  value  of..  R? ,  we  see 
that  r  and  R  will  =  o  if  / 

_a    (2  +  vtanacos^)2 
4  "     1  +tan*oco8-^ 


252  LieuL-Qen.  Tennant,  Notes  an  xlvii.  5, 

and  we  find  that  this  will  also  be  the  case  if 

cos  * = ****  ^«(4g-4*+^) 

(4*— ao*)  tan  a 

This  value  of  coe  f  becomes  impossible  if 

<■♦*)■ 


x>a\ 


When  x  exceeds  this  value,  R  cannot  be  =  o,  but  z  will  =  o 
when  sin  <£  =  o.  Otherwise  cos  <f>  may  have  two  different  values 
for  which  R  and  z  vanish :  these  correspond  to  a  point  which  is 
either  double  or  quadruple. 

It  is  needless  to  spend  labour  on  seeking  the  place  where  the 
rays  are  most  concentrated.  The  question  of  focus  of  the  whole 
speculum  in  such  a  case  seems  to  me  likely  to  be  affected  a  good 
deal  by  the  causes  which  would  make  the  image  of  a  point  of 
light,  even  in  the  case  of  a  perfect  reunion  of  the  rays,  to  be  a 
disc  surrounded  by  rings. 

I  purpose  adding  some  numerical  results.  As  a  circle,  whose 
diameter  is  1  -s-  4/2  of  that  of  the  speculum,  will  separate  its 
surface  into  two  zones,  receiving  equal  amounts  of  light,  I  will 
only  consider  that  ring  as  a  mean  case,  and  I  shall  assume 
x  =  a  cos'a.  In  other  respects  I  have  used  the  dimensions  I  have 
taken  before  for  the  data  of  the  telescope  and  calculated  co- 
ordinates. 

I  shall  assume  a  to  be  equal  to  20,  or  the  field  to  be  40  in 

diameter,  and  from  the  values  of  y  I  shall  omit  Ix—™  j  tan  a  ; 

the  whole  of  the  co-ordinates  will  be  expressed  in  thousandths  of 
an  inch. 

When  R=o,  besides  the  two  universal  values  of  cos^  ±  1,  we 
shall  only  have  one  value  of  cos  ^  possible,  namely,  that  corre- 
sponding to  ^=117°  42*  49"* 73.  And  I  may  remark  that 
only  one  such  value  of  cos  <f>  will  be  possible  when  we  are 
dealing  with  practical  oases ;  because  near,  and  at  the  focus,  x 
will  not  differ  much  from  a ;  therefore  the  quantity  under  the 
radical  sign  in  the  numerator  will  not  vary  much  from  <mr,  and 
the  two  values  of  thenumeratorwiflbe,  one  very  small,  and  the  other 
not  very  far  from  2  av ;  the  denominator,  on  the  other  hand,  will 

approach  4a  tana  (—  being  small  compared  with  1  ),  but  tan  a 

will,  for  the  outer  part  of  the  speculum,  which  alone  is  avail- 
able, be  much  smaller  than  v  -,  and,  of  the  two  values  of  f,  one 
will  be  small  as  possible,  the  other  greater  than  1. 


keflecliwj  Telescopes. 


-(-"> 


.-(-•;> 


+  43*a 

000 

9° 

-  000 

+  2585 

+  4299 

+   7-5* 

100 

-  304 

+  "7-45 

+  4135 

+  15-04 

■  to 

-  270 

+  7-42 

+  383' 

+  2178 

110 

+   ■-« 

-   113 

+  3378 

+  2886 

13° 

+  83- 

-   9-9° 

+  2776 

+33'°9 

140 

+  17-47 

-1466 

+  20-60 

+  35-68 

150 

+  37-20 

-'571 

+  12  91 

+  35-48 

160 

+  3579 

-13-29 

+   5'67 

+  33'29 

170 

+  41-74 

-   7-3 1 

+   000 

+  2585 

180 

+  4375 

-  000 

The  co-ordinates  for  tho  values  of  <p  from  180°  to  360°  will  be 
those  for  st  —  f  with  the  sign  of  a  changed. 

Of  the  portion  of  the   value  of  y   which  I  hare   omitted, 


x  tana  ia  the  value  ofy  for  centrally  incident  rays,   and  the 

remainder —  tana,  equal  to  10-96  thousandths  of  an  inch,  is 

the  amount  by  which  the  focus  of  centrally  incident  rajs  is 
farther  from  the  axis  than  the  point  from  which  the  values  in  the 
table  are  reckoned :    its  cause   will  be  evident  if  we  observe 


254  Lient.-Gen.  Tmnant,  Notes  on  XLVir.  5, 


av* 


that  —  is  the  portion  of  the  axis  of  the  parabola  intercepted 

4 
between  the  vertex,  and  the  plane  by  whose  intersection  with 

the   parabolic  surface  the  reflecting  ring  is   defined.    I  have 

plotted  the  curve  in  Fig.  III.  mnch  enlarged,  and  shown  on 

it  the  position  of  the  focus  of  a  centrally  incident  ray.     The 

width  perpendicular  to  the  trace  of  the  principal  plane  is  39*5 

seconds  of  span. 

When  sp  S3  a  we  shall  have  the  case  of  the  plane  of  the  image 

being  defined  by  its  passing  through  the  principal  focus  and 

being  perpendicular  to  the  axis.     In  this  case 


/ 


R  =  a  v  ■ 


\       4  / 1  —     r  +  v 


I  +  tan2acos2^ 


tan  a  cos  <p 


-  —  tan  a  cos  <p 

4 

=  a  v  tan  a  cos  A 

n 
1+  tan  a  cos  d> 

i-t 


If  we  assume 


V 

tan  A  = ;, 

I  — 


4 
tan  B  s  tan  a  cos  <P, 


and 

we  shall  have 

y  =  ai  1  —  -j tan  o  +  aycos  4>  tan  B  tan  (A— B) 

z—  nusijup  tan  B  tan  (A  — B) 

Moving  the  origin  to  the  point* 

tana,  o 


■(-3 


and  using  R  and  <f>  as  the  polar  co-ordinates  of  the  curve,  we  shall 

have 

R  =  ai«tanBtan(A-B) 

where  A  and  B  have  the  values  above  given,  in  which  A  depends 
only  on  v  and  B  on  a  and  <f>. 

In  this  case  the  values  of  cos<j>  for  z  =  o  will  be 

:  l  -J  v 

+  I,  —  1,  o,  mid 


.lTl    T:;  . Itana 


(-3' 


*'  If'tthe,1phiri«:'5of  the  reflecting  ring  were  itself  a  Reflecting  plane,  then 
the  toy  imddtnt 'id Jits'  intersection  with!  the  axis  would  pass  through  this 

point*  •'.     ..*    u   ' n 0 V.  ~     '■■ 


Monthlv  Notices  of  Roval  Astronomical   Society. 


Vol  Tim.  Plate  2. 


Length  of  Curve  i,  solid  line,    5".oo;  dotted  line,  2". 69;  whole,    8".  10 

2,  „  1 5".  86;             „  2".  28;       „      16".  54 

3,  „  29". 62;            „  5".  25;       „      29".  62 

4,  „  47".  28;             »  14"  73;       »      47".  28 

5,  „  68".86;            „  28".o8;       „      68".86 


i» 


»» 


t« 


»» 
*» 
it 


it 


»» 


-T-'J   Z>T..JCrX 


Monthly  Notices  of  Roval  Astronomical  Society. 


VolITW.  Plate  1 


'r&Cbth  london 


March  1887.  Reflecting  Telescopes,  255 

for  both  the  last  values  y  is  reduced  to  the  term 

tana  and  R«o, 


hence  the  corresponding  points  will  be  quadruple  if 

be  <  1,  and  doublo  it  if  it  be  >  1 . 

This  position  would  be  that  of  most  interest  for  photography, 
I  have  therefore  computed  the  values  of  B  for  five  equidistant 
rings  of  the  speculum  I  have  so  often  spoken  of,  and  plotted 
them  on  a  large  scale  in  the  annexed  Plate  2*  in  which  the 
dotted  portion  of  each  curve  is  due  to  the  portion  of  the  ring 
where  cos^  is  positive,  and  the  continuous  portion  to  the  re- 
mainder :  a  is  assumed  as  20. 

The  place  of  the  ray  reflected  at  the  vertex  of  the  speculum 
is  marked.  It  will  be  seen  that  as  the  ring  increases  in  size  the 
multiple  point  recedes  towards  the  axis  of  the  speculum  ;  at  first, 
while  v  is  small,  the  curve  is  four-looped  with  two  small  loops ; 
as  v  increases  the  loop  towards  the  axis  becomes  smaller,  while 
the  others,  and  particularly  the  two  side  loops,  increase  in  size. 
When 

V 

tana  = * 

1-? 

4 

the  loop  towards  the  axis  vanishes,  the  multiple  point  is  mo- 
mentarily triple,  and  two  of  the  branches  form  a  cusp,  the  trace 
of  the  principal  plane  being  a  tangent  to  both  branches.  As  v 
continues  to  increase,  this  cusp  becomes  a  salient  point,  recedes 
from  the  axis,  and  gradually  becomes  effaced,  the  loops  swell, 
and  the  curve  gradually  becomes  one  with  only  two  rounded 
loops,  with  a  common  point  in  the  axis. 

We  can  form  some  idea  now  of  the  general  distribution  of 
the  illumination,  by  picturing  to  ourselves  a  greatly  increased 
number  of  these  images  from  rings — the  total  image  will  be  that 
of  course  arising  from  considering  v  to  vary  continuously  from 
o  to  its  maximum  value.  It  would  seem,  that  just  behind  the 
place  of  the  ray  reflected  from  the  vertex,  there  will  be  a  maxi- 
mum of  illumination  in  a  bright  ray  extending  from  the  place  of 
the  central  ray  towards  the  axis ;  from  this  the  light  will  decrease. 
The  lines  of  equal  brightness  will  have  a  tendency  to  an  oval 
form,  and  beyond  this  the  light  will  spread  out  in  the  well- 
known  fan  shape. 

If  we  consider  what  would  be  the  result  of  photographing  an 
object  of  this  sort,  I  think  it  will  be  seen  to  be  as  follows.  With 
comparatively  short  exposures  the  image  will  be  elongated  in 

*  Plate  I  shows  the  innermost  curve  on  a  larger  scale. 

u 


256  Lieut.-Qen.  Tennant,  Notes  on  xlyii.  5, 

the  direction  of  the  trace  of  the  principal  place ;  as  the  exposure 
is  increased  the  image  will  become  more  round,  and  probably 
only  a  very  long  exposure  indeed  would  exhibit  the  outer  parte 
of.  the  fan.  After  the  exposure  has  been  long  enough  to  efface 
the  nucleus  by  rendering  lees  illuminated  portions  of  the  image 
opaque,  the  centre  of  the  imago  will  seem  to  move  outwards 
from  the  axis  with  increasing  exposure.  No  donbt  such  an  effect 
would  be  very  small,  but  it  seems  to  me  it  will  exist. 

On  the  whole,  I  am  disposed  to  think  that  the  parabolic 
speculum  will  have  great  advantages  for  a  small  field  in  photo- 
graphing planets,  nebulas,  Ac,  but  that  if  a  large  area  be  required, 
there  will  be  rapidly  increasing  astigmatism,*  soon  becoming 
unbearable.  For  eye  views,  when  the  field  is  small,  whether 
used  in  the  Newtonian,  the  Herschelian,  or  even  the  Brachy 
form,  it  will  work  satisfactorily,  especially  if  the  focal  length  be 
long  in  proportion  to  the  aperture.  Whether  opticians  may  be 
able  to  produce  a  surface  in  which  by  sacrificing  some  of  the 
perfection  of  the  central  image  a  bearable  average  result  can  be 
obtained  over  a  large  field,  I  cannot  say,  but  I  donbt  it.  It  is 
true  that  the  image  for  photography  does  not  need  to  be  so 
perfect  as  for  vision  of  a  small  object  under  a  high  power,  bnt 
1  he  image  of  a  star  should  be  round,  and  its  position  should  not 
vary  with  the  aperture.  The  devices  by  which  opticians  have 
sought  to  gain  large  fields  in  achromatic  lenses  for  photography 
do  not  seem  applicable  in  any  way  to  specula,  and  I  do  not  see 
any  others. 

Lastly.  To  find  the  focus  of  a  ring  of  a  parabolic  mirror, 
when  the  centre  of  curvature  at  the  vertex  is  the  origin  of 
light,  and  also,  under  the  same  circumstances,  to  find  the  focus 
of  a  small  patch  of  the  speculum. 


In  Fig.  IV.  let  P  be  a  point  in  the  ring  and  A  the  vertex  of 
tho  parabola,  by  whose  revolution  round  its  axis  AX  the  speeu- 

*  It  mum  be  remembered  that  in  order  to  photograph  we  mat  block  oat 
the  centre  of  the  field  which  gives  a,  nnclenn  to  the  imago.  When  the  field 
in  lurge  we  ton;  from  thi»  ceoee  even  have  a  dark-centred  image. 


March  1887.  Reflecting  Telescopes.  257 

lum  is  defined.  Let  S  be  tbe  focus  of  the  parabola,  G  the  centre 
of  curvature  at  the  vertex,  then  AG  =  2  a.  Also  draw  PM  per- 
pendicular to  the  axis  AX,  and  PN  the  normal  at  P,  then 
MN  =  2a.  And  if  PF/  be  the  reflected  raj  (PC  being  incident) 
we  shall  have  the  angle  GPN  =  angle  NPF.  I  shall  assume  A 
as  the  origin  of  rectangular  co-ordinates,  and  AX  as  the  axis 
ofX.     PM  =  y',  AM  =  a/. 


*., 


a 

as  before,  and  consequently 


av* 


The  angle 
and 

also 
Hence 


4 
CPN  =  PCM-PNM 


ten  PCM ^->-c4% 

za-x'    8-v* 


tanPNM-^'--. 

2a    2 


4V    _v 

tanCPN-  — -^-tf+a,.. 
J8-v* 


Whence 


tan  AFP  -  (MNP  -  C£N) - 


v  v* 

2     16  +  21;'  iSv 

1+       v*      mi2  +  4v*  +  vv 
32  +  40* 


The  equation  to  PF/  will  therefore  be 


y  —  av=  - 


16*         /^'X 
+  4u2  +  v4\4        / 


or 


32»+8vt+tf»  160 

y  =  a.± -.  — x. —  . 

*         32+4«;8+t;4         32  +  4«si'* 

When 

32  +  1 8w* + 1;4    „„  ,  at'*  .av* 
9  16  2       16 

which  value  corresponds  to  F,  and  this  will  manifestly  be  the 
place  of  the  bright  image  from  the  ring  whose  diameter  is  av  or 
MP.     Also 


-t(«+?) 


OF 

2  \       »/ 

V  2 


258  Lieut. ~Q en.  Tennant,  Notes  on  xlvii.  5, 

Reverting  to  the  equation 

a   32v  +  &v*+vi_x         i6u 
"  32  +  41/*+  vA        '32  +  4ua  +  v4 

and  differentiating  with  effect  to  v  we  have 

d if  _     1 024  +  640V* + 96t»4  +  4**  +  tr8 _  ,     32— 4t>a— 3P4 
c/v"0'  "  (32  + 4"*  +  i'r)'J_  '  (32  +  4»2  +  vAY 

and  since  when 

v  =  0,    x-  A/(/  being  the  focus  of  the  ray) 
dr 

we  have 

.        a  ,  a  (       «  .  ^  «  ,  7  ..  .  *.    t  I024  +  640l'2  +  96?'l  +  4^'•  +  »• 

A»  =      =  2a  +   ,    24i;2  +  9u4  +  ii^  +  &c.  \    — *  —  -~ f --I 

16  16 (.  2  j  32— 4^  — 31/4 

and 

C»  =  aj?v*+-%t>4  +  -Z-vi  +  &c.} 

l2  ID  32  j 

Also  Babstitnting  the  value  of  Ap  for  x  in  the  equation  for 

y  we  have 

/.  .  512+ I92y2+32i>4  +  4t*i  .  ( 1      3    ,,    9    «  .,     \ 

pf=-av*.D g-         3         *»    M-flg»i~+-g-t;»+   ~_t;4  +  &c.[ 

i024-8o«4+i6y-— 3«  (2     16         128  * 

the  values  of  Ap  and  |?/  being  true  to  v7,  which  is  more  than 
enough. 

These  values  of  C/,  Ap  and  pf  will  serve  in  verifying  the  form 
of  a  speculum  during  the  polishing  process. 

Data  for  Light  Curves. 

a  -  360*000  inch ;  a-2°:oof. 

The  unite  for  the  values  of  R  is  o*ooi  inch. 

No.  I.— »  =  ^j. 


4> 

R 

* 

R 

+ 

R 

+ 

R 

a-  tana 

4 

0 
0 

— 

3*82 

0 

50 

— 

078 

0 
100 

-  083 

0 
150 

— 

8*52 

10 

— 

3"66 

60 

— 

Oil 

no 

—  206 

160 

— 

985 

20 

— 

325 

70 

+ 

034 

120 

-  35o 

170 

— 

1054 

087 

30 

— 

246 

80 

+ 

039 

130 

-  5"27 

180 

— 

IO'82 

40 

I  62 

90 

o*oo 

140 
No.  2.- 

-  704 

* 

R 

4> 

R 

4> 

R 

* 

R 

a— tana 

4 

0 
O 

— 

I  24 

0 
5o 

+ 

293 

0 
100 

-   287 

0 
150 

— 

23*10 

^ 

IO 

— 

0"43 

60 

+ 

333 

no 

-  649 

160 

— 

2608 

20 

.4. 

• 

02I 

70 

+ 

307 

120 

- 10*65 

170 

— 

2798 

349 

30 

+ 

ri2 

80 

+ 

198 

130 

-1508 

180 

- 

2804 

4° 

+ 

2*11 

90 

000 

140 

-19*31 

March  1887. 

Reflecting  Telescopes. 

25S 

* 

R 

+ 

R 

No.  3.- 
* 

R 

* 

R 

a     tana 

4 

0 
0 

+    949 

0 
50 

+  11-13 

0 
100 

-   613 

0 
150 

-  4377 

10 

+    967 

60 

+ 10-23 

no 

"  13  33 

160 

—  49-02 

20 

+  ICVI6 

7o 

+  815 

120 

—  21-23 

170 

-  5236 

7'86 

30 

+  IO76 

80 

+  546 

130 

-2932 

180 

-  5350 

40 

+  IT20 

90 

+    O'OO 

140 

-3703 

+ 

• 

R 

4> 

R 

No.  4.- 

-tr-A. 
R 

* 

R 

a-  tan  a 

0 
0 

+  26*60 

0 
5o 

+  2383 

0 
100 

-IO56 

0 
150 

-    70*53 

4 

10 

+  2664 

60 

+  20*63 

no 

-22*57 

160 

-    78-58 

20 

+  26  66 

70 

+  1570 

120 

-3533 

170 

-    8366 

1245 

30 

+  2644 

80 

+   8  83 

130 

-48-12 

180 

-    8540 

40 

+  2563 

90 

O'OO 

140 

-6013 

+ 

R 

* 

R 

No.  5.- 
* 

R 

4> 

R 

a-  taua 

4 

0 
0 

+  5072 

0 
SO 

+  4I-02 

0 
100 

-  l6'28 

0 
150 

-  IO344 

10 

+  50  5° 

60 

+  34*53 

no 

-  34*22 

160 

—  114*80 

20 

+  4976 

70 

+  25*60 

120 

-5295 

170 

-121-93 

I946 

30 

+  4844 

80 

+  1408 

130 

-7146 

180 

—  124-40 

40 

+  45*42 

90 

o-oo 

140 

-8866 

P.S. — I  have  said  that  the  devices  for  gaining  a  large  field 
in  achromatic  combinations  for  photography  are  not  available 
with  the  reflector.  Of  course  there  is  no  possibility  of  combining 
curves,  and  the  other  means  is  the  use  of  a  diaphragm  to  exclude 
from  acting  those  parts  of  the  surface  which  cause  most  diffusion. 
The  position  of  this  diaphragm  should  be  so  chosen  that  it  flattens 
the  field — that  is,  that  the  centre  of  the  acting  surface  for  oblique 
rays  will  have  its  focus  in  the  plane  perpendicular  to  the  axis 
and  passing  through  the  principal  focus. 

Suppose  we  desire  that  this  shall  be  the  case  for  rays  inclined 
to  the  axis.  If  we  make  xx  in  the  formula  giving  the  distance  of 
this  focus  from  the  vertex  =  a,  we  shall  have — 

t^  +  6v%  tan  o  —  1 2v  —  8  tan  a  —  o. 

When  a  is  small  one  root  is  very  nearly  §  tan  a,  and  can  readily 
be  determined;  the  other  roots  are  large,  one  being  positive, 
and  the  other  negative.  Practically  v  =  §  tan  a  will  be  a  suf- 
ficient approximation  to  the  useful  root.     The  place  of  the  dia- 

phragm  will  be  at;  cot  a+a —  (sensibly  §a)  from  the  vertex,  and 

4 
this  being  nearly  independent  of  a,  it  follows  that  the  position 
flattens  the  focus  for  all  obliquities.   If  D  be  the  diameter  of  the 


260  Gapt.  Abney,  on  the  Atmospheric  xlvii.  5, 

speculum,  then  that  of  the  largest  opening  of  the  diaphragm  will  be 

D  —  2av  =  D  —  —  tan  a  for  the  limiting  value  of  a. 

3 
If  now  we  assume  a  =  20  we  shall  find  the  diameter  of  the 

diaphragm  about  43  J  inches.     The  image  for  the  field  will  be 

25*14  inches  in  diameter,  and  probably  the  carriers  will  require 

to  have  a  space  of  27  inches  in  diameter  allowed  for  them.    This 

would  leave  only  28  percent,  of  the  surface  available  to  form  the 

image  of  any  object ;  excluding  all  the  central  part. 


On  the  Atmospheric  Transmission  of  Visual  and  Photographically 
Active  Light.    By  Captain  Abney,  R.E.,  F.R.S. 

In  his  publication, '  Researches  on  Solar  Heat,'  which  appears 
in  the  Professional  Papers  of  the  Signal  Service,  Professor  S.  P. 
Langleyha3  been  somewhat  hard  on  those  astronomers  who  have 
made  a  speciality  of  observing  star-magnitudes.  In  the  report 
on  the  transmissibility  of  our  atmosphere  for  light,  in  which  is 
embodied  the  observations  made  by  his  party  at  Mount  Whitney, 
and  which  appears  in  the  above-named  volume,  he  makes  the  fol- 
lowing remarks:  '  For  it  may  be  observed  in  general  terms  that 
since  the  rays  with  large  coefficients  are  represented  by  diminish- 
ing geometric  progression,  whose  common  ratio  is  near  unity, 
these  rays  will  persist  whilst  others  with  small  coefficients  are 
very  nearly  extinguished ;  and  something  like  this  was  shown 
by  Biot  at  the  time  when  Melioni's  first  observations  on  the 
transmission  of  heat  through  successive  strata  attracted  atten- 
tion. But  what  we  desire  now  further  to  point  out  is,  that  ac- 
cording as  the  difference  of  these  coefficients  of  transmission  for 
the  different  portions  of  the  light  of  the  same  star  is  greater,  so 
will  the  error  of  the  result  in  treating  them  as  equal  be  larger — 
a  consequence  so  obvious  that  it  is  only  necessary  to  make  the 
statement  in  order  to  have  its  truth  recognised. 

• Since  it  has  now  been  demonstrated  that  the  formula  ordi- 
narily employed  leads  to  too  small  results,  it  might  properly  be 
left  to  those  who  still  employ  it  to  show  that  their  error  is  negli- 
gible ;  but  this  has  never  been  done.  There  is  possibly  an  im- 
pression that  if  there  were  any  considerable  error  its  results 
would  become  apparent  in  such  numerous  observations  as  have 
been  made  all  over  the  world  in  stellar  photometry  during  this 
century.  But  it  is,  in  my  opinion,  a  fallacy  to  think  so ;  and  I 
believe,  as  I  have  elsewhere  tried  to  show,  that  the  error  might 
be  enormous ;  that  the  actual  absorption  might  be  twice  what  it 
is  customarily  taken,  or  40  per  cent,  instead  of  20  per  cent, 
without  the  error  being  detected  by  such  observations  as  are  now 
made.1 

In  a  paper  which  I  have  recently  communicated  to  the  Royal 
Society,  on  the  transmission  of  sunlight  through  our  atmosphere,  I 


March  1887.  Transmission  of  .  .  .  Light  261 

have  described  in  detail  observations  which  I  have  carried  out 
during  the  past  year  on  this  subject,  using  the  visible  solar 
spectrum  for  the  particular  object  I  had  in  view.  My  wish  was 
to  ascertain  the  loss  of  luminosity  of  each  visible  ray  after  trans- 
mission through  varying  atmospheric  thicknesses.  The  definite 
conclusion  which  I  came  to  was  that,  as  a  rule,  the  loss  of  light 
followed  Lord  flayleigh's  law  for  scattering  by  small  particles — 

I'«If-*rA-4, 

where  I'  and  I  are  the  transmitted  and  original  intensities,  x  the 
thickness  of  air,  and  A.  the  wave-length.  These  observations 
which  I  made  it  is  needless  to  describe  again  in  this  note ;  suffice 
it  to  say  they  were  made  by  means  of  the  colour  photometer 
described  by  General  Festing  and  myself  last  year  in  the  Bakerian 
lecture.  My  standard  luminosity  curve  was  one  taken  at  8,500 
feet  altitude  in  the  Alps,  and,  as  I  have  already  said,  nearly  every 
curve- of  luminosity  through  other  air  thicknesses  obeyed  the  above 
law.  Now,  having  got  this  result,  it  was  easy  to  construct 
curves  of  luminosity  of  the  spectrum  for  1,  2,  3,  .  .  .  <fcc.  air 
thickness  in  which  the  ordinates  were  the  relative  intensities  of 
the  rays  transmitted.  The  areas  of  such  curves  when  con- 
structed could  very  easily  be  found,  and  such  areas  would  re- 
present the  total  luminosity  of  white  light  coming  from  the  Sun 
though  with  varying  thicknesses.  It  would  then  be  easy  to  see 
what  variation  from  the  law  usually  employed  in  stellar  observa- 
tions would  occur,  and  which,  according  to  Langley,  would  be 
serious.     The  law  in  question  is  that — 

r-ia-**, 

I'  and  I  being  the  transmitted  and  original  intensities  and  a  the 
coefficient  of  transmission,  0  being  the  zenith  distance,  the  secant 
of  which,  within  certain  limits,  is  a  measure  of  the  air  thickness. 
I  found  that  the  minimum  value  of  &  in  Lord  Rayleigh's  formula 
was  '0013,  when  the  value  of  X-4  for  X=6ooo  was  taken  as  78*3. 
In  this  case  the  areas  of  the  curves  representing  o,  1,  2,  3,  4, 
and  5  atmospheres  were  represented  as  761,  662,  577,  504,  439, 
and  385  respectively.  It  may  be  supposed  that  an  observer  when 
observing  sunlight  integrally  would  have  obtained  the  same 
values,  and  then  attempted  to  adapt  the  formula  just  given  to  it. 
Probably  he  would  have  used  '  least  squares,9  and  arrived  at  a 
result,  but  it  would  hardly  have  been  necessary  to  do  so.  I  had 
first  omitted  to  calculate  the  area  of  the  curve  of  the  spectrum 
through  5  atmospheres,  and  I  simply  took  o  and  4  atmospheres 
as  lying  on  the  curve  by  the  formula— 

where  /i  is  the  coefficient  of  absorption,  and  in  which  c";"=a  in 
the  above  formula.     From  this  I  found  that  /x=i378,  and  this 


262  Capt.  Abney,  on  the  Atmospheric  xlvii.  5, 

gave  for  j,  2,  and  3  atmospheres  664,  578,  and  504,  the  results 
from  the  spectrum  being  662,  577,  and  504.  Calculating  next 
the  absorption  through  5  atmospheres,  I  found  it  to  be  383  instead 
of  385 .  The  coefficient  of  transmission  in  the  usual  formula  from 
the  above  is  a=862,  a  somewhat  high  value ;  but  it  must  be 
recollected  it  was  mj  maximum  value.  Taking  a  larger  value 
of  k,  via.  £=0019,  the  areas  for  o,  1,2,  3,  and  4  atmospheres  were 
9T7»  755*  623,  513,  418.  Taking  the  first  and  last  as  lying  on 
the  logarithmic  curve,  the  values  obtained  were  917,  755,  626, 
508,  418,  a  very  close  approximation,  p  being  '  19708,  and  the 
coefficient  of  transmission  being  '822.  I  may  mention  that  with 
any  value  for  k  that  I  tried  the  same  result  held  good.  It 
thus  appears  that  the  logarithmic  formula  is  more  than  a  close 
approximation  to  the  truth  with  the  values  arrived  at  from  my 
observations. 

Professor  Langley's  values  and  my  own  for  the  transmissi- 
bility  of  the  different  visible  rays  differ  somewhat,  so  it  occurred 
to  me  that  it  would  be  right  to  take  his  own  values  for  trans- 
missibility,  and  treat  them  in  the  same  manner.  Taking  my 
Riffel  observations  of  the  luminosity  of  the  spectrum  as  correct, 
I  calculated  from  them  the  value  of  the  areas  of  the  curves  of 
luminosity,  using  Langley's  own  coefficients  of  absorption. 
They  were  as  follows,  1,  2,  3,  4,  and  5  atmospheres,  657,  392, 
235,  142,  and  52.  Taking  1  and  4  atmospheres  as  being  on  the 
logarithmic  curve,  the  values  derived  from  the  formula  were 
657,  394,  237,  142,  and  51,  fx  being  '5106  and  a  being  '602;  a 
value  which  is  extremely  low. 

This  shows  that  still  the  agreement  is  complete  between 
them.  It  must  be  borne  in  mind  that  in  observations  such  as 
these,  which  are  for  settling  stellar  magnitudes,  there  is  no 
desire  to  know  the  intensity  of  light  outside  our  atmosphere. 
All  that  concerns  the  astronomer  is  to  compare  light  coming 
from  a  star  at  the  zenith  with  that  coming  from  it  at  a  reasonable 
zenith  distance ;  5  atmospheres  is  represented  by  a  Z.D.  of  about 
7 8°  30'*,  and  it  is  unlikely  that  anyone  would  set  much  value  on 
observations  made  at  a  greater  Z.D.  than  that.  Hence  for  the  com- 
parison of  star  magnitudes  the  usual  formula  may  safely  be 
adopted.  A  much  more  serious  matter  is  the  absorption  coefficient 
used,  and  we  find  that  it  varies  between  791  and  '843,  according 
to  previous  observations,  whilst  I  have  found  my  maximum  at 
sea  level  to  be  '869,  though  my  mean  is  not  far  from  the  '825, 
which  value  has  been  adopted  by  some  astronomers. 

The  Z.  distances  of  two  observed  stars  may  vary  very  greatly. 
This  discrepancy  of  course  would  alter  the  calculated  magnitudes 
very  considerably,  but  if  the  difference  be  small  the  calculated 
magnitude  will  not  be  far  out,  even  if  the  absorption  coefficient 
be  a  little  out  from  the  truth.  I  may  remark  that  in  taking 
his  stellar  magnitudes,  Professor  Pritchard  seems  to  have  taken 
every  care  as  to  this,  his  comparison  star  being  Polaris,  and  the 
star  observed  being  about  the  same  zenith  distance. 


March  1887.  Transmission  of  .  .  .  Light.  263 

Having  arrived  at  the  conclusion  regarding  visual  observa- 
tion, it  struck  me  that  absorption  of  the  photographic  spectrum 
ought  to  follow  the  same  course.  Now  in  the  '  Proceedings  of 
the  Royal  Society  '  I  have  given  a  very  careful  measurement  of 
the  photographic  sensitiveness  to  various  rays  of  light  of  bromo- 
iodide  of  silver,  besides  which  I  had  the  spectrum  sensitiveness 
of  other  salts  of  silver  by  me,  and  I  knew  the  air  thickness  and 
the  spectral  luminosity  on  the  day  when  these  measures  were 
takeb*  Assuming  that  the  ultra  violet  rays  obeyed  the  same  law 
as  the  visible  rays,  it  was  easy  to  calculate  the  photographic 
value  of  each  ray  for  any  air  thickness  ;  and  this  1  accordingly 
did. 

Using  a  value  of  '00 183  for  k  in  Lord  Rayleigh's  formula, 
the  same  process  as  before  was  gone  through,  supposing  a  plate 
of  bromo-iodide  of  silver  had  been  used :  the  areas  were  for 
o,  1,  2,  3,  and  4  atmospheres,  835,  621,  457,  340,  and  254. 
Tbe  values  arrived  at  by  the  logarithmic  formula  were  837,  621, 
461,  342,  and  254.  This  gave  ^='2980,  and  the  coefficient  of 
transmission,  '742. 

Taking  chloride  of  silver  as  the  sensitive  salt,  its  spectrum 
value  being  known,  and  proceeding  as  before,  the  following  areas 
were  found  for  o,  1,  2,  3,  and  4  atmospheres  :  693,  413,  246, 147, 
and  87.  Calculated  by  the  logarithmic  formula,  they  became  689, 
413, 248, 148,  and  87,  /i=*5 1 15,  and  the  coefficient  of  transmission 
=•603. 

Taking  these  two  results  it  is  evident  that  before  any  definite 
knowledge  of  a  value  of  a  star  magnitude  by  photography  can 
be  arrived  at  (supposing  all  stars  were  of  the  same  colour)  a 
definite  acquaintance  must  be  made  with  the  kind  of  sensitive 
salt  that  is  employed.  Thus  the  bromo-iodide  plate  gave  a 
value  of  transmission  of  742  ;  the  chloride,  of  '603  ;  whilst  the 
optical  value  was  only  *88o  when  k  =  00 11 83. 

Now  it  may  be  considered  that  these  results  are  only  theo- 
retical deductions,  but  luckily  they  are  capable  of  proof  in  the 
laboratory  by  experiment. 

Water  can  easily  be  made  turbid  by  alcoholic  solutions  of  mastic 
or  by  other  fine  precipitates,  and  last  year  General  Festing  and 
myself  proved  that  these  artificially  prepared  turbid  media 
strictly  obeyed  Lord  Rayleigh's  law.  Now  it  was  easy,  having 
proved  this,  to  ascertain  whether  when  the  light  passing  through 
such  media  was  measured  integrally  by  optical  and  photographic 
means  the  logarithmic  formula  was  followed. 

Experiment  showed  that  it  did  so.  Here  is  one  of  several 
results.  A  cell  measuring  exactly  6  inches  by  4  inches  was 
taken,  and  the  values  of  light  passing  through  these  thicknesses 
of  clear  and  turbid  water  were  found  to  be — 


Clear 
Turbid 


4-in. 

6-in. 

75'6 

754 

265 

155 

264  Capt.  Abney,  Atmosplieric  Transmission  etc.        xlvii.  5, 

Taking  the  clear  or  incident  light  as  the  mean  of  the  two,  75*5, 
and  using  the  6  inches  of  the  turbid  medium  as  lying  on  the 
curve,  the  logarithmic  formula  gave  /i=*2639  *n  *ne  formal* 

I'  =  ic-**, 

and  the  absorption  consequently  for  4  inches  of  the  fluid  =26*3. 
Taking  the  photographic  values  a  bromo-iodide  plate  was  ex- 
posed to  the  clear,  the  4-inch  and  the  6-inch  turbid  water  for 
definite  times,  and  the  values  of  the  light  acting  on  the  plate 
found  to  be 

4-inch  clear         1 

I  —  4-inch  turbid  - 

io- 125 

6-inch  turbid     — 
33* 

Using  the  logarithmic  formula  as  before,  taking  the  clear 
and  6-inch  turbid  light  as  lying  on  the  curve,  the  value  of  the 

4-inch  turbid  would  be  nr3J  and  the  value  of  ^='5832. 

The  optical  value  of  /*  is  2*639.  The  ratio  of  the  optical  to 
the  photographic  value  of  fi  is  1  :  2*21,  as  determined  by 
experiment. 

Taking  the  optical  and  photographic  values  of  /1,  say,  for  a 
value  of  £=001183,  they  are  '1324  and  2980,  or  1  :  2*25. 

This  shows,  I  think,  that  the  values  of  /*  determined  experi- 
mentally in  the  laboratory  and  by  appeal  to  the  atmosphere  are 
as  consistent  as  can  be  expected. 

Further  we  have  this  curious  fact,  that  if  we  take  the  optical 
value  of  unanalysed  light  passing  through  the  atmosphere,  and 
also  the  photographic  value  of  the  same,  we  are  able  to  form  two 
equations  which  give  the  value  of  k,  which  must  be  applied  to 
every  wave-length,  and  also  enable  a  curve  of  light  to  be  con- 
structed which  takes  into  account  general  absorption  by  mist 
which  is  not  composed  of  sufficiently  fine  particles  to  scatter 
light.  Calculation  shows  that  k  is  derived  from  either  by 
dividing  /i  by  110  and  250  respectively  when  k  is  less  than  '0013. 
These  gradually  alter  in  value  till  they  become  104  and  255, 
when  £='0015  is  reached.  The  values  of  1 10  and  255  are  inverse 
fourth  power  of  wave-lengths  in  the  green  and  violet  respectively, 
showing  that  when  light  is  integrally  measured  it  is  equivalent 
to  measuring  definite  rays  in  these  parts  of  the  spectrum. 

I  have  not  touched  upon  the  question  of  how  star  magnitudes 
are  to  be  measured,  but  merely  ventured  to  give  a  means  of 
applying  a  correction  for  loss  caused  by  the  atmospheric  trans- 
mission. It  will  be  seen  how  much  greater  is  the  loss  of  those 
rays  which  are  photographically  active  than  the  visual  rays, 
and  it  would  appear  that  to  enable  a  proper  correction  to  be 


March  1887.     I  Mr.  Roberts,  Photographic  Search  etc.  265 

made  to  photographs  of  stars  taken  at  different  times,  the  visual 
absorption  at  the  time  should  also  be  calculated.  I  am  not 
alluding  now  to  the  fact  that  the  angle  included  in  any  star 
photograph  is  small;  stars  on  such  a  plate  may  be  compared 
inter  se;  but  in  order  to  make  comparisons  general  the  atmo- 
spheric absorption  for  the  photographically  active  rays  must  be 
studied,  and  it  is  absolutely  necessary  that  the  spectrum  value  of 
the  sensitive  salt  should  be  known  beforehand. 


Photographic  Search  for  the  Minor  Planet  Sappho. 

By  Isaac  Roberts. 

From  1872  to  the  present  time  no  observations  of  the  minor 
planet  Sappho  have  been  published  except  those  of  1882,  in 
which  year  Mr.  Gill  took  measures  for  a  determination  of  the 
solar  parallax. 

Mr.  Bryant,  who  is  engaged  in  determining  the  orbit  of  this 
planet,  prepared  an  ephemeris  for  the  opposition  of  this  year, 
and  in  order  that  no  time  might  be  lost  in  identifying  it  from 
the  neighbouring  faint  stars,  and  further  that  the  error  of  the 
ephemeris  might  be  obtained  as  early  as  possible,  he  sent,  on 
December  16,  1886,  the  positions  he  had  calculated,  and  appealed 
to  me  to  find  the  planet  if  possible  by  photography. 

The  brightness  of  the  planet  is  estimated  at  eleventh  magni- 
tude, and  since  its  orbital  movement  in  sixty  minutes  is  equal  to 
about  4*2  times  its  photographic  diameter,  the  trail  it  would 
leave  would  probably  not  exceed  in  density  a  thirteenth  magni- 
tude star. 

On  December  30  I  obtained,  with  an  exposure  of  sixty 
minutes  between  sidereal  time  at  Maghull,  7h  35™  and  8h  35°*, 
a  negative  of  which  the  accompanying  photograph  marked 
chart  No.  1  is  an  enlargement  to  three  diameters.  The  trail  of 
the  planet  is  to  be  seen  near  the  centre,  and  to  make  it  more 
easily  recognisable  a  white  circle  is  drawn  round  it. 

Another  photograph  was  taken  on  January  1,  and  a  third  on 
the  14th.  These  are  marked  respectively  charts  Nos.  2  and  3. 
Each  of  the  three  charts  shows  the  difficulties  to  be  encountered 
in  finding  a  planet  so  faint  as  this  one  amongst  such  numbers  of 
other  faint  stars,  and  as  an  illustration  I  may  refer  to  chart  No.  3 
upon  which  I  estimate  that  there  are  about  2,000  stars  below 
the  seventh  magnitude  on  each  square  degree. 

Mr.  Bryant  informs  me  that  the  error  of  the  ephemeris 
deduced  from  the  photographs  is  in  very  close  agreement  with  that 
from  two  meridian  observations  of  the  planet  made  about  the  same 
time  at  Dunecht,  results  that  must  be  considered  satisfactory. 

This  is  probably  the  first  instance  in  which  photography  has 
been  successfully  applied  to  the  purpose  here  described,  and  as 
an  historical  fact  it  may  be  worth  recording.     There  are  also 


266  Mr.  Qore,  Orbit  of  14  (1)  Ononis.  xlvii.  5, 

some  inferences  which  might  be  drawn  from  these  experiments. 
First,  it  is  here  demonstrated  that  asteroids  of  eleventh  magni- 
tude leave  very  strong  trails  on  the  films  of  the  photographic 
plates,  and  probably  others  down  to  the  thirteenth  or  fourteenth 
magnitude  could  under  favourable  atmospheric  conditions  be 
photographed. 

Another  inference  is  that  all  the  asteroids  which  up  to  the 
present  time  have  been  discovered,  together  with  those  that  may 
exist  but  are  not  recorded  down  to  the  fourteenth  magnitude, 
could  by  one  astronomer  alone  be  found  and  accurately  charted 
in  the  coarse  of  two  or  three  years'  time. 


On  the  Orbit  of  14  (i)  Ononis  (0.  Struve  98).     By  J.  E.  Gore. 

I  have  computed  the  orbit  of  this  binary  star  by  means  of  the 
graphical  method,  and  find  the  following  provisional  elements  : — 

Elements  of  14  (t)  Orionis. 

P  » 190*48  years  Q  =  990  35' 

T  =  195905  a.d.  A  =  3020  42' 
*  =  0-2465  «=i"-22 

7  =  44°  57'  /i=-i°-89 

From  these  elements  we  have  the  following  formulas  : — 

(1)  w- 14- 12  sin  «= —1*89  (£—1959-05) 

(2)  tan  £V- 1286  tan  £«. 

(3)  tan  (0C  -  990  35')  =  07077  tan  (V  +  3020  42') 

<*>  ,-™<«-« 465 ~«).^^-$. 

where  u  is  the  exoentric  anomaly,  and   V  the  true  anomaly 
for  the  epoch  t ;  6C  the  required  position-angle,  and  p  the  distance. 
The  following  is  a  comparison  between  the  recorded  measures 
and  the  positions  computed  from  the  above  elements  : — 


Epoch. 

Observer. 

Oo 

*c 

60 -Be 

Po 

pc 

PO-PC 

1844*05 

Madler 

0 
2588 

0 

25444 

0 
+  436 

II 

136 

II 

184453 

0.  Strove 

25083 

253*95 

-3'12 

114 

135 

-0*21 

1849*22 

»» 

249*60 

24897 

+  063 

0*98 

i*33 

-O35 

1852-15 

Madler 

2454 

24580 

—  040 

— 

— 

— 

1854*82 

Dawes 

2409 

24275 

-1-85 

I  29 

1*29 

OOO 

1859*22 

0.  Strove 

23780 

237-55 

+  025 

1*24 

1  26 

—  0*02 

1865*98    Dembowski      234*0        228*95       +5*05       1*25       1*20       +005 


March  1887.     Mr.  Ooret  Observations  of  Variable  Star. 


267 


Epoch. 

Observer. 

Oo 

ec 

0°-Sc 

?o 

1* 

Po-f* 

I867'I5 

Dembowski 

0 
232'I 

0 
227*4 

0 
+  470 

II 

128     1 

rig 

11 
+  OO9 

186814 

11 

228'S 

226*1 

+  2*40 

1-05     1 

18 

-OI3 

1869*19 

Dnner 

224*6 

22463 

-0-03 

095     1 

17 

-C22 

1 8708 1 

Dembowski 

2233 

222-25 

+  I*05 

I'2I         1 

16 

+  OO5 

187087 

0.  Strove 

22413 

222-17 

+  1*96 

I*09         J 

[•16 

-007 

187342 

Dembowski 

2I9'2 

21845 

+  0  75 

1*26         1 

[•14 

+  0*12 

187618 

Duner 

211*9 

21425 

-2*35 

122         ] 

[•1 1 

+  o*n 

1876*88 

Dembowski 

212*8 

213-17 

-0*37 

I'll         ] 

en 

OOO 

1877-18 

Schiaparelli 

209'9 

21271 

-2*8l 

O98         ] 

[*IO 

-0-I2 

I878-35 

Dembowski 

208'2 

210-8 

—  2*60 

099        1 

['IO 

-0*11 

1879-10 

Hall 

205*8 

209*61 

~3"8i 

089        ] 

[-09 

—  0*20 

1 88014 

Jednejewicz 

209I 

207*91 

+  1*19 

IO3         ] 

[•08 

-OO5 

188113 

Hail 

203'2 

206-28 

-308 

IO3         I 

•07 

—  0*04 

l88ll6 

Jedrzejewicz 

205*9 

206*23 

-033 

ro8      i 

[•07 

+  0*01 

1882-14 

i» 

201 -3 

204*62 

-3*32 

I'OO        ] 

[■06 

—  0-06 

188276 

Engelmann 

2033 

20353 

-023 

115      1 

106 

+  009 

1886*917 

Tarrant 

1964 

196*15 

+  025 

113      ^ 

104 

+  0-09 

1886977 

it 

1958 

196*11 

-031 

116      i 

[•04 

+  0*12 

1887*019  Young 

1955 

196-07 

-o-57 

0*98 

104 

-0*06 

The  magnitudes  of  the  component*  are  about  6  and  7.  Ac** 
cording  to  the  above  elements  the  distance  will  remain  nearly 
constant  during  the  next  fifty  years,  the  angle  diminishing  to 
about  1070  in  the  year  1936.  As  far  as  I  know  the  orbit  has  not 
been  previously  computed.  Some  of  the  measured  angles  in  late 
years  are  very  discordant.  Professor  Young's  measure  this  year 
was  communicated  to  me  by  private  letter. 


Observations  of  the  Variable  Star  S  (10)  Sayitte. 

By  J.  E.  Gore. 

The  following  are  my  observations  of  this  interesting  vari- 
able star  in  the  year  1886.  They  form  a  continuation  of  the 
observations  given  in  the  Monthly  Notices  for  January  1 886. 

The  comparison  stars  are,  as  before : — 


II  Sagitta 
9  Sagittm 
DM  +  16°  4086 


Meg. 
5*8 
6*6 
7*0 


268  Mr.  Gore,  Observations  of  Variable  Star.        xlvii.  5, 

Observations  of  10  Sagitta. 


Date. 
1886,  Jan. 

6 

h    m 

5  45 

Ma*. 

57 

Date. 
1 886,  Sept 

■    30 

h    m 
IO  25 

Mag. 
6*2 

13 

6    0 

64 

30 

II   20 

6l 

May 

19 

10  25 

61 

Oct. 

1 

7  55 

57 

21 

10  50 

5-8 

1 

10  40 

57 

22 

10  15 

59 

7 

9  30 

64 

26 

10  30 

64 

9 

7  10 

6*o 

3i 

10  45 

59 

10 

6  45 

57 

June 

12 

10  30 

64 

12 

7    5 

57 

July 

12 

10  15 

58 

13 

10  10 

5*9 

19 

10    0 

57 

16 

7  15 

63 

21 

9  45 

5*9 

21 

10  54 

5*9 

22 

10  10 

61 

23 

6  45 

6*4 

Aug. 

8 

9  15 

64 

23 

10  30 

64 

14 

9    0 

59 

24 

6  26 

64 

22 

8  40 

58 

25 

9  57 

6*2 

28 

9    0 

59 

26 

6  37 

5'8 

29 

8  15 

5'8 

■ 

26 

10  40 

5'85 

3i 

8  20 

57 

28 

7    7 

59 

Sept. 

1 

10  45 

60 

3' 

6  20 

61 

2 

825 

615 

Nov. 

1 

8  40 

6*4 

3 

8  20 

6*2 

3 

6  56 

60 

5 

8  42 

60 

4 

9  30 

5-65 

6 

7  58 

5*8 

5 

7  5o 

575 

6 

"  35 

57 

8 

6  45 

625 

8 

8  25 

5"8 

10 

8    0 

6-4 

14 

10    2 

58 

16 

5  50 

61 

15 

7  40 

57 

1/ 

5  43 

625 

16 

7  50 

585 

23 

5  27 

58 

17 

7  55 

5'8 

26 

5  3o 

6*3 

18 

7  40 

60 

30 

8  IS 

5*9 

18 

11  20 

605 

Dec. 

4 

5  26 

64 

20 

8  10 

64 

12 

6  10 

6*2 

20 

11    0 

64 

16 

5  22 

5-6 

22 

7  10 

5*9 

22 

5    4 

6-35 

25 

11  30 

5*9 

24 

6  25 

5'8 

27 

7    5 

6*2 

25 

5  3o 

5'65 

March  1887.  Mr.  FraiJcs,  Star  Colours.  269 


A  Proposed  Nomenclature  for  Star  Colours.    By  W.  S.  Franks. 

It  is  generally  admitted  that  the  nomenclature  of  star  colours 
is  at  present  in  a  very  unsatisfactory  state,  and  not  at  all  in 
keeping  with  the  exact  methods  employed  in  other  departments 
of  astronomical  observation.  The  hitherto  popular  fashion  of 
naming  star  tints  after  fruit,  flowers,  precious  Btones,  <fec.,  is 
both  vague  and  arbitrary,  and  also  objectionable  on  account  of 
the  frequent  diversity  in  tint  of  the  object  referred  to.  Any 
standard  whatever,  to  be  of  real  utility,  must  be  readily  accessible 
and  also  of  uniform  tint — the  same  at  all  times  and  in  all  places. 
It  is  very  evident  that  the  terrestrial  objects  just  mentioned  do 
not  fulfil  any  one  of  these  conditions  ;  and  so  they  should  now 
be  definitely  rejected,  as  their  retention  only  serves  to  per- 
petuate the  existing  confusion.  The  late  Admiral  Smyth,  who 
was  doubtless  responsible  for  the  introduction  of  many  of  these 
poetic  but  exceedingly  vague  terms,  felt  the  force  of  the  objec- 
tions to  their  use,  when  he  wrote  the  brochure  entitled  "Sidereal 
Chromatics  " — a  book  which,  was  unfortunately  only  intended  for 
private  circulation,  and  therefore  not  so  well  known  as  it  deserves 
to  be.  It  contained  a  plate  of  coloured  discs,  with  four  gradations 
each  of  red,  orange,  yellow,  green,  blue,  and  purple,  which  was 
intended  as  a  scale  upon  which  star  colours  could  be  more  defi- 
nitely expressed.  But  this  chromatic  diagram,  pretty  as  it 
looked,  had  several  serious  faults.  Its  twenty- four  tints  were 
not  so  carefully  selected  as  they  might  have  been,  nor,  indeed, 
were  they  sufficient  to  meet  the  requirements  of  the  observer ; 
and  further,  an  opaque  wafer  of  colour,  necessarily  viewed  by 
artificial  light  (which  of  course  modified  its  appearance),  could 
not  well  be  compared  with  a  glittering  stellar  point.  The  suc- 
cessive depths  of  tint,  also,  were  inversely  put  with  regard  to 
the  numerical  order.  Thus,  the  deepest  tint  of  red  was  called 
"  Bed  *,"  and  the  palest  "  Bed.4  "  Some  of  the  colours  them- 
selves are  open  to  criticism.  For  instance,  the  two  deeper  shades 
of  orange  are  not  pure,  but  have  a  perceptible  tinge  of  red,  whilst 
the  two  corresponding  shades  of  yellow  are  really  orange-yellow. 
Neither  the  red  nor  the  green  are  typical  colours,  as  anyone 
may  see  by  comparing  them  with  the  ordinary  daylight  spec- 
trum ;  the  former  is  too  crimson,  and  the  latter  too  bluish-green. 
There  is  some  reference  to  the  colours  of  stars  in  Professor  Piazzi 
Smyth's  "  Madeira  Spectroscopic,1 '  and  a  chromo-lithograph  at 
the  end  of  that  work  gives  a  graduated  series  of  primary, 
secondary,  and  tertiary  spectrum  colours,  with  their  corre- 
sponding wave-numbers. 

It  is  pretty  evident  that,  in  the  future,  we  must  look  to  the 
spectrum  for  our  standard  colours.  But  as  these  star  observa- 
tions are  confined  to  the  period  when  the  sun  is  below  the 
horizon,  it  is  equally  obvious  that  they  cannot  be  directly  so 


270  Mr.  Franks,  A  Proposed  Nomenclature.  XLVii.  5, 

compared.  This  difficulty  might  be,  however,  got  over  by 
having  a  series  of  coloured  gelatine  discs  carefully  matched  with 
the  spectrum,  and  then  viewing  them  as  transparencies  by  the 
light  transmitted  from  an  incandescent  electric  lamp.  In  at- 
tempting to  devise  any  plan  for  the  more  systematic  observation 
of  star  colours,  there  are  several  essential  points  to  be  con- 
sidered. The  standard  mnst  be  uniform,  and  easily  accessible 
anywhere  for  reference,  if  it  is  to  meet  with  universal  adoption. 
The  solar  spectrum  answers  this  end  completely,  since  it  affords 
a  well-marked  range  of  colours,  which  can  be  expressed  in  wave- 
lengths, or  referred  to  certain  Frannbofer  lines.  The  nomen- 
clature should  be  as  simple  as  possible,  yet  copious  enough  for 
ordinary  requirements,  and  be  arranged  on  some  methodical 
plan,  so  as  to  be  easily  remembered.  Its  terms  should  have  a 
precise  and  definite  meaning,  and  be  capable  of  numerical 
reduction,  so  as  to  get  mean  results  from  a  number  of  observa- 
tions. How  far  these  conditions  are  fulfilled  in  the  scheme 
which  I  have  the  honour  to  lay  before  the  Society  may  be  best 
judged  of  by  reference  to  the  annexed  diagram.  The  germ  of 
the  present  plan  is  due  to  certain  suggestions  made  by  Professor 
Pickering,  that  I  should  reject  all  modifications  of  white,  as 
applied  to  stars,  except  in  the  direction  of  the  prismatic  colours, 
and  that  I  should  take  white  as  one  end  of  a  series  for  -each 
colour,  giving  a  numerical  ratio  to  each  term  in  the  series.  It 
then  occurred  to  me  to  call  white  the  zero,  from  which  the 
spectral  colours  radiate  as  a  centre,  each  concentric  ring  corre- 
sponding to  a  given  depth  of  each  colour.  Starting  with  red, 
the  primary  and  subordinate  colours  are  placed  at  equal  dis- 
tances round  the  circle  up  to  violet,  and  the  opposite  ends  of  the 
spectrum  connected  by  the  intermediate  tint  of  purplish  red. 
On  this  plan,  too,  each  colour  is  opposite  to  its  complementary ; 
the  sum  of  any  two  opposite  colours  forming  white  light.  This 
may  be  convenient  in  estimating  the  colours  of  "  double  "  stars. 
As  to  the  fiducial  points  to  which  the  chief  colours  are  referred  I 
would,  provisionally,  adopt  Professor  Smyth's  definition  of  them. 
They  would  then  run  as  follows  : — 

Red  ...    '    ...  #  WN  36,000 :  Nearest  Solar  lines  a  and  B. 

Orange  ...         ...       „    40,000:  „  „  a  (alpha). 

Yellow  „    43,000:  „  „  D!andD*. 

Green  .,    49,000:  „  „  b1,  b2,  &c. 

Bine  ...         ...       „     56,000:  „  „  d.     . 

Violet  „    60,000:  „  „  G  and  g. 

With  regard  to  the  names  of  the  colours,  I  have  tried  to 
avoid  even  such  terms  as  "citron,"  "glaucous,0  &c.,  because, 
though  need  by  Professor  Smyth,  they  would  certainly  be  mis- 
interpreted by  many  observers.     In  adopting  Professor  Picker- 

*  The  wave-number  10  for  the  centre  of  each  colour. 


March  1 81 


for  Star  Colours. 


ing's  restriction  of  "  white,"  I  have  sacrificed  all  anoh  qualifying 
adjectives  as  very,  intense,  pale,  greyish,  ifcc.,  for,  aa  generally 
used,  these  refer  to  the  relative  brigktnett  of  the  light  rather 
than  to  its  colour.  The  terms  I  have  proposed  for  the  sub- 
ordinate tints  carry  their  own  meaning,  as  they  are  compounded 
of  the  two  adjacent  primaries.  And,  by  inverting  the  order,  a 
minuter  subdivision  might  be  made,  exactly  analogous  to  the 
case  of  star  magnitudes ;  as  we  oould  divide  the  interval  between 
green  and  bine,  say,  into  "  bluish-green  "  and  "  greenish-blue," 
according  to  whether  green  or  blue  was  the  strongest  compo- 
nent. Bat  probably  there  would  be  no  necessity  for  this,  as 
the  number  of  tints  (forty-eight  in  all)   seems  sufficient  for 


the  required  purpose,  and  is  twice  as  many  as  the  number  on 
Smyth's  chromatic  diagram.  Commencing,  now,  with  tiie 
centre  as  "white"  (see  diagram),  the  symbol  for  which  is 
"0":  the  first  circle  will  represent  ruddy  white,  creamy 
white,  yellowish  white,  greenish  white,  bluish  white,  and  pur- 
plish white,  their  symbols  being  B1,  Or',  T1,  G\  IS1,  and  V  i 
the  next  circle  pale  red,  pale  orange,  pale  yellow,  &c. ;  symbols, 
If,  Or1,  Y\  Ac. :  the  snooseding  circle  is  intended  to  be  equiva- 
lent to  the  normal  shade  of  red,  orange,  yellow,  Ac  ;  symbols, 
R3,  Or3,  T1,  &e. :  the  outer  circle  corresponds  to  the  deepest 
shades  of  colour,  as  very  rfed,  very  orange,  very  yellow,  Ac,  ; 
symbols,  B*,  Or1,  T1,  &c.    Thus  the  four  terms  in  each  series 


272  Mr.  Toddy  On  the  Best, Device  xlvh.  5, 

are  supposed,  to  be  equal  to  four  corresponding  increments  of 
depth  of  shade,  the  numerical  ratios  being  direct,  instead  of 
inverse,  as  in  Smyth's  scale.  And  it  is  at  once  apparent,  how 
readily  these  terms  admit  of  redaction  in  discussing  a  number 
of  observations.  I  have  not  thought  it  necessary  to  specify  the 
subordinate  colours  here,  as  their  corresponding  symbols  appear 
on  the  diagram.  But  though  they  all  follow  the  same  invariable 
rule — that  is,  the  inner  circle  means  white  tinged  with  the  given 
colour :  circle  2,  a  pale  tint  of  the  colour;  circle  3,  the  normal 
colour  ;  and  circle  4,  the  deepest  tint  of  colour,  yet  it  will  not, 
in  all  probability,  be  requisite  to  use  the  first  term -in  their 
series,  as  six  different  tints  of  white  are  as  many  as  can  be  well 
distinguished  from  each  other. 

P.S. — The  original  diagram,  of  which  the  annexed  is  a  copy, 
was  executed  in  water-colours,  and  gives  a  much  better  idea  of 
the  proposed  scheme  than  one  in  black  and  white  can  possibly 
do,  but  it  would  probably  be  difficult  and  expensive  to  repro- 
duce in  a  satisfactory  manner. 


On  the  Best  Device  for  "Revolving  a  Dome.     By  Professor 

David  P.  Todd. 

(Communicated  by  the  Secretaries.) 

The  various  methods  which  have  been  devised  for  applying 
power  to  revolve  a  dome  show  that  it  is  a  matter  of  considerable 
importance  in  observatory  construction.  The  number  of  these 
methods  shows  also  that  many  of  them,  at  least,  are  imperfect 
either  in  principle  or  construction.  A  very  common  method,  espe- 
cially in  the  older  observatories,  consists  of  a  continuous  rachet 
or  cog-wheel  run  around  the  bed-plate  or  interior  of  the  dome, 
in  which  a  cog-wheel  on  a  short  journal  runs,  the  power  being 
communicated  to  this  latter  in  the  simplest  manner.  The  diffi- 
culties in  the  way  of  this  device  consist  rather  in  the  imperfec- 
tion of  the  running-gear  of  the  dome  itself.  In  constructing  the 
large  dome  pf  the  Washburn  Observatory,  at  Madison,  Wisconsin, 
the  late  Professor  Watson  sought  to  overcome  these  difficulties 
by  a  double  cog-wheel,  which  should  work  into  the  rachet  of  the 
dome  on  exactly  opposite  sides,  of  the  latter.  In  order  to  secure 
this  end,  a  somewhat  cumbersome  apparatus  was  devised  and 
applied,  consisting  of  two  vertical  shafts  on  opposite  sides  of  the 
dome  geared  into  a  rigid  horizontal  shaft,  running  across  from 
one  side  to  the  other,  underneath  the  floor  of  the  dome.  This 
apparatus  is  described  in  Vol.  I.  of  the  publications  of  this 
Observatory.  In  constructing  the  smaller  dome  of  the  lick 
Observatory,  the  idea  occurred  to  Mr.  Fraser,  the  superintendent 
of  construction,  that  the  dome  itself  might  be  considered  as  a 
large  pulley,  and  a  rope  run  around  it  as  such,  and  brought  into 
the  inside  of  the  dome,  where  it  was  carried  around  a  suitable 


I     I 


March  1887.  for  Revolving  a  Dome.   .  2^3 

pulley  connected  with  the  gearing  and  a  crank.  This  device 
works  in  the  moat  perfect  manner,  and  there  is  no  objection  to 
it  except  that,  the  rope  being  ran  around  the  outside  of  the 
dome,  it  is  not  easy  to  secure  perfect  weather  protection  at  the 
point  where  the  rope  passes  to  the  inside  of  the  dome.  In  addi- 
tion to  this,  the  rope  itself  where  exposed  on  the  exterior  of  the 
dome  would  require  protection  from  the  weather,  especially  in 
our  northern  latitudes. 

When  Mr.  Warner,  of  the  firm  of  Warner  and  pwasey,  of 
Cleveland,  was  at  the  Lick  Observatory  in  May  last,  the  idea 
occurred  to  him  that  the  wire  rope  employed  in  turning  the 
dome  could,  by  means  of  a  suitable  device,  be  run  around  the 
inside  of  the  dome  quite  as  well  as  the  outside,  thus  rendering 
special  weather  protection  unnecessary,  and  reducing  the  appara- 
tus to  a  very  compact  form.  The  accompanying  plate  (figs.  1-3) 
gives  a  good  idea  of  this  new  device  as  constructed  by  Mr.  Warner 
For  the  first  time,  and  applied  to  the  22-feet  dome  of  the  new 
observatory  at  Smith  College,  Northampton.  It  will  be  seen 
that  there  are  attached  to  the  projecting  uprights  of  the  dome  a 
series  of  horizontal  grooved  pieces,  curved  to  the  same  radius  as 
that  of  the  dome  itself.  These  pieces  form  a  continuous  grooved 
pulley  on  the  inside  of  the  dome,  and  concentric  with  it  Im- 
mediately underneath  the  bed-plate  of.  the  dome,  and  rigidly 
attached  to  the  wall,  is  a  framework  carrying  the  pulleys  as 
represented  in  the  plate  (fig.  3).  Around  the  largest  of  these 
Jralleys  passes  an  inch  rope,  to  which  the  necessary  power  iB 
applied  by  the  hand/  On  the  same  axle  with  this  large  pulley 
is  a  small  pulley,  around  which  a  wire  cable  passes  which  revolves 
the  dome  directly.  To  facilitate  the  running  of  the  wire  rope 
from  this  small  pulley  into  the  large  grooved  pulley  of  the  dome 
itself,  a  pair  of  idle  pulleys  are  plaoed  immediately  underneath, 
the  grooved  pulley  attached  to  the  dome.  As  these  loose  pulleys 
are  placed  very  near  together,  they  serve  also  the  purpose  of 
giving  the  rope  a  larger  bearing  service  upon  the  motor-pulley 
below  them.  It  will  be  seen  that  the  device  is  a  very  simple 
and  compact  one.  It  is  all  contained  in  a  shallow  niche,  in,  the 
wall,  and  is  thus  entirely  beyond  the  reach  of  the  observing- 
chair  as  it  moves  upon  the  floor  of  the  dome.  Tfye  distri- 
bution of  the  power  to  every  part  of  the  circumference  of 
the  dome  by  means  of  the  wire  rope  is  an  important  ad- 
vantage not  secured  in  any  form  of  cog-wheel  apparatus. .  t  The 
bearing  surface  of  the  wire  rope  upon  the  dome  is  nearly 
70  feet  long;  so  that,  although  the  rope  may  be  quite 
loose,  there  is  still  friction  enough  to  move  the  dome  readily. 
The  perfection  of  the  running-gear  of  the  dome  itself ,  has,  of 
course,  much  to  do  with  the  ease  of  movement  of  this  revolving 
apparatus.  In  the  case  of  the  dome  alluded  to  above,  a  three- 
pound  weight  is  sufficient  to  set  the  dome  in  motion,  the  ratio  of 
descent  of  the  weight  to  the  movement  of  the  periphery  of  the 
dome  itself  being  about  as  three  to  one. 

12 


e74  •&&•  Crossley,  A  Centering  Tube.  xlvii.  5, 

In  connection  with  the  accompanying  illustration  of  a  section 
of  the  running-gear  of  the  dome,  the  following  brief  description 
will  make  its  construction  clear.  First,  being  assured  that  the 
tracks  on  the  wall-plate  and  the  conical  wheels  are  turned  to 
their  exact  cones,  the  next  important  point  is  to  hold  these 
wheels  so  that  their  axes  produced  will  converge  to  a  point  at 
the  centre  of  the  tracks.  Messrs.  Warner  and  Swasey  have 
found  it  impossible  to  accomplish  this  by  any  system  of  bearing 
of  the  live  ring.  They  therefore  provide  a  yoke  for  each  conical 
wheel.  In  addition  to  carrying  the  journals  of  the  conical  wheel, 
each  yoke  carries  also  two  guide-wheels,  which  run  between  the 
tracks  of  the  wall-plate.  These  guide- wheels  are  so  adjusted  as 
to  keep  the  axis  of  the  conical  wheel  coincident  with  the  true 
radios  of  the  circle~of  the  wall-plate.  These  guide- wheels  obviate 
also  the  necessity  of  flanges  on  the  conical  wheels,  while  the  yokes 
merely  require  connection  with  each  other  by  single  flexible  rods, 
forming  thus  the  continuous  live  ring.  By  these  simple  devices 
the  friction  is  so  largely  reduced  that  the  dome  may  be  readily 
revolved  by  the  application  of  a  direct  tangential  pressure  of 
1£  pound  for  each  ton's  weight. 


A  Centering  Tube  for  Reflecting  Telescopes.    By  Edward 

Crossley. 

To  facilitate  the  centering  of  the  "  Common"  3-foot  Reflector 
I  have  constructed  a  tube  with  diaphragms,  by  means  of  which 
the  mirrors  can  be  adjusted  with  the  greatest  ease. 

The  tube  I  use  is  10  inches  long  and  2$  inches  in  diameter. 
This  is  placed  in  the  eye  end  at  the  side  of  the  telescope.  The 
end  of  the  tube  towards  the  eye  has  a  small  pin-hole.  The  other 
end  towards  the  mirrors  has  two  diaphragms  which  will  replace 
each  other  concentrically.  The  large  diaphragm  is  1*96  inch 
in  diameter,  the  small  one  is  0*37  in  diameter.  The  large  dia- 
phragm just  embraces  the  large  mirror,  which  can  be  centered  by 
means  of  the  flat.  The  small  diaphragm  is  then  put  in  its  place, 
and  the  flat  centered  by  means  of  the  adjustment  of  the  large 
mirror,  or,  better  still,  by  the  adjustment  of  the  eye  end. 

Thus  the  telescope  can  be  centered  in  any  position  with 
accuracy  during  the  day  or  with  illumination  at  night. 

The  sizes  of  the  diaphragms  are  proportionate  to  the  diameters 
of  the  large  and  small  mirrors  respectively,  and  the  length  of  the 
tube  is  a  little  less  in  proportion  than  the  focal  length  so  as  to 
embrace  a  rather  larger  angle. 

At  night  time  a  reflector  is  necessary  within  the  tube  at  an 
angle  of  45°  to  the  tube,  with  an  opening  at  the  side  so  as  to 
throw  the  light  of  a  lamp  held  in  the  hand  upon  the  inner  face 
of  the  diaphragm,  and  a  white  sheet  of  paper  stretched  on  a 
hoop  can  fee  set  in  front  of  the  telescope  and  illuminated  by 
another  lamp.  This,  however,  is  not  necessary  if  the  work  is 
properly  done  in  the  daytime. 


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Observation*  0/  Comets. 


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*&o  R.  Observatory,  (Jape  of  Good  Hope,  xlyh.  5, 

Comet  1886  .  .  .  (Fabry). 

Adopted  Mean  FUea  of Comparimm  Stan. 

Camp.  B^  Declicatkn  .   ,t .. 

SUrKo.  1886a  1W60.  AnthoriQr. 

h    m       »  ©     #       « 

1  4    5  16-15       +   5  *3  3<>*5  Greenwich  7-jear  and  9-jear. 

2  4  32  50-32       -  o  37  312  Qottingen,  1263. 

3  4  55    9*o       -  6  15  191  8|  mag.  Equat.  diff  from  a. 

*  4  54  45*6*       -  6  21  443  W.B.  iv.  1177. 

4-     5  19  1968       -11     5443  J(W.B.V.  407  +  Sant.  519). 

5        5  18  1246       -11  18  387  J(W.B.V.  382  +  Saot  516). 

*  5  36   (27)        -15  23  (42)  (  =  Lal.  10807). 

7  5  55  5432       - 19  14  3»*5  9|  «*g.  Equat.  diff. from,*. 
*•  -  62  4392       -19    9  135  Stone  2801. 

8  654    872       -2849    35  €  Can.  Maj.  N.A. 
i    9        7    321*98       -30  19  198  Coid.  Z.  Tii.  209. 

10        7    9  4X'45       -3126473  Cord.  Z.  vii.  626. 

-II         7  20  42*58       -32  26  370  8J  mag.  Equat  diff.  from  <?. 

'     e        7  17  4907       -32  22  133  Stone  3602. 

;  It        7  40  2234       -34  51  253  Cord.  Z.  vii.  2889. 

13  7  44  36'76       -35  27  144  8  mag.  Equat.  diff.  from  d. 
'd..     746    781       -35  30    4'8  Cord.  Z.  Tii.  3384. 

14  8    3  3403       -37    5  423  Coid. Z.  Tiii.  242. 

15  .    o    8  4070       -37  34  531  Stone  4207. 

16  8  28  -38  57  9  mag. 

17  8283519       -39  11  565  Cord.  Z.  Tiii.  2355.  .    ^ 
18.      84742-30      -4033288  Stone  4707. 

19  8  47  4877       -40  38  122  C.  Z.  Tiii.  3879 and Eq.  diff.  from  18. 

20  85416-86      -41    o    61  10  mag.  Equat.  diff  from  e. 
.«'.      8  53  2089      -40  54  362  Cord.  Z.  Tiii.  4288. 

.     21!       857    677       -4125     1-6  Stone  4803. 

;  22 1.     9  13  3<>*22       -42  38  146  10 mag.  Equat.  diff.  from  /. 

i.  /,       9  16  2932       -42  35  561  Cord.  Z.  ix.  1284. 

.    23!      9  15  55'8i       -42  48  49*  dnpL  10  mag.  Eq.  diff  from  24. 

'-"**!.      9  15    8*43       -4244176  CordZ.  ix.  1175. 

{   *$  -     9  19    739       -43    6  470  Cord.  Z.  ix.  1498. 

:  26!:     929    2*io       -44    3365  10 mag.  Equat  diff.  from g. 

'g        9  25     1-44       -44    2  254  Cord.  Z.  ix.  1985.  .      . 

-44  21  55-2  9  mag.  Equat.  diff.  from  h. 

-44  18  289  Coid.  Z.  ix.  2418. 

-44  29  317  9J  mag.  diff.  from  OZ.  ix.  2776. 

-44  39  287  Ooid.  Z.  ix.  2746. 

-44  49  12-5  ioj  m.  diff.  from  C.Z.  ix.  2715. 

-46  38    53  loj  m.  diff.  from  C.Z.  ix.  4184. 

-47  39    30  io^m.  diff.  from  C.Z.X.  #2>'     ; 

-48  22  1 3-9  Coid.  Z.  x.  493. 


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10    7    285 

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March  1887  Observations  of  Comets.  283 


Comet  1886  .  .  .  (Barnard  L) 

Adopted  Mean  Places  of  Comparison  Stars. 

Comp.  RA.  Declination  .    .fc    .. 

Star  No.  1886.  1886.  Authority. 

h    m       a  o       /       « 

1  4  33  42-53       -16  57  140    Oeltz.  Arg.  8.  3251. 

2  5  13  2866       -27  36  26-6    Oeltz.  Arg.  S.  3846. 

3  5  59    975       -37  3*  401    8101162762. 

4  6  10  3526       -39  24  592    9J  mag.  =  Stone  2926 1  ~$™  27"23- 

I  +  I    12  *2. 

5  6  22    753       -40  54  310    Stone  2995. 

-I  51  *3- 

7  6  48  (6)   -44  38     9  mag. 

8  6  49  (53)   -44  46     9  mag. 

9  7  6  52-    -  46  23  55*4  10  mag.  =  C.Z.  vii.  260 1  +  2"  5^'28* 
10    7  27  204   -48  21  527  Cord.  Z.  vii.  1876. 

n   8  13  (9)   -51  6     9  mag. 

12  814    288       -5120449    8Jmag.  =  C.Z.viii.i47i|"3™5^"57" 

{  —  o  44  *6. 

13  8  57  5745       -53  33  40-5     ioinag.  =  C.Z.viii.4702|^^ 

14  9    3    6'3i       -53  37  53*4    C.Z.  ix.  229. 

15  9    4  3787       -53  49  543    *$  mag.  =  C.Z.  ix.  4i6J  ~*£  *££' 

16  98  5078       -53  48  376    C.Z.  ix.  666. 

17  941  12*82       -552942-3    C.Z.ix.3183. 

18  9  49  2497       -55  51  401     C.Z.  ix.  3790. 
19.       9  54  52'*1       -56    7  423    C.Z.  ix.  4203. 


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Coma  1886  .  .  .  (Brooks!.). 
Adopted  Mean  Places  of  Comparison  Stan. 

h    m       s  o     /         « 

i  8  25    (42)  -  9    3  8  mag. 

2  8  31     897  —  9  19     76  Yarnall  3507, 

3  8  36  25-06  —  9  27  42*6  9  mag.  Equat.  diff.  from  a. 
«,  8  37  2363  -  9  23  495  W.B.  viii.  942. 

4  8  41    (48)  -  9  44  10J  mag.  =  ft|  +  j,  ^,'*°; 
•    6  8  40   (21)  —  9  49  9  mag. 

5  8  49    (7)  -  9  57  10J  mag.  =  <•  j  _  f/  ^  ' 
e  8  51   (32)  -  9  55  9n»g. 

6  97  44*44  —10  19  44' i  Santini  1142. 

7  9  14  1469  —10  42  410  Santini  1155. 

8  9  16    (3)  - 10  45  9  mag. 

9  941  1469  -11  24  411  |( Yarnall +  Santini). 

10  9  42  4704  —11  27  32:5  Santini  1199. 

11  9  57    651  -11  45  1 1-9  104  mag.  diff.  from  d. 
d  10    040*92  -11  51  37-6  9i  mag.  diff.  from  e. 

e  10    1     6-25  -11  55    s*i  W.B.  ix.  1277. 

12  10    3     i-oi  —11  57400  J(Schj.  +  diff.  from  \  Hydrse). 

13  10  12  25*08  -12    6     i*7  9linag. diff. fromW.B.X.U4 and X.204. 

14  10  14  30*74  .    -12    7  35*3  10  mag.  diff.  from  *  13  and  Lam,  711. 

15  10  19  51*90  —12  11     5-8  LamontZ.  711. 


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% 

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^▼m^ro**     —     rim  ^t-    ^  10    »n  —  ^    po 

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00     bsci     »sin»nitin»nbNd\^bvob     c>»    *»*    n     w     h   n    q 

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OflCI      **      OsM      N     in   00      ^-POOsOOsO      —      m     M      O      C»     O      «      *•      «*> 

Si    ^00     ts>r^i^vo     NNNNNNNNNNNO^OOOOOOOO 

O    O      O      **      «     toOv^vOsO     t>»00      O     O      u^vOl^O     —      »*     «** 
MffMCIClMClMM       —       mm       MMMCItO  •• 

*<  03  O 


March  1887. 


Observations  of  Comets. 


287 


•  o 

§**       O     **     «     to    *•    *o    »o  so     *^    *> 
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m  CO  to  co  ^  <*■ 

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+  +  +  +  +  +  +  +  +  + 


*  ^  «*>  v>  w  *  ro 

o  p  p  p  o  o  p 

fc  «  ei  ct  «  c*  « 

+  +  +  +  +  +  + 


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288 


R.  Observatory,  Cape  of  Good  Hope, 


xlyii,  5, 


Winnecke. 

Adopted  Mean  Placet 

r  of  Comparison  Stars. 

Coma 
Star  No. 

BJL 

z886'o. 

Declination 
z886'o. 

Authority. 

h    m       ■ 

0     /         u 

I 

13    7  5001 

—    O  30  56*2 

10  mag.  Eqnat.  diff  from  *  a. 

a 

13  13  791 

-  0  40    3-1 

Gopeland  and  Borgen  3986. 

2 

13    9  2976 

-  1    8  339 

Gopeland  and  Borgen  3979. 

3 

13  11  36-07 

-  1    4  568 

Gopeland  and  Borgen  3982. 

4 

13   12   I2'OI 

-  1  44  34*8 

9  mag.  one  Eqnat  diff.  from  *  b. 

b 

13  18  31-41 

-  1  42  543 

Gopeland  and  Borgen  3996. 

5 

13  16  (58) 

—  2  20 

10  mag.                                                                      j 

1 

6 

13  29  29-82 

-  4  20  585 

1 

W.B.  xiii.  465. 

7 

13  42  4132 

-  6  56  123 

io£  mag.  Eqnat.  diff.  from  *  c. 

c 

13  44  3332 

-  7    1  507 

Schjel.  4937-8. 

8 

14    7  4429 

-11    5  335 

10  mag.  Eqnat.  diff  from  *  d. 

d 

14    4  34- 19 

-11    5  55*9 

W.B.  xiv.  33. 

9 

IS    0  47*57 

- 19  46  540 

Oelts.  Arg.  S.  14264-5. 

10 

15    8  31-10 

-20  24  55-9 

o£  mag.  Eqnat.  diff.  from  *  e. 

e 

15    9  I3-I5 

-20  30  507 

Oelts.  Arg.  S.  14402. 

II 

15  11    S$S 

—21    9    7-6 

Wash.  Zones  255-18. 

12 

15  17  1560 

—21  56  407 

9  mag.  Eqnat.  diff.  from  *  /. 

/ 

15  14  5645 

-21  55  55  1 

Oelts.  Arg.  S.  14484. 

13 

15  22  2277 

-22  32    48 

9j  mag.  Eqnat  diff  from  *  g. 

9 

15  20  3067 

—  22  29  23*1 

Oelts.  Arg.  S.  1456 1. 

14 

15  52    095 

-26    0  593 

9  mag.  Eqnat.  diff.  from  *  h. 

h 

15  48  3685 

-25  55  43-6 

Stone  8647. 

IS 

15  56  4789 

—26  40  41*1 

i  (CZ.  3944  +  Eq.  diff.  C.Z.  4023). 

16 

16    1    7-41 

-27  25  27-3 

C.Z.  xvi.  30. 

17 

16  20  10' 10 

—29  12  14-0 

i  (OZ.  1357 +Eq.  diff.  C.Z.  1559). 

18 

16  24  5217 

-29  48  31-1 

i(CZ.  1653 +  Eq.  diff  C.Z.  1592). 

19 

18    1  39*62 

-35  56  22*6 

9$  mag.  Eqnat  diff  from  *  k. 

k 

17  58  41*47 

-36   I  367 

\  (Stone  9855  +  C.Z.  3937). 

March  1887. 

Observations  of  Comets.                             2 

Camp. 
Star  No. 

B.A. 

7886*0. 

Declination 
18860. 

Authority. 

h    m        b 

0      i       u 

20 

18  22    (13) 

-36  35 

.                ^  ,  [  +  2m  16*00. 
9*ma*'=  **{-!' 28"7. 

I 

18   19    (57) 

-36  33 

9  mag. 

21 

18  29  35-34 

-36  47    0*0 

g\  mag.  Eqnat.  diff.  from  *  m. 

m 

18  36  25*26 

-36  49  395 

Stone  10182. 

22 

18  42  4808 

-36  5*5  36*4 

OZ.  xviii.  2375. 

23 

18  48  27-34 

-37    1    81 

C.Z.  xviii.  2633. 

24 

19  34  3904 

-3*5  53  437 

J(C.Z.  1443  +  Stone  10615). 

25 

19  49  (28) 

-3*5  40 

9}  mag. 

26 

20    2  23*42 

-36  21  570 

9}  mag.  Equat  diff.  from  *  ». 

» 

20    3  4219 

-36  23  12-4 

Stone  10813. 

27 

21    2    (0) 

-33  45 

1                   f-o»37,*5o. 
9jmag.=  *.(_4/43;,25 

0 

21    2  (38) 

-33  40 

9jmag. 

28 

21    IO  10*21 

-32  25  494 

C.Z.  xxi.  608. 

29 

21  27  45  01 

-31  42  318 

oj  mag.  one  Eqnat.  diff.  from  *  p. 

p 

21  35  1581 

-31  46  43*8 

OZ.  xxi.  1065. 

30 

21  45  3440 

-30  21     56 

10  mag.  Eqnat.  diff.  from  #  q. 

9 

21  43  59*27 

-30  16  405 

C.Z.  xxi.  1353. 

3i 

21  52  5662 

—29  36    i*8 

£(OZ.  1644  + Stone  11567). 

32 

21  59  42*80 

-29  15  326 

C.Z.  xxi.  1870. 

33 

22    8  16*71 

—28  16  13*9 

$(<XZ.  232  +  Eq.  diff.  Stone  11657) 

T2 


290 


R.  Observatory i  Cape  of  Good  Hope, 


xlyii.  5, 


I 


I 


a 


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g,p         ^«mW  «n*ni/»«4w>«*^««Mnv'« 

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MMMMdeiMticteicotoM 


March  1887. 


Observations  of  Comets. 


291 


Is 


i- 
f 


MMMttcottcOttcONCOciCirororOro 


N    m    «     N    O      O      ^     O 

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• .      •        •        •        •        •        •        •        . 

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NSNNNNNOOOO      ^     »     <h     O 


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S 

3 
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a 
o 


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•        •••        •        •        •• 

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292  Cape  Observations  of  Comets.  XLvn.  5, 

Comet  18860  .  .  .  (Fiftiay). 
Adopted  Mean  Places  of  Comparison  Stars. 

•£?&  ££'  ^i^"011  Authority. 

Star  No.        x886'o.  1886  o.  * 

h     m        ■  a        1        it 

i  17    3  29*17  -26    5  52*8  =A.0. 16394 comp. with 0^5.373, 550. 

2  17    7  22*60  —26  10  40-4  9J  mag.  Equat.  diff.  from  *  1. 

3  17  11  1566  -26  11  250  J(OZ.  728  +  Equat diff. ftomOZ. 934). 

4  17  14  20*02  —26  19    7*6  C.Z.  xvii.  927. 

5  171421-17       -2623    4*1    G.Z.  xvii.  928. 

1  n  r,  .  „    f  + 1"  10*36. 

6  17  22  5409       -27  30  120    9$mag.  =  aZ.  I43°  {  +  7*  43*4. 

7  17  38  3393      -2636    00    9jmag.  =  A.O.  17142^^  **,**' 

8  17  54   (37)       -26  38  9i  mag.  =  *  a  j  ^  Jjj£j* 
a      17  58   (14)       -26  39            9  mag. 

9  18    4  10*42       —26  39  56*0    Wash.  Zones  100-56  and  36-93. 

(— om  5Q"*qo. 
-I9"*3. 
6       18  10   (10)       —26  36  9  mag. 

11  18  17    4*05  -26  30  16*8  I  (C.Z.  1037  +  Yamall). 

12  18  17  3371  -2633    33  J(C.Z.  1071+Yamall). 

13  18344440  -2624    31  9i  mag.  =  C.Z.l732{*l~*J* 

14  1844    8-22  —26    856*4  C.Z.  xviii.  2438. 

15  18  48  4462  —26    4  44*7  Wash.  Zones  127-24. 

16  19  48    700  - 23  56  511  9J  mag.  =  C.Z.  xix.  2002 1  ~^w.^°" 

17  20    5  2396      -22  56  556    9im^.  =  A.O.ao2d4J^r^i5' 


1—  O*  23B*6o. 


19  20304072  -2130    32  9jmag.  =  *c|~*"Ji7* 

e  20  31  48*47  -21  23  221  J(A.O.  20678  +  Wash.  i860). 

20  20345607  -21  13    48  (  =  A.0. 20744)  Wash  Zones  (2  obs.). 

21  20  45    0*76  —20  25  147  10}  mag.  Equat  diff.  from  *d. 
d  20  40    616  —20  26  457  9i  mag.  Wash.  Zones  190. 

22  20494778  —20    048*6  9  J  mag.  Equat.  diff.  from  *  «. 
e  20  45  4488  -20    4  12*8  Radclifie  Obs.  1 88 1. 

23  21     3  5645  -18  55  123  A.O.  21180. 

24  21  28  55*51  - 16  46  27*4  9  mag.  Equat.  diff.  from  */. 

/  21  27  22-21  -1642  157  (  =  A.O.  21468)  Edinburgh  Catalogue. 

25  21  39   (59)  - 1 5  48  9i  mag-  =  *  9  {  ~  ^T  *  „**5* 
g  21  42   (25)  -15  50  9  m*g. 

6  22173682  -12    445*8  10  mag.  Equat  diff.  from  *  h. 

h  22  12  5080  -12    7  387  £(Schj.  9115  +  Sant  2507). 

27  22  27  44-24  - 10  56  35-2  9$  mag.  Equat.  diff.  from  *  A. 


March  1887.  Mr.  Tebbutt,  Winnecke's  Comet.  293 

Comp.  RA.  Declination  a«*v— i*. 

No.        18W0.  1886-0.  Authority. 


// 


Ster  No.        1886-0.  1886-0. 

h    m       b 

*      22  31  1330  -10  51  39:i  J (Yaraall  9932  +  Sant.  2550). 

28  22  31  5993  - 10  25  27-6  9 J  mag.  I  Equat.  diffi  from  *  /. 

/      22  36  3073  -10  30  507  (  =  Lal.  44394-5)  Pa™  Obs.  1862. 

29  22  37     102  -  9  44  587  J(Sdg>SantiirJ). 

30  22  42  21-57  -911  131  9}  mag.  Equat.  diff.  from  *  m, 
m      22  45  48*20  -  9    9  45*1  Schjellerup  9365. 

31  23    930*02  -  6    931*0  10  mag.  Equat.  Diff.  from  * ». 

»      23  12    217  —  6    8  22*5      9  mag.  Aatr.  Nach.  lxxzri.  p.  215. 

32  23  27    3*80  -  3  38  44*1  Karlsruhe  Zones  (Valentaoer). 

33  23  33  (22)  -  3    5  9*  mag. 


Observations  of  Winnecke's  Oomet,  1886,  made  at  Windsor,  New 

South  Wales.     By  John  Tebbutt. 

Notice  of  the  discovery  of  this  comet  at  the  Gape  of  Good 
Hope  was  received  here  on  August  25.  The  comet  was  found  on 
the  same  evening,  and  observations  of  it  continued  as  long  as 
possible.  As  it  was  at  no  time  bright  enongh  to  admit  of  ob- 
servation in  an  illuminated  field,  and  there  were  no  means  of  illu- 
minating the  threads  of  the  filar  micrometer  on  a  dark  field,  I 
was  obliged  to  have  recourse  to  a  dark  field  micrometer.  Of  the 
accompanying  positions  those  for  August  were  determined  with 
a  square  bar-micrometer  on  the  Cooke  4^ -inch  Equatorial.  On 
Sept.  1  a  ring-micrometer,  whose  mean  radius  =  242^*6,  was 
fitted  to  the  recently  mounted  Grubb  8-inch  Equatorial,  and  with 
this  instrument  observations  were  continued  till  Sept.  18,  when 
the  square  bar-micrometer  hitherto  employed  with  the  4^-inch 
telescope  was  adapted  to  the  large  instrument.  With  this  micro- 
meter, whose  adjustment  and  errors  of  form  were  carefully 
attended  to,  the  remaining  positions  were  obtained.  The  comet 
was  at  no  time  a  good  object  for  observation,  and  in  consequence 
of  either  bright  moonlight  or  haze,  such  was  particularly  the  case 
on  Sept.  2,  7,  10,  11,  12;  Oct.  6,  7,  11,  25  and  29.  On  Oct.  25 
it  approached  so  close  to  star  No.  59  as  to  be  observed  with  the 
greatest  difficulty.  On  the  whole  I  think  the  positions  yielded 
by  the  square  bar-micrometer  will  be  found  more  satisfactory 
than  those  obtained  with  the  ring.  Finlay's  comet  was  observed 
with  the  large  Equatorial  from  Oct.  8  to  Dec.  30. 

I  may  add  that  the  tail  of  a  large  comet  was  visible  on  the 
W.S.W.  horizon  immediately  after  sunset  on  the  evenings  of  the 
19th,  20th,  and  21st  inst.  at  several  places  in  the  neighbouring 
colonies.  At  Windsor,  however,  the  past  few  days  have  been 
characterised  by  dense  cloud,  with  rain,  so  that  no  opportunity 
whatever  was  afforded  for  getting  even  a  glimpse  of  the  stranger. 


294 


Mr.  Tebbutt,  Observations 


xlyii.  5, 


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302  Mr.  Finlay,  Elements  of  Oomet  1886  e.         xlyil  5, 


Elements  of  Oomet  1886  e  (Finlay).    By  W.  H.  Finlay,  M.A. 

The  following  elements  represent  my  observations  of  this 
comet  closely.  A  normal  place  was  deduced  from  the  observa- 
tions on  September  26,  27,  29,  and  30,  and  another  from  those 
on  December  13,  15,  16  and  17 ;  these  were: 


Sept.  28*5 

a -256  48  3#* 

8»  —  26  10  51-0 

Dec    15*5 

a=336  51  52*2 

5= -10  49  160 

From  these,  by  varying  the  geocentric  distances  to  satisfy  the 
observations  on  October  21,  November  13,  and  December  27  (on 
which  dates  very  good  places  were  available  for  the  comparison 
stars),  I  obtained  the  elements 

T-  Nov.  22391 8,  G.M.T. 


Ecliptic  and  Mean 
Equinox  18860 


00 

0        /      // 
3i5    5  47*o| 

Q 

52  29  152 

i 

3     1  38-6J 

* 

45  5*  51*6 

log  a 

0*5482066 

M 

534"'19» 

The  representation  of  the  observations  on    October  21,  No- 
vember 13,  and  December  27  is 

C-0 


<2Aas  0 

d$ 

Oct. 

21 

+  07 

u 

+  3'3 

Nov. 

13 

+  o-6 

+  5'i 

Dec. 

27 

-0-8 

—  2-9 

I  discontinued  my  observations  when  the  oomet  passed  to 
the  north  of  the  equator,  and  was  more  favourably  situated  for 
observation  in  the  northern  hemisphere,  so  that  I  have  no  later 
date  than  December  27  to  compare  with  the  elements.  The 
discordances  in  latitude  are  persistent  in  all  the  variations  of  the 
distances.     The  heliocentric  co-ordinates  are 


u 


x- [99996185]  r  sin  (97  32  430  +  v) 
y  ■  [9*9562980]  r  sin  (8  40  46-9  +  1/) 
£.[96324689]  r  sin    (2  28  49'5  +  v) 


Royal  Observatory,  Cape  of  Good  Hope: 
1887,  February, 


March  1887.  Mr.  Finlay,  Comet  1887  a.  303 


Comet  1887  a.     By  W.  H.  Finlay,  M.A. 

The  tail  of  this  remarkable  comet  was  first  seen,  so  far  as  I 
am  aware,  by  a  farmer  and  a  fisherman  at  Blauwberg  (near 
Cape  Town),  on  Tuesday  night,  January  18 ;  the  next  evening 
it  was  seen  at  Grahamstown,  Fraserbnrg,  Ac. ;  our  first  view  of 
it  at  the  observatory  was  on  January  22.  It  presented  the 
appearance  of  a  pale  narrow  ribbon  of  light,  quite  straight,  and 
of  nearly  uniform  brightness  throughout  its  length.  There  was 
no  head  or  condensation  of  any  kind  visible  near  the  end,  the 
light  simply  fading  away  to  nothing.  The  comet  was  lost  in  the 
6-inch  Equatorial  long  before  the  end  of  the  light,  as  visible  to 
the  naked  eye,  was  reached.  The  following  rough  observations 
were  made  by  tracing  the  tail  down  as  far  as  possible  with  the 
finder  of  the  6- inch  and  reading  the  circles  of  the  Equatorial. 
On  January  24  and  27  the  circles  were  also  read  for  the  centre 
of  a  very  slightly  more  condensed  part  of  the  tail,  extending  over 
about  half  a  degree.  A  star  near  the  same  position  was  also 
observed  in  a  similar  manner  each  evening.  The  resulting 
places  are : 


Date. 
Jan.  22 

Cape  M.T. 
h  m 
8  50 

App.  R.A, 

h  oi   1 

21  30  O 

App.  Dec 

-45  47j 

23 

8  44 

21  47  54 

-46  32J 

24 

8  50 

22  8  15 

-47  35 

24* 

8  55 

22  9  20 

-47  54-V 

25 

9  4 

22  30  44 

-48  39 

27 

8  58 

23  16  10 

-49  38 

27* 

9  35 

23  17  11 

-49  5o 

28 

9  38 

23  37  12 

-49  22 

The  observations  marked  *  are  of  the  centre  of  the  slightly 
brighter  part  of  the  tail.  Moonlight  put  a  stop  to  any  further 
observations.  The  tail  was  sketched  each  night  on  a  map 
copied  from  Gould's  Uranometria ;  it  was  quite  straight  at  first, 
but  on  the  27th,  28th,  and  29th  a  slight  curvature  was  per- 
ceptible. 

The  physical  appearance  of  the  comet,  its  long  straight  tail 
of  no  greater  brilliancy  than  the  smaller  Magellanic  cloud,  and 
the  absence  of  head  at  once  recalled  to  mind  the  comet  of 
February  1880,  and  as  soon  as  I  had  secured  a  place  on 
January  22  I  tried  whether  the  observed  place  could  result 
from  the  elements  of  that  comet.  I  found  that  it  could  very 
nearly  with  a  true  anomaly  of  i68°*7  and  perihelion   passage 

z 


Mr.  Finlag,  Comet  1887  a. 


XL VII.  J, 

a  very  similar 


From  the  observations  t 
following  orbit : 


jHDUiiy  37,  9*  15-  C.M.T. 
»8,  g"  35-      „ 
29,  9*  15"      « 


:  Janaary  22,  25,  and  28  I  find  the 


T  =  J«n   Il°l44,  G.M.T. 


Thin  orbit  satisfies  the  middle  place  in  longitude,  bat  leaves  a 
discordance  of  4'  in  latitude.  These  elements,  though  of  conrse 
rough,  prove  conclusively  that  the  comet  belongs  to  the  family 
of  '  Sun-grazers,'  of  which  1843  I.,   1880  I.,  and  1882  II.  are 

members. 


March  1887.     Mr,  Todd,  Obsereation*  of  Cumet  1 


Observations  of  Comet  1887  a,  made  at  the  Observatory,  Adelaide. 
By  Charles  Todd. 

[Extracts  from  letters  to  ths  Atlronomer  Royal.) 

A  few  words  about  the  new  comet  which  baa  suddenly  burnt 
into  view  ha  the  8.  W.  1  sent  yon  a  telegram  through  Mr.  Hesse 
on  Friday,  the  21st,  which  I  hope  yon  received,  and  I  now  en- 
close a  rough  sketch-map  showing  its  positions  on  Jan.  20th  to 
Jan.  27th.  It  was  first  seen  on  the  19th,  bnt  at  the  Observatory, 
by  myself,  not  till  the  20th,  shortly  before  9  p.m.  The  head  of 
the  comet  was  then  hid  by  the  mists  of  the  horizon,  bnt  the  tail 
pawed  nearly  midway  between  a  Gruis  and  a  Pavonit,  or  over 
y  Indi,  extending  to  and  a  little  to  the  right  of  y  Pavonit. 


On  the  21st  it  was  better  seen  aad  the  head  of  the  comet  was  close 
to  a  small  star,  or  roughly  (at  9  p.m.)  11. A.  2ih  $m,  Dec].  42"  34'. 
The  tail  of  the  comet,  as  measured  round  the  horizon,  had  sensibly 
moved  to  the  north  or  towards  a  Qruis  ;  it  passed  a  little  to  the 
right  of  y  Indi,  and  to  the  left  of  a  and  8  Toucini,  and  could  be 
traced  a  little  higher  in  the  direction  of  fi  Hydri,  On  the  22nd, 
at  8h  30™,  the  position  of  the  head  of  the  comet  was  roughly 
H.  A.  2i1,2om3o*,  Peel.  44°  17'.  The  comet  has  a  long  narrow  tail 
of  about  30s,  bat  no  well-defined  nucleus,  resembling,  in  fact, 
very  closely  in  appearance  the  comet  of  Feb.  1880,  which  during 
its  short  season  of  visibility,  you  will  remember,  occupied  the 
same  part  of  the  sky,  and  came  into  view  equally  suddenly.  I 
will  follow  it  np  on  every  clear  night  and  advise  you  again.  In 
the  meantime  this  will  bo  usofnl  in  comparing  with  observations 
made  elsewhere,  and  may,  perhaps,  be  of  some  uxo  in  getting  a 
rongh  orbit. 


306  Mr,  Stone,  The  Moon  and  Aldebaran.         xlvii.  5, 

The  following  are  the  only  positions  of  the  comet  I  was  able 
to  secure  before  the  Moon  shut  it  oat.  Although  a  conspicuous 
object,  about  as  bright  at  first  as  the  Magellan  clouds,  it  became 
rapidly  fainter,  and  at  no  time  was  there  any  defined  nucleus*  or 
condensation  about  the  head.  It  was  simply  a  narrow  nebulous 
streak  of  about  300  long,  and  although  with  the  naked  eye,  or 
with  an  ordinary  field-glass,  the  position  of  the  head  of  the  comet 
could  be  fairly  determined,  yet  seen  through  the  Equatorial  the 
head  was  so  diffused  and  died  awayso  gradually  that  it  was  quite 
impossible  to  say  where  it  was.  The  positions  I  give  are  con- 
sequently mere  rough  approximations  obtained  by  the  Equatorial, 
checked  by  the  naked  eye. 

On  the  24th,  at  9  p.m.,  the  head  of  the  comet  was  partly  over 
and  a  little  to  the  right  of  a  Oruis,  which  star  appeared  as  a 
bright  stellar  nucleus. 

On  the  20th  the  head  was  in  the  midst  of  the  group  rl,  r*,  t3 
Qruis,  the  tail  passing  between  A2  and  58,  and  overt  Toucani  and 
to  the  left  of  a  Hydri. 

On  the  27th  the  head  of  the  comet,  a  very  diffused  nebulous 
mass,  appeared  to  be  cut  off  by  a  wide  break  or  rift,  from  the  tail, 
and  higher  up  there  was  another  narrow  break  in  the  continuity 
of  the  tail.  Both  of  these  breaks  might  be  attributable  to  small 
clouds,  but  we  could  see  faint  stars  through  the  breach  which 
seemed  to  forbid  such  a  supposition  : 


21 

h 
9 

R.A. 
h     111 

21      5 

Dec. 

0     1 

-42  34 

22 

9 

21    21 

44  17 

25 

9* 

22   22 

48  18 

26 

940 

22  47 

49  14 

27 

915 

23    9 

49  39  guess  work 

I  shall  be  curious  to  know  how  these  agree  with,  perhaps 
better,  positions  obtained  elsewhere.  I  send  them  hoping  they 
may  at  least  be  useful  in  identifying  the  comet  which  I  am 
disposed  to  regard  as  a  fragment  of  some  previous  visitor. 


The  Moon  and  Aldebaran,  1887,  March  2,  5h  45m  to  6b  om  Q.M.T., 
ob  seen  at  the  Badcliffe  Observatory,  Oxford.  By  E.  J.  Stone, 
M.A.,  F.R.S. 

The  occultation  of  Aldebaran  by  the  Moon  predicted  to  take 
place  on  1887,  March  2,  was  carefully  looked  for  at  the  Radcliffe 
Observatory,  but  though  an  extraordinarily  near  appulse  took 
place  there  was  no  occultation  at  Oxford.     The  overlapping  of 

*  A  nucleus  was  observed  by  Mr.  Eddie  of  Grahamstown,  on  Jan.  24,  25, 
and  26. — Ed. 


March  1887.    Mr.  T.  O.  Elger,  Approach  of  Moon  to  a  Tawri.      307 

the  image  of  the  Moon's  limb  and  the  diffraction  image  of  the 
star  appears  to  render  a  record  of  these  observations  desirable. 
The  following  notes  were  made  by  the  observers : 
Mr.    Wickham,  with    heliometer,   7^-inch   object-glass,   and 
power  as  200 : 

*  The  star  did  not  disappear,  but  skirted  the  north  limb. 
The  exterior  flames  of  the  star's  image  on  the  side  next  the 
Moon  were,  at  times,  lost  in  the  Moon's  disc,  although  there 
was  a  strong  contrast  between  the  quality  of  the  Moon's  light 
and  that  of  the  star.  The  Moon's  colour  was  a  dead  creamy 
white,  the  star's  a  brilliant  light  orange.  The  close  contact  of 
the  star's  disc  to  that  of  the  Moon  lasted  without  apparent  change 
for  nearly  three  minutes.  The  nearest  appulse  took  place  close 
to  the  division  of  the  illuminated  and  defective  limbs.  There 
was  very  strong  twilight.' 

Mr.  Robinson,  with  Marlborough  telescope,  3^-inch  object- 
glass,  and  power  =  80 : 

'The  star  was  not  occulted,  but  it  apparently  grazed  the 
Moon's  N.  limb ;  three  or  four  minutes  previous  to  this,  or  about 
5h  47m  G.M.T.,  the  Moon's  periphery  when  produced  beyond  the 
N.  cusp  appeared  to  bisect  the  star.  The  dark  limb  of  the  Moon 
was  not  visible  owing  to  twilight.  The  colour  of  the  star  greatly 
contrasted  with  that  of  the  Moon,  being  orange-red  throughout.' 

Mr.  Bellamy,  with  10-foot  telescope,  7 -inch  object-glass, 
power  125  : 

*  The  star  was  not  occulted,  but  the  outer  rings  of  the  image 
were,  at  times,  in  contact  with  and  a  small  portion  lost  sight  of 
in  the  illumination  of  the  Moon's  limb.  The  time  when  I  esti- 
mated that  the  star  was  nearest  the  bright  limb  of  the  Moon  was 
about  5h  5i£m  G.M.T.' 


Note  on  the  Near  Approach  of  Moon  to  a  Tauri. 
By  Thomas  Gwyn  Elger. 

Though  this  object  was  not  actually  occulted  here  on  March  2, 
the  exceedingly  near  approach  of  the  Moon  and  star  was  watched 
with  much  interest,  as  it  seemed  probable,  when  the  time  drew 
near,  that  it  might  suffer  a  momentary  eclipse  by  some  of  the 
elevations  on  the  Moon's  northern  limb.  Between  5h  49™  and 
5h  54m  it  appeared  to  be  almost  in  contact  with  one  of  these, 
without,, however,  its  light  being  visibly  affected.  The  position 
of  my  observatory,  according  to  the  6-inch  scale  map  of  the 
Ordnance  Survey,  is  N.  Lat.  520  7'  10",  W.  Long.  2  mins.  04  sec. 
A  power  of  150  was  used  on  a  8^-inch  Calver  Reflector. 

Kempston,  Beds  : 

1887,  March  5. 


£o8  Mr.  Prince^  Occtdtation  of  Aldebaran.  xlvh.  5. 


Second  OccuUation  of  Aldebaran,  1887.     By  the 

Bev.  S.  J.  Johnson. 

In  marked  contrast  to  the  occult ation  period  of  1866-9,  when 
only  one  emersion  of  Aldebaran  was  visible  from  my  place  of 
observation  and  no  immersion,  the  second  passage  of  the  Moon 
over  the  star  visible  here  this  year,  on  March  2,  was  seen  nnder 
a  sky  even  more  favourable  than  the  first.  Parallax  slightly 
lengthened  the  duration  as  compared  with  Greenwich.  Immer- 
sion 5h  40™  53s,  quite  as  instantaneous  as  last  January.  Sun 
had  reached  the  horizon  but  had  not  descended.  At  6h  om  56s 
Aldebaran  clear  of  the  Moon's  limb,  but  visible  on  the  bright  edge 
five  seconds  before  this.  The  illusion  conveyed  to  the  eye  at 
emersion,  probably  from  the  smallness  of  the  instrument  and 
power,  50  on  3^  inches,  was  that  the  star  was  shining  through 
the  bright  limb.  The  only  time  I  have  had  this  impression  be- 
fore was  during  the  totality  of  the  eclipse  of  August  23,  1877, 
when  three  or  four  small  stars  appeared  within  the  reddened 
disk  for  8  or  10  seconds  before  actually  disappearing.  The  same 
impression  appears  to  have  been  conveyed  to  the  eyes  of  ob- 
servers at  Greenwich  and  elsewhere  on  the  occasion  of  the 
bccultation  of  October  15,  1829. 

Mdplash  Vicarage,  Dorset : 
March  9. 


The  OccuUation  of  Aldebaran.     By  C.  Leeson  Prince. 

I  observed  the  occupation  of  Aldebaran  this  evening  under 
very  favourable  circumstances ;  the  Moon  being  so  near  the 
meridian,  the  Sun  had  just  set,  and  the  atmosphere  was  very 
calm,  clear,  and  diaphanous;  nevertheless,  the  non-illuminated 
portion  of  the  Moon  was  not  visible. 

The  disappearance  occurred  at  4b  25™  57*,  and  the  reappear- 
ance at  4h  48™  37s,  local  sidereal  time.  The  star  was  occulted, 
therefore,  exactly  22m  40s. 

The  disappearance  was  absolutely  instantaneous,  but  the 
reappearance  not  quite  so,  a  very  minute  point  of  light  being 
visible  for  nearly  a  second  before  the  star  completely  emerged  ; 
this  may  perhaps  have  been  occasioned  by  a  slight  elevation  on 
the  lunar  surface  at  the  exact  point  of  reappearance.  Telescope 
68  inches  aperture,  focal  length,  12  feet;  mag.  power,  144. 

The  Observatory,  Crowhorough,  Sussex : 
1887,  March  2. 


MONTHLY    NOTICES 

or  THE 

ROYAL  ASTRONOMICAL  SOCIETY. 

Vol.  XLVIL  April  6,  1887  No.  6 

Edwin  Dunkin,  F.R.S.,  Vice-President,  in  the  Chair. 

The  Rev.  John  Bone,  St.  Thomas's  Vioarage,  Lancaster ; 

W.  F.  Caborne,  Lieut.  R.N.R.,  F.R.G.S.,  F.R.Met.Soc,  4 
Cambridge  Gardens,  Notting  Hill,  and  Royal  Navy  Club, 
Grafton  Street,  W. ; 

Campbell  M.  W.  Hepworth,  Lieut.  R.N.R.,  60  Matlock  Lane, 
Ealing  Dean ;  and 

William  Frederick  Smith,  F.R.Hist.Soc,  51  Perham  Road, 
West  Kensington,  S.W., 

were  balloted  for  and  duly  elected  Fellows  of  the  Society. 


On  the  Choice  of  Instruments  for  Stellar  Photography. 
By  Howard  Grubb,  F.R.S. 

In  view  of  the  Astronomical  Congress  about  to  be  held  in  Paris, 
the  subject  matter  of  its  deliberations,  viz.  stellar  photography,  is 
naturally  attracting  much  attention  at  present  among  astronomers ; 
and  I  venture  to  hope  that  a  few  notes  which  I  have  put  together 
on  this  snbject  may  not  be  without  interest  to  the  Fellows  of  the 
Society.  At  the  same  time  I  desire  to  premise  that  I  submit  them, 
not  with  an  idea  that  they  possess  any  peculiar  originality,  but 
more  as  suggestions,  and  as  tending  to  show  the  great  number  and 
diversity  of  points  which  will  require  to  be  thoroughly  discussed 
before  coming  to  a  satisfactory  conclusion  as  to  the  best  instru* 
^mental  equipment  to  satisfy  all  the  conditions  which  arise  in 
undertaking  this  new  class  of  astronomical  work. 


310  Mr.  Grvbb,  On  the  Choice  of  xlvii.  6, 

The  first  and  most  important  question  to  be  decided  is 
whether  a  refracting  or  reflecting  telescope  is  likely  to  give  the 
best  results.  Theoretically  considered,  the  reflector  would  appear 
to  have  a  considerable  advantage,  for  in  it  there  is  no  dispersing 
of  the  rays.  If  the  spherical  aberration  be  properly  corrected, 
all  the  rays  are  brought  to  the  same  focus ;  whereas  in  the  refrac- 
tor it  is  not  so.  If  the  curve  formed  by  the  foci  of  the  different 
rays  of  the  spectrum  be  examined,  in  the  case  of  a  refractor,  it 
will  be  seen  that  with  any  possible  combination  of  existing 
glasses,  or  arrangements  of  same,  a  very  small  portion  only  of 
the  whole  light  can  be  brought  to  one  focus  on  the  photographic 
plate ;  again,  the  field  of  the  reflector  is  theoretically  flatter ;  but 
at  the  same  time,  as  pointed  out  by  Lieut.-Gen.  Tennant  at  last 
meeting,  a  considerable  amount  of  "  coma  "  is  to  be  found  in 
lateral  pencils  of  the  reflector,  which  coma  causes  distortion  of 
the  star  discs. 

Generally,  however,  the  advantage  appears  to  be  on  the  side 
of  the  reflector.  It  was  for  these  reasons  that,  when  consulted 
some  time  ago  by  Mr.  Roberts  of  Liverpool,  I  advised  his  adop- 
tion of  the  reflector  in  preference  to  the  refractor  for  photo- 
graphic purposes. 

The  value  of  Lieut.-Gen.  Tennant's  papers  would  have  been 
largely  increased  had  he  gone  a  little  further,  and  shown  what 
the  comparative  results  would  be  for  the  lateral  pencils  of  a 
refractor.  Nor  would  this  be  at  all  impracticable ;  for,  although 
the  result  may  vary  with  different  constructions  of  objectives,  it 
would  still  have  been  interesting  to  study  the  effect  on  the  one  ordi- 
nary form  of  double  objective  (corrected,  of  course,  for  chemical 
rays)  such  as  I  have  constructed  for  Dr.  Gill,  and  such  as  is,  I 
believe,  also  used  by  the  MM.  Henry.  At  the  time  I  came  to 
the  above  conclusion  respecting  the  superiority  of  the  reflector  I 
had  nothing  to  guide  me  but  deductions  from  theoretical  con- 
siderations. Since  then,  however,  the  work  of  the  MM.  Henry 
at  Paris,  and  Dr.  Gill  at  Cape-Town,  with  refractors,  and 
Mr.  Roberts  at  Liverpool,  with  a  reflector,  present  some  prac- 
tical results  from  which  to  draw  further  deductions,  and  while 
I  readily  admit  that  the  refractors  have  done  better  work  than  I 
had  expected,  I  am  by  no  means  prepared  to  admit  without 
further  demonstration  that  under  equal  conditions  they  may  be 
expected  to  do  better  work  than  the  reflectors. 

I  have  not  myself  had  an  opportunity  of  comparing  the 
negatives  taken  by  the  reflector  and  refractor ;  but  I  understand 
from  those  who  have  that  while  the  star  discs  in  Roberts'  (re- 
flector) photographs  show  in  all  parts  a  slight  want  of  symmetry, 
there  is  no  decided  elongation  of  the  discs  up  to  8o;  from  centre 
of  field,  whilst  in  the  refractor  photographs  there  is  a  decided 
distortion  at  that  distance.  The  want  of  perfect  symmetry  in 
Roberts'  photographs  is  probably  due  to  the  fact  that  the  power 
of  his  finder,  as  compared  to  the  main  telescope,  is  not  nearly  so 
great  as  is  used  in  the  case  of  the  refractor. 


April  1 88  7 .       Instru merits  for  Stellar  Photography.  311 

No  doubt  Mr.  Roberts  has  not  produced  the  same  Dumber  of 
equally  fine  plates  as  the  MM.  Henry ;  but  when  we  wish  to 
compare  results  with  a  view  of  drawing  a  comparison  between 
the  value  of  the  instruments  which  have  produced  those  results, 
it  is  right  and  just  to  take  the  best  specimens  of  each  (not  the  aver* 
age),  for  the  inferiority  of  any  examples  which  are  of  an  excel- 
lence less  than  the  best  must  be  attributed  to  some  unfavourable 
conditions  outside  the  instrument,  not  in  it.  An  inferior  instru- 
ment cannot*,  under  any  circumstances,  give  a  good  result ;  and 
Mr.  Roberts1  best  specimens  appear  to  me  to  compare  vary 
favourably  with  those  done  by  the  refractors. 

In  making  the  comparison  due  regard  must  be  had  to  the  fact 
that  the  atmosphere  of  Liverpool  is  of  very  inferior  quality  as 
compared  to  that  of  either  Paris  or  Gape-Town,  and  also  that  Mr. 
Roberts'  photographs  show  an  enormously  increased  number  of 
stars  on  account  of  the  large  aperture  of  his  instrument ;  but  that 
very  large  aperture  requires  of  course  a  still  greater  degree  of 
perfection  of  atmosphere  in  order  that  its  full  power  may  be 
utilised.* 

I  do  not  for  a  moment  dispute  the  fact  that  most  excellent 
results  can  be,  and  have  been,  produced  by  a  refractor ;  but  it 
appears  to  me  that  it  would  be  very  unwise  to  spend  large  sums 
ex  money  in  the  installation  of  several  large  refractors  over  the 
world  without  some  further  and  more  crucial  comparative  expe- 
riments as  to  the  relative  fitness  of  refractor  and  reflector  for 
this  particular  work.  Mr.  Roberts  has  certainly  shown  that  most 
excellent  work  can  be  done  with  the  reflector  ;  but  his  instrument 
is  not  comparable  with  the  refractors  which  have  been  at  the 
same  work  either  as  regards  size,  position,  or  many  other  respects. 

It  i«,  no  doubt,  highly  desirable  that  the  important  work  of 
mapping  the  heavens  should  be  commenced  with  as  little  delay 
as  possible  ;  but  it  would  be  equally  regrettable  if  in  the 
beginning  a  large  amount  were  expended  on  instruments  which 
proved  after  a  little  to  be  not  the  very  best  for  the  purpose.  I 
would  venture  to  suggest,  therefore,  that  a  really  fair  competitive 
trial  be  made  between  refractors  and  reflectors,  to  test  their  fitness 
for  celestial  photography,  before  any  definite  decision  be  arrived 
at.  This  need  by  no  means  impede  or  hamper  the  work  of  the 
Congress  in  deciding  other  questions  which  could  be  made 
dependent  on  the  results  of  these  trials,  and  six  months  would 
probably  decide  the  question. 

In  the  photographing  of  nebula?  there  can  be  no  doubt  what- 
ever as  to  the  superiority  of  the  reflector,  for  in  this  case  increase 
of  angular  aperture  means  increase  of  light  and  reduction  of  ex. 

*  Since  writing  above  I  hare  received  information,  founded  on  practical 
results,  which  materially  strengthens  my  views.  Professor  Pritchard  has  suc- 
ceeded in  producing  photographs  with  the  Be  la  Rue  reflector,  in  which  the 
images  at  80'  from  centre  are  sensibly  circular,  while  at  same  distance  in  MM. 
Henry's  (refractor)  plates  the  small  star  discs  are  ellipses,  the  proportion  of 
whose  major  and  minor  axes  are  9  to  4. 

A  A  2 


312  Mr.  Qrubb,  On  the  Choice  of  xlvii.  6, 

posure,  and  the  angular  aperture  of  reflectors  can  be  increased 
far  beyond  what  is  possible  in  case  of  refractors. 

In  connection  with  the  optical  portion  of  the  instrument  there 
are  a  great  number  of  important  points  which  it  would  be  most 
desirable  to  discuss  ;  and  I  mention  some  of  these,  not  so  much 
with  a  view  of  giving  my  own  individual  opinion  about  them, 
as  in  the  hope  of  eliciting  opinions  from  others,  and  having  them 
fairly  and  folly  discussed. 

Effect  of  Increase  of  Actual  Aperture. — Theoretically,  so  far  as 
star  discs  are  concerned,  the  brilliancy  shonld  increase  as  the 
square  of  the  aperture.  Long  since,  in  discussing  this  with  Dr. 
Huggins  and  Mr.  Roberts  (before  I  had  any  practical  results  to 
guide  me),  I  stated  that  I  thought  it  very  likely  that  the  increase 
of  brilliancy  would  not  be  in  such  a  high  ratio ;  for  practically 
the  discs  (of  large  stars  at  least)  are  not  mathematical  points. 
Practice,  I  think,  has  corroborated  this  view ;  but  more  details 
are  required  to  make  it  quite  clear. 

Effect  of  Increase  of  Angular  Aperture. — The  actual  aperture 
remaining  the  same,  reduction  of  focus  or  increase  of  angular 
aperture  ought  not  to  increase  the  brilliancy  of  star  discs ;  but, 
for  the  same  reason  as  above,  it  would  appear  that  it  does  so  to 
some  considerable  extent. 

This,  however,  is  also  a  question  that  requires  more  experi- 
ments to  enable  us  to  come  to  a  decision  upon. 

Field  of  View. — In  a  refracting  telescope  the  field  of  view  is 
limited  simply  by  the  amount  that  can  be  covered  by  the  objective 
with  sufficiently  good  definition. 

In  a  reflector  the  conditions  are  much  more  complicated. 

If  the  focus  be  made  long  the  field  is  flatter  and  can  be  used 
larger ;  but,  on  the  other  hand,  the  photographic  plate  and  carrier 
begin  to  stop  out  an  inconveniently  large  portion  from  the  centre 
of  the  pencil  of  light. 

If  the  focus  be  shortened  a  smaller  plate  will  take  in  the  same 
angular  quantity  of  field,  but  that  field  will  not  be  so  flat. 

There  appears,  therefore,  to  be  some  proportion  that  will  be 
found  to  be  best. 

So  far  as  present  results  go,  they  tend  to  show  that  with 
either  a  refractor  or  reflector  a  field  of  about  2°  x  2°  is  the  maxi- 
mum attainable  with  really  good  definition.  Much  larger  fields 
may  be  obtained  with  combination  of  lenses ;  but  these  are  useless 
for  the  purpose,  as,  the  pencils  not  being  all  centrical,  a  certain 
amount  of  distortion  is  inevitable. 

Silver.on- Glass  or  Metallic  Mirrors  to  be  used, — Silver-on- glass 
mirrors  are  now  so  universally  used,  and  so  cod  venient  on  account . 
of  their  lightness,  that  it  may  seem  almost  useless  to  discuss  this. 
However,  if  the  very  best  result  is  aimed  at,  I  am  inclined  to 
think  it  might  be  well  to  institute  some  experiments  to  test  the 
relative  reflective  powers  of  speculum-metal  and  silver  for  those 
rays  which  are  used  for  forming  the  image  on  the  photo- 
graphic plate.     There    are    good    grounds  for  supposing  that 


April  1 887 .       Instruments  for  Stellar  Photography.  313 

speculum-metal  is  more  highly  reflective  for  chemical  rays  than 
silver. 

Long  since  I  obtained  photographs  of  the  Moon  with  the  Mel* 
bourne  telescope,  with  exposure  of  from  quarter  to  half  a  second, 
using  the  old  collodion  process  and  no  peculiarly  rapid  process. 
Plates  are  now  made  50  to  100  times  as  rapid  as  this  old  process, 
but  I  have  never  aB  yet  heard  of  any  photographs  of  the  Moon 
having  been  taken  with  a  silver-on-glass  mirror  in  -g^-th  or  ?-J  6th 
of  a  second.  An  idea  has  been  thrown  out  that  the  field  of  a 
reflector  could  be  improved  by  modifying  the  figure  of  the  mirror. 
This  is  quite  impracticable,  as  any  modification  whatever  would 
affect  the  definition  of  the  central  pencil. 

It  has  been  objected  to  reflectors  that  the  film  or  surface  is 
liable  to  tarnish,  and  therefore  these  instruments  are  not  so 
stable,  and  are  therefore  less  suited  for  long-continued  observa- 
tions. 

Metallic  mirrors,  if  the  metal  is  good,  I  believe  to  be  almost 
as  stable  as  an  object-glass;  but  even  if  not  so,  this  is  a  point  of 
little  consequence,  for  Mr.  Roberts  tells  me  that  under  ap- 
parently equal  conditions  of  atmosphere  he  sometimes  obtains 
three  times  the  number  of  Btars  in  the  same  locality  as  at  other 
times. 

With  such  an  enormously  variable  factor  as  this  to  deal  with, 
B  slight  variation  in  the  condition  of  the  film  is  of  little  account. 

Best  Size  of  Instrument  to  adopt. — The  larger  the  instrument 
the  shorter  the  exposure  necessary  to  obtain  an  image  of  a  star  of 
any  given  magnitude;  but  the  difference  in  this  respect  will 
probably  not  (as  I  have  before  said)  be  on  as  high  a  ratio  as 
the  theoretical — viz.  square  of  aperture. 

On  the  other  hand,  the  larger  the  instrument  the  more 
difficult  will  it  be  to  find  a  night  sufficiently  good  to  use  it 
advantageously. 

The  question  of  size  is  therefore  mixed  up  with  many  others, 
such  as  geographical  position,  accuracy  of  clockwork,  minimum 
magnitude  of  star  desired  to  be  mapped,  rapidity  of  plates,  &c. 

In  order  to  determine  the  best  size  of  instrument  it  would  be 
necessary  to  determine  first  the  minimum  magnitude  of  star  it 
is  desired  to  photograph ;  secondly,  for  what  time  the  clock- 
work could  be  depended  upon  to  go  sufficiently  accurately  to 
.preserve  the  symmetry  of  the  image. 

The  problem  would  then  resolve  itself  into  this  :  What  is  the 
least  size  of  telescope  which  would  photograph  that  particular 
magnitnde  of  stars  in  that  particular  period  with  the  quickest 
plates  obtainable  ? 

General  Form  of  the  Equatorial  Mounting. — If  a  reflector  be 
used,  and  more  especially  if  the  mirror  be  metallic,  the  ordinary 
so-called  German  form  of  equatorial,  slightly  modified  so  as  to 
give  circumpolar  motion,  will  fulfil  all  necessary  conditions ;  but 
in  case  of  a  refractor  it  has  been  suggested  that  the  eld  English 
split  polar  axis  might  be  more  convenient. 


314  Mr,  Gruhb,  On  tlie  Choice  of  xlvii.  6, 

In  ordinary  eye  and  raicrometrical  observations  the  necessity 
which  exists  in  all  eqnatorials  of  the  German  form  of  reversal 
is  not  any  great  inconvenience,  bnt  in  stellar  photography 
absolute  circnmpolar  motion  is  almost  a  necessity. 

It  would  not  be  possible  to  stop  during  the  exposure  of  a 
plate,  reverse  the  telescope,  and  commence  again  at  the  other  side. 
It  is  possible  to  make  the  German  form  circnmpolar  in  this  lati- 
tude np  to  the  zenith ;  bnt  to  do  so  for  refractors  beyond  that 
involves  a  construction  somewhat  of  the  form  of  Colonel  Tom. 
line's,  which  is  clearly  impracticable  for  instruments  which  have 
to  be  transported. 

With  a  reflector,  however,  the  whole  telescope  being  short, 
the  lower  end  being  short  in  case  of  a  metallic  mirror,  and  the 
person  of  the  observer  being  at  the  upper  end,  it  is  perfectly  prac- 
ticable to  make  the  German  form  circnmpolar — at  least  for  these, 
and  even  a  lower  latitude. 

Effect  of  Refraction. — It  is  very  important  to  study  the  effect 
of  refraction  in  disturbing  the  position  of  the  images ;  for  if,  as 
has  been  stated,  the  effect  is  so  great  that  even  in  favourable 
altitudes  and  with  a  perfect  clock  a  hand  correction  must  be 
made  every  two  or  three  minutes,  it  would  appear  almost  useless 
to  go  to  very  much  trouble  about  the  clock,  at  least  in  control- 
ling it  so  as  to  keep  its  rate  correct  for  long  periods. 

Dr.  Dreyer  of  Armagh  has  kindly  made  some  calculations 
for  me  respecting  the  effect  of  refraction.  I  have  only  just 
received  his  calculations  as  I  send  this  paper  to  the  printers;  but 
the  results  are  so  interesting  that  they  appear  worthy  of  further 
investigation. 

Taking  a  star  near  the  equator  and  on  the  meridian,  the  differ- 
ence in  Declination  lor  short  periods  is  very  small.  I  hn  ve  assumed 
that  a  shift  of  star  image  in  plate  of  o"*5  would  be  the  least  that 
could  sensibly  affect  the  symmetry  of  image.  That  o"'5  error 
would  not  occur  in  Declination  for  nearly  half  an  hour;  but  in 
Right  Ascension  the  error  would  amount  to  this  quantity  in 
two  minutes.  The  curious  part,  however,  is  that  this  difference 
in  Right  Ascension  is  nearly  constant  for  a  considerable  distance 
from  meridian:  thus,  one  hour  off  meridian  it  is  still  about o'''5 
in  two  minutes,  and  nearly  the  same  at  two  hours  off  meridian. 

The  practical  deductions  to  be  drawn  from  this  are : — 

(i)  That  a  really  perfect  controlled  clock  can  be  fully 
utilised,  even  for  long  periods,  and  that  it  is  highly 
desirable  to  have  such  ; 

(2)  That  this  clock  should  be  provided  with  an  arrange- 
ment for  introducing  very  slight  changes  in  its  rate. 

Clockwork. — This  is  of  course  the  most  important  of  all  the 
details  of  an  equatorial  intended  to  be  devoted  to  stellar  photo- 
graphy. 

There  are  many  uniform  motion  clocks  which  go  smoothly 
and  uniformly  for  short  periods ;  bat  for  long  periods  it  is  abso* 


L  t  , 


O 


7- 


V 


Tv 


J 


jonthly  Notices  of  Royal  Astronomical  Society.  VbLMEH  Piutf 


April  1887.       Instruments  for  Stellar  Photography.  315 

lately  necessary  to  have  some  controlling  action  from  a  pen- 
dulum.  The  form  of  control  which  I  have  found  best  consists 
of  two  parts — 

(1)  A  detector  apparatus  f  jr  detecting  the  errors  of  equa- 
torial clock,  using  as  a  standard  a  mercury  or  other 
good  pendulum  driven  by  a  remontoire,  so  as  to  be 
uninfluenced  by  the  incorrect  rate  of  the  equatorial 
clock. 

(2)  A  correcting  apparatus  for  correcting  any  errors 
found  in  the  equatorial  clock  by  the  detector.  This 
corrector  itself  naturally  consists  of  two  parts — an 
"  accelerator  "  and  a  "retarder." 

It  will  be  necessary  to  describe  first  this  accelerator  and 
retarder. 

Any  of  the  clock- shafts  between  the  clock  and  the  endless 
screw  which  drives  the  Bight  Ascension  sector  is  cut  into  three 
pieces— Plate  4,  ^g.  1 — S,  S',  and  S". 

On  the  end  of  the  shaft  S  is  fixed  the  wheel  1.  On  the  end 
of  the  shaft  S',  next  S,  is  fixed  the  wheel  2,  close  up  to  and  almost 
touching  1. 

On  the  other  end  of  shaft  S'  is  fixed  the  wheel  3,  and  on  nearest 
end  of  shaft  S"  the  wheel  4.  Also,  on  the  shafts  S  and  S"  are 
placed  discs  of  brass,  d  and  d\  close  to  the  pair  of  wheels  1-2 
and  3-4  ;  bnt  these  discs  are  free  to  turn  on  sJutfts. 

On  a  stud  on  these  discs  are  pinions,  p  and  p\  which  gear 
across  both  wheels  of  each  pair,  p  gearing  across  Nos.  1  and  2, 
p'  across  Nos.  3  and  4.  In  general  the  whole  of  this  apparatus 
revolves  together  and  as  one  piece ;  but  it  is  possible  during  the 
action  to  arrest  the  motion  of  one  or  other  of  discs  d  and  d'y  which 
causes  the  pinion  to  revolve  on  its  own  axis,  and  the  motion 
is  transmitted  to  the  adjacent  wheel  through  the  pinion.  If  the 
two  adjacent  wheels  have  exactly  the  same  number  of  teeth  the 
speed  remains  the  same ;  but  if  one  wheel  has  (say)  one  tooth 
more  than  the  other,  a  slight  difference  in  speed  takes  place 
between  the  driving  part  and  the  driven  part  of  the  spindle. 
For  example : 

Suppose  wheel  1  to  have  30  teeth  and  wheel  2  to  have  29 
teeth,  and  that  spindle  S  be  revolving  at  the  rate  of  once  in  60 
seconds.  If  now  the  motion  of  disc  d  be  stopped,  the  wheel 
No.  2  and  its  spindle  S'  will  be  revolving  once  in  58  seconds  in- 
stead of  once  in  60  seconds.  By  reversing  the  position  of  the 
wheels  at  the  other  end  of  spindle  S'  a  retardation  occurs  on 
stopping  its  disc  d'. 

If,  therefore,  the  normal  rate  of  spindle  S,  S',  and  S"  be  once 
in  60  seconds,  a  stopping  of  disc  d  will  cause  screw  to  revolve 
(as  long  as  disc  d  is  held)  once  in  58  seconds,  while  a  stopping 
of  disc  d'  will  canse  same  to  revolve  once  in  62  seconds. 

This  stopping  is  actually  accomplished  by  cutting  the  edge 
into  a  set  of  very  fine  teeth  (see  tig.  2)  into  which  a  comb  or 


316  Mr.  drubb,  On  the  Choice  of  XLVii.  6f 

the  armature  of  an  electro-magnet  engages.  When  therefore  a 
current  is  sent  through  the  magnet  of  the  accelerator  the  screw 
ia  accelerated  ^V^h  p**t»  an^  when  sent  through  the  magnet 
of  retarder  the  screw  is  retarded  ^th  part. 

To  understand  how  these  currents  are  sent  from  the  detector, 
see  figs.  2  and  3. 

A  scape- wheel,  W,  is  mounted  ona6o-second  spindle  of  clock, 
and  driven  from  that  spindle  by  a  spiral  springs  g,  fig.  1,  so  that 
no  error  of  equatorial  clock  can  affect  its  rate  or  the  rate  of  the 
pendulum.  On  same  clock- spindle  behind  scape- wheel  is 
mounted  an  ebonite  disc,  E  E,  fig.  2,  on  which  are  fixed  two  brass 
insulated  rings,  b  b,  fig.  1,  connected  metallically  with  two  plati- 
num plates  B  B',  inserted  in  face  of  ebonite  disc  E  E. 

Between  scape- wheel  and  ebonite  disc  is  an  arm,  A  A,  also 
mounted  on  spindle  and  loose  on  it,  having  at  its  end  a  little 
platinum  bridge  G,  of  such  a  length  as  to  fit  between  the  two 
platinum  plates  B  and  B'. 

The  ebonite  disc  moves  uniformly  with  the  equatorial  clock. 

The  scape- wheel  works  absolutely  correctly  with  the  peu- 
dulnm  and  is  uninfluenced  by  error  in  clock. 

The  arm  A  A  moves  by  friction  from  the  ebonite  disc,  and 
remains  with  its  bridge  exactly  between  the  two  platinum  discs 
B  and  B'  so  long  as  the  rate  of  clock  is  exactly  coincident  with 
the  rate  of  scape- wheel;  but  if. the  clock  goes  the  least  faster 
or  slower,  a  pin  on  the  scape- wheel  touches  arm  A,  moves  bridge 
C  into  contact  with  B  or  B',  and  sends  a  current  through  the 
accelerator  or  retarder  until  that  error  be  corrected. 

A  piece  of  rock-crystal  is  inserted  between  the  two  pieces  of 
platinum  for  the  bridge  to  slide  on. 

The  current  is  guided  to  brass  rings  b  V  by  the  fine  platinum 
wires  0  0',  which  wipe  against  them. 

The  time  which  the  accelerator  or  retarder  is  kept  in  action 
depends  on  the  amount  of  error  it  is  necessary  to  correct. 

Assuming  the  proportions  given  above  for  teeth  of  wheels, 
and  that  an  error — of,  say,  £th  of  a  second — is  by  some  means 
introduced,  the  corrector  will  be  held  in  contact  for  6  seconds, 
because  for  every  revolution  it  is  held  in  contact  (that  is,  for 
every  60  seconds)  a  correction  of  2  seconds  will  be  made,  so 
6  seconds'  contact  will  correct  £th  of  a  second, 

The  advantages  of  this  control  are—- 

( 1 )  It  not  only  brings  the  rate  of  the  clock  right  after  any 
temporary  disturbance,  but  it  corrects  any  errors  that 
may  have  already  occurred.  This  is  absolutely 
necessary  for  photographic  work,  as  otherwise  the 
star  would  occupy  a  new  position  on  the  plate  though 
rate  of  clock  were  corrected.  [N.B. — all  ordinary 
forms  of  fan,  frictional  governor,  isochronous  pen- 
dulum, &c,  only  tend  to  correct  the  rate  of  the  clock, 
but  do  not  deal  with  any  error  already  existing,] 


April  1887.       Instruments  for  Stellar  Photography.  317 

(2)  The  detector  arrangement,  being  attached  close  to 
screw-spindle,  lakes  cognisance  of  all  the  errors  of 
the  various  spindles  and  wheels  between  clock  and 
screw  as  well  as  clock  itself. 

(3)  It  is  more  smooth  and  eqnable  in  its  action  than  any 
other  form,  for  instead  of  endeavouring  to  alter  the 
rate  of  a  heavy  moving  governor  it  allows  it  to  go 
wrong\  but  introduces  a  corrective  arrangement  into 
the  gearing  so  as  to  compel  the  screw  to  revolve  exactly 
correctly. 

The  practical  result  of  this  control-clock  I  find  to  be  that  it 
is  admirable  for  long  periods ;  but  the  delicacy  of  the  detector  part 
is  not  as  great  as  I  could  desire. 

Owing  to  the  fact  that  the  linear  measure  of  a  second  of  time 
on  the  detector  disc  (revolving  once  in  60  seconds)  is  a  small 
quantity,  I  find  that  practically  the  detector  will  not  detect 
errors  less  than  £th  to  -^th  of  a  second ;  but  it  will  keep  the  clock 
right  within  that  error  for  any  number  of  hours.  In  other 
words,  the  correcting  portion  of  the  apparatus  (the  accelerator 
and  retarder)  work  perfectly,  but  the  detector  is  not  quite  deli, 
cate  enough.  I  think  it  likely  that  a  combination  of  Dr.  Gill's 
detector  (that  used  at  Dun  Echt)  and  my  corrector  would  give 
the  most  perfect  clock-control  possible. 

I  prefer  my  corrector  because  it  takes  into  its  influence  all 
the  errors  of  the  various  connecting  shafts,  <fcc.,  between  clock 
and  sector,  which  Dr.  Gill's  does  not. 

Dr.  Gill  has  suggested,  in  order  to  avoid  all  unnecessary 
wheels  and  gearing  between  governors  and  screw,  that  the 
governor  spindle  should  have  an  endless  screw  cut  on  it,  gearing 
directly  into  a  toothed  wheel  on  screw-spindle,  and  that  this 
governor  should  be  driven  by  a  small  electric  motor  and  governed 
from  the  control  by  a  variable  resistance  apparatus.  The  first 
part  of  this  I  consider  a  most  admirable  suggestion ;  but  instead 
of  driving  by  electricity  and  regulating  by  the  varyipg  resistance, 
I  would  still  drive  by  a  weight  and  introduce  the  correction  by 
my  accelerator  and  retarder,  which  I  find  to  work  so  well. 

There  are  many  reasons  for  which  I  prefer  this  to  the  electric 
driving,  among  which  are : — 


(a)  That  whenever  possible  I  prefer  gravity  (which  never 
fails  us)  to  batteries,  as  a  motive  power. 

(b)  That  when  we  apply  a  corrector  which  necessitates 
the  alteration  of  speed  of  a  heavy  and  quick-moving 
mass  (such  as  the  governor)  we  are  apt  to  set  up  a 
slight  swing  in  the  motion.  The  accelerator  and 
retarder  above  described  are  free  from  that  defect. 

(c)  If  we  adopt  the  electric  driver,  the  control  would  have 

to  correct  all  the  errors  due  to  want  of  constancy  of 


318  Mr.  Grubb,  On  the  Choice  of  xlvii.  6, 

tho  battery  as  well  as  the  mechanical  errors  of  the 
clock,  and  as  the  former  would  probably  amount  to 
20  per  cent,  of  the  whole,  while  the  latter  need  not  ex- 
ceed £rd  per  cent.,  it  is  evident  that  J^ths  of  the  work 
of  the  control  would  be  used  in  correcting  a  factor  (the 
driving  pow*er)  which,  by  adopting  gravity,  we  render 
practically  constant. 

The  form,  therefore,  of  clockwork  I  would  recommend  as 
probably  the  best  at  present  possible  would  be  one  driven  by  a 
weight,  the  governor  gearing  directly  into  a  wheel  or  screw 
shaft.  A  dettctor  similar  to  Dr.  Gill's  at  Dun  Echt,  but  driven, 
not  from  clock,  but  directly  from  screw- spindle,  with  only  one 
pair  of  wheels  intervening,  and  a  pair  of  correctors  on  the  prin- 
ciple of  my  accelerator  and  retarder. 

Slow  Motion  of  Equatorial. — For  stellar  photography  it  is 
absolutely  necessary  to  have  a  slow  motion  of  far  greater  delicacy 
and  precision  than  that  which  suffices  for  micrometrical  work.  If  in 
micro  metrical  work  a  slight  turn  of  the  handle  to  bring  the  star 
central  causes  the  telescope  to  oscillate  very  slightly  it  is  of  no 
consequence,  as  the  eye  can  wait  till  the  oscillation  subsides  (I  am 
speaking,  of  course,  of  extremely  small  quantities) ;  but  in  an 
instrument  for  stellar  photography  this  is  not  admissible,  as  it 
would  cause  the  star  disc  to  be  elongated.  Special  arrangements, 
therefore,  must  be  made  for  the  slow  motion  in  the  photographic 
telescope. 

Slow  Motion  i?i  Right  Ascension. — For  this  purpose  (beside  the 
ordinary  slow  motion  used  to  bring  star  to  centre  of  field)  I  find  the 
best  arrangement  is  to  have  another  accelerator  and  retarder, 
similar  to  those  described  above  for  clock  control,  and  to  have  the 
electro-magnets  of  these  connected  to  a  little  commutator  with 
two  keys  held  in  the  hand  of  the  observer.  By  pressing  one  the 
oJock-spindle  is  caused  to  revolve  g^th  part  faster,  and  continues 
at  this  faster  speed  ho  long  as  the  key  is  held  down.  By  pressing 
the  other  a  corresponding  retardation  occurs. 

By  using,  this  arrangement  there  is  no  possibility  of  causing 
any  jerk  or  sudden  movement  in  the  instrument.  The  key  is 
held  in  the  hand  and  is  totally  independent  of  the  instrument. 
Pressing  the  key  simply  causes  the  screw  to  revolve  ^th  part 
faster  or  slower  for  the  time  being. 

Slow  Motion  in  Declination. — I  would  be  glad  if  possible  to 
have  an  equally  perfect  arrangement  for  the  Declination  slow 
motion ;  but  I  do  not  see  how  this  can  be  accomplished;  and,  for- 
tunately, it  is  not  quite  so  important  as  it  is  not  so  often  in  use. 
1  incline  to  think  that  the  German  form  of  slow  motion — i.e.  a 
fine  screw  acting  against  a  stiff  spring — would  be  the  best  form, 
only  that  the  strength  of  the  spring  is  not  constant,  and,  unless 
made  very  stiff,  does  not  work  well.  I  have  introduced  a  modi- 
fication of  this  which  removes  these  objections. 

A  B  C  D  (fig.  4)  is  a  portion  of  the  arm  attached  to  telescope 


April  1887.       Instrument*  for  Stellar  Photography.  319 

or  cradle,  on  which  is  planted  tbe  block  (6)  forming  the  bearing 
of  the  screw.     Tbe  nut  (n)  is  in  the  form  of  a  ball,  working  in  a 

socket  on  the  extremity  of  the  clamp-arm  E  F  Q.  A  short  stiff 
spring  (S)  is  attached  to  this  clamp-arm,  bearing  not  directly 
against  any  part  of  other  arm,  bat  against  end  of  a  second  screw 
of  same  pitch  as  the  main  screw,  the  nnt  of  which  (o  0)  is  toothed 
on  edge  and  works  into  a  wheel  of  equal  size  (pp)  on  main 
screw.  The  point  of  this  second  screw,  therefore,  advances  as 
much  in  one  direction  as  the  frame  ABC  D  is  carried  m  tbe  other, 
according  as  the  milled  head  is  turned  1  and  consequently  the 
point  of  the  screw  does  not  sensibly  vary  in  its  position  with 
respect  to  the  clamp  arm  E  F.G.  A  shnrt  stiff  spring  can  there- 
fore be  used,  and  the  disadvantage  above  mentioned  disappears. 


The  most  serious  difficulty  in  using  reflectors  appears  to  be 
that  of  the  want  of  constancy  of  the  axis  of  collimation.  A 
mirror  cannot  be  fixed  into  its  cell  with  tbe  same  rigidity  as  is 
possible  in  case  of  an  object-glass,  and  if  the  smallest  shift  occurs 
during  the  exposure,  any  attempt  to  make  the  clock  drive  cor- 
rectly or  to  keep  a  stai*  on  cross-line  of  finder  by  laborious  eye 
.  observations  are  utterly  futile. 

The  shorter  the  exposure^  of  course,  the  less  danger  of  any 
shift  during  an  exposure  j  but  some  system  most  be  devised  by 
which  the  axis  of  the  tinder  can  be  kept  in  a  constant  position — 
not  as  regards  the  tube  or  mechanical  fixtures  of  the  reflector, 
but  as  respects  its  true  optical  axis. 

This  is  not  a  very  simple  problem,  but  1  feel  quite  sure  that 
it  is  quite  capable  of  being  solved. 

The  necessity  of  its  solution  did  not  arise  till  now,  and  there- 
fore no  attention  has  been  given  to  it. 


o  Jfr.  Gr*bb,  On  the  Choice  of  xltii.  6, 

Let  it  be  remembered  that  we  have  three  poasible  a 


.  sliding  bodilj  on  its  snp- 


( i)  Lateraj  shift  of  mirror,  i 

ports. 
(i)  Flexnreoftnbe. 
($)  Tilling  of  mirror. 

By  giving  the  back  of  the  mirror  a  convex  curve  equal  in 
radios  to  concave  at  front  +  thickness  of  disc  the  lateral  shift  has 
no  effect  on  the  cotlimation.  The  other  two,  however,  have  a 
very  serious  effect.  An  arrangement  irach  as  the  following  wonld 
take  into  account  the  error  in  collimation  produced  br  either 
or  both  these. 


Fig-  5- 


Beside,  and  a  little  behind,  the  photographic  plate,  lid  attached 
to  same  supports,  let  there  be  a  small  electric  lamp,  e,  enclosed  in 
a  little  box,  and  having  in  front  h  silvered  glass  window  on  which 
is  scratcbud  a  minute  circle    Let  a  prism  and  Ion?,  jj,  be  mounted 


April  1887.       Instruments  for  Stellar  Photography.  321 

on  large  mirror  itself,  in  such  position  as  to  form  an  image 
of  that  little  illuminated  circle  at  t.  Let  the  finder  tele* 
scope  be  provided  near  eye-end  with  a  diagonal  mirror,  a  a,  having 
a  hole  in  centre,  so  that  the  image  is  thrown  oat  to  side  of  its 
tnbe  at  i ;  and  let  a  lens  be  mounted  in  centre  hole  of  that  mirror, 
which  will  re-form  the  image  of  circle  at  %'.  On  looking  into  field 
of  finder  a  ghost  image  of  this  circle  will  be  seen  in  field,  and 
the  position  of  this  ghost  in  field  of  finder  will  be  affected  by 
flexure  of  the  tnbe  of  great  telescope  or  tilting  of  great  mirror. 
Therefore,  if  instead  of  keeping  any  certain  star  on  fixed  cross- 
lines  of  finder  it  be  kept  in  centre  of  this  ghost  ring,  the  optical 
axes  of  finder  and  reflector  will  be  kept  constant,  and  the  image 
on  photo-plate  will  be  absolutely  steady,  provided  any  star  in 
field  of  finder  be  kept  constantly  in  centre  of  that  ghost  circle. 

It  is  quite  possible  that  a  better  arrangement  than  this  will 
be  devised  ;  but  I  mention  the  first  that  occurs  to  me  in  order  to 
show  that  it  is  at  least  possible.* 

Curved  Plates. — It  appears  quite  possible  that  the  adoption  of 
slightly  curved  plates  might  add  considerably  to  the  possible 
amount  of  field  to  be  photographed  with  sufficient  sharpness. 

The  curvature  necessary  to  place  the  lateral  portions  of  the 
plate  in  the  place  of  least  confusion  would  be  very  slight.  In  the 
case,  say,  of  a  reflector  of  10  feet  focus  and  for  a  field  of  20  the 
versed  sine  of  this  curve  would  only  be  about  ^\th  of  an  inch. 

There  could  be  no  manipulatory  difficulties  in  coating  a  plate 
of  this  curve,  for  the  common  plates  in  ordinary  use  by  photo* 
graphers  have  often  more  curvature  (accidentally)  than  this. 

There  would  be  no  danger  of  any  distortion  occurring  in  re- 
ducing the  observations  from  these  plates  if  proper  precautions 
were  taken,  and  any  extra  expense  of  plates  would  be  more  than 
compensated  for  if  even  £°  of  additional  field  could  be  obtained 
with  the  same  distinctness. 

Many  other  points  beside  those  above  mentioned  will  have  to 
be  considered  and  discussed  before  it  is  possible  to  come  to 
a  definite  conclusion  as  to  the  best  instrumental  equipment  for 
stellar  photography  ;  but  the  object  of  this  paper  will  have  been 
attained  if  I  have  succeeded  in  showing  that  the  subject  is  one 
in  which  new  and  unexpected  conditions  are  continually  pre- 
sented for  our  consideration ;  and,  that  while  we  know  enough 
now  to  be  able  to  say  that  a  certain  instrument  will  give  a  good 
result,  we  really  have  not  as  yet  sufficient  data  to  enable  us  to 
say  what  will  be  likely  to  give  the  best  result.  For  instance,  the 
different  conditions,  instrumental  and  otherwise,  under  which 
Mr.  Roberts  and  the  MM.  Henry  have  been  working  preclude 
any  idea  of  drawing  a  decisive  conclusion  from  a  comparison 
of  their  results. 

It  appears  to  me  that  the  most  useful  work  the  Paris  Congress 

*  It  may  be  observed  that  fig.  5  is  only  a  diagram,  and  that  the  comparative 
site  of  the  various  parts  of  this  collimating  apparatus,  as  compared  to  telescope, 
are  very  much  exaggerated  for  clearness'  sake. 


322  Prof.  Pritchard,  Present  Aspects  xxvii.  6, 

could  do  would  be  to  formulate  a  series  of  experiments  which 
won  Id  clear  up  all  debatable  points.  Arrangements  might  also  be 
made  to  enable  the  work  to  be  carried  on  immediately  after  these 
experiments  were  completed,  the  general  features  of  the  instru- 
mental equipment  to  be  contingent  upon  the  result  of  the  ex- 
periments. If  it  be  possible  for  me  to  take  advantage  of  the 
kind  invitation  of  the  French  Astronomers,  this  is  the  view  which 
I  propose  to  put  forward  at  the  Congress. 


Remarks  on  someoftlis  present  Aspects  of  Celestial  Photography. 
By  Professor  C.  Pritchard,  D.D.,  F.R.S. 

When  a  new  science,  or  a  new  application  of  an  old  one,  is  in 
the  early  stages  of  its  development,  as  is  now  the  case  with 
stellar  photography,  any  practictil  remarks  connected  with  its 
history  and  progress  will  certainly  possess  a  peculiar  interest 
when,  in  the  distant  future,  the  art  shall  have  been  brought  to 
comparative  perfection.  It  is  under  this  view  that  I  venture  to 
occupy  for  a  few  minutes  the  attention  of  the  Society. 

We  are  greatly  indebted  to  General  Tennant  for  his  recent 
contribution  to  our  theoretical  knowledge  of  the  nature  and 
position  of  the  foci  of  cylindrical  pencils  of  light  incident  on 
parabolic  mirrors,  when  the  axes  of  these  pencils  are  inclined 
to  each  other  at  considerable  angles.  By  considerable  angles  I 
mean  such  as  extend  through  one  to  three,  or  even  four,  degrees. 
These  investigations  have  a  very  close  and  important  bearing  on 
questions  relating  to  the  angular  extent  of  the  photographic 
pictures  of  the  heavens,  which  may  be  hoped  for  through  the 
instrumentality  of  reflecting  telescopes.  One  result  which  I 
gather  from  General  Tennant' s  labour  is  that,  even  at  angles 
slightly  exceeding  one  degree  from  the  axis  of  the  mirror,  dis- 
cernible astigmatism  and  distortion  may  be  expected  to  com- 
mence ;  and  if  such  be  found  to  be  the  actual  result  in  practice, 
then  photographic  pictures  of  the  distribution  of  stars  will  be 
necessarily  confined  within  Very  narrow  limits  indeed ;  and  if 
the  whole  heavens  are  to  be  photographically  charted,  then  the 
number  of  the  plates  will  become  unavoidably  enormous,  inas- 
much as  no  single  plate  could  be  expected  to  contain  more  than 
five  or  six  square  degrees,  in  at  all  events  such  perfection  as  not 
to  offend  the  eye,  and  remind  it  forcibly  and  continuously  of  the 
comparative  imperfection  of  the  means  adopted  for  the  formation 
of  the  pictures.  Passing  for  a  moment  from  these  inauspicious 
expectations  of  aid  from  telescopic  mirrors,  I  find  from  a  recent 
printed  note  of  Mr.  Common  that  the  photographic  results,  at 
present  derived  from  specially  constructed  object-glasses,  are,  in 
respect  of  accuracy  of  form  and  extent  of  available  field,  not 
much  more    hopeful  than  those  predicted  by  mathematical  in- 


April  1887.  of  Celestial  Photography.  323 

vestigation  in  the  case  of  reflectors.  Mr.  Common,  speaking  of 
the  really  beautiful  results  obtained  by  MM.  Henry,  says : 
"  Looking  now  at  a  picture  of  one  of  the  faintest  stars  on  the 
plate,  and  about  the  centre  of  the  field,  these  images  are  quite 
distinct  and  perfectly  symmetrical;  it  is  only  when  we  get 
about  i°  from  the  centre  that  distortion  begins.  .  .  .  We  must 
therefore  consider  that  the  field  of  this  instrument  is  a  circle  of 
about  20  diameter  .  .  ." 

It  was  with  a  view  of  ascertaining,  in  respect  of  circularity 
of  the  stellar  images  and  available  extent  of  the  field,  within  the 
limits  of  agreeable  representation,  that  I  recently  commenced  some 
experiments  with  the  De  la  Rue  reflecting  telescope  of  13  inches 
aperture.  The  ordinary  plate-holder  of  this  instrument  is  a 
circle  of  two  inches  only  in  diameter,  at  a  focal  distance  of  120 
inches,  and  consequently  it  comprehends  a  field  scarcely  exceed- 
ing a  single  degree  in  diameter.  Beautifully  perfect  as  this 
field  is,  and  presenting  images  of  the  fainter  stars  admitting 
of  refined  measurements,  suitable  even  for  the  purposes  of  stellar 
parallax,  it  affords  no  adequate  extent  of  picture  practically 
adapted  for  the  larger  scheme  of  charting  the  heavens.  I 
accordingly  caused  to  be  constructed  a  camera  of  more  than 
double  this  diameter,  and  affording  a  circular  field  extending 
to  about  20' 7 ;  and  although  its  construction  with  home  re- 
sources  was  very  rough  and  temporary  in  its  character,  never- 
theless a  series  of  negatives  was  obtained  exhibiting  not  the 
slightest  discernible  deformity  in  the  figures  of  the  stars.  This 
encourages  me  to  hope  that  the  field  may  be  safely  extended 
yet  further  with  suitable  appliances,  and  possibly  sufficiently  so 
for  efficient  and  general  charting.  One  of  these  negatives  thus 
considerably  passing  the  angular  limits  indicated  by  the  mathe- 
matical analysis,  I  have  very  recently  submitted  to  the  judgment 
of  some  members  of  the  committee  delegated  by  the  Society  to 
inquire  into  such  matters. 

Independently  of  this,  at  a  meeting  of  the  Photographic 
Committee  of  the  Royal  Society,  comprising  several  of  the 
members  of  the  former  body,  it  was  proposed  that  experiments 
should  be  made  with  two  mirrors  of  widely  different  focal  lengths 
in  order  to  determine  what  is  the  greatest  extent  of  available 
field  to  which  photographic  pictures  can  be  thereby  carried. 
Mr.  De  la  Rue,  with  his  well-known  and  thoughtful  generosity, 
undertook  to  provide  two  such  mirrors  for  the  determination  of 
the  question,  and  he  has  placed  them  in  my  hands  at  Oxford 
with  the  view  of  mounting  them  temporarily  on  the  solid  frame  of 
his  reflector  in  the  University  Observatory.  The  aperture  of 
each  is  15  inches,  with  focal  lengths  respectively  of  80  inches 
and  T20  inches.  Cameras  are  now  in  process  of  construction 
capable  of  photographing  fields  of  30  20',  and  extending  to 
nearly  50  in  diameter.  What  the  result  may  be  cannot  be  told 
until  after  the  inquiry  has  been  completed. 

There  is  also  another  question  of  some  importance  to  be 


324  Prof.  Prltehard,  Celestial  Photography.  xltii.  6, 

decided.  It  relates  to  the  conical  or  trumpet- shaped  form  of  the 
telescope  tube,  indicated  in  General  Tennant's  paper  already 
referred  to.  There  can  be  no  doubt  that  owing  to  the  ordinary 
cylindrical  form  of  the  tube  very  much  light  from  stars  whose 
images  are  formed  near  the  edge  of  the  field  is  cut  off  from 
incidence  on  the  mirror.  This  fact  will  also  necessarily  interfere 
with  the  correct  estimation  of  the  magnitude  of  snch  stars.  On 
the  other  hand,  it  is  indicated  in  the  analysis  referred  to  that 
there  is  much  probability  of  astigmatism  and  distortion  in  the 
images  of  these  widely  angular  pencils,  and  it  may  even  turn  oat 
that  deformation  is  partially  prevented  by  the  month  of  the 
ordinary  cylindrical  tube ;  for  it  is  one  of  the  results  of  the 
mathematical  investigation  that  a  diaphragm  placed  within  the 
tube  may  conduce  in  some  degree  to  the  flatness  of  the  field. 
All  this  is  a  subject  for  further  practical  inquiry,  and,  as  Mr. 
Common  reminds  us  by  a  forcible  remark,  "  there  is  not  (at 
present)  mach  information  available,  and  what  there  is  is  such 
as  rather  raises  than  removes  doubts." 

Should  it  so  happen  that  considerably  wider  fields  than  those 
indicated  by  the  mathematical  analysis  can  be  successfully 
pictured  on  t'  e  plates,  this  need  not  be  regarded  as  contravening 
the  correct  interpretation  of  General  Tennant's  research.  For 
the  photographic  images  are  not  in  any  sense  mathematical 
points.;  and  as  to  their  physical  genesis,  we  are  greatly  in  the 
dark.  One  thing  is  certain,  that  they  grow  under  continuous 
exposure ;  but  whether  that  growth  is  due  to  the  diffusion  of  the 
light,  or  in  some  degree  to  the  unsteadiness  of  the  atmosphere 
or  of  the  instrument,  or  to  some  molecular  action,  extending  as 
it  were  from  a  centre  of  disturbance,  who  can  at  present  tell  r 

One  conclusion,  I  think,  is  clearly  deducible  from  the  fore- 
going remarks,  to  the  effect  that  the  method  and  final  plan  of  a 
general  charting  of  the  heavens  is  not  yet  wholly  ripe  for 
decision.  For  my  own  part,  I  do  not  think  it  a  chimerical  hope 
that  before  long  it  may  be  within  the  power  of  a  single  obser- 
vatory, provided  with  two,  or  it  may  be  three,  capable  assistants, 
to  procure  a  series  of  charts  of  the  heavens,  extending  from  the 
Pole  to  the  Equator,  photographed  on  an  efficient  scale,  without 
unpleasant  distortion,  extending  to  stars  nearly  as  faint  as  the 
fifteenth  magnitude,  and  reproduced  in  a  permanent  form  nearly 
to  the  fourteenth,  and  then  circulated  among  astronomers  within 
a  space  of  time  not  exceeding  four  years.  The  plates,  however, 
must  necessarily  be  duplicated  by  a  second  instrument  for  the 
purposes  of  rectification. 

These,  however,  are  questions  which  await  discussion  at  the 
approaching  Conference  at  Paris.  Meanwhile  there  are  two 
mottoes  applicable  to  the  present  condition  of  the  matter  before 
us.  The  one  is  "Fonvards!"  and  the  other  is  "  Festina 
Lente" 

1887,  April  5. 


April  1887.      Mr.  Turner,  Variations  of  Level  etc.  325 


On  the  Variations  of  Level  and  Azimuth  of  the  Transit  Circle  at 
the  Royal  Observatory,  Greenwich.  By  H.  H.  Turner,  M.A., 
B.Sc. 

In  Vol.  XXIX.  of  the  Memoirs  of  the  Royal  Astronomical 
Society,  Mr.  William  Ellis  has  given  a  very  complete  account  of 
the  changes  of  level  and  azimuth  errors  of  the  Transit  Circle 
during  the  early  years  of  its  history  (1851-1858).  He  found 
that  there  were  fluctuations  in  the  position  of  the  instrument  in 
both  these  elements  which  followed  very  closely  the  changes  of 
external  temperature,  especially  those  of  long  period,  such  as 
the  annual  variation.  As  the  changes  of  position  of  an  instru- 
ment which  has  been  in  constant  use  for  so  long  a  period  are  of 
interest,  the  following  tables  have  been  recently  formed,  show- 
ing the  simple  arithmetical  mean  of  the  adopted  level  errors  in 
each  month,  and  of  the  adopted  azimuth  errors  in  each  month,  for 
the  period  185 1-1884.  From  the  means  for  each  month  that  for 
the  year  has  been  formed  (in  the  column  on  the  right)  ;  and 
similarly  the  means  for  the  separate  months  have  been  formed  (in 
the  bottom  line),  excluding  those  years  in  which  the  changes 
mentioned  in  the  notes  have  been  made. 


B  B 


326 


Mr.  Turner,  Variations  of  Level  etc.,  xltii.  6, 


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328 


Mr.  Turner,  Variations  of  Level  etc., 


XL VII.  6, 


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3JO  Mr.  Turner,  Variation*  of  Level  etc.  XLvn.  6> 

The  last  columns  exhibit  the  secular  change  in  the  position 
of  the  instrument.  The  lowest  lines  exhibit,  after  correction  for 
that  part  of  the  secular  change  which  takes  place  throughout 
the  year,  the  annual  variation.  I  have  thought  it  of  interest 
to  express  this  variation  in  harmonics  of  annual  and  semi-annual 
period,  giving  at  the  same  time  the  corresponding  expression 
for  the  temperature  of  the  air,  whose  connection  with  these 
fluctuations  Mr.  Ellis  has  already  pointed  out.  The  results  are 
as  follows — the  unit  of  time  being  one  year,  and  the  months 
being  assumed  of  equal  length  :< — 

Level  - 1"96  sin  (2980  45'  +  *.  36o°)-o"*45  sin    (670  55'  +  2*.  3600). 

Azimuth         +  3"7$  sin  (204     7  + 1.  360  )  +  o"*44  sin  (341    30  +  2*.-  360). 
Temperature   I2°*22  sin  (247    13  +*.  360  )+  i°*23  sin    (30  42  +  2/.  360). 

I  have  only  given  two  terms  of  the  harmonic  series,  although 
the  residuals  of  the  means  of  so  many  years  show  traces  of 
being  capable  of  further  analysis.     They  are  as  follows : — 


LereL 

Azimuth. 

Temperatnr 

January 

... 

it 

+  o*oi 

// 
-OI3 

0 
O'O 

February 

>*• 

+  O*0I 

+  006 

+  0-3 

March    ... 

... 

+  0*04 

—  0-07 

-07 

April      ... 

... 

-0-13 

+  o*o8 

+0*5  • 

May 

... 

+  0*09 

—004 

—  0-2 

June 

• . . 

+  002 

+  005 

+  0*4 

July 

... 

—0*04 

-0-03 

-P"3 

August  ... 

... 

—  0'02 

—002 

—  0'2 

September 

... 

+  0*03 

+  002 

+03 

October... 

»• » 

O'OO 

+  0-15 

+07 

November 

•  a. 

—O'O  I 

-0-32 

-13 

December 

•  •  a 

-005 

+  0*29 

+07 

If  these  changes  are  due  to  temperature,  which  we  may 
suppose  to  be  only  gradually  taken  up  by  the  masses  of  stone 
and  metal,  and  the  ground  on  which  the  instrument  stands,  we 
should  expect  the  lagging  effect  behind  the  temperature  which 
is  exhibited  by  the  azimuth.  The  difference  of  epoch  for  the 
first  harmonic  is  about  430,  or  about  a  month  and  a  half;  and 
for  the  second  480. 

We  may  get  some  idea  of  the  kind  of  phenomena  to  be 
expected  by  studying  the  law  generally,  assumed  for  under* 
ground  temperature,  though  we  must  remember  that  this  law 
is  deduced  for  a  homogeneous  infinite  body  bounded  by  a  plane 
surface,  while  we  are  here  dealing  with  a  mass  of  variable 
density  and  shape,  and  that  we  do  not  know  more  than  very 


April  1887.      •    of  the  Greenwich  Transit  Circle.  331 

roughly  which  part  of  it  contributes  most  to  the  effect  under 
consideration. 

A  wave  of  temperature  expressible  by  the  term 

A  sin  (nt  +  a) 
reaches  the  depth  x  under  the  form 

A*-**Vn  sin  (nt-  kx Vn  +  a), 

where  h  is  a  constant  depending  on  the  conductivity  of  the  soil. 
If  the  variation  of  azimuth  were  due  to  the  variation  of 
temperature  at  a  definite  depth  below  the  surface  of  some  part 
of  the  instrument,  we  should  expect  the  lagging  for  the  second 

harmonic  to  be  about  >J  2  times  that  for  the  first  harmonic.  We 
see,  however,  that,  although  the  former  is  decidedly  the  greater, 
it  is  not  quite  so  large  in  proportion  as  this.  Again,  the  ratio  of 
the  coefficient  of  the  second  harmonic  to  that  of  the  first  is 
a  little  greater  than  the  corresponding  ratio  for  temperature, 
whereas  we  should  expect  it  to  be  a  little  less. 

But  it  is  probable  that  this  case  of  the  temperature  at  a 
definite  depth  is  not  fairly  comparable  with  that  before  us  ;  we 
are  more  likely  to  get  a  fair  analogy  by  considering  the  sum- 
mation of  a  series  of  small  changes  at  continually  varying 
depths,  i.e.  by  integrating  the  above  expression  in  some  way. 

Simple  integration  with  respect  to  the  depth  from  the  surface 
to  a  considerable  distance  within  the  earth  would  give 

I*  A 

Ac-**V»  sin  («*-&r*/»  +  aW*  «---  sin  (nt—-  +  a). 
0  kVn  4 

which  would  represent,  say,  the  elevation  of  the  surface  owing 
to  expansion  below.  And  in  this  sort  of  integrated  effect  we 
notice  an  important  difference  from  the  former ;  viz.  the  lagging 
is  constant  for  waves  of  all  period.,  and  is  nearly  45  °.  Without 
laying  too  much  stress  on  the  point,  it  is  interesting  to  notice 
that  the  actual  lagging  is  430  and  480  for  the  two  harmonics. 
The  truth  thus  apparently  lies  between  this  hypothesis  and  the 
former,  as  we  might  expect. 

On  proceeding  to  consider  the  level,  however,  we  find  that, 
so  far  from  its  lagging  behind  the  temperature,  it  actually  pre- 
cedes it  by  nearly  as  much  as  the  azimuth  falls  behind.  In 
considering  a  periodic  term  it  is  of  course  always  possible  to 
express  it  as  either  preceding  another  of  like  period  by,  say,  an 
eighth-period,  or  following  it  by  seven-eighths ;  or  if  we  are  at 
liberty  to  consider  a  crest  of  one  to  correspond  to  either  a  crest 
or  trough  of  the  other,  we  may  express  the  same  anticipation  of 
one-eighth  of  a  period  as  a  lagging  of  three-eighths.  The  only 
reason  for  considering  a  decrease  of  level  to  correspond  to  an 
increase  of  temperature  is  that  such  is  found  to  be  the  case  in 
the  irregular  and  sudden  changes  which  occur  from  day  to  day ; 


332  Mr.  Turner,  Variations  of  Level  etc.  xltii.  6, 

but  it  is  of  course  quite  possible  that  these  rapid  changes  may- 
be caused  by  the  expansion  of  quite  a  different  part  of  the  in- 
strument, e.g.  much  nearer  the  surface  of  some  part  of  it.  We 
have  then  the  alternative  of  considering  that  the  level  lags  at 
least  4^  months  behind  the  temperature,  perhaps  iot  months  ; 
and  when  we  consider  that  this  would  mean  that  the  seat  of 
these  changes  would  be  at  a  depth  of  about  24  feet  (or  perhaps 
56  feet)  if  the  conductivity  of  the  parts  of  the  instrument  be 
even  so  small  as  that  of  rock,  this  does  not  seem  very  likely.* 
I  was  led  therefore  to  speculate  as  to  whether  this  apparent 
anticipation  of  the  temperature  might  not  be  real ;  and  I  venture 
to  hazard  the  suggestion  that  a  difference  of  conductivities  in 
the  two  piers  of  the  transit  circle  would  produce  such  an  effect. 
If  we  differentiate  the  expression 

A*-*XV»  sin  (nt-  kxVn  +  a) 
to  &  we  obtain 

-A**Ai«~laV»  sin  (nt-kx<Sn  +  -  +  a); 

4 

that  is,  this  differential  effect  anticipates  the  former  by  an  eighth- 
period,  and  the  relative  value  of  the  terms  of  short  period  for 
which  n  is  larger  is  increased  in  the  proportion  of  «/»  to  1. 
This  result  is  not  to  be  taken  numerically,  but  only  as  a  very 
rough  qualitative  illustration  of  the  way  in  which  the  tempera- 
ture possibly  influences  the  level.  It  will  be  noticed  that  the 
supposition  of  a  difference  of  conductivities  will  thus  explain 
the  apparent  anticipation  by  the  level  of  the  change  of  tempera- 
ture, and  at  the  same  time  the  large  relative  value  of  the  second 
harmonic  in  the  case  of  level,  which  is  much  more  marked  than 
in  the  case  of  azimuth. 

Now,  we  have  above  differentiated  the  expression  for  the 
temperature  at  a  definite  point  within  the  mass;  but  it  is 
probable  that  some  process  of  integration  should  first  have  been 
employed  as  in  the  case  of  azimuth.  We  have  however  previously 
studied  the  general  effect  of  integration,  and  know  that  it  is  in 
the  opposite  direction  to  that  just  mentioned.  Generally  we 
should  expect  these  two  causes — the  gradual  filtering  of  the 
temperature  into  the  solid  mass  producing  an  effect  of  retardation, 
and  the  difference  of  conductivity  between  the  various  parts 
producing  an  anticipatory  effect,  to  counterbalance  one  another 
to  a  considerable  extent,  both  in  the  case  of  azimuth  and  level. 
They  have  been  assigned  respectively  to  the  one  and  the  other,, 
first  for  simplicity,  and  secondly  because  the  amormt  of  the  effect 
to  be  expected  from  theso  respective  causes  compared  with  the 
actual  differences  of  epoch  observed  in  the  two  cases  seems  to 
point  to  the  fact  that  the  variation  of  azimuth  is  mainly  due  to 
the  first,  and  of  level  to  the  second.    If  it  be  worth  while  to 

*  See  Greenwich  Observations  for  i860.    Redaction  of  the  observations 
of  the  deep-sunk  thermometers,  by  Prof.  Everett 


April  1887.     Mr.  Marth,  FormuhB  for  Computing  etc.  333 

hazard  farther  conjecture  as  to  the  reason  of  this  difference  of 
behaviour  of  the  instrument  in  the  two  elements  -we  might 
suppose  more  definitely  that  the  level  error  is  caused  by  a 
warming  of  the  eastern  pier  more  rapidly  than  the  western, 
whose  conductivity  is  not  so  great ;  so  that  it  expands  vertically 
and  affects  the  level,  while  at  the  same  time  the  lateral  expansion, 
being  symmetrical  about  the  central  vertical  plane  which  passes 
nearly  through  the  pivots,  would  not  affect  the  azimuth.  The 
piers,  or  that  part  of  them  at  least  which  supports  the  pivots, 
not  being  very  thick,  the  lagging  due  to  gradual  conduction  will 
not  be  very  large,  and  we  have  the  effect  of  difference  of  conduc- 
tivity nearly  free  from  any  counteraction. 

On  the  other  hand,  we  must  refer  the  azimnthal  variation  to 
changes  of  temperature  probably  at  some  depth  below  the 
surface  of  the  soil,  which  do  not  happen  to  affect  the  level 
appreciably. 

I  have  examined  the  variations  of  level  and  azimuth  at  other 
observatories  for  a  few  years  to  see  if  there  is  any  similarity 
between  these  fluctuations  for  different  instruments.  It  is 
somewhat  difficult,  without  expending  more  time  than  I  can 
well  spare  at  present,  to  disentangle  their  annual  variations 
from  changes,  secular  and  irregular,  and  generally  larger  than 
those  noticed  at  Greenwich.  I  look  forward  with  interest  to  a 
discussion  by  Mr.  Finlay  of  the  errors  of  the  Cape  Transit 
Circle  promised  in  the  last  volume  of  "Cape  Observations' ' 
(1879-81).  Roughly  speaking,  there  does  not  seem  to  be  much 
similarity  between  the  fluctuations  of  position  of  different  instru- 
ments; for  instance,  the  difference  of  epoch,  which  has  been 
chiefly  considered  above,  is  very  variable.  And  indeed  Mr.  Ellis 
pointed  out  in  his  paper  above  referred  to  how  largely  the 
variations  of  the  present  Transit  Circle  differ  from  those  of 
Troughton's  Transit,  which  occupied  nearly  the  same  site.  As 
I  have  already  said,  however,  in  suggesting  the  above  explana- 
tions of  the  changes  in  position  of  the  Greenwich  Transit  Circle, 
we  have  at  our  disposal  two  causes  which,  combined  in  varying 
relative  proportion,  are  capable  of  explaining  fluctuations  follow- 
ing or  anticipating  the  temperature  by  very  different  periods  of 
time. 


On  the  Formula  for  Computing  the  Apparent  Positions  of  a  Satellite, 
and  for  Correcting  the  Assumed  Elements  of  its  Orbit.  By  A. 
Marth. 

The  methods  of  computation  connected  with  the  investiga- 
tion of  a  satellite's  orbit  are  comparatively  simple  and  convenient, 
if  they  are  duly  selected  to  suit  directly  the  coordinates  furnished 
by  the  observations.  If  polar-coordinates  have  been  observed, 
there  exists  apparently  no  good  reason  for  not  employing  polar- 
coordinates  also  in  the  corresponding  computations.   The  present 


334  ^Ir.  Marihy  Formulas  for  Computing  xxvn.  6, 

paper  contains  the  formulae,  which  seem  to  me  the  most  advan- 
tageous and  handy  for  computing  the  apparent  positions  and 
the  corrections  of  the  assumed  elements  in  the  chief  cases  which 
come  under  consideration. 

Referring  the  plane  of  the  satellite's  orbit  to  the  plane  parallel 
to  the  terrestrial  equator,  let  N  denote  the  longitude  or  Bight 
Ascension  of  the  ascending  node ;  J  the  inclination ;  Q  the  angle 
between  the  line  of  apsides  and  line  of  nodes  or  the  departure  of 
the  lower  apside  from  the  node ;  e  =  sin  <f>  the  eccentricity :  ft,  c,  v 
the  mean,  eccentric,  and  trne  anomaly  of  the  satellite ;  u  =  Q-f-v 
its  trne  longitude  in  the  orbit  reckoned  from  the  node ;  «0  =  Q  +/* 
its  mean  longitude ;  r  the  radius  vector ;  a  the  major  semi-axis  of 
the  orbit  or  the  satellite's  linear  mean  distance  from  the  planet's 

centre ;  -  =  p,  so  that  p  is  the  radius  vector  expressed  in  parts  of 
a 

the  major  semi- axis  of  the  orbit.     Further,  let  A,  D  denote  the 

apparent  Bight  Ascension  and  Declination  of  the  planet's  centre  ; 

a,  8  those  of  the  satellite  ;  A  the  linear  distance  of  the  observer 

from  the  planet.    If  the  origin  of  the  coordinates  is  placed  in  the 

satellite  instead  of  in  the  centre  of  the  planet,  the  strict  formal© 

become  somewhat  simplified,  but  for  the  purpose  a  and  8  must  be 

known.     In  case  approximately  correct  values  of  a  — A  and 

8— D  are  available,  like  those  of  the  three  outer  satellites  of 

Saturn,  published  for  some  years  past  in  the  Monthly  Notices,  or 

if  they  can  be  derived  directly  from  the  observations,  it  will  be 

worth  while  to  take  advantage  of  the  favourable  circumstance. 

As  most  of  the  observed  positions  of  satellites  consist  of 
measures  of  position- angles  p  and  distances  *,  or  are  given  in 
polar-coordinates,  the  formulae  for  their  proper  computation  may 
first  be  taken  into  consideration. 

If  the  Earth's  position,  as  seen  from  the  satellite,  is  referred 
to  the  plane  of  the  satellite's  orbit  by  the  longitude  U+  i8o°  and 
latitude  B,  and  if  P  is  the  position-angle  of  the  pole  of  the  orbit 
(in  Bight  Ascension  N — 900  and  Declination  900— J)  at  the  geo- 
centric place  of  the  satellite,  the  values  of  U,  B,  P  are  found  from 
those  of  N,  J,  a,  8  by  means  of  the  equations  : 

cos  B  sin  IT  »  cos  8  sin  (a— N)  cos  J  +  sin  8  sin  J 

cos  B  cos  U  =  cos  5  cos  (o— N) 

sin  B  =  cos  8  sin  (a— N)  sin  J— sin  8  cos  J 

cos  B  sin  P  =3       —  cos  (a— N)  sin  J 

cos  B  cos  P  =  sin  8  sin  (a— N)  sin  J  +  cos  8  cos  J 

or  by  equivalent  formulae. 

The  satellite's  orbital  longitude  «=Q+v,  and  also  p  being 
deduced  from  the  mean  anomaly  /x,  either  by  the  usual  formulae : 

€-*»*sine«/*  wo  =  s7^296  =  __L_ 

p  sin  v  =  sin  €  cos  ^  4WV  * 

p  cos  &*■  cost—* 


April  1887.      the  Apparent  Positions  of  a  Satellite.  335 

or  by  the  series  for  the  equation  of  the  centre  v — fi  and  log  p, 
the  values  of  the  position«angle  p  and  of  the  distance  $  corre- 
nponding  to  u  are  found  by  means  of  the  equations 

sin  <r  sin  (p — P)  ■»  sin  (u — U) 

sin  <r  cos  (p — P)  «  cos  (« — U)  sin  B 

a 

sin*™—  .  psin<r 

A    r 

in  -which  <r  is  the  arc  on  the  sphere  between  the  geocentric  and 
planetocentric  place  of  the  satellite,  or,  without  the  introduction 
of  <r,  by 

sin e sin  p—'P)=~pan(u—V) 

sin e cos (^>— P)  =-  pcos(«— U)sinB 

A 

The  position-angle  p  thus  oomputed  refers  to  the  Declination-circle 
passing  through  the  satellite.  In  case  the  observed  position- 
angle  refers  to  the  Declination-circle  passing  through  die  point 
midway  between  the  planet's  centre  and  the  satellite,  a  correction 
=  —  A*sinjp  tan  8  must,  when  a  strict  comparison  is  required, 
be  added  to  the  computed  p. 

If  A,  D  are  substituted  for  a,  8  in  the  formulas  for  U,  B,  P,  so 
that  their  ensuing  values  refer  to  the  centre  of  the  planet 
instead  of  the  satellite,  the  correction  of  the  computed  p  will  be 
=  +  \  s  sin  p  tan  D,  the  computed  <r  (which  must  be  taken 
between  90°  and  1800,  when  cos  (u—TJ)  is  negative)  represents 
the  arc  between  the  geocentric  place  of  the  planet  and  the  planeto- 
centric place  of  the  satellite,  and  the  value  of  8  must  be  found 
indirectly  from  the  equation 

sin  a  =  -  p  sin  (<r— «), 
A 

if  the  employment  of  the  equations 

Aj  sin  *  sin  (p— P) =a/>  sin  («— U) 

Al  sin  8  cos  (p — P) «=  ap cos(m— U)  sin  B 

A,  cos*  =apcos(u— U)cosB  +  A, 

in  which  A,  denotes  the  distance  of  the  satellite  from  the  earth,  is 
to  be  avoided. 

The  equations  of  condition  for  correcting  the  assumed  ele- 
ments of  the  orbit  gain  in  clearness  and  simplicity  by  the  intro- 
duction of 

sin  (T  sin  t  =  sin  B 

sin  <r  cos  t  «  cos  B  sin  (u — U) 

cos  ft «  cos  B  cos  (u — U) 

which  serve,  at  the  same  time,  as  a  partial  control  upon  the 
equations  for  finding  p : 


336  Mr.  Marth,  Formulas  for  Computing  xlytt.  6, 

sin  a  sin  (p— P)  =  sin  (• — U) 

sin  *  cos  (  p — P)  =  cos  (• — U)  sin  B 

a 

sin*=  — .pain<r 

A 

The  differentiation  of  these  equations  gives : 

sin  &dp=  sin  r .  <£(«  — U)  —  cost  cos  («— U)  dB  +  sin  tftfP 
<fo-«  cos  t  .  d  («  —  U)  +  sin  t  cos  (•— U)  dB 

But 

cosBrfU^-cosUsinBdJ-cosPcosMN 

cosBrfP«-cosUrfJ         +einUsinJ<*N 

c?B= +ainU(/J         — cosUsin  J4N. 

Hence,  after  some  reductions : 

sin  tftfp  ■■  sin  rdu — cost  sin  udJ  +  (cos  acoup  cos  5— sin  «•  sin  8)dN 
da  =*  cos  rdu  + sin  r  einvdJ  +  Bin  p  coaWN 

p  sin  <r . «°  —  «  0  cos  ffdff  +  sin  au°dp  +  p  sin  oV* . 

5  a 

The  differential  expressions  of  u,  the  satellite's  true  longitude, 
-with  respect  to  its  mean  longitude  u0  and  Q  and  <£,  are : 

pdu-—+du0+(p  -22!^W  +  (i+ps6cV)sin».cos^ 
-=(1  +  ecos  y)8ec<^«0—  {2cos v]  ten<pdQ,+  {2sintr}  coe <pd*f> 

in  which  the  coefficients  in  {}  brackets  denote  the  following 
equivalents,  among  which  the  most  convenient,  according  to 
facilities  at  hand,  may  be  selected  : 

J  2  cos  v]  =  cos  v  +  cos  e  cos  $  +  tan  £$ 

_  (2  +  «  cos  t>)  cos  v  +  «  +  tan  \<f>  cos*£ 
I  +  e  cos  t; 

(ecosv   \          .  *  cos  6  + tan  A* 
2— icosi?  + I. £2- 
1  +  e  cos  »/                 1  +  e  ccs  t; 

-  ( 1  +  p  sec  V)  cos  v  +  p(tan  ^  +  tan  J^  sec» 

{2  sin  t/}  »  sin  v  +  ran  «  sec  $> 

2  +  tfcoav   . 

= sin  t; 

I  +  «  cos  0 

(* COS  V    \    .     _ 
2  — 1  gin  v 
I  +«COSt'/ 

=  (1  +  psec*^)sin  v. 

The  substitution  of  these  expressions  and  of 

flp°<2pstan$sin  vrf«0— sinv.  tan^Q— cos  v.cosftty 

in  the  equations  for  sin  <rdp  and  ds  leads  to  the  equations  be-  ' 


April  1887.      the  Apparent  Positions  of  a  Satellite.  337 

tween  the  variations  of  the  computed  coordinates  and  the  varia- 
tions of  the  assumed  elements 

p  sin  alp  -  sin  t  .  — T .  lu0 

P 

— sin  t  .  {2  cos  v)  «°(tan  <p  +  Be)  sin  8Q 
+  sin t  .  {2  sin  v] «°[(tan  $  +  le)  cos  8Q — tan  <f>] 
— p  cost  sin  ttlJ 

+  p(cos  <r  cos  p  ccs  S -  sin  a  sin  8)  8N 
ftdjf      /  cop  A  .  •       \» 

p  sin  a  . «°  —  -  (cos  a  cos  t  .  — ■£■  +  tan  <p  sin  *  sin  v)©«0 

—  (cos  0-  ccs t {2  cos  t>|  +  sin  a  sin  v)«°(tan  ^  +  9e)  sin  9Q 

+  (cos  <r  cost {2  sin  v\  —  sin<rco8  v)«°[(tan<p  +  8tf)cos8(J— tan<f>] 

+  pcos  <rsin  rsinu.SJ 

+  p  cos  a  sin  j>  cos  8 .  8X 

+  p  sin  a .  o»°—  . 
a 

In  order  to  guard  against  some  possible  oversight  or  error 
in  the  interpretation  of  tho  variations  connected  with  the  eccen- 
tricity if  they  are  written  in  the  form  tan  <f>  8  Q  and  cos  <£  8<£,  I 
have  substituted  in  these  equations  for 

tan  <f>3Q «°(tan  <f>  +  le)  sin  «Q 

and  for 

cos  $ty ....  «°[(tan  <p  +  **)  cos  ftQ—tan  ^] 

expressions  which  represent  the  true  meaning  of  these  variations, 
and  will  lead  to  right  deductions  of  the  corrections  of  Q  and  e  in 
all  cases.  If  not  thus  interpreted  the  expressions  tan  <f>  8  Q  and 
cos  <f>  8  <f>  or  8  e  may  obviously  be  misleading,  and  may  give  very 
incorrect  results  whenever  the  assumed  values  of  Q  and  e 
require  more  than  small  corrections. 

If,  instead  of  8  Q  and  8  e,  the  variations  of  suitable  functions  of 
Q  and  e  are  to  be  introduced,  the  equations  for  pdu  and  dp  suggest 
the  advantage  of  selecting  for  the  purpose  not  e  sin  Q  and  e  cos  Q, 
but  E  sin  Q  and  E  cos  Q,  where  E  is  such  a  function  of  e  or  </>  that 

tan^cfEsEcfc-Ecosfcty. 

Putting  accordingly 

E=« .  secJ£* .  c-«*,na  J*»2  tan  \* .  (?-»■**' »♦  (c  basis  of  nat.  log.) 

the  differential  coefficients  of  u  and  p  with  respect  to  E  sin  Q  and 
E  cos  Q  will  be 

od  «  (2  +  *  cos  v)  cos  u+ (e  cos  <p  +  tan  ^>)  cos  Q    ^Q    tan  ft  jw£asnQ\ 

^  ™  '.*  i+ccosv  E    "^  ' 

f2  +  «cost>)8in«  +  («cosft+tani$)sinQ      0     tan*     ,,_  ^^  nx 
+ - — .  •    .  — — -  •  (tip  COS  ii). 

<7p-....-sini«.  *l£.  <*(E  sin  Q)- cost*  .  ^1*  .  d(E  cos  Q). 

E  E 


f  |g  J£r.  Martk,  Formula  for  Computing  xlyii.  6, 

Hence  the  eccentricity  terms  in  the  equations  of  condition  for  Sp 
and  3  #  become 

piionv  =•  •  •  —  nor  . ■ — - — •  •    • 

*!L*  .  «(E  «n  Q) 

^ -;-.   («+•«»  r)«n«  +(««»  + + tan  If)  an  Q      0 

+■  nil  t  .  — ^^— — — — — ^ — — —  ■  »    • 

1+  eoos  v 

*!L*.l(EcosQ) 

Sf  ,  (24-  eeo8»)eos«+(ecoe$+taii£+)eo8Q 

$  I+fC08V 

+  anran«)  .  ^^  .  S(EnnQ) 

E 

+  (co6rcG6r  .  (*  +  '«»  p)8ill»+freo«0+tluli*)8i||Q 

I+CCOSV 

—  an  rco6«) t .  5(E  eos  Q). 

Though  in  this  way  the  corrections  of  the  assumed  values  of 
Q  and  e  might  he  properly  found  and  mistaken  deductions 
avoided,  the  way  would  be  needlessly  circuitous ;  for,  by  substi- 
tuting in  the  foregoing  expressions  for  S(E  sin  Q)  and  S(E  cos  Q) 
their  values 

.  (E  +  ftE)siii(Q+tQ)-E8inQ,aDd 
(E  +  tE)cos(Q+SQ)-EcosQ, 

and  by  eliminating  Q,  the  expressions  are  obtained  which  are 
already  given  in  the  equations  of  condition,  and  which,  while  of 
equal  strictness,  are  obviously  preferable  on  account  of  their 
greater  simplicity  and  directness.  Moreover,  they  allow  the 
motion  of  the  apses,  if  approximately  known,  to  be  easily  taken 
into  account. 

The  equations  of  condition  have  yet  to  be  so  adjusted  that 
the  differences  between  the  observed  and  the  computed  co-ordi- 
nates are  measured  by  the  same  unit.  It  will  depend  on  the 
character  of  the  measured  position-angles  and  distances  whether 
it  is  preferable  to  express  the  differences  in  seconds  of  arc  or  in 
units  corresponding  to  an  arc  of  one  degree  on  a  circle  of  suitable 
radius,  and  also  how  far  the  ensuing  rules  are  better  modified  or 
altered. 

Ifsina0=— ,  where  A0  is  some  conveniently  fixed  value  of  A 

° 
(not  differing  greatly  from  the  average  of  the  distances  A  at 

which  observations  are  taken),  and  if  ^-2=  v,  the  angular  distances 
$  of  the  satellite  will  be 

*  =  a0v  .  p  sin  a. 


April  1887.       (he  Apparent  Positions  of  a  Satellite.  339 

Making 

573 
the  adopted  unit,  the  equations  of  conditions  will  be 

S  •  COS*      * 

_8p»+rsinr .  V^lr  .  8»0 
«o  P 

—  r  sin  t  .  {2 cost'}  .  »°  (tan^>'+  Ze)  sin  8Q 

+  rsinr.  {2sinv}  .  «o[(tan^  +  8«)eos8Q-tan0 

—  vp  cos  t  .  sin  u .  8J 

+  vp  (cos  *  cos^»  cos  8 — sin  <r  sin  8) .  8N 

-£-  +  y(cos  er  cos  r  .  ?°£x  +  tan  ^  sin  or  sin  0) .  8k0 

K  p 

— v(cob  <r  cos  r  .  {2  cos  t>}  +  sin  <r sin  «)  .  «°  (tan  $  +  8e)  sin  8Q' 

+  y(co8<rco8T  .  {2  sin  t?}— Bin<rco8  v)  .  »°  [(tan ^  +  8*) cos 8Q  — tan  ^] 

+  vp  cos  <r  sin  t  .  sin  u  .  8  J 

+  vp  cos  er  sin  p  cos  8 .  8N 

«     8a0 
a*     k 

If  the.  differences  between  the  observed  and  computed  coor- 
dinates are  expressed  in  seconds  of  arc,  the  equations  become 

8     »                                 COS  6        » 
8p«  +  v sin T  . -L  .  *8«0 

— vsinr  .  {2cosv}  .  a0  (tan  $  +  8e)  sin  8Q 

+  vsinT.  {2sinu}  .  a0  [(tan  <f>  +  te)  cos  8Q— tan^] 

— rpcosT  .  sinw  .  k8J 

+  *7>(cos0'co8^cos8  — sin«rsin8)  .  «c8N 

85=  +  r  (cos  <r  cos  t.^-T  + tan  ^  sin*  Bint?)  .  *8w0 

P 

— v (cos  <r cost  .  {2  cost;}  +  8in<rsint>)  .  a,  (tan  $  +  80)  sin  8Q 

+  v(cos0'cost  .  {2sinv}—  sincrcose)  .  <z4[(tan^  +  8e)cos8Q— tan^t] 

+  *p  cos  (f  sin  t  .  sin  u  .  *8 J 

+  vp  cos  a1  sin  p  cos  8  .  k8N 

H —  .  Sa^ 

The  formulra  are  here  written  out  in  full.  Abbreviated 
notations  for  the  quantities  which  are  to  be  determined  and  for 
their  coefficients  will,  of  course,  be  substituted  in  actual  com- 
putations. 

The  preceding  equations  are  valid  for  orbits  of  any  assumed 


340  Mr.  Marihy  Formula  for  Computing  XLVir.  6, 

ellipticity.    For  assumed  circular  elements  they  get  considerably 
simplified,  and  become 

Ltpm  +  rsinr .  *k 


*o 


—  rrinr  .costs  .  2^sinQ 

+  ?sinr  .  sin*  .  2$cosQ 

— vcoer  .  sinu  .  SJ 

+  *(cos<rcos^)coe8— Bin<r8in5)  .  &N 

_«  +  v cos <r cost  .  to 

— v (cos <r cost  .  co8«+£sin<rsintf)  .  2$sinQ 
+  v(co8(fC08T  .  sintt— £  sin  <r cost*)  .  2$cosQ 
+  r  cos  <r  sin  r  .  sin  ti  .  W 
+  rcos<rsinpcos8  .  8N 

a0      it 

They  most  be  multiplied  by  k  if  the  differences  are  to  be  ex- 
pressed in  seconds. 

The  orbital  longitudes  u,  U,  Q  employed  in  the  preceding 
formulae  are  reckoned  from  the  node  N,  and  this  reckoning  is 
most  suitable  whenever  the  inclination  J  is  considerable.  But  if 
J  is  only  of  moderate  amount,  as  in  the  case  of  the  orbits  of 
Satu/rn's  satellites,  the  determination  of  the  nodal  point  is  con- 
siderably uncertain,  and  this  uncertainty  rapidly  increases  with 
the  decrease  of  J.  By  adding  the  longitude  of  N  to  the  longi- 
tudes reckoned  from  N  the  uncertainty  is  evaded,  and  the 
longitudes  in  the  orbit  start  from  a  properly  fixed  point. 

tutting  ti+N  =  Z  andU+N  =  L,  the  formula  for  finding  p 
and  the  sin  and  cos  of  a  and  r  require  merely  the  substitution 
of  Z— L  for  t*— U: 

shuffling— P)  =  sin  (/— L)  sinrsinTasinB 

sin  *  cos (p—P)  -cos  (/— L) sin  B  sin  cr  cost = cos  B sin  (J— L) 

Bin8=*  - .  psina  or  s **aj> .  p  sin  <r  cos<r=cosBeos(J— L). 

A 

The  differential  expressions  for  sin  <rdp  and  da-  become  by  the 
substitution  of  dl—dN  for  du 

rin<rdp**BinT  .  <2i— cosrsinti  .  <ZJ+(co8<rcosj>cos8  — sin  cr  sin  8— sinrViN 
<J<r=cosT  .  dl  +  sin  t  sin  u  .  (ZJ  +  (sinj>cos8— cost)<2N. 

But 

cot  «r  conp  cos  J —sin  9  sin  J—  sin  t  cos  J  +  cos  r  cos  u  sin  J 

sin  p  cos  8  -  cos  t  cos  J — sin  t  cos  u  cos  J. 

Henoe 

sin  cdp  »  sin  t  .  dl  +  [cos  t  cos(Z  -  N)  -  tan  £J  sin  t]  sin  J .  dN  -cost sin  (/ — N>JJ 
dff  -  cost  .  dl  -  [sin  t  cos  (/  -  N)  +  tan  JJ  cos  t]  sin  J .  <*N  +  sin  t  sin  (I  -  N)dJ 


April  1887.      the  Apparent  Positions  of  a  Satellite.  341 

The  equations  of  condition  between  the  variations  of  the  coordi- 
nates and  the  variations  of  functions  of  the  elements  become 
accordingly 

57'3 r  o 

—  v  sin  t  .  { 2  oofl  v} .  aj(t&n  $  +  Be)  sin  3(Q  +  N) 

+  v  bin  t  .  (2  sin  v } .  a0[(tan  Q  +  &)  cos  5  (Q + N) — tan  0] 
+  vp[«osTcos(/-N)-tanJJMnT].fl/sinJ  +  ?£,\sin5y 

— rpcosTsin^/— N).a0[(sin  J  +  — \cosJN -- sin  J] 

5*=  +  jY  cos  <r  cost  .  ^-?  4-tanf  sin<rsintA.*&/0 

—  r  (cos  <r  cost  .  {2  cost;}  +  Bin<rsinv).at(tan4>  +  80)sin8(Q  +  N) 

+  r  (cos  (f  cos  t.  {2  sin  »}  -  sin*  cos  v) .  a0[(tan  <p  +  8*)cos  &(Q + N) — tan<?>] 

— r p  cos  <r  [sin  t  cos(/ —  N)  +  tan  £J  cos  t]  .  aJ  sin  J  +  —  \  sin  8N 

+  ?/> cos <r. sin r sin (£— N).at[/sinJ  +  —   o  s&N-sinJ] 

+  -.3a0 

In  order  to  guard  against  incorrect  deductions  of  the  cor- 
rections of  the  node  and  inclination,  which  might  occur,  if  the. 
terms  sin  J  .  8N  and  8J  were  kept  without  proper  interpretation, 
I  have  substituted  for 

*.sinJ.8N  ....  aJ  sin  J  +  —  J  sin  8N 

and  for 


.  V  .  .  .  .  aa[(sin  J  +  — jcosSN— tinJ] 


expressions  which,  as  in  the  analogous  case  of  the  eccentricity 
terms,  represent  the  true  meaning  of  these  terms,  and  cannot 
mislead.  By  this  simple  substitution  all  the  advantages  for  the 
correctness  of  the  deductions  are  secured,  which  otherwise  might 
be  gained  by  the  introduction  of  the  variations  of  tan  \  J  sin  N 
and  tan  ^J  cos  "N",  but  without  their  attending  drawbacks,  as 
mathematical  readers  may  easily  satisfy  themselves. 
The  quantities 

*M»  a9(txn  ^  +  Be)  sin  &(Q  +  N),  a0[(tah  ^  +  Be)  cos  9  (Q  +  N)  -  tan  f ] , 
a  J  Bin  J  +  —  J  sin  5N,  a9[(  sin  J  +  —  j  cos  &N  —  sin  J] 

which  are  to  be  treated  as  the  unknown  quantities,  will  in  the 
formnl®  for  actual  computation,  of  course,  be  represented  by 
single  letters. 

For  assumed  circular  elements  the  equations  of  condition 
become 

c  c 


342  Mr.  Marth,  Formula  for  Computing  xlvii.  6, 

— 8— ftp  m  +  rsinr .  *W 
573 

— r  sinr .  ooe  I .  zxf  sin  (Q  +  N) 

+  r  sinr.  sin /.2*£  cos  (Q  +  N) 

+  r  [cos  t  cos  (/ — N)  —  tan  J  J  sin  t  ] .  aJsin  J  +  ~  j  sin  JN 

— rcOiTiin(i-N).at[jiin  J  +  — jcoiJN -sin  J] 

8*=  +  vcos<rcos«r .  kZ19 

— *(co8<rcoar  .  cosJ+JsuKTsin  J)  .  2x$sin(Q+N) 
+  r(cos<rcosr  .  sin /— £sin<rcosJ) .  2k^cos(Q  +  N) 

— r  cos  <r  [sin  r  cos  (J— N)  +  tan  £Jcos  t ] .  a9  ( sin  J  +  -—  J  sin  JN 
+  roosf  .  sinTsin(/— N)  .  a0[fsin  J  +  -g)  cos  JN— sin  J] 


«0 


In  turning  from  the  consideration  of  the  proper  treatment  of 
measured  polar  coordinates  to  that  of  rectangular  coordinates, 
it  is  obviously  expedient  to  take  first  the  special  case  of  Saturn's 
satellites,  when  their  rectangular  coordinates  parallel  to  the  axes 
of  the  ring  are  either  measured  or  estimated.  In  measuring  the 
distances  from  the  axes  it  is  essential  that  the  position-angles  in 
which  the  measures  are  taken  should  be  distinctly  stated,  so 
that  if  they  differ  from  the  computed  position-angles  of  the  axes 
which  represent  the  fundamental  plane,  to  which  the  orbits  of  the 
satellites  are  to  be  referred,  the  necessary  corrections  may  be 
applied. 

If  L,  B,  P  have  the  same  significance  as  before  in  reference  to 
the  assumed  plane  of  the  ring,  the  coordinates  s",  y"  parallel  to 
the  axes  of  the  ring  are 

»*m(p— P)  =  *"»a0i' .  psin(2— L) 

8C0B(p—¥)=y"*=ajr .  poos (Z~L)  sin B 

•*"*»  +* [cos(J— L)+* cosM] .  k  secf8/0 

—  *[cos(J— L)(cos€cos<f>  +  tan£^)  +  cosM]  .  <r0(tanf +  te)sin&(Q+N) 

+  r  [cos  (/— L)  sin  c  sec  ^  +  sin  M]  .  a^  [(tan  <p  +  9e)  cos  9  (Q+ N) — tan  f] 


—vp  .  tan  \J  cos  (2— L)  .  a9  fsin  J  +  —  \  sin  8N 


+  —  .  8a0. 


8y  =  —  rein B [sin (Z—L)—c sin M]  .  jrsec$8?0 

+  v  sin  B  [sin  (I — L)(cos  c  cos  <f» + tan  \Q) — sin  M].a0  (tan  <t>  +  te)  sin  &(Q  +  N) 
—  *sinB[sin(J— L)sinfsec^  +  cosM].a0[(tan^+8tf)cos8(Q  +  N)— tan^] 

+  vp  [cos  B  cos  (I — N)  -  tan  J  J  sin  B  sin  (I — L)]  .  a0  (sin  J  +  -M  sin  8N 

+  vp cos B sin  {I— N)  .  a9  [/sin  J  +  —  j  cos  &N — sin  J] 
V"    * 


*o 


April  1887.      the  Apparent  Positions  of  a  Satellite.  343 

For  convenience  M  is  put  instead  of  L  —  (Q +N).  If  the  eccentric 
anomaly  c  is  not  available 

cost;+ecos»+tanfrfr  mwgt  be  pafc  for  ^s,  cog  ^  +  Un  ^ 


I  +  4COSV 

and 


sinv      *      .  . 

for  sin  «  sec  <p. 


i+ecoHV 


For  assumed  circular  elements  the  equations  of  condition 
become 

Sx"- +vcoe(Z-L).«M 

— r[co8(l— L)cosf  +  cosL]  .  a«6  sin  (Q  +  N) 
+  r  [cos  (I— L)  sin  /+  sin L]  .  <V cos (Q  +  N ) 


— v tan  JJcos (/— L)  . a, (sin  J + -^  j sin &N 


x 


+  — .  8ar 


*o 


Jy"  —  —  ysinB  .  sin(J— L)  .  uZl 

+  ysinB[sin(i— L)cos2— sinL]  .  <70«sin(Q,  +  N) 
— *  sin  B  [sin  (J— L)  sin/  +  cos  L]  .  a05cos(Q+N) 


— r  [cos  B  cos  (J— N)  —  tan  JJ  sin  B  sin  (J— L)] .  a0(  sin  J  +  —  j  sin  5N 
+  rcosBsin(/— N)  .  a0  [(sin  J  +  ~)  cosJN— sin  J] 


«o 


In  case  the  x  ordinates  are  not  measured  micrometrically,  but 
estimated  by  comparison  with  certain  definite  points  of  the  major 
axis  of  the  ring,  the  proper  unit  for  x  and  for  the  semi-axis  of  the 
satellite's  orbit  will  obviously  be  the  semi-diameter  of  Saturn's 
equator.    If  (a)  is  the  length  of  the  semi-axis  expressed  in  suoh 

units,  the  computed 

• 

x=(a)psin(/— L) 

and  the  equations  of  condition  require  merely  the  substitution  of 
(a)  for  a0  v. 

Though  the  range  of  such  estimations  of  x  is  limited,  there  is 
the  great  advantage  that  they  can  be  made  without  micrometer, 
and  even  with  a  rather  unsteady  instrument,  and  that  when 
taken  with  due  care  and  circumspection  at  the  right  times,  they 
yield  in  accuracy  only  to  the  best  micrometrical  measurements. 
Observations  which  fix  the  times  of  the  conjunctions  of  the 
satellites  with  the  limbs  of  the  ball  and  the  ends  of  the  ring  in 
the  four  quadrants  are  of  great  value,  not  only  in  investigations 

cc  a 


344  Mr.  Marthy  Formula*  for  Computing  xlvii.  6, 

of  the  orbital  longitudes  of  the  satellites,  bat  also  in  examining 
the  dimensions  of  the  ball  and  ring. 

If  the  observed  positions  of  the  satellite  in  reference  to  the 
planet's  centre  consist  of  differences  of  Bight  Ascension  and 
Declination,  or  are  given  in  equivalent  rectangular  coordinates, 
the  frequently  used  method  for  their  computation  may  be 
followed,  which  Bessel  employs  in  his  investigation  of  the  orbit 
of  Titan  ("  Astr.-Nachr.,"  Nos.  193-195).  His  auxiliary  angles 
/,  F,  g,  G,  h,  H,  referred  to  the  geocentric  place  of  the  planet 
A,  D,  may  be  found  by  means  of  the  formul®  * 

sin /sin  F  =  —  sin  (A — N)  sin  g  sin  (Q — F)  =  —  sin  (D  +  E) 

sin/cosF  =  +  cos  (A  -  N)  cos  J  sin  ^  cos  (G— F)  =  +cos(D  +  E)cos/ 

cos/—  —  cos  (A— N)  sin  J  cos  g  ■■  +  cos  (D  +  E)  sin/ 

sin/sin  E  =  —  sin  ( A  —  N)  sin  J  sin  h  sin  (H — F)  =  +  cos  (D  +  E) 

sin/ cos  E  «  +  cos  J  sin  A  cos  (H  —  F)  =  — sin  (D  +  E)  cos/ 

cos  h  =  +  sin  (D + E)  sin/ 


*  The  values  of  0,  B,  c,  C  in  the  expressions  for  a  planet's  or  comet's  helio- 
centric coorli nates  referred  to  the  equator — 

x = r  sin  a  sin  (A'  +  v), 

y  =■  r  sin  6  sin  (B'  +  v), 

e  ■■  r  sin  c  sin  (C  +  v), 

may  be  found,  in  a  similar  manner,  by  means  of  the  formulae 

sin  a  sin  E  —  +  sin  t  cos  8  sin  b  sin  (B — A)  ■  —  cos  (E  +  c) 

sin  a  cos  E  -  +  cos  t  sin  6  cos  (B — A)  -  +  sin  (E  +  c)  cos  a 

cos  a«  +  sin  f  sin  Q  cos  6-  —  sin  (E  +  c)  sin  a 

sin  a  sin  A-  +  cos  8  sincsin  (C— A)=  — sin(E  +  c) 

sin  a  cos  A—  —sin  Q  cost  sin  c  cos  (C  — A)—  — cos(E  +  c)cosa 

A'«A  +  »  cos<?» +C08(E  +  e)sina 

so  that  the  B'  +  u  and  C  +  v  in  the  expressions  for  y  and  e  are  obtained  by 
simply  adding  B — A  and  C — A  to  the  values  of  A'  +  v. 

Are  these  convenient  formulas  for  b,  B,  c,  C  not  to  be  found  anywhere  in 
print?  Considering  that  they  refer  to  computations  of  such  frequent  recur- 
rence, it  is  not  easy  to  assume  that  they  have  not  been  pointed  out  before. 

In  case  the  inclination  t  is  of  moderate  amount,  it  may  be  worth  while,  for 
greater  accuracy,  to  determine  A  by  computing 

sin  v  =  tan  jt  .  sin  8  .  sin  E 

which  makes  A  «  Q  +  900  —  v. 

If  formulae  for  control  are  required, 

sin  6  sin  B  —  sin  Q  cos  e 
sin  c  sin  C  a  sin  Q  sin  e 

Un(C-B)-     ™*a 

COS  0  COS  c 

may  serve  the  purpose. 


April  1887.       the  Apparent  Positions  of  a  Satellite.  345 

The  positions  of  the  satellite  are  then  found  by 
A  sin  *  sin p  »  r  sin/sin  (F + 1«)       «=  A .  £ 
A/8in«co6j>«r«in£Bin(G+«)        -A.y 

A,  cos*  sA  +  rsinifcsin(H+a)-A.(i  +  0; 

or,  if  the  difference  between  s  and  <a"  tan  s  is  neglected,   the 
rectangular  coordinates  by 


*" -—  .  _— vsin  / sin  (F  +  m) 


**. 


A     i  +  f 

By  the  substitution  of  a,  8  for  A,  D  in  the  computations  of  the 
auxiliary  angles/,  F,  g,  G,  or  by  computing  their  values,  not  for 
the  apparent  place  of  the  planet,  but  for  that  of  the  satellite,  the 
divisor  1  +£  will  be  got  rid  of,  and  the  formulae  become  simpli- 
fied.    If  that  course  is  adopted  they  will  be 

*"  -  »" sin  s  sin  p  -  »" cos  D  sin  (o  -  A)  -  app .  sin/ sin  (F  +  ») 

y"  =  »" sin  s  cos  p  ■■  •" sin  (8 — D) — *" .  tan  J(a  -A)  sin  8  =  a,*/* .  sin  g  sin (G  +  «) 

or,ifF=F+Q,  G'=G+Q, 

*"  -  a9v  sin/,  p  sin  (F'  +  v) 
y" =  a9v  ninff .  p  sin  (G'  +  v). 

The  equations  of  condition  are 

$y  s  +  v  tin/  [cos  (F'  +  v)  +  e  cos  F']  .  k  sec  ^8/0 

— v  sin/  [cos  (F' + 1?)  (p  cost;  cos  f  +  ecos$  +  tan  J  ^)  +  cosF']. 

a#(tan  <p  +  9e)  sin  8  (Q  +  N) 

+  k  sin  /[cos  (F  +  u) .  pain  usee* $>- sin  F'] .  a0[(tan  <p  +  8«)  cos  8  (Q+N) 

-tanf] 

+  vp .  tan  JJ .  cos  (/— N  +  o— N) .  a0  J  sin  J  +  —  j  sin  8N 

+  vp  sin  (/— N)  cos/.  a0[sin  (J  +  —J  cos  8N — sin  J] 

x" 
+  — 8a0 

ac 
3/'  =  +  vsin#[cos(G'  +  t;)  +  <?co8G']  .*sec^.  8/0 

-K8in^[cos(G'  +  v)(/>cost;co8^  +  eco8^  +  tani^)  +  oo8G[]  . 

<z0(tan <p  +  Ze)  sin  8  (Q  +  N) 

+  v  siny  [cos  (G'  + 1>) .  p  sin  v  sec*  ^  -  sin  G'] .  a0[(tan  <p  +  8e)  cos  8(Q  +  N) 

-tan<f>] 
— vp  [cos  (/— N)cos  8  +  tan  J  J  sin  (J— N  +  a— N)  sin  8] . 

a4  (sin  J + —j  sin  8  N 
+  vp  sin  (/ — N) .  cosy .  a0[(  sin  J  + — \  cos  8N  —  sin  J] 

+•— .8a,. 

If  the  assumed  elements  are  circular,  and  if  F/  =  F— N, 
Gy  =  G— N,  the  coordinates  become 

*"  =  a0  v  sin/ .  sin  (F/  +  V) 

y/'  =  at>'sin^.8in(G/  +  ^ 


346  Mr.  Gore,  On  the  Orbit  of  OS  400.  xlyii.  6, 

and  the  equations  of  condition 

fcr"=  +  rsin/cos(F, +  /).«*<• 

—  r  sin/  [cos  (F,  +  /)  cos/ + en  F,] .  a.  *  sin  (Q  +  X) 
+  y  sin/  [cos  (F, +/)  sin  f— sin  FJ  .  a,  c  cos  (Q  +  X ) 

+  *tan|J.eos(/-X  +  a-X).fl.(siflJ  +  ^8mSX 
+  rsin(Z— X)cos/.  a0[sinj  J0  +—  jcos  JX  — sin  J] 

a, 
3y"  =  +  *  h\ng  cos(G,  +  /) .  «W0 

—  rsin^ [oos(G,  +  Z) cos  J  +  cosG,]  .a,«8in  (Q  +  X) 
+  ysiny[cos(G,  +  l)sini— sinG,]  .  a.  «  cos  (Q  +  X) 
-ir[cos(/-X)cos«  +  tanJJsiii(/-N  +  a-X)8iii«].«#8in'J  +  ??Wn8N 

+  r  psin  (/— X)cos^ .  a0sin  [J  J  +  —  J  cos  $X  —sin  J] 
+  20  .  8a0 


a. 


The  auxiliary  angles  are  found  by  the  formal® 

sin/sin  E  =  +  sin  J  sin  (a— N)  sin  g  sin  (G— F)  «  —sin  (E  +  5) 

sin/cos  E  «=  +  cos  J  sin  g  cos  (G— F)  «  —  cos(E  +  8)  cos/ 

cos/=— sin  Jcos(a— X)  cos^«  +  cos(E  +  &)sin/' 

sin/sinF  =  —  sin  (a— X) 
sin/cos  F  s»  +  cos  (0 — X)  cos  J 

orF-Nby 

sin  (F— N  +  o)  -  tan  \Z .  cos  (a— X) .  sin  E. 

The  values  of  B  and  P  used  in  the  formulas  for  polar-coordinates 
are 

cosBsinP=  —  cos  (a  —  X)  sin  J  «  cos/ 
cos  B cosP»  +  cos  (E  +  Z)  sin/ *=  cos g 
sinB=  —  sin(E  +5)  sin/ 


On  the  Orbit  of  OS  400.     By  J.  E.  Gore. 

Some  measures  of  this  close  binary  star,  made  in  1885  with 
the  23-inch  Refractor  of  the  Princeton  (U.S.A.)  Observatory,  and 
kindly  sent  me  by  Professor  Young,  show  that  the  companion 
lias  described  about  190°  of  its  apparent  ellipse  since  its  discovery 
by  0.  Struve  in  1844. 

I  have  computed  the  orbit,  and  find  the  following  provisional 
elements : — 

Elements  of  OS  400. 
P«  170-37    years  Xl«i46°  20' 

T  =  188209  A=  430  307 

£  =  0-669  **=     °""59 

7-36°  58'  /*=-2°-ii3 

The  following  table  shows  a  comparison  between  these  ele- 
ments, and  the  observations  used  in  the  calculation  of  the  orbit: — 


April  1887.        Mr.  Gore,  On  the  Orbit  of  OS  4°o. 


347 


^^        •*>  «  m  •  •  •  ■  •••• 

I      "O     OOOOOOOOO 
i        I        I        I        I        I       +       I       +      +     + 


I        I        I        I        I        i 


o 

+ 


I  I 


I     o 

+ 

A 


&    * 


■  •••••••■••  Z^. 

OOOOOOOOOOO 


O       f*    NO       2?0      N     n     J? 

obbobobobobo 


\o    NO 


s 


*  *b    b    o 


>©      On     "">     N      « 
vr>    "">    v©     v©     vo 

b    b    b    b    b 


a 

•3 
.5  -a 


& 

a 

•— « 
o 


-*3 


O     VO     VO     J  g     3      g 

o     O     O    '3      '-So 


4 
hi 

s 

d 

=    §  b 

1     »° 


b   o 

A 


9 


s>  = 


.O 
O 


t^r^roN     O     »2    £•     £>    O     £*    g     J    O      n    O 
\0      m     vO      m     •-•       ^■vOON^ONNWOvf^r' 

•~    bb    bfo>biob    bo^Mb^00 
4.+     1      1     1      1      l      I      I+    +    +I+    + 


o 
I 


0    ,^   o 

On    "«      O 

+  +   + 


.a  *>  «*> 

8    +    I 

a 

X 

00 


tO     *>.     CO     «      O 
N     m    »>.    to    **• 


8n    n    Q     «    .    ^     O     £•    „ 
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34&  Jfr-  Chamber*,  A  Working  xlyii.  6, 

Considering  thai  the  errors  in  the  measures  of  so  close  a  pair 
are  necessarily  considerable,  the  above  comparison  may  be  con- 
sidered as  fairly  satisfactory. 

The  position  of  the  binary  is  for  1880 — 

BJL    2oh    6-  14- 

+  43°  35' 
Magnitudes,  7*3,  77,  according  to  Burnham. 


A  Working  Catalogue  of  "Bed  "  Stars.     By  G.  F.  Chambers. 

The  following  catalogue  is  the  outcome  of  many  hundreds  of 
observations,  extending  over  (more  particularly)  a  period  of 
about  seventeen  years  (1870-86),  though  not  a  few  of  the  stars 
were  examined  in  an  unmethodical  fashion  during  several  yean 
previous  to  1870.  Between  1870  and  1881  the  telescope  em- 
ployed was  a  4-inch  Refractor  by  Cooke,  but  all  the  observations 
since  1884  have  been  made  with  a  6-inch  Refractor  by  Grubb, 
almost  always  charged  with  an  eyepiece  of  very  low  power, 
having  a  field  of  1  j°.  The  observations  of  colour  cited  with  the 
name  '*  Brodie  "  appended  were  made  by  my  cousin,  Mr.  C.  G. 
Brodie,  of  Fernhill,  I.W.,  with  an  8^-inch  Refractor,  in  the  years 
1884-86.  He  has  seen  most  of  the  stars  which  I  have  observed, 
but  I  have  quoted  from  his  notes  only,  as  a  rule,  in  cases  where 
we  did  not  agree  in  our  estimates  of  colour. 

The  existing  catalogues  of  red  stars  from  which  contribu- 
tions have  been  levied  are  the  following :  but  I  have  not  limited 
myself  to  these,  having  been  in  the  habit  for  many  years  past  of 
making  notes  of  all  red  stars  wheresoever  mentioned  : — 

1804.  Lalande,  J.  de.     Tables  des  fitoiles  Rouges. 

(Connaissances  des  Temps,  An.  xv.  p.  378.) 
1822.  De  Zach,  Baron.     fitoiles  Rouges. 
(Corresp.  Ast.  vol.  vii.  p.  298.) 
1847.  Herschel,  Sir  J.     Ruby-coloured,  or  very  Intense  Red 
Stars. 
{Cape  Observations,  p.  448.) 
1866.  Schjelleeup,  H.  C.     Catalog  der  rothen,  isolirten  Sterne. 
(Ast.  Nach.  vol.  lxvii.  No.  1591,  June  18,  1866  ; 
Addenda,  vol.  lxviii.  No.  1613,  October  30, 1866.) 
1872.  Schmidt,  J.  F.  J.     Verzeichniss  rothgelber  Sterne. 

(Ast.  Nach.  vol.  lxxx.  No.  1902,  September  5, 1872.) 
1874.  Schjellebup,  H.  C     Zweiier  Catalog  der  rothen,  iso- 
lirten Sterne. 
(Vierteljahrsschrifl  der  Astronomischen  GeseUschaft, 
vol.  ix.) 

1876.  Burnham,  S.  W.     Catalogue  of  Red  Double  Stars. 

(Month.  Not.  vol.  xxxvi.  p.  331,  1876.) 

1877.  Birmingham,  J.  Observations  and  Catalogue  of  Red  Stars. 

(Trans.  Roy.  Irish  Acad.  vol.  xxvi.  p.  249,  1877.) 
1877.  Fearnley.     Des  JBtoiles  colorSes. 

(Ast.  Nach.  vol.  Ixxxix.  No.  2121,  March  27, 1877.) 


April  1887.  Catalogue  of "  Red "  Stars.  349 

1879.  Lindemakn,   E.      Verzeichniss   von    42    neuen    rothen 
Sternen. 
{Bulletin  de  VAcad.   de  St.-Pelersbourg,  vol.  xxv. 

P-  I55-) 
.  1882.  Likdemann,    E.       Zweites    Verzeichniss    neuer    rother 

Sternen. 

(Bulletin  de  VAcad.  de  St.-Petersbourg,  vol.  xxviii. 

p.  278.) 

1885.  Espin,  Rev.  T.  E.     Some  New  Bed  Stars. 

(Journal  of  Liverpool  Ast.    Soc.  vol.    iii.    p.   82, 
March  1885.) 

1886.  Espin,  Rev.  T.  E.    Some  New  Red  and  Orange-red  Stars. 

(Month.  Not.  R.A.S.  vol.  xlvi.  p.  293,  March  1886.) 

This  catalogue  makes  no  pretence  to  being  exhaustive;  it 
must  not  be  regarded  as  more  than  it  professes  to  be,  namely,  a 
working  list  of  the  best  of  the  red  stars,  almost  always  excluding 
known  variables,  many  of  which  are  notoriously  red  in  colour. 
My  reason  for  excluding  known  variables  was  this :  their  inclusion 
would  have  been  a  trap  to  observers  using  this  list  for  the  pur- 
pose  for  which  alone  it  is  designed,  namely,  to  facilitate  the  study 
of  any  red  stars  which  are  always  -within  reach  of  their  instru- 
ments (regard  being  had  to  the  season  of  the  year  and  the  lati- 
tude of  the  place  of  observation). 

And  in  another  senso  this  catalogue  is  not  exhaustive;  it  only 
includes  stars  of  decided  colour  and  not  less  than  8£  magni- 
tude. It  may  be  that  my  eyes  are  not  so  sensitive  to  red  hues  as 
many  other  eyes  are,  but  I  certainly  have  often  considered  that 
many  of  my  predecessors  in  the  observation  of  red  stars  have 
greatly  exaggerated  the  colours  they  have  ascribed  to  particular 
objects.  Taking  the  so-called  "red  "  stars  all  round,  my  opinion 
is  that  a  more  generally  accurate  generic  term  for  them  would  be 
"  orange  "  stars,  and  that  very  few  indeed  rise  to  real  "  red,"  and 
that  less  than  a  dozen  can  be  truly  termed  "  carmine  "  or  "  ruby." 
These  remarks  seem  requisite  by  way  of  caution  in  order  to 
guard  inexperienced  observers  from  being  disappointed  when  they 
come  to  examine  for  themselves  stars  described  by  Sir  W. 
Herschel,  Sir  J.  Herschel,  Schmidt,  and  others,  as  "red"  or  "very 
red."  There  can  be  no  doubt  that  these  observers  saw  many 
stars  to  possess  a  redder  tinge  than  they  have  since  been  found 
to  exhibit.  This  may  have  been  in  the  case  of  the  Herschels 
some  effect  of  their  metallic  mirrors,  or  of  their  eyesight,  or  may 
have  been  due  to  both  causes  combined ;  and,  speaking  generally, 
it  may  be  said  that  the  vast  majority  of  the  stars  here  catalogued 
are  "  orange  "  more  than  anything  else.  I  would  for  this  purpose 
define  as  "  orange "  the  colour  exhibited  by  the  gilding  inside 
articles  of  silver  plate  newly  gilt. 

A  few,  and  only  a  few,  explanations  are  requisite  as  to  the 
principles  on  which  the  catalogue  has  been  constructed.  In 
column  1  one  asterisk  indicates  objects  of  particular  interest ; 
two  asterisks  objects  of  very  special  and  remarkable  interest. 


35©  -M**.  Chambers,  A  Working  xlvii.  6, 

Column  2  gives  the  progressive  numbers,  if  any,  from  Birming- 
ham's catalogue.  The  places  in  columns  4  and  5  have  been 
taken  from  the  best  authorities  available,  brought  np  to  1890.  I 
have  freely  consulted  the  catalogues  of  Stone  and  Yarnall,  and 
the  Armagh  catalogue,  and  the  two  Radcliffe  catalogues,  besides 
Birmingham's.  The  places  of  such  of  the  stars  as  are  to  be  found 
in  the  Nautical  Almanac  for  1890,  or  the  American  Ephe- 
meris  for  1889,  are  taken  from  those  works  respectively.  Espin's 
places  are  as  given  by  him,  but  brought  up  from  1885  to  1890. 
As,  however,  he  only  quotes  the  Durchmusterung  to  the 
nearest  minute  of  Bight  Ascension  and  Declination,  my  1890 
places  of  his  stars  will  be  less  exact  than  in  the  case  of  all  the 
other  stars.  The  magnitudes  in  column  6  are  in  all  cases  from 
Pickering's  Harvard  Photometry,  where  the  star  was  to  be 
found  in  that  important  and  interesting  record;  one  of  the 
most  valuable  contributions  to  practical  astronomy  that  has 
appeared  for  many  years.  The  magnitudes  of  many  of  the 
remaining  stars  have  been  determined  by  Mr.  C.  G .  Brodie  by 
Dawes's  method.  In  the  column  headed  "  Colour;  Remarks  "  the 
information  given  within  inverted  commas  has  been  generally 
taken  from  published  sources,  although  the  authority  is  not  in  all 
cases  mentioned.  All  other  details  not  in  inverted  commas  re- 
produce the  results  of  my  own  original  work.  The  stars  examined 
by  myself  amount  to  589,  out  of  a  total  of  719,  being  virtually 
nearly  all  those  visible  in  England. 

It  would  not  be  difficult  to  offer  many  interesting  and  sug- 
gestive reflections  as  the  result  of  a  prolonged  study  of  the  red 
stars ;  but  one  would  soon  be  apt  to  drift  away  into  speculations, 
which,  however  attractive  to  some  minds,  would  not  only  be  mere 
speculations,  but  would  relate  to  matters  quite  beyond  the 
domain  of  astronomy  proper.  I  will  therefore  here  only  record 
the  well-known  facts  that  many  of  the  stars  certainly  variable 
are  red,  and  that  many  of  the  red  stars  have,  since  they  were 
first  noted  as  such,  been  found  to  be  variable.  The  instances 
that  could  be  cited  in  support  of  these  statements  are  very 
numerous,  and  it  is  quite  impossible  for  the  coincidence  between 
the  redness  of  the  colour  and  the  variability  of  the  light  of  several 
hundred  stars  to  be  accidental.  What  it  means  I  do  not  presume 
to  suggest.  Amongst  observers  who  have  paid  much  attention 
to  the  colours  of  stars  a  foremost  place  must  be  given  to  the  late 
Mr.  J.  Birmingham,  of  Tuam,  whose  labours  in  the  matter  of  red 
stars  added  much  to  our  knowledge  of  stellar  colours.  It  was 
he  who  remarked  that  "  a  space  of  the  heavens,  including  the 
Milky  Way,  between  Aquila,  Lyra,  and  Cygnus,  seems  so  pecu- 
liarly favoured  by  red  and  orange  stars  that  it  might  not  inaptly 
be  called  *  the  red  region,'  or  *  the  red  region  of  Cygnus ' ;  and, 
although  the  chances  of  finding  a  star  of  any  stated  colour  must, 
of  course,  be  greater  among  the  countless  multitudes  of  the  Milky 
Way  than  elsewhere,  still  its  other  portions  visible  in  this  latitude 
show  no  such  special  richness  in  red  stars." 

One  other  remark  of  Birmingham's  will  be  useful  in  this 


April  1887.  Catalogue  of "  Bed "  Stars.  351 

place :  "  The  red  stars  seem  as  liable  to  change  of  tint  as  to  change 
of  magnitude  ;  and,  although  modifications  of  colour  may  have 
been  remarked  without  any  striking  change  of  size,  still  I  have 
observed  that  as  a  red  variable  increases  it  grows  paler,  and  that  it 
reddens  deeper  towards  the  minimum.  Schmidt  has  made  the 
same  observation,  and  it  well  accords  with  the  fact  that  all  the 
very  red  stars  are  telescopic,  and  none  of  them  visible  to  the 
naked  eye.  This  is  noteworthy,  and  seems  difficult  of  explana- 
tion ;  but  the  cause,  as  I  would  suggest,  may  be  found  in  the 
quality  of  light  received  from  the  object.  As  we  do  not  see  the 
stars  by  their  discs,  but  by  the  amount  of  their  light,  according 
to  apparent  magnitude,  it  seems  evident  that  the  very  red  stars, 
shining  with  only  a  part  of  the  components  of  white  light,  must 
appear  less  bright  than  the  white  stars,  and  seem  therefore 
generally  small.  According  to  this  view,  it  might  be  assumed 
that  the  few  naked  eye  reddish  stars  would  appear  larger  if 
white  ;  so  that  Aldebarau,  Betelgeuse,  &c.,  if  of  that  colour,  might 
be  rivals  of  Sirius.  The  redness  of  a  star  has  given  rise  to  the 
singular  conceit  that  it  shows  a  cooling  down,  or,  as  we  might 
say,  an  approach  to  a  final  snuffing  out  of  the  luminary ;  but  one 
might  think  that  the  fact  of  periodic  variation  of  tint  in  many  of 
the  red  stars  ought  to  go  far  in  disproving  this  proposition." 

The  reason  why  I  have  not  included  stars  below  the  9th 
magnitude  is  that  where  one  is  dealing  with  a  star  which  is  near 
the  minimum  visibils  of  a  telescope  estimations  of  colour  are  apt 
to  become  very  imaginary  in  many  cases.  I  say  this  without  any 
desire  to  impute  bad  faith  to  an  observer  who  might  talk  about 
" magnitude  13,  colour  red";  but  I  nevertheless  should  view 
his  chromatic  notions  with  a  certain  amount  of  distrust.  I  do 
not  believe  that  it  is,  as  a  rule,  possible  to  assign  colour  to  stars 
of  the  12  th  or  lesser  magnitudes,  except  a  very  large  telescope 
indeed  happens  to  be  employed  in  viewing  them. 

The  question  has  often  been  discussed  as  to  how  far  flat 
surface  diagrams  of  colour  are  of  any  use  as  standards  of  com- 
parison for  coloured  stars.  For  my  part  I  am  disposed  to  question 
their  usefulness,  notwithstanding  that  I  caused  Smyth's  well- 
known  diagram  of  coloured  discs  to  be  reproduced  for  the  new 
edition  of  the  Cycle  of  Celestial  Objects,  I  have  often  thought 
of  trying  whether  a  series  of  transparent  discs  of  coloured  glass, 
arranged  in  gradations  of  colour,  and  mounted  in  a  frame  suf- 
ficiently portable  to  be  held  in  the  hand  by  the  observer  whilst  his 
eye  is  looking  through  the  telescope,  might  not  be  used  for  com- 
parisons of  star  colours.  Probably  the  chief  difficulty  would  be 
the  obtaining  of  a  sufficiently  pure  white  light  wherewith  to 
illuminate  the  discs.  If  this  were  got  over  by  the  use  of  elec- 
tricity or  otherwise,  I  think  such  an  apparatus  might  be  effective 
and  trustworthy,  whilst  it  need  not  be  very  expensive  nor  very 
cumbersome. 

The  notes  bearing  the  names  of  Bellamy  and  Robinson  were 
sent  to  me  in  MS.  by  Mr.  E.  J.  Stone,  Director  of  the  Radcliffe 
Observatory,  Oxford. 


35*  ***>  Chamben,  A  Working  xlyii.  6, 


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369 


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Catalogue  of  "Bed"  Stan. 


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388  Mr.  Orossley,  Description  of  xltii.  6, 


Description  of  a  New  Measuring  Bod.     By  Edward  Crossley. 

Some  ten  years  ago  I  had  occasion  to  triangulate  across  a 
valley  3,000  feet  wide  on  the  south  side  of  my  observatory  at 
Bermerside,  Halifax.  In  order  to  accomplish  this  with  sufficient 
accuracy  it  was  necessary  to  measure  a  base  line  to  1  in  io,ooo. 
I  soon  discovered  that  no  simple  and  accurate  method  had  yet 
been  devised  for  this  purpose.  The  ordinary  surveyor's  chain 
or  steel  tape  was  quite  inadequate  for  the  purpose,  especially 
as  the  ground  was  more  or  less  uneven.  The  elaborate  methods 
used  in  geodetic  surveys  were  also  out  of  the  question  on  account 
of  their  great  complexity.  I  therefore  determined  to  construct 
a  measuring  rod  on  simple  geometric  principles,  capable  of 
doing  accurate  and  rapid  work  over  uneven  ground,  with  or 
without  the  aid  of  an  assistant. 

The  first  rod  I  designed  for  this  purpose  was  made  for  me 
by  Messrs.  T.  Cooke  and  Sons  of  Tork.    It  was  made  of  well- 
seasoned  red  deal,  1  inch  thick,  6  feet  in  length,  with  a  T  section 
2\  inches  wide  and  4  inches  deep  in  the  centre.    At  each  end,  on 
the  under  flat  surfaces,  brass  plates  were  attached  with  spherical 
cups  in  their  centres,  facing  downwards.     In  the  middle  of  the 
rod  was  placed  a  clinometer  reading  to  30"  of  arc.     Three  stout, 
firm  tripods  were  used  for  carrying  the  rod.     Each  tripod  termi- 
nated in  a  flat  iron  ring,  faced  in  the  lathe,  6\  inches  in  outside 
diameter  and  4  inches  internal  diameter.    On  these  rings  were 
placed  brass  pedestals  with  circular  bases  6  inches  diameter,  sur- 
mounted by  spheres  or  balls  \  inch  diameter,  the  top  of  the  balls 
not  being  more  than  2\  inches  above  the  surface  of  the  rings. 
Each  pedestal  had  a  spindle  going  through  the  ring,  with  a  brass 
tribrach  "washer"  and  clamp,  milled  head  screw  nut  on  the 
under  side  of  the  iron  ring,  so  that  the  pedestal  could  be  clamped 
anywhere  within  the  area  of  the  ring.    The  spherical  heads  were 
turned  of  equal  size,  to  fit  the  cups  on  the  measuring  rod.      In 
the  first  instance  stout  posts  with  brass-headed  nails  in  their 
centres  were  used  for  terminals. 

The  method  of  procedure  was  as  follows.  A  tripod  was  set 
up  over  the  first  po9t  and  the  spherical  head  clamped,  with  the 
plumb  bob  over  the  brass  nail.  A  correction  was  applied  for  any 
inclination  of  the  ring.  A  piece  of  string  60  feet  in  length  with 
tabs  every  6  feet  was  stretched  on  the  ground  in  the  direction  of 
the  base  line,  to  facilitate  the  setting  of  the  tripods.  B  tripod 
was  set  over  the  first  tab  and  C  tripod  over  the  second,  with 
the  heads  undamped.  The  measuring  rod  was  now  placed  upon 
the  heads  of  A  and  B  tripods.  The  head  of  B  tripod  being  un- 
damped was  free  to  take  the  position  necessary  to  fit  the  cup 
at  the  end  of  the  rod. 

After  lining,  B  head  was  clamped  and  the  clinometer  read 
off.     Then  the  same  process  was  repeatod  on  B  and  C  tripods. 


April  1887. 


a  New  Measuring  Bod. 


389 


A  tripod  was  set  forward  oyer  the  tab  in  advance  of  C,  and  so 
on  to  the  end  of  the  base. 

The  following  results  were  thus  obtained  in  1883  from  three 
measurements  of  the  same  base  line : — 


L 

Feet. 
442635 

Differences. 
*5        34 

in. 

1 

5 

II. 

442612 

8 

18 

1 
10 

III. 

442*612 

8 

18 

1 
10 

442*620 

10 

23 

1 
ff 

N.B. — /*= million  ths  of  the  whole  distance. 

These  results  were  so  encouraging  that  I  determined  to  go  a 
step  further,  and  secure  results  of  an  accuracy  of  not  less  than 
1  in  100,000. 

For  this  purpose  I  made  another  rod,  10  feet  in  length,  of 
well-seasoned  pine,  with  a  T  section,  but  with  an  opening  £  inch 
square  from  end  to  end,  through  which  a  steel  rod  £  inch  diameter 
passed.  The  steel  rod  was  firmly  attached  at  each  end  to  brass 
plates  with  spherical  cups,  and  two  thermometers  were  also 
attached  to  the  rod.  Fresh  terminals  were  used,  consisting  of 
iron  castings,  with  ^-inch  vertical  holes  in  their  centres,  buried 
in  the  ground,  the  surface  of  the  ground  being  made  good  by 
iron  box  frames  and  lids. 

Adopting  precisely  the  same  method  as  before,  the  following 
results  were  obtained  in  1886  : — 


I. 

Feet 
83633022 

Differences. 

461      5*5 

in. 
1 

IS 

Feet. 
44289724 

Difference!. 
72       i-6 

in. 

1 

III 

II. 

83633786 

303 

36 

1 

44289682 

114 

23 

1 

III. 

83633640 

iS7 

19 

l 

442*89981 

185 

4-2 

1 

45 

83633483 

307 

37 

1 
57 

44289796 

124 

28 

1 
65 

Thus  a  greater  accuracy  than  1  in  100,000  was  obtained. 

The  10-feefc  measuring  rod  was  afterwards  further  improved 
by  making  the  wood  portion  of  square  box  section,  and  supporting 
the  steel  rod  on  rollers  along  the  centre  of  the  box.  Simple 
means  were  also  adopted  for  measuring  intermediate  lengths 
with  an  accuracy  of  i-iooth  of  an  inch.  The  thermometers 
were  bedded  to  the  steel  rod  with  mercury  amalgam.  A  de- 
tached thermometer  was  also  placed  inside  the  box  near  to  one 
of  the  other  thermometers,  and  the  steel  rod  was  blackened 
throughout  its  whole  length  to  increase  its  thermal  conductivity, 
the  weight  of  the  whole  rod  being  about  1 2  lbs. 

In  order  to  determine  the  exact  value  of  the  measuring  rod 
I  have  designed  a  variable  end  standard,  which  Messrs.  Troughton 
and  Simms  have  constructed  for  me. 

F  F 


390  Mr.  Crowley,  Description  of  xlvii.  6, 

It  consists  of  a  cold-drawn  steel  tube  i£  inch  external 
diameter,  with  a  telescopic  or  sliding  piece  at  one  end  having  a 
range  of  i  inch.  The  ends  are  parallel  plane  surfaces.  By 
means  of  a  vernier,  scale,  and  reading  microscope,  the  position 
of  the  telescopic  end  in  reference  to  the  tube  is  easily  deter- 
mined by  estimation  to  00005  incn,  and  with  care  to  0*00025, 
the  reading  being  to  o'ooi. 

The  tube  is  supported  in  a  stoat  mahogany  box  at  two  points, 
on  a  roller  at  one,  and  suspended  by  a  vertical  arm  and  cross- 
piece  at  the  other.  The  box  is  provided  with  brass  brackets 
at  each  end,  by  means  of  which  it  rests  upon  the  spherical  heads. 
One  bracket  has  a  spherical  cup,  the  other  bracket  a  cylindrical 
groove. 

By  means  of  suitable  screws  and  springs  the  plane  ends  of 
the  steel  tube  are  brought  into  firm  contact  with  the  spherical 
heads,  so  that  the  centres  of  the  spheres  lie  in  the  axis  of  the 
tube.  The  temperature  of  the  tube  is  indicated  by  two  thermo- 
meters. 

Most  of  the  comparisons  have  been  taken  on  two  iron 
brackets  firmly  attached  to  the  stone  wall  of  the  observatory, 
but  I  have  constructed  a  wooden  bench  carrying  two  iron  plates 
at  each  end,  connected  by  two  steel  rods  from  end  to  end  in 
such  a  manner  as  to  withstand  the  springs  of  the  steel  tube  or 
standard  10-feet  measure.  In  this  way  I  have  got  results  about 
0*0002  inch  less  than  when  the  comparisons  were  made  on  the 
iron  brackets. 

Six  sets  of  comparisons,  consisting  of  five  each  set  on  the 
iron  brackets,  gave  10*00296  feet  as  the  value  of  the  measuring 
rod,  with  a  mean  error  of  each  set  of  o*oooo  1 5  foot.  Another  six 
sets  on  different  days  gave  10*002951  feet  as  the  value,  with  a 
mean  error  of  each  set  of  0*000012  foot.  With  greater  reading 
power  I  have  no  doubt  that  one  set  of  comparisons  would  give 
the  value  of  the  rod  to  o*oooi  inch  or  0*00001  foot. 

The  average  difference  of  the  two  thermometers  on  the 
10-feet  standard  in  125  comparisons  was  o°*93  F.,  and  the  10- feet 
measuring  rod  under  similar  circumstances  o°*69  F.  The  differ- 
ence between  the  attached  and  detached  thermometers  adjoining 
one  another  on  the  measuring  rod  in  145  comparisons  was 
o°*i6  F.,  showing  a  close  approximation  of  the  steel  rod  to  the 
temperature  of  the  air.  Two  persons  can  make  five  comparisons 
in  12^  minutes. 

Experiments  for  expansion  gave  a  coefficient  of  61*5  ten- 
millionths  for  i°  F.  for  both  rods,  with  a  probable  error  of 
i*o  ten- millionth.  One  hundred  feet  have  been  set  off  with  the 
measuring  rod  eight  times  with  a  mean  error  of  0*0005  f°°t> 
showing  that  the  apparatus  is  capable  of  doing  reliable  work  to 
1  in  200,000.  One  hundred  yards  can  be  measured  easily  in  one 
hour  with  one  assistant. 

The  accompanying  drawings  will  make  the  above  description 
clear. 


OF 
^    **• 


i  &3 


April  1887.  a  New  Measuring  llod.  391 


Plate  1. 

Fig.  1  is  the  measuring  rod  of  square  box  section  resting  on 
two  tripods. 

Fig.  2  is  a  section  of  the  rod.  The  steel  rod  is  indicated  in 
both  drawings  passing  through  the  middle  of  the  box  on 
rollers.  At  each  end  of  the  rod  are  sights  for  lining.  In  the 
centre  is  the  clinometer,  and  between  these  the  two  thermo- 
meters. 

Underneath  the  rod  is  a  sliding  piece,  with  clamps  and  slow 
motion  and  hook  for  plumb  bob  for  measuring  part  lengths,  the 
rod  being  divided  every  six  inches,  an  ivory  scale  divided  on 
both  edges  giving  intermediate  lengths  to  the  hundredth  of  an 
inch. 

Fig.  3  shows  the  end  of  the  rod  and  the  top  of  the  tripod  in 
section,  and  fig.  4  the  top  of  the  tripod  in  plan. 

Figs.  5  and  6  show  a  method  of  supporting  the  tripods 
so  as  to  facilitate  the  levelling  of  the  rings,  by  moving  the  feet 
along  the  grooves  tangentially,  and  thus  tilting  the  rings  to  any 
desired  position. 

Fig.  7  shows  the  terminal  mark,  consisting  of  an  iron 
casting  A,  surmounted  by  a  brass  step  with  cap  at  B.  C  is  the 
box  frame  and  lid  for  making  good  the  surface  of  the  ground. 

Fig.  8  is  a  plan  of  C. 

Fig.  9  is  a  plan  of  A. 

Figs.  10  and  n  show  a  pedestal  suitable  for  supporting  a 
theodolite  centrally  over  the  spherical  head  on  one  of  the 
tripods. 

Plate  2. 

Fig.  1  shows  the  standard  10- feet  rod  resting  upon  two 
spherical  heads  upon  the  wooden  comparing  bench. 

Fig.  2  shows  the  above  in  longitudinal  section. 

Figs.  3  and  4  are  sections  of  the  rod. 

Figs.  5  and  6  show  the  telescopic  end  of  the  steel  tube,  with 
reading  microscope  and  adjusting  screws. 

Figs.  7  and  8  show  a  telescopic  tubular  rod,  which  is  more 
convenient  than  the  plumb  bob.  The  lower  end  is  conical, 
and  fits  into  the  brass  step  on  the  terminal.  The  upper  end  is 
cylindrical,  and  embraces  the  spherical  portion  of  the  milled 
head  as  shown  in  section,  fig.  9.  The  rod  will  then  rotate  on 
these  two  centres,  and  by  means  of  the  attached  level  the  vertical 
position  is  easily  found  with  considerable  accuracy. 


392 


Oreenunch  Observations  of 


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394 


Mr.  Prince,  Lunar  Occultations  etc. 


XLVII.  6. 


Lunar  Occultations  on  March  29,  1887.     By  C.  Leeson  Prince. 

I  observed  the  occultations  of  fire  stars  this  evening  under 
very  favourable  conditions. 

The  grey  light  of  the  non-illuminated  portion  of  the  Moon 
was  remarkably  distinct  at  the  limb,  and  its  gradual  approach 
to  each  star  could  not  be  watched  with  greater  exactness. 


Local  Sidereal  Time. 
Disapp. 


0»  Tauri 

0*      „ 

A  small  star 

A  bright  red  star ... 

B.A.G.  1 391 


h    m       s 

9  46  1 75 
9  55  22 
10    o  47*5 
10  31  23 
10  44  545 


Reapp. 

h     m      a 
10  42    6 

10  36  56 


About  three  or  four  seconds  before  occultation  of  the  three 
principal  stars  I  noticed  a  diffraction  phenomenon  which  I  do 
not  recollect  to  have  previously  observed,  viz.  that  as  the  Mood 
approached  each  star  the  brilliancy  of  the  latter  completely 
obliterated  the  grey  tint  of  the  lunar  surface  at  the  point  of 
contact,  and  a  dark  semicircle  appeared  thereupon  up  to  the 
moment  of  disappearance,  which  in  the  case  of  each  star  was 
quite  instantaneous. 

The  reappearance  of  Bl  and  02  Tauri,  so  far  as  I  could  judge, 
was  not  so  immediate. 

I  employed  my  Equatorial  telescope  of  6*8  inches  aperture  and 
12  feet  focal  length,  mag.  power  144. 

The  Observatory,  Crowborough,  Sussex : 
April  2,  1887. 


Errata. 

In  General  Tennant's  paper,  "  The  Orbit  of  Comet  II.,  1883,"  page  26, 
line  II, 

/or  L=U4  39  019 
read  I- 114  59  01*9 

In  General  Tennant's  paper,  "  Notes  on  Reflecting  Telescopes,"  page  258, 
line  8, 

for  Ap  a    ,  *  la  +  .  .  \  241;*  +  gv*  +  '  tf  +  &c.  [ A " - -2 

J        ^     16  16  l  2  '  32-4y*-3(;* 

j  .         a    1024.  +  6401;*  +  o6»l  +  4«a  +  u8  a  (       .        .    7  -     »     • 

readAp**    -.       *      *  -     f—    ,  **2a+   ^  1 24^  +  90*+  '-tfi  +  &c.\ 

r     16  32-4v,i-3u«  16 l  2  > 


MONTHLY    NOTICES 

OF  TUB 

ROYAL  ASTRONOMICAL  SOCIETY. 

Vol.  XLVII.  May  13,  1887  No.  7 

J.  W.  L.  Glaisuer,  M.A.,  F.R.S,  President,  in  the  Chair. 

W.  Austin  Ashe,  Director  of  the  Observatory,  Quebec  ;  and 
Guatavus  William  Nicolis,  Caixa  162,  Pernainbuco,  Brazil, 

were  balloted  for,  and  duly  elected  Fellows  of  the  Society. 


On  the  Images  formed  by  Reflecting  Mirrors,  and  their  Aberration. 

By  the  Hon.  Lord  McLaren. 

The  application  of  reflecting  telescopes  to  photography  renders 
it  desirable  that  their  suitability  for  large  fields  should  be  tested 
by  an  accurate  investigation  of  the  caustic  images  produced  by 
the  reflection  of  oblique  pencils  from  their  surfaces.  This  is  the 
purpose  of  the  present  paper. 

It  has  been  suggested  that  for  large  fields  a  mirror  of  spherical 
figure  possesses  some  advantages  over  that  of  the  parabolic  form, 
on  the  ground  that  the  spherical  mirror,  while  it  does  not  bring 
any  parallel  pencil  to  an  accurate  focus,  reflects  always  a  circular 
image,  and  gives  images  of  equal  intensity  at  all  angles.  The 
present  investigation  shows  that  for  fields  of  any  angle  likely  to 
be  required  in  practice — say  fur  any  angle  under  two  degrees — 
the  lateral  aberration  of  the  paraboloid  is  inconsiderable.  But 
it  also  brings  oat  a  variation  of  focal  length  for  different  dis- 
tances from  the  centre  of  the  field,  which  even  for  a  field  of  20  is 
considerable.  It  will  be  shown  in  the  sequel  that  the  cycloidal 
mirror  possesses  some  advantages  in  this  respect  over  mirrors  of 
the  parabolic  type. 

The  form  of  the  caustic  surface  produced  by  direct  reflexion 
from  a  spherical  surface  is  well  kuown  :  it  is,  near  the  imarre,  a 

6  G 


396  Lord  McLaren,  On  the  Images  formed  by        xltii.  7, 

cone  generated  by  the  revolution  of  an  epicycloid,  and  presents 
its  apex,  or  cusp,  to  the  observer's  eye.  I  have  not  found,  how- 
ever, in  any  work  accessible  to  me,  a  solution  of  the  problem  of 
the  caustic  surfaces  produced  by  the  reflexion  of  oblique  pencils 
from  a  paraboloid.  Sir  William  Hamilton,  in  his  great  Memoir 
on  the  "  Theory  of  Systems  of  Bays,"  *  finds  expressions  for  the 
caustics  formed  by  reflecting  surfaces  of  any  form.  The 
distinguished  author  has  not  shown  how  these  expressions  are 
to  be  integrated  for  parabolic  reflecting  surfaces,  and  I  am  not 
aware  that  his  differential  equations  have  been  integrated  for  the 
general  equation  of  a  surface  of  the  second  degree. 

The  .solution  which  I  offer  for  the  case  of  a  parabolic  mirror 
is  obtained  in  a  different  way,  and  is  perhaps  of  some  practi«-al 
interest.  It  will  be  seen  that  for  rays  of  any  inclination  to  the 
axis  of  symmetry  the  caustic  is  a  curve  resembling  a  parabola, 
confocal  with  the  reflecting  surface,  and  having  its  axis  inclined 
to  that  of  the  reflector  at  an  angle  depending  on  the  inclina- 
tion of  the  ray.  The  equation  of  the  caustic  curve,  referred  to 
its  own  axis,  is 

3 

The  small  arc  of  the  caustic  which  constitutes  the  image  of  a 
non-central  star  is  a  diminished  copy,  or  nearly  so,  of  the  arc  of 
the  reflector,  but  turned  round  so  as  to  lie  nearly  in  the  line  of 
sight.  The  image  of  the  whole  field  is  convex  to  the  observer's 
eye,  and  is  aplanatio  only  in  this  sense,  that  equal  arcs  of  the 
heavens  are  represented  by  equal  arcs  in  the  image  ot  the  field. 

Case  I. — To  find  the  equation  to  the  caustic  of  the  parabola  for 
parallel  rays  in  the  principal  plane.     (See  Plate  7.) 

Let  SjS^So  be  an  axial  section  of  the  parabolic  reflecting 
surface  in  the  plane  of  reflection,  O  the  focus  and  origin  of 
polar  coordinates. 

SjO,  S20  two  consecntive  vectors. 

Si  Pi,  SsPa  two  consecutive  reflected  rays,  on  which  let  the 
perpendiculars  OPb  OP3  be  let  fall  from  the  origin. 

S0O  (or  X)  is  the  axis  of  the  parabolic  reflecting  surface. 
S0P0  the  reflected  ray  proceeding  from  the  vertex,  and 

making  with  the  axis  an  angle  =  (<£). 
OP0  is  the  perpendicular  on  S0Po  from  0. 

Then  the  cnrve  P1P2Po  represents  the  locus  of  the  inter- 
sections of  the  reflected  rays  with  the  perpendiculars  drawn  from 
O,  and  the  curve  C^PqCj  represents  the  caustic,  or  locus  of  the 
intersections  of  consecutive  reflected  rays. 

Let  the  axis  of  the  reflecting  surface  be  the  reference  line 
for  the  polar  equation  /  (pO)  of  the  parabola,  and  also  for  the 

•  Trans.  Roy.  Irish  Acad.  Vol  XV. 


Monttilv 


O 


J%Xs*t.L?wrO* 


J 


May  1S87.    Inflecting  Mirrors,  and  their  Aberration.  397 

respective  polar  equations  f{p>ff)  and  /'O>"0")»  °f  the  curve 
PjP^Po  and  the  curve  C]P0C2. 

Then,  because  the  incident  pencil  is  a  pencil  of  parallel  rays, 
all  the  rajs  which  are  incident  on  the  parabola  at  points  S,,  32, 
Ac.  are  inclined  at  the  same  angle  (=  <j>)  to  the  lines  parallel 
to  X  which  pass  through  these  points ;  and  all  the  reflected  rajs 
are  inclined  at  the.  same  angle  (=—<£)  to  the  corresponding 
vectors. 

Or,  if  (x)  be  the  angle  between  the  normal  and  the  x 

coordinate  at  any  point  Slf 
(~~x)    the  angle  between    the    normal   and  the  radius 

vector  at  the  same  point, 
(X  +  $)  w*^  ^°  the  ang'e  °^  the  incident  ray  at  point  St, 
""  (x  +  t^)   wiN  b*  the   angle    of  the  reflected  ray  at  the 

same  point. 

In  other  words,  all  the  reflected  rays  SxP}i  S2P2,  Ac.  make 
equal  angles  (=  —  <£)  with  the  vectors  passing  through 
Sj,  S2,  &°. 

Therefore,  in  the  series  of  triangles  OSjP^  OS2Ps,  <fcc.  all 
the  angles  at  Slf  S2,  Ac.  are  =  <f>; 

and  all  the  angles  at  P19  P2,  Ac.  are  by  construction  right 
angles* 

Therefore  the  remaining  angles  S 1  OP lt  S2OP2,  <fcc.  are  each 
=  900  -  *. 

if  6  be  the  angle  between  the  reference  line  and  any  vector, 
OS  1  of  the  parabola,  then 

a^e+too9-*)* 

will  be  the  angle  between  the  reference  line  and  the  correspond- 
ing vector  OP!  of  the  curve  P^Pq.      Also 

vector  OP!  —vector  08,  x  sin <p, 

or 

/  -  p  sin  <p. 

Now,  if  the  reference  line  for  the  curve  Pi^2Po  be.  turned 
round  to  OP0,  while  the  reference  line  for  the  parabola  SlS2S0 
is  unchanged,  then,  for  any  correlative  points  SjPj  in  the  two 
curves  whose  current  coordinates  are  (Op)  and  ($V),  we  have 

$'  =  $, 

and 

pf  sm  p  sin  <p  —  p  x  constant. 

The  curves  are  therefore  similar  in  figure,  and  the  curve 
P,P2P0  is  a  parabola  with  parameter 

4a' = 4a  sin  <^ (a) 

where  (4  a)  is  the  parameter  of  the  reflecting  curve. 

*  In  the  figure  0  is  negative,  being  in  the  fourth  quadrant. 

G  G  2 


$98  Lord  McLaren,  On  the  Images  farmed  by        xi.vn  "7, 

The  equation  of  the  curve  P»PjP0  may  he  time  written  : 

^cos^-a'* (J>) 

From  this  construction  the  equation  of  the  caustic  may- 
he  immediately  deduced.  By  construction  the  derived  parabola, 
P,PjP0,  is  the  loons  of  intersecticns  of  perpendiculars 
drawn  from  O  to  the  reflected  rays.  By  definition  the  reflected 
rays  are  tunsrents  to  the  caustic  curve,  CjP0C2,  aud  the  caustic 
is  thus  the  first  negative  pedal  of  the  derived  parabola. 

The  equation  of  the  caustic  is  dednced  as  follows : 

By  a  known  property  of  pedal  curves,  if 

p*  cos  n&  »  am 
he  the  equation  to  a  curve, 

p"i*-H  cos  — TT*"4* a"*"*1 

r  m  +  1 

is  the  equation  of  its  first  negative  pedal.* 

Hence,    from    the    expression     for    the    derived    parabola 

[Equation  (&)] 

p'tcosjfrstf'l 

we  may  at  once  write  the  equation  of  the  caustic. 

It  is 

/i  cos  }r -41 (c) 

where  a'  is  the  prime  vector  in  both  curves,  and  is  =  a  sin  <£. 
The  caustic  touches  the  pedal,  or  derived  parabola,  at  the  vertex: 
P0.  For  any  value  of  0"  not  greatly  exceeding  900  the  caustic 
lies  within  the  pedal  parabola. 

When  0"  =s  2700,  cos  $$  =  o,  and  p"  becomes  infinite. 

The  caustic  is  evidently  a  looped  curve,  with  branches -inter- 
secting at  fhe  point  where  6"  =  1800,  and  tending  to  ultimate 
parallelism  with  a  line  at  right  angles  to  its  axis  of  symmetry. 

Locus  of  Cavstics. — If  we  suppose  the  inclination  of  the 
pencil  to  vary  we  shall  have  as  many  caustic  curves  as  there  are 
radiant  points  on  the  celestial  arc,  the  quantity  a'  representing 
in  each  case  the  distance  of  the  star  image  from  the  centre  of 
the  telescopic  field.  Before  proceeding  to  the  analysis  for  the 
surface  of  revolution,  it  may  be  noticed  that  in  the  parabolic 
mirror  the  locus  of  the  vertices  of  the  caustic  curves  is  the 
point  (P0),  being  the  angular  point  of  the  right-angled  triangle 
<">P0S0.  It  therefore  lies  on  a  circle  (shown  in  the  diagram) 
whose  diameter  is  the  focal  length,  OS0,  and  radius  =  ±  radius 
of  curvature  of  the  parabola  at  the  vertex.  That  is  to  say, 
all  the  foci  for  pencils  of  different  degrees  of  obliquity  (or 
star-images  of  variable  distances)  lie  on  the  circle ;  and  all  the 

*  Williamson,  Differential  Calcidus,  p.  231. 


May  1887.     Reflecting  Mirror*,  and  their  Ab«i*tttit>n.  39 

nUr-ioiagss   in   r.lio   field  lie  oo  a  spherical   surface  whose  culm 
=£  radius  of  curvature  of  parabola  at  vertex. 


Cask  II.  Caustic  Surface  for  the  Paraboloid  of  Revolution. — 
The  caustic  surface  mar  be  obtained  by  investigating  the  equa- 
tion of  the  plane  curve  for  any  plane  section  of  the  paraboloid 
passing  through  the  axis  or  at  right  angles  to  it. 

Except  in  the  case  already  considered,  neither  the  incident 
nor  the  reflected  ray  lies  in  the  plane  of  the  section,  nor  do  any 
two  consecutive  reflected  rays  lie  in  the  same  plane.  The 
solution  is  therefore  a  little  complicated,  bnt  it  may  he  found  by 
projective  geometry  commencing  with  the  following  preliminary 
proposition.* 

The  normal,  the  aiscitia  of  the  paraholoid,  and  the  incident 
ray  at  any  point  S  constitute  a  solid  angle,  whose  six  edges  and 
tingles  are  respectively  equal  to  those  of  the  solid  angle  formed 
by  the  rarmal,  the  vector,  and  the  reflected  ray.     (See  Figure  a.) 

If  we  denote  these  five  lines  by  their  initial  letters  we  have 
normal         —  a   abscissa,  parallel  to  X  — » 
incident  r.tj  —  i  radios  vector  ■  f 

reflected  rsy  -r       8  is  the  incident  point. 

The  same  letters,  n,  2, 1,  r,  and  p,  also  denote  the  points  of 

*  In  what  follows  the  reference  plane  for  projection!  is  s  lection  tliroiifih 
the  axis  of  the  paraboloid,  and  hanng  so;  required  inclination  to  thu  prin- 
cipal plane.    It  u>  assumed  that  the  reflected  rave  intersect  in  some  regular 


400  Lord  McLaren,  On  the  Image*  farmed  by         jlvii.  j, 

the  two  spherical  triangles  from  which  the  angles  at  8  are  to  be 
deduced. 

To  shout  that  the  tolid  angle  i,  n,  x  is  equal  to  the  solid  angle 
p  n  r. — The  three  lines  x,  n,  p  are  in  one  and  the  samerplane,  vis. 
the  given  axial  section  of  the  paraboloid,  and  angle  niS:i=angle 
n8p.  Also  the  three  lines  inr  are  in  one  plane,  being  the  plane 
of  refleii'in  ;  and,  hj  the  law  of  reflexion,  angle  iSn={ngle  nSr. 
Now  these  equal  angles  are  proportional  to  the  corresponding 
Rides  of  the  two  spherical  triangles ;  also  the  contained  angles 
formed  by  the  intersection  of  the  plane  laces  inrS,  mpS  are 
equal.     Therefore  the  remaining  sides  and  angles  are  eqnal. 

,-.  tf8»-i  iSx-f .     .     (i) 

£  betwooii  fnoes  rSp,  xSp^  L  batweep  faceoiS x,  xSp^-i      .     .     (*) 

These  equations  are  fundamental.  Equation  (d)  is  independ- 
ent of  the  particular  section.  It  affirms  that  for  any  point  S 
on  the  snrfaoe  of  a  paraboloids!  mirror  the  plane  angle  (rSp) 
between  the  reflected  ray  and  the  radius  vector  is  invariable, 
and  is  eqnal  to  #,  the  inclination  of  pencil  to  mirror  axis. 

In  Equation  (e)  it  is  easily  seen  that  the  quantity  i/<  is  the 
angle  between  a  given  axial  section  and  the  principal  plane. 
This  equation  affirms  that  for  any  point  S  on  the  given  mirror 
section  the  inclination  of  the  plane  faces  T|S(p,,  rfiipt.  &-'-  to 
the  plane  of  th.  >  section  is  constant,  and  eqnal  to  if/. 


From  these  equations  it  follows  directly  that  at  the  variable 
point  S  the  projection  of  the  reflected  i  ay  on  the  plane  of  the 

section  makes  a  constant  angle   (<£')  with  the  radius  rector,  and 


May  1887.     Reflecting  Mirrors,  and  their  Aberration.  401 

also  tbat  the  projection  of  the  reflected  ray  makes  a  constant 
angle  with  the  reflected  ray  itself.  (See  Figure  ft,  where  cx  is- 
a  point  in  the  caustic,  and  cx'  a  point  in  its  projection  on  the 
plane  of  the  axial  section,  OSjc/.) 

Because  if  we  consider  any  of  the  solid  angles  formed  at 
Si,  S2,  <fec.  by  the  vector,  the  reflected  ray  and  the  projection 
of  the  reflected  ray  (which  may  be  denoted  by  r7),  we  see 
that  its  edges  and  angles  are  proportional  to  the  angles  and 
sides  of  a  right-angled  spherical  triangle,  of  which  one  of 
the  sides =<£  and  one  of  the  angles  (other  than  the  right 
angle) =i^.  Now,  as  these  quantities  are  the  same  for  all  the 
solid  angles  at  S,,  Ss,  Ac.  it  follows  that  all  the  solid  angles 
hare  their  third  edges  and  throe  angles  respectively  equal ;  or 
generally,  for  the  solid  angles  at  points  Slf  S2,  Ac.  we  have 

Three  edges  respectively = ^,  90*,  900 — ♦» 

and  three  plane  angles  <f>y  <f>,  and  <£",  whose  equations  are  <f>, 
=  4  between  incident  ray  and  x. 

tan  <£'«=  tan  <£  coe  4  ~  constant (/) 

sin<p"«6in^einf .     .    (g) 

To  form  the  equation  of  the  caustic  curve  in  the  plane  of  pro- 
jection. 

With  the  same  diagram  and  notation  as  in  Case  I.,  the  plane 
of  the  paper  is  now  the  plane  of  the  given  axial  section,  making 
the  angle  (\j/)  with  the  principal  plane.  The  lines  AS] ,  AS9,  &c. 
are  the  projections  of  the  parallel  incident  rays  on  the  section. 
They  are  therefore  also  parallel,  and  make  a  constant  angle 
f(<t>ty)  with  the  corresponding  abscissae.  SP,,  SP2,  Ac.  are  the 
projections  of  the  reflected  rays,  to  which  the  perpendiculars 
OP,,  OPa,  Ac.  are  drawn  from  the  focus. 

Then  for  any  one  of  the  points  Si,  S9,  Ac.  we  observe  that 
the  plane  of  projection  intersects  the  plaue  of  reflexion  in  the 
normal  N ;  and  it  is  evident  that  equal  angles  measured  from  N, 
in  the  plane  of  reflexion,  are  represented  by  equal  angles  in  the 
plane  of  projection.  Therefore  the  projections  of  the  incident 
and  reflected  rays  make  equal  angles  with  the  normal  at  any 
point,  Si,  S3,  Ac.  of  the  series.  Then,  as  before,  pl$lt  p/0/, 
pi"#i",  are  the  current  coordinates  of  the  original  and  the  two 
derived  curves,  whence  we  deduce  the  curve  in  the  plane  of 
projection  identically  as  in  Case  I. 

Angles  OS.P,,  OSjP*  &<?.«**' [-constant,  by  Equation  (/)], 

Angles  S^Oj,  S2P302,  Ac.  are  by  construction  right  angles. 

Therefore 

Angles  S^Pj,  SsOP,=- 90- ^-constant. 

Hence  0P=0S  .  sin  <£',  or 

p'  =  ph\ntf  o/=-aeinf'  - 

0  (measured  from  iU  own  axia  0P#)—#  (measured  from  x). 


402  Lord  McLaren.  On  the  Image*  formed  by        XLvn.  7, 

Hence  the  curve  P^P,,  or  derived  parabola  f(p'9)y  is 
the  locus  of  intersections  of  perpendiculars  on  the  projections  of 
the  reflected  rays. 

1  ts  parameter  4a' -  4«  tin  +'. 

And  finally  the  negative  pedal  of  the  derived  parabola  is  the 
projection  of  the  caustic  of  the  given  section,  or  locus  of  inter, 
section*  of  the  consecutive  projections  of  the  reflected  ray*. 
It  is  as  before 

/(,"*")  -  /cos  !T  -  a:  ~  o, 

3 

where,  approximately, 

a'-atiiifeosf. 

We  thus  see  that  for  any  axial  plane  of  the  paraboloid  the 
projections  of  the  reflected  rays  form  a  caustic  curve,  having  the 
same  equation  as  the  caustic  curve  in  the  principal  plane. 

By  projective  geometry  two  curves  which  are  connected  by 
a  projective  relation  are  of  the  same  decree  and  the  same  class, 
and  differ  only  in  their  constant  coefficient's.* 

We  therefore  conclude  that  the  equation  of  the  caustic  is  of 
the  same  form  as  the  equation  of  its  projection,  and  it*  parameter 
only  remains  for  determination. 

Caustic  deduced  from  its  Projecfiott. — The  reflected  ray  from 
the  vertex  of  the  mirror  is  evidently  common  to  all  the  axial 
sections.  It  is  therefore  invariable  in  position  and  magnitude. 
The  prime  vector  d  of  the  caustic  deduced  in  the  principal 
plane  is  necessarily  also  common  to  all  the  axial  sections; 
because  it  is  tbe  line  drawn  from  the  origin  to  the  extremity  of 
the  ray  reflected  from  the  mirror  vertex.  That  is  to  say,  for  all 
axial  sections  of  the  mirror  we  have  caustic  curves,  of  the  same 
form  and  with  parameter  invariable  in  length  and  position ;  and, 
therefore,  if  the  axial  section  of  the  mirror  is  turned  round,  so  as 
to  generate  a  surface  of  revolution,  the  caustic  curve  also  will 
generate  a  surface  of  revolution  about  its  axis  of  symmetry. 

Circular  Section  of  the  Paraboloid. — The  result  jijst  obtained 
may  be  found  more  easily  by  considering  a  circular  section  of 
the  mirror  in  the  plane  YZ. 

In  such  a  section  let  pi,pj,  Ac.  be  tbe  vectors  drawn  from 
consecutive  points  Sj,  S2,  Ac.  of  the  circular  section  to  the 
focus  O.  They  are  evidently  of  equal  length,  and  their  integral 
is  a  right  cone,  having  its  vertex  at  O.  Let  r,,  rt,  Ac.  be  con- 
secutive reflected  rays  drawn  from  the  earn  a  series  of  points  Sl9 
8  j,  Ac. 

Thenby  Equation  (d)  (which  is  general  for  the  whole  reflect- 
ing surface)  all  the  angles  piS,r,,p,S2r2,  &a.  (although  lying  in 
different  planes)  are  equal  to  one  another,  being  equal  to  the 
constant  <f>. 

*  Cremona,  Projective  Geometry,  Chap.  II. 


May  1887.     Reflecting  Mirrors,  and  iheir  Aberrafion.  403 

Let  perpendiculars  OP,,  OP, be  drawn  from  O  to  the  reflected 
rays  rl9  r9,  Ac.  and  we  haye 

pi  nee  all  the  vectors  p{,  p^  Ac.  of  the  circular  section  are 
equal. 

The  locus  of  P  accordingly  is  a  small  circle,  described  on 
the  surface  of  a  sphere  whose  radius  p'  =  p  sin  <f>. 

This  small  circle  is  the  caustic,  because  the  consecutive 
reflected  rays  are  tangents  to  it. 

If  we  now  consider  two  opposite  points  of  the  mirror  section 
in  the  plane  of  the  luminous  pencil  we  see  that  for  one  of  tbe*e 
the  point  P  lies  outside  the  cone  of  vectors,  and  for  the  other 
it  lies  inside  the  cone.  The  line  joining  the  two  points  P  is  a 
diameter  of  the  caustic  circle ;  and  by  drawing  the  diagram  in 
perspective  for  two  parallel  circular  sections  of  the  mirror  it 
will  be  seen  that  the  caustic  circles  are  parallel  and  co-axial. 
Their  integral  is  therefore  a  surface  of  revolution  whose  equa- 
tion is  that  of  the  caustic  curve  in  the  principal  plane. 

Lateral  Aberration. — In  the  caustic  of  the  parabola  we  have 
not  to  find  a  circle  of  least  aberration,  because  at  the  focus 
the  aberration  is  nil,  and  we  have  only  to  determine  for  any 
particular  point  or  image  the  diameter  of  a  section  of  the  cone 
of  rays  through  the  plane  of  the  field  of  view.  The  aberration, 
whether  in  a  direction  radial  or  transversal  to  the  field,  is  to  be 
obtained  from  the  equation  to  a  section  of  the  surface,  in  terms 
of  the  focal  length  (a),  the  setoi-arc  of  mirror  (0),  and  the  in- 
clination of  pencil  (<j>). 

In  the  principal  plane  the  required  aberration  is  the  dif- 
ference of  the  distances  of  the  surface  of  caustic  and  its  tangent 
from   centre  of  field,  or  focus  of  paraboloid. 

The  latter 

=  a"  sec  B9  where  a"  —  a  si  n  $. 


The  former 


Therefore 


COS«(i*)  V3 


W!); 


aberration — a  si  0  $  [sec*  -sec*(-j  | (&) 


0  is  determined  by  the  aperture  of  mirror. 

The  rays  proceeding  from  that  half  of  the  caustic  surface 
which  lies  on  the  negative  side  of  its  prime  vector  constitute  the 
right  half  of  the  pencil  which  enters  the  eye-piece ;  those  pro- 
ceeding from  the  positive  side  of  the  prime  vector  constitute  the 
left  half  of  the  visual  pencil  It  is  evident  that  near  the  centre 
of  the  field  the  images  are  symmetrical. 

Except  near  the  centre  of  the  field  th^re  will  obviously  *>e 
a,  greater  dispersion    of  the    rays    in  the   plane  XZ  than  in 


,1«'. 


404  Lord  McLaren,  On  the  Images  formed  by       xlvti.  7, 


the  plane  XY  of  the  incident  pencil ;  and  the  diameter  of  the 
visible  image  will,  apparently,  oe  smaller  in  proportion  to  the 
dispersion.*  If  we  assume  that  the  visual  pencil,  in  the  direction 
XZ,  is  only  offeotive  to  the  extent  of  one-half  of  its  angular 
divergence,  then  we  have  for  this  aberration  the  quantity 

and 

Therefore,  by  Equation  (ft),  we  have,  in  a  direction  transverse 
to  radius  of  field, 

lateral  aberration  from  centre  of  image— a  sin  f  -?-  ]  [see0— sec-M-)  |    .  (0 

The  breadth  of  the  image  will  be  twice  this  quantity. 

Example  of  Computation  of  Lateral  Aberration. 

Assume  focal  length  =  16  feet  =192  inches  =  (a)  and  dia- 
meter of  mirror  =  24  inches. 

The  semi-arc  of  mirror  will  be  about  30  30'  =*=(0) 
For  a  star  i°  from  centre  of  field,  i°  =  (<£) 

log  sin  ft  — 8*2419 
— - —  -  o°7o72  "  43' 

log  sin  -I-  -  8  097  2 

V2 

sec0«=sec3°  30'  -1*0019 

«rc^  =  sec  i°  10'  :  log  s©c= -00009 


log  sfrc*  (  -  J  -  -00027     *         V3/ 


1  0006 


sec 


a-8ecf  (-)  - 00013=/  (secant). 


Then 

(1)  In  the  principal  plane  by  Equation  (&)  we  have 

log  192  inches  =  2*2833 

log  sin  ft -8  2419 

log/ (secant)  « log  0*0013-  -3"39 

log  latere  1  aberration  =  —3*6391 

lateral  aberration  =  '0044  ^ncn- 

*  Since  this  paragraph  was  written  the  writer  has  fonnd,  by  making  a  large 
*cale  perspective  drawing  of  the  course  of  the  rays,  considered  as  tangents  to 
the  caustic  surface,  that  the  converging  pencils  are  apparently  truly  symmetri- 
cal cones,  and  that  their  images  are  therefore  round.  This  agrees  with  the 
results  obtained  experimentally  by  Mr.  Howard  Grubb  {Monthly  Notice*  for 
April,  p.  .310);  and  it  is.  evident  from  the  equations  that,  if  the  images  are 
circular  near  the  centre  of  the  field,  they  will  be  circular  through  its  entire 
«xt*»nt,  provided  the  images  are  received  on  a  concave  plate  of  the  proper  cub- 
vature,  as  suggested  in  Mr.  Grubb's  paper. 


May  1887.     Reflecting  Mirrors,  and  their  Aberration.  405)- 

(2)  In  the  transverse  plane  by  Equation  (I)  we  have 

log  192       2*2833 


log  abV-X-       8-0972 

log  0*0013     -3*«39 
log  aberration  »  —  3*4944 
transverse  lateral  aberration  from  centre  of  image  « '0031  iaoh 

transverse  diameter  of  image  -  '0062  inch. 

III.  Elliptic  and  Hyperbolic  Reflecting  Surfaces. 

Although  the  writer  has  not  been  able  as  yet  to  obtain  an 
exact  solution  of  the  caustic  for  parallel  rays  incident  on  an 
elliptic  surface,  it  may  be  here  mentioned  that  if,  in  tbe  case  of 
the  ellipse,  a  similar  figure  to  tbat  of  Case  I.  in  this  paper  be 
drawn  with  divergent  and  convergent  pencils,  making  a  given 
angle  with  the  focal  pencils,  the  locus  of  intersections  of  per* 
pendiculars  on  the  reflected  pencil  will  be  a  small  ellipse- 
placed  obliquely  to  the  primary  ellipse,  and  the  caustic 
will  be  tbe  first  negative  pedal  of  the  derived  ellipse. 
Tbe  divergent  pencil  traced  backwards  will  be  found  to  proceed 
from  a  radiating  surface  conjugate  with  the  caustic  surface. 
The  caustic  curves  thus  derived  do  not  differ  sensibly  from  the 
CHustic  of  the  parabola  when  they  are  represented  graphically, 
and  from  the  manner  of  their  derivation  they  are  obviously 
curve*  involving  the  cubic  radical.  It  would  add  needlessly  to 
the  bulk  of  this  paper  to  give  the  demonstration  for  the  case  of 
the  elliptic  caustic.  By  drawing  the  diagram  with  divergent 
and  convergent  pencils,  and  using  the  same  notation  and  analysis 
as  in  Case  I.,  the  reader  will  have  no  difficulty  in  finding  tbat 
the  caustic  of  the  divergent  pencils  is  the  first  negative  pedal  of 
an  ellipse  whose  axis  is  inclined  to  the  minor  axis  of  the  reflect- 
ing ellipse  at  the  angle  (<j>)  which  the  divergent  pencil  makes 
with  the  major  axis.  The  same  notation  and  analysis  gives  for 
the  hyperbola,  with  converging  incident  pencils,  and  diverging 
reflected  pencils,  a  caustic  whose  equation  is  the  first  negative 
pedal  of  a  small  hyperbola  inclined  to  the  reflecting  hyperbola  as 
in  the  case  of  the  ellipse. 

The  relation  found  in  Case  I.  between  the  caustic  of  the 
parabola  and  the  equation  of  the  parabola  itself  is  thus  shown 
U>  he  only  a  limitiug  case  of  a  more  general  theorem  which 
includes  all  curves  of  the  second  degree.  For  if  in  the  case  of 
the  ellipse,  for  example,  the  major  axis  be  supposed  infinite,  then 
the  converging  pencil  (whose  rays  are  supposed  to  make  a 
constant  angle  with  those  of  a  focal  pencil)  becomes  a  pencil 
of  parallel  rays  having  the  given  inclination  to  a  pencil  parallel 
to  the  axis  of  the  reflecting  surface. 


406  Lord  McLaren,  On  the  Images  formed  by        xlytl  -jx 

IV.  Gycloidal  Surfaces  of  Revolution  — The  investigation  of 
the  conditions  necessary  to  the  prod  action  of  a  perfect  image  by 
reflexion  has  led  to  the  conclusion  that  these  conditions  are  better 
fulfilled  by  the  cycloid  than  by  the  parabola.  This  results  from 
two  well-known  properties  of  this  carve:  (i)  the  base  or  line 
on  which  the  gene  »*a  ting  circle  rolls  bisects  all  the  radii  of  cur- 
vature ;  (2)  equal  linear  intervals  measured  along  the  base  from 
its  centre  correspond  to  equal  angles  between  the  radii  of 
curvature. 

From  the  first  condition  it  results  that,  whatever  may  be  the 
angular  extent  of  the  6 eld  of  view,  the  geometrical  foci  of  the 
images  lie  on  the  base-line  of  the  cycloid  or  on  the  base-plane  of 
its  figure  of  revolution. 

From  the  second  condition  it  results  that  the  field  of  view  is 
a  true  stereographic  projection  of  an  area  of  the  celestial  sphere, 
equal  intervals  of  arc  in  the  sphere  being  represented  by  equal 
straight  lines  in  the  field  of  view. 

Caustic  of  the  Cycloid. — Consider  first  the  case  of  a  direct 
pencil  parallel  to  the  axis  of  symmetry  of  the  mirror  (represented 
in  the  left  quadrant  of  the  plate).  The  figure  represents  an 
axial  section,  the  base  being  parallel  to  the  axis  of  (a?),  and  the 
axis  of  symmetry  parallel  to  (//). 

IiS,,  I3S2,  Ac.  are  the  incident  rays. 

Ni'S|V  N2S2,  Ac.  the  normals. 

PiS^  P2Sa,  <fcc.  the  reflected  rays. 

/  (x  tf)  denotes  the  equation  of  the  reflecting  surface. 

/  (jxf  yf)  the  equation  of  the  caustic. 

IjSiNt,  I3S3Na  are  the  angles  which  the  normals  make  with 
lines  parallel  to  the  axis  of  x. 

Then  in  the  equation  of  the  reflecting  surface 


IA^-IAN.-ltan-^g). 


In  the  equation  of  the  caustic  I|StPi,  IaSsPs  are  the  angles 
which  its  tangents  make  with  the  axis  of  x.  And  because 
IiS]?},  IS88PS  are  the  sums  of  the  angles  of  incidence  and 
reflexion 

W\-IAP,«2(l|S,N,-IAN.). 

or 

\dx  J  ax 

That  is,  the  curvature  of  the  caustic,  at  Pt,  measured  by  the  deflec- 
tion of  its  tangent  for  unit  increment  of  arc  is  double  the  curva- 
ture of  the'  reflecting  surface  at  the  corresponding  point  S,, 
measured  by  the  deflection  of  its  normal  for  an  equal  increment 
of  arc. 

If  </>,  <£2  be  the  angles  between  consecutive  normals  to  the 
cycloid  and  the  relative  incident  rays  (parallel  to  y), 


May  1887.     'Reflecting  Mirrors,  and  their  Aberration,  407 

<£i'  <£a'  the  angles  between  the  same  normals  and  the 
base  x 

If  0X  02  be  angles  between  the  incident  rays  and  the  reflected 
rays  which  are  tangents  to  the  caustic 
#i'  02',  the  angles  made  by  the  normals  to  the  caustic  with 
the  base 

Bx  -ft,**,'— ft,'. 

Therefore,  from  Equation  («),  we  have 

0/-0,'«2(K-^). 

We  may  now  directly  compare  the  angles  made  by  the 
normals  of  the  two  carves  with  the  base-line.  If  we  make  the 
base-line  the  reference-line  for  angular  measure,  then  at  the  point 
O,  where  the  cycloid  and  the  caustic  are  in  contact,  <£'=o,  0'=o, 
and  for  any  other  position  the  normals  drawn  from  S  and  P  to 
the  respective  carves  make  angles  with  the  base-line,  having  the 
relation  0'  =  2<f>r. 

If  now  we  join  NjP,,  N2P2,  <fcc.  without  making  any 
assumption  as  to  the  valne  of  the  angles  at  Plf  P3,  <fcc.  we  have, 
by  the  geueral  equation  for  reflecting  surfaces  :* 

Length  of  reflected  ray  =  $  radius  of  curvature  x  cosine  of  angle  of  reflexion, 

or 

SP-NS.cosNSP. 

Therefore  the  angle  at  P  is  a  right  angle,  and  NP  is  a  normal 
to  the  caustic.  In  other  words,  the  normals  drawn  to  the 
respective  curves  from  the  extremities  of  the  rpflected  ray  intersect 
%n  the  base.     Also 

NP-NS.cosSNP-NS.coa^-^O-NSco**', 

which  may  be  written : 

p'^pcosf («) 

Now  consider  ON,  the  intercept  on  the  base-line  made  by  the 
normals  NS  and  NP  at  any  point. 

If  »=v  be  the  length  of  ON,  measured  from  0,  and  a  the 
radius  of  the  generating  circle  of  the  cycloid,  we  have  by  the 
"  tangential  equation  "  of  the  cycloid  and  trochoid 

v=2a<p {h) 

as  an  equation  between  coordinates  of  the  reflecting  surface 
(Williamson,  Diff.  Calc.  p.  339). 

*  In  ihe  Memoir  by  Sir  Willi  am  Hamilton,  before  referred  to,  this  relation 
i»  deduced  from  the  general  differential  equation  of  the  reflected  ray,  and 
is  shown  to  be  true  for  any  reflecting  surface,  where  the  my  is  contained  in  the 
plane  of  t  he  greatest  or  least  osculating  circle  to  the  mirror  ( Trans.  Roy. 
Irish  Acat'Vol.  XV.  r.  97)- 


408  Lord  McLaren,  On  the  Images  formed  by        xlyii.  7, 

And  in  the  equation  of  the  caustic  we  have,  for  the  same 
values  of  ON  or  v, 

r-2^.\  r-ar-aaV («) 

The  caustic,  therefore,  satisfies  the  *'  tangential  equation  "  for 
the  cycloid  and  trochoid  generated  by  a  circle  of  radius  a'=2<z. 
It  mast  be  a  cycloid  if  its  normal  vanishes  at  two  pointa  on  the 
base-line.  At  the  point  0,  where  the  reflecting  curve  and 
the  caustic  are  in  contact 

SN  or  p  -  o  :  /  -  o  [by  Equation  (a)]. 

At  the  centre  of  base-line 

2 

The  caustic  meets  the  base  in  two  cusps,  one  of  them  being 
coincident  with  the  cusp  of  the  reflecting  curve,  and  the  other 
being  at  the  middle  of  the  base-line. 

The  caustic  is  therefore  a  cycloid  with  radius  of  generating 
circle: 

«'-£ (<*) 

2 

and  base 

2*a'~£  base  of  reflecting  cycloid («) 

The  whole  caustic  surface  is  generated  by  the  revolution  of 
the  caustic  section  about  the  axis  of  symmetry. 

In  connection  with  the  caustic  of  oblique  pencils  we  shall 
have  occasion  to  refer  to  the  simultaneous  equations  (a)  and  (c)  : 

Caustic  of  Oblique  Pencils. 

With  similar  notation  and  construction  (see  the  right  qua- 
drant of  the  plate),  and  denoting  by  (^)  the  inclination  of  the 
obliquely  incident  rays  to  the  axis  of  symmetry  of  the  reflector, 
and  by  2  the  point  where  the  oblique  pencil  is  normal  to  the 
surface,  we  have,  as  before,  from  the  general  equation  of  re- 
flecting sufaces, 

SP'-NS.cosNSF, 

and  from  the  preceding  analysis  we  have :  angle  at  P,  a  right 
angle :  NP',  a  normal  to  the  cans  tic,  intersecting  NS,  the  normal 
to  the  reflecting  surface  at  a  point  N  in  the  base-line.  Now  if 
we  imagine  a  direct  ray  and  an  obliqne  ray,  both  incident  on  the 
reflector  at  the  same  point  S,  so  that  the  construction  in  figure 
(1)  is  superposed  on  that  of  figure  (2),  we  see  that  the  normal 
SN  and  the  po  nt  N  are  common   to  both  systems.      We  see 


May  1887.    BffleciUig  Mirrors,  and  their  Aberration.  409 

also  that  the  reflected  rajs  SP  and  SP'  (of  direct  and  oblique 
reflexion)  are  inclined  to  each  other  at  the  angle  \f/ ;  also  that  the 
normals  PN  and  PN  (of  the  caustics  of  direct  and  oblique  re- 
flexion) have  the  same  inclinations^.  Hence  for  any  one 
point  in  the  base-line, 

and  for  any  two  points  in  the  base-line,    (*-  r,)    (x-  rj 
we  have,  by  subtraction, 

that  is,  for  equal  differences  of  base  (or  progression  of  the  rolling 
circle)  the  differences  of  deflection  of  the  normals  in  the  two 
caustics  are  equal. 

The  caustic  of  oblique  reflexion  is  therefore  a  cycloid  satis- 
fy in  g  an  equation  of  the  form 

It  consists  of  two  unequal  branches  meeting  in  the  focus  of 
the  oblique  pencil,  or  rather  of  two  separate  cycloids  on  unequal 
bases,  and  together  occupying  the  base  of  the  reflecting  cycloid. 

Observing  that  the  length  of  base  of  the  caustio  of  direct 
reflexion  is 

it  is  easily  peen  that  for  the  caustic  of  oblique  reflexion  the  bases 
of  the  two  branches  are 

2»a"«2a'(ir+*) (/) 

and 

2»a'"-2a'(ir-^) (jg) 

by  which  the  generating  radii  a"  and  a'"  are  determined. 

It  is  supposed  that  in  the  case  of  the  ohliqne  pencil  the  whole 
caustic  surface  is  formed  by  revolution  with  varying  parameter 
about  the  line  2N,  which  is  thus  an  interior  tangent  to  the 
surface.  For  direct  pencils  the  caustic  surface  is  obviously  a 
true  figure  of  revolution  about  S0P0. 

The  rtsult  of  a  careful  investigation  of  the  aberration  is  that 
at  the  circles  of  least  aberration  or  least  confusion  there  is  very 
little  difference  between  the  sphere  and  the  cycloid  in  the  matter 
of  lateral  aberration,  while  if  the  preceding  analysis  be  well 
founded  there  would  be  little  or  no  longitudinal  aberration  for  the 
images  formed  in  a  cycloidal  mirror.  The  epicycloidal  caustic  of 
the  circle  of  curvature  falls  within  the  cycloidal  caustio  in  the 
figure. 

The  limits  of  this  paper,  however,  do  not  admit  of  the  further 
discussion  of  this  subject. 


41  o  Lord  McLaren,  On  the  Images  formed  by        XLVii.  7, 


Results. 

The  chief  interest  of  the  discussion  turns  on  the  possibility 
of  obtaining  symmetrical  images  from  the  caustics  of  oblique 
pencils  of  parallel  rays. 

1.  In  every  caustic  there  are  two  principal  points  in  the  curve 
to  be  considered.  One  of  these  (usually  denoted  by  the  letter 
q)  is  the  focus  of  the  elementary  pencil  reflected  from  the  central 
point  of  the  mirror.  Tde  other  principal  point  is  the  focus  of 
that  particular  element  of  the  pencil  which  is  a  normal  to  the 
reflecting  surface  (F). 

In  astronomical  instruments,  where  the  celestial  arc  viewed 
in  the  field  is  of  less  angular  extent  than  the  aic  of  the  mirror, 
either  of  the  points  described  is  a  possible  focus.  The  question 
which  of  the  two  is  the  true  visible  *bcu3  of  the  infinitely  distant 
point  is  one  which  must  be  considered  separately  for  each  kind 
of  reflecting  surface ;  because,  in  general,  a  visible  image  will 
only  be  formed  at  or  near  the  point  where  the  curvature  of  the 
caustic  is  a  maximum,  and  the  point  of  maximum  curvature  can 
only  be  determined  from  the  equation  of  the  caustic  itself. 

2.  Other  conditions  being  supposed  equal,  that  form  of  mirror 
is  to  be  preferred  in  which  the  visible  image  is  formed  at  the 
point  q  ;  that  is  to  say,  at  the  focus  of  the  element  of  the  con- 
verging pencil  which  comes  from  the  centre  of  the  mirror. 

It  is  proved  in  the  preceding  paper  that  for  a  paraboloids! 
mirror  this   point  constitutes  the  vertex  of  the  cubic  radical, 

which  is  the  caustic.     At  the  vertex  —   is  a  maximum ;  and  a 

dp 

greater  number  of  tangent  rays  will  pa*>B  through  a  small  finite 
arc  of  the  caustic  at  the  vertex  than  will  pass  through  a  con- 
secutive arc  of  equal  length.  Near  this  point  is  the  visible 
image,  and  it  is  a  remarkable  and  apparently  unique  property  of 
the  paraboloid  that  all  its  visible  images  are  formed  by  the  rays 
proceeding  from  the  central  part  of  the  mirror.  Moreover  the 
image  point  is  not  a  cusp,  but  only  a  point  of  maximum  intensity 
in  the  luminous  surface. 

It  is  possible  that  there  is  also  a  secondary  focus  at  the  point 
F  where  the  oblique  pencil  is  normal  to  the  parabola ;  but  this 
focus  has  not  been  investigated. 

3.  It  has  been  shown  for  the  case  of  the  paraboloid  that  the 
locus  of  the  field  of  view  is  a  sphere  touching  the  paraboloid  at 
the  vertex,  and  whose  radius  is  one-fourth  the  radius  of  curvature 
at  that  point;  and,  generally,  whatever  be  the  nature  of  the 
reflecting  surface  (provided  it  is  symmetrical  about  a  centre), 
the  sphere  here  found  will  be  the  locus  of  the  focus  of  rays  inci- 
dent near  the  centre  of  the  mirror.  I  am  indebted  to  Professor 
Oayley  for  the  following  proof  of  this  interesting  theorem  : — 
In  any  small  mirror  for  parallel  rays  inclined  to  the  axis  in 


May  1887.     Reflecting  Mirror*,  and  their  Aberration.  411 

the  principal  plane,  the  locos  of  the  focus  is  ft  oirc'e  whose  dia- 
meter =\  radius  of  curvature  at  vertex.     (See  Figure  e.) 


a  the  radius  of  curvaru,*  0  A. 
a  tlie  inclination  I  A  0. 
$  the  small  angle  A'  O  A. 

The  inclination  of  A'  q  to  axis  —0  +  26;  whence  if  xy  are 
coordinates  of  A',  and  X  T  current  coordinates, 
Equation  of 

X'qU  T-y--(X-*)tan(.4al) 

Aj  is  y     =-xtHQB 
*-a(i   «o»  »)--§»•« 

j  =  nBiiitt  -oS, 


Equations  are 


Y-y-.-(X-r)(tan«  +  a8.sec,<«) 


T+X  tan  «-o*-*X  mc*«.« 

Y  +  Xtans  =  o 


«9-aX>ec'o.»=o,  i.e.  X-l*eo»'B.-.^ 

X'  +  Y'-fl'MB'a 


—  *•« 
-i«X, 


which  is  circle  on  diameter  A F  (if  A  F=£  AO). 

In  the  case  of  the  paraboloidal  mirror  the  UMym metrical 
form  of  the  visible  images  near  the  bonndary  of  the  field  is  attri- 
butable mainly  to  the  curvatnre  of  the  field-snrfare,  which  has 
of  conrse  the  effect  of  throwing  the  non-central  part  of  the  6eld 
ontside  the  focus  of  the  eye-piece  or  ontside  the  plane  of  the 


412  Dr.  Dreyer,  Nebula  suspected  of  xlttj.  7, 

•photographic  plate,  as  the  case  may  be.  With  a  photographic 
})late  ground  to  a  concave  surface  of  the  proper  curvature,  there 
is  reason  to  believe  that  symmetrical  star  images  may  be  obtained 
in  a  field  of  the  usual  angular  extent.  Bnt  this  is  subject  to  the 
objection  that  the  plate  will  always  stop  out  the  central  and  best 
part  of  the  pencil. 

4.  In  the  spherical  Mr&tftR  the  visible  image  will  not  coincide 
with  the  focus  for  rays  incident  at  the  centre  of  the  mirror  unless 
the  angle  subtended  by  the  arc  of  the  mirror  is  supposed  to  be 
small  relatively  to  the  angle  of  incidence  of  the  oblique  pencil. 
For  the  actual  conditions  of  astronomical  images  the  visible 
field  will  be  the  locus  of  the  point  F,  or  locus  of  the  epicycloidal 
cusps,  which  are  the  points  of  greatest  condensation  for  the 
respective  pencils.  For  any  given  pencil  the  cusp  of  the  caustic 
lies  in  the  line  where  the  ray  is  a  radius  of  the  spherical  surface. 
Hence  the  geometric  field  is  a  spherical  surface  concentric  with 
the  mirror  and  having  half  the  radius  ;  and  the  visible  field  lies 
very  near  it. 

5.  Evidently  a  spherical  mirror  will  not  give  symmetrical 
images,  except  near  the  centre,  because  it  is  only  at  the  centre 
of  the  field  that  the  visible  images  are  formed  by  the  central  part 
of  the  mirror.  Neither  will  the  sphere  give  a  flat  field,  though 
it  will  give  a  nearer  approach  to  one  than  the  parabola.  Against 
this  advantage  we  must  set  off  the  objection  that,  except  at  the 
centre  of  the  field,  its  images  are  not  formed  by  the  central  part 
of  the  mirror. 

6.  As  to  the  ctcloidal  mirror,  if  the  preceding  analysis  be 
correct,  the  locus  of  the  cusps  of  the  cycloidal  caustio  is  a  plane 
surface,  but  the  images  become  unsymmetrical  as  they  recede 
from  the  centre  of  the  field.  It  is  not  meant  to  be  asserted  that 
the  visible  field  will  be  a  true  plane,  because  the  visible  field  is 
the  locus  of  the  circle  of  least  aberration,  which  is  not  identical 
-with  the  locus  of  the  caustic  cusps.  But  the  field  will  be  very 
nearly  a  plane  surface. 

It  is  right  to  add  that  the  possibility  of  obtaining  a  flat  field 
by  reflexion  has  been  doubted  by  mathematicians  of  high 
authority,  and  it  must  be  left  to  the  reader  to  form  his  own 
opinion  of  the  validity  of  the  reasoning  by  which  the  conclusion 
last  announced  has  been  reached. 


On  some  Nebulce  hitherto  suspected  of  Variability  or  Proper  Motion. 

By  J.  L.  E.  Dreyer,  Ph.D. 

The  discrepancies  met  with  in  comparing  observations  of 
nebulce  by  different  observers  are  frequently  so  great  that  more 
or  less  positive  assertions  have  naturally  from  time  to  time  been 
made  as  to  variability  or  changes  in  the  objects.  While  many 
of  these  assertions  can  at  once  be  dismissed  as  showing  that  too 


May  1887.  Variability  or  Proper  Motion.  413 

little  regard  has  been  paid  to  the  great  difficulties  attending 
observations  of  neb u lee  or  to  the  vast  influence  of  the  state  of  our 
atmosphere  from  night  to  night,  others  are  either  founded  on 
undoubted  facts  or  appear  at  least  to  others  than  practised  ob- 
servers of  nebulee  to  be  so.  It  seems  that  the  only  well  authenti- 
cated cases  of  change  in  nebulee  are  changes  of  brightness  only, 
while  we  so  far  do  not  possess  any  clear  evidence  of  change 
of  form  or  change  of  place. 

The  most  generally  known  case  of  a  nebula  having  disap- 
peared— that  of  Hind's  nebula  in  Taurus — is  also  the  most 
certain  and  undisputed  one.  Chacornac's  nebula  (GkC.  1191)9 
though  only  seen  by  that  observer,  doubtless  also  existed  in  a 
place  where  no  nebulosity  has  since  been  seen ;  but  these  two 
cases  are  the  only  ones  which  are  quite  certain.  It  is  true  that 
some  of  William  Herschel's  nebulee  cannot  now  be  found,  but 
these  may  either  have  been  comets,  or,  more  probably,  some 
error  of  observation  has  vitiated  the  position  he  gives  for  the 
object  in  question.  The  latter  case  must,  e.g.,  have  occurred  on 
April  2,  1 80 1,  when  he  compared  a  number  of  nebulas  (among 
which  are  three  of  the  first  class)  with  one  comparison  star, 
which  he  identifies  as  "  208  (N)  Gamelop.  of  Bode's  Cat."  As 
not  one  of  these  objects  can  now  be  found,  it  is  evident  that  he 
made  a  mistake  either  in  identifying  the  star  or  in  making  or 
recording  the  observation  of  it.  Another  case  is  G.C.  2179 
s=  I  26,  which  possibly  may  be  an  erroneous  observation  of  the 
neighbouring  M  95.  The  remarkable  nebula  at  Merope,  and  a 
less  notable  one,  G.C.  710,  were  by  d' Arrest  and  others  sup- 
posed to  be  variable,  because  the  difficulty  of  seeing  them  with 
a  large  aperture  made  it  appear  strange  that  they  had  been 
described  as  conspicuous  in  small  instruments.  This  difficulty 
is,  however,  now  universally  understood  to  arise  from  the  use  of 
too  high  a  power  with  consequent  smallness  of  field ;  and  nobody 
now  suspects  these  two  nebulas  of  variability. 

I  shall  not  enter  into  an  examination  of  the  numerous  in- 
stances where  observers  disagree  as  to  the  brightness  of  an 
object.  Probably  atmospheric  or  instrumental  circumstances 
could  in  most  cases  account  for  this  disagreement ;  but,  all  the 
same,  the  possibility  of  nebulas  changing  in  lustre  cannot  be 
denied,  since  we  have  witnessed  the  total  disappearance  of  two 
of  them.  Bat  I  propose  to  go  through  all  the  objects  which 
have  been  suspected  of  having  changed  in  form  or  position,  and 
I  trust  I  shall  be  able  to  prove  that  not  one  of  the  cases  can  be 
considered  as  well  established. 

Most  of  the  nebulas  examined  in  the  following  are  double 
nebulas,  which  have  been  suspected  of  being  in  motion.  They 
have  been  collected  (from  d' Arrest's  work)  by  M.  Flammarion 
in  an  appendix  to  his  "  Catalogue  des  Etniles  doubles  et 
multiples  en  mouvement  relatif  certain."  In  all  cases  the  sus- 
picion is  founded  on  differences  in  their  relative  positions,  as  re- 
corded by  Sir  William  and  Sir  John  Herschel  and  by  later 

h  H  2 


414  Dr-  DteyeTt  Nebula  suspected  of  xlvii.  7, 

observers,  and  it  does  not  seem  to  have  been  generally  noticed 
that  Sir  W.  Herschel  never  employed  a  micrometer,  but  merely 
estimated  the  position-angles  and  distances  of  neighbouring 
nebulae,  and  that  Sir  John  Herschel  did  the  same  from  the  com- 
mencement of  his  observations,  and  np  to  July  5,  1828.*  After 
this  date  the  eye-piece  of  his  18-inch  Reflector  was  famished 
with  a  wire  micrometer,  with  which,  however,  only  position- 
angles  could  be  measured,  while,  as  formerly,  distances  (both  of 
nebula?  and  doable  Ktars)  were  only  estimated.  Even  then  be 
frequently  estimated  angles,  in  which  case  they  were  given  only 
to  whole  degrees;  whenever  a  decimal  is  given  it  shows  that 
the  position-angle  was  measured.  Although  such  estimations 
should  evidently  not  be  used  (or  at  least  only  with  great 
caution)  in  drawing  conclusions  as  to  orbital  or  proper  motion, 
I  have  thought  it  desirable  to  re-observe  many  of  the  objects  with 
the  new  10- inch  Refractor  at  the  Armagh  Observatory,  which  I 
am  devoting  to  micrometric  observations  of  nebula?.  The  pair 
h  444-445  were  measured  with  a  filar  micrometer ;  the  others 
with  a  small  micrometer  with  steel  bars  instead  of  spider  lines, 
and  requiring  no  illumination.  Although  distances  measured 
with  the  latter  kind  of  micrometer  are  doubtless  subject  to 
systematic  errors  (which  I  intend  to  investigate),  their  accuracy 
is  quite  sufficient  for  the  present  purpose. 

Great  Nebula  in  Andromeda. — The  question  as  to  variability 
of  this  object,  first  raised  by  Le  Gentil,  has  been  thoroughly  dis- 
cussed by  G  P.  Bond  in  bis  well-known  Memoir,  and  he  comes 
to  the  conclusion  that  the  views  of  Le  Gentil  are  "  far  from  being 
supported  by  an  amount  of  evidence  adequate  to  such  a  con- 
clusion." The  nucleus  has  been  drawn  or  described  in  a 
remarkably  different  manner ;  by  some  (e.g.  Schultz,  Schonfeld, 
Vogel)  as  starlike,  by  others  at  the  verv  same  time  (e.g. 
Schmidt:  see  Vogel's  note  in  A$tr.  Nachr.  No.  2681)  as  a  very 
soft  and  gradual  condensation.  These  strange  discrepancies 
are,  however,  explained  by  the  valuable  experiments  made  by 
Dr.  Gopelandf  with  different  eyepieces,  which  show  what  an 
immense  influence  the  magnifying  power  has  on  the  appearance 
of  the  nucleus,  the  lower  powers  making  it  more  starlike,  the 
higher  ones  more  soft-looking  and  extensive.  Whether  the  new 
star  of  1885  really  belonged  to  the  nebula  or  not  does  not 
concern  us  here ;  but  Dr.  Copeland's  experiments  with  artificial 
stars  and  different  illumination  of  the  field  prove  that,  even  if  a 
real  change  had  taken  place  in  the  nebula  at  the  time  of  the  out- 
burst, it  could  not  have  been  detected  as  long  as  the  star  was 
shining  brightly.  Since  the  fading  of  the  star  the  nebula  has 
quite  resumed  its  former  appearance. 

IJI.  228-229  as  h  251-252. — M.  Flammarion  remarks  that  W. 
Herbchel  estimates  the  distance  at  about  1',  while  d' Arrest  gives 

*  See  Mem.  R.A.S.,  toI.  iv.  p.  331. 
t  Monthly  Notices,  vol.  xlrii.  p.  60. 


May  1887.  Variability  or  Proper  Motion.  41 5 

A  a  =  8s,  and  estimated  (on  one  occasion)  the  distances:  n  2"  ±. 
There  is,  however,  perfect  accordance  between  J.  Herschel  and 
d' Arrest,  for  the  former  gives  Aa=  7»*5,  while  the  distance 
resulting  from  his  positions  is  134".  Both  nebulae  are  very  faint, 
especially  the  following  one,  which  d' Arrest  describes  a9  "in- 
dubitatnm  nebulae  vestigium,  adeo  tenne  tamen,  ut  vitmm  eagre 
sustineat."  His  estimated  distance  is  too  small,  as  one  can  see 
by  a  glance  at  his  A  a. 

III.  574-575  =  h  294-295. — While  Sir  W.  Herschel  does  not 
say  anything  about  the  relative  positions  of  these  two  very  faint 
objects,  Sir  John  gives  the  following  positions  for  1830  (one 
observation) : — 

h     m        ■         o  «     (The  np  of  2.     Pos.  from  the  following 

h  294      3     10    25  8      49     1822   J  which  i8  the  largest,  3520-4,  dist.  100' . ' 

295      3     10    269      49     1644.     The  ttf  of  two. 

while  according  to  d' Arrest  Aa  =  48,  the  following  one  being 
124"  south  of  the  preceding  one.  A  glance  at  Sir  J.  Herscbel's 
positions  and  remarks  shows  that  no  conclusion  can  be  drawn 
from  them.  If  the  tirst  one  was  "  the  tip  of  2,"  the  second  can- 
not have  been  "  the  nf  of  2,"  and  if  the  position-angle  of  the 
first  one  from  the  second  one  was  352°*4,  the  N.P.D.  of  the  first 
one  most  have  been  smaller  than  that  of  the  second,  and  not 
greater.  D'  Arrest's  A  a  and  A  8  give  the  position-angle  of  the 
first  one  =  339°'9  and  the  distance  =  132";  but  he  remarks: 
"  Situs  relativi  observatio  plurimis  laborat  difficultatibus,"  so 
that  the  difference  of  120  between  Herschel  and  d* Arrest  is  net 
surprising.  Probably  Sir  John  Herschel  determined  the  R.A. 
and  Decl.  of  the  following  one,  measured  the  position-angle, 
estimated  the  distance,  and  afterwards  from  these  data  made  out 
the  A  a  and  A  8,  in  doing  which  he  accidentally  gave  the  latter 
the  wrong  sign,  placing  the  preceding  nebula  south  of  the 
following  one,  instead  of  north  of  it. 

II.  8-9  =  h  316-317. — M.  Flammarion  says  that  in  1830 
(should  be  1827)  the  position-angle  was  300  to  400 ;  while 
d' Arrest  in  1862  (should  be  1863-65)  found  it  =  8o°±.  This  is 
however  not  correct,  for  Herschel  says :  "  Pos.  by  a  drawing  made 
at  the  time  300  .  .  .  400  n/,"  which  means  that  he  estimated  it 
equal  to  6o°  .  .  .  500.  At  Birr  Castle  the  angle  was  in  1850  on 
two  nights  measured  =  770  and  75°*5,  and  in  1876  =  78°*8.  In 
1783  Sir  W.  Herschel  determined  the  places  of  these  two  nebulae, 
according  to  which  the  second  one  should  then  have  been 
1'  south  of  the  first  one;  but  as  his  earliest  observations  are  very 
inaccurate,  no  conclusion  can  be  drawn  from  them.  At  any  rate, 
the  objects  were  stationary  from  1850  to  1876. 

Great  Nebula  in  Orion, — This  object  has  more  frequently  than 
any  other  nebula  been  suspected  of  having  varied  in  form,  bat 
on  the  other  hand  it  has  been  more  thoroughly  examined  and 
discussed  than  any  other.     From,  his  own  observations  and  his 


416  Dr.  Dreyer,  Nebula  suspected  of  xlyii.  7, 

examination  of  the  principal  monographs,  d 'Arrest  drew  the 
conclusion  that  "  the  observed  changes  in  this  vast  mass  of  gas 
peem  exclusively  to  turn  oat  to  be  temporary  fluctuations  of 
brightness,"*  and  the  elaborate  discussion  of  all  previous  obser- 
vations in  connection  with  his  own  led  Professor  Bolden  to 
state  "  that  the  figure  of  the  nebula  in  Orion  has  remained  the 
same  from  1758  till  now  (if  we  except  a  change  in  its  apex  about 
1770,  which  appears  quite  possible),  but  that  in  the  brightre** 
of  its  parts  undoubted  variations  have  taken  place,  and  that 
such  changes  are  even  now  going  on."f 

IV.  25  =  h  428. — A  double  star,  h  749,  involved  in  (or  pro- 
jected on)  a  fan-shaped  nebula.  In  1827  the  position-angle  was 
estimated  =  1250,  and  the  distance  12";  in  1863  d'Anest  esti- 
mated them  1200  and  4".  There  has  been  no  change,  as  two  ob- 
servations made  at  Birr  Castle  in  1874-76  give  119°  it".  But 
even  if  there  had  been  a  change  in  the  distance  of  the  double 
star,  this  could  not  really  be  called  a  change  in  a  nebul  t.  Sir 
W.  Herschel  did  not  notice  the  duplicity  of  the  star. 

II.  316-317  =  ^444-445. — In  the  Astr.  Nachr.  No.  1366, 
d 'Arrest  called  attention  to  the  following  remarkable  disci**  |'ati<y 
between  tbe  then  existing  observation  of  this  fine  double 
nebula : — 


H 

1785 

Pos. 

O 

#/ 
List.  60 

h 

1827 

M 

45 

,»    45 

d'A 

1862 

»» 

56*5 

„    285 

At  first  sight  this  certainly  looks  like  orbital  motion.  But, 
unfortunately,  Sir  John  Herschel  only  estimated  the  angle  and 
distance,  and  his  two  estimates  of  the  latter  differ  very  much 
inter  se,  being  30"  and  60''.  It  is,  however,  only  fair  to  add 
that  d* Arrest  merely  showed  the  disagreement  without  makiug 
it  out  to  be  a  sure  case  of  motion.  Tbe  following  later  measures 
show  that  the  pair  have  been  at  rest  during  the  last  twenty-five 
years : — 

Schultz     1864-65       Pos.  591        Di&t.  3r6  (4  nights). 

Dreyer     1876  „     53-9  „     277  (Birr  Castle,  I  night). 

Dreyer    1887  „     57-3  „     323  (2- nights). 

Tbe  two  nebulaa  are  connected  (see  Phil.  Trans.  1850,  pi. 
xxxviii.,  and  Birr  Obs.  1848-78,  pi.  ii.).  The  following  one  is 
fainter,  smaller,  and  far  less  condensed  in  the  middle  than  the 
preceding  one. 

h  705. — This  iB  a  very  interesting  object :  a  double  star 
(h  2529)  with  nebulosity  attached.  In  "The  Observatory," 
vol.  viii.,  p.  127,  Mr.  H.  Sadler  suggested  that  here  might  be  a 
possible  case  of  proper  motion  in  a  nebula,  since  Mr.  Burnham 

*   Underwogelser  over  de  nehulose  Stjerner  (1S72),  p.  42. 
+  Holders  Monograph,  p.  225.. 


May  1887. 


Variability  or  Proper  Motion. 


417 


in  1879-82  saw  the  nebula  "  19"  from  the  principal  star," 
-while  Sir  J.  Herschel  in  1830-31  said  the  nebula  was  about  the 
principal  star.  It  will  bo  well  to  put  together  all  the  observa- 
tions made  by  Herschel,  both  as  they  are  recorded  in  his  fifth 
list  of  double  stars  *  and  in  the  Phil.  Trans.  1833. 


Sweep. 


Double  Star  Ob*. 


« 


243 


J 


Pos.    95*3    Dist.  1 J 


»i 


10  8 


*t 


Obe.  of  Neb. 
.A  most  curious, deli-. 

^iKS   *T*  *.  D  *   of  the 

examined  .nth  3*>,  }"n<*»lou«  ™P-     "A  most 
-  •    J         ctihou6,  delicate,  and  inter- 
esting object." 


proves     to    be    dis- 
tinctly a   first-class 
Mouble  star.  } 


242  • 


338 


1* 


»t 


l» 


>I 


95  4 
80 

33o  ±t 
70 


ii 


i» 


1 

7 
6 


l  A     nebula    strongly . 

suspected  about  the )  A  ..  ,     .  .    . 

closVdoubleHtar.  and  I A  «"Ple  8Ur  ,n  *  »eon,a'  a 
a   fourth    star  also  I fourth  *  ">"¥«*•*• 
suspected.  J 

{A  double   star  in  a] 
very  faint  nebula  (a   A  double* in  a  v  F  nebula, 
hurried  observation)., 


In  the  "  Remarks "  on  the  double-star  observations  (I.e. 
p.  78)  Herschel  alludes  to  this  object,  Raying  that  "  a  minute  and 
very  close  double  star  forms  the  nucleus  of  a  small  round  nebula ; 
one  or  two  other  small  stars  in  the  immediate  vicinity  seem  un- 
connected with  it,  but  the  exactly  central  position  of  the  double 
star  strongly  points  to  a  physical  relation  between  them."  It  is, 
however,  not  to  these  remarks,  written  several  years  afterwards, 
but  to  the  observations  themselves  that  we  must  look  for  evidence 
of  motion.  D*  Arrest  observed  the  object  three  times  in  1864-65  ; 
he  saw  a  star  of  1011  magnitude  with  a  star  13  mag.  about 
12"  nnf.,  the  latter  being  the  centre  of  a  nebula  which  reached  to 
the  former  star.  In  1872  the  following  observation  was  made  at 
Birr  Cas'le:  "Neb.  to  *  9  m  Pos.  i93°o,  Dist.  19"' 7,  *  9  to  *  12m 
243°'3,  8"'8,"  and  in  1876:  "Double  star,  1011  and  15*16  mag. 
5°'o,  21",  vF  neby  round  it,  E  north  and  south."  Mr,  Burnham  J 
in  1879  and  1882  saw  only  the  wide  pair  in  Pos.  70  9, 
Dist.  i9"*o  (and  once  the  faint  companion  sp  the  brighter  star), 
and  remarks,  "  The  nebula  is  now  19"  from  the  principal  star." 

All  this  does  not  seem  to  prove  that  the  nebula  has  moved 
away  from  the  close  double  star,  for  it  is  only  in  the  remarks 
that  Herschel  calls  the  latter  the  nucleus  of  the  nebula,  while  the 
observation  in  sweep  243  merely  says  that  it  was  involved,  which 
is  not  contradicted  by  the  later  observers.     Mr.  Burnbam  of 


*  Mem.  R.J. 8.,  vi.  p.  32. 

f  Should  be  2300.    See  d'Arrest  and  Burnhara. 

J  Mem.  R.A.S.  xlvii.  p.  270. 


4i 8  Br.  Dreyer,  Nebulce  inspected  of  xlvii.  7, 

coui>e  did  oot  mean  that  the  edge  of  the  nebula  was  19"  from 
the  close  double,  but  that  the  nucleus  was  at  that  distance,  which 
it  is  still.  Having  during  the  two  years  elapsed  since  Mr.  Sadler's 
note  appeared  quite  forgotten  all  the  details  about  this  object,  I 
looked  it  up  on  March  15  last  on  finding  it  on  my  working  list, 
and  noted : — 

"  Nebulosity  nearly  reaches  the  south  *  if  it  does  not  actually 
touch  it.  '  It  is  oval  in  shape,  £  in  the  same  pos.  angle  as  the 
two  stars.  I  saw  only  the  two  stars,  but  definition  was  not 
particularly  good.  The  north  star  looks  more  like  a  nucleus 
than  a  *." 

This  agrees  perfectly  wirh  d' Arrest's  observations,  so  that 
there  can  have  been  no  "  proper  motion "  between  1865  and 
1887,  and  it  may  safely  be  inferred  that  there  has  been  none 
since  1830,  unless  we  are  to  believe  in  this  and  similar  cases  that 
nebula  in  the  good  old  days  moved  about  as  they  liked,  but 
have  been  on  their  good  behaviour  since  1861  and  kept  quiet. 

Great  Nebula  around  17  Argils. — It  is  sufficient  to  refer  to 
the  various  papers  on  the  alleged  discovery  of  vast  changes  in 
this  nebula  in  the  Monthly  Notices,  vol.  xxxi.  There  has  ever 
since  been  perfect  unanimity  among  astronomers  that  the 
changes  were  "altogether  imaginary  "  (Ibid,  xxxii.  p.  178). 

I.248,  11.832  =  ^983-984. — W.  Herschel  in  1790  made 
Aa  =  12s,  giving  both  nebulas  same  N.P.D.  In  1832  J.  Herschel 
.  found  Aa  =  128,  the  second  nebula  being  (estimated)  45"  north 
of  the  first.  In  1866  d'Arrest  found  I3B*5  and  57''.  "Mouvement 
certain,"  says  M.  Flammarion.  On  the  27th  April  last  I  found 
Pos.  angles  6i°*i,  Dist.  =  i2o"*o,  or  A«  =  i4,#o,  A3  =  58". 
Both  are  pretty  large  and  vgb  M  to  a  very  soft-looking  nucleus. 
No  change. 

III.  394-395  =  /*  1065-1067. — M.  Flammarion  considers  that 
the  position-angle  has  changed  200  since  Sir  J.  Herschel  in  1830 
twice  estimated  it  =  70° ;  while  d'Arrest  in  1864  on  three 
occasions  states  that  they  are  on  the  same  parallel.  But  in  1865 
he  says  that  the  second  one  is  "pauxillnm  quid  ad  boream,"  and 
so  it  is,  for  at  Birr  Castle  in  1872  it  was  measured  in  Pos.  82°'7, 
Dist-  69//,5,  and  on  April  11  last  I  found  Pos.  79°*5,  Dist,  68"#5- 

II.  751-752  =  ft  1905. — Two  connected  nebulsB,  the  pre- 
ceding one  very  little  elongated,  the  following  one  much  so ; 
figured  in  Phil.  Trans.  1833,  fig.  77  (one  observation)  and  1861, 
fig.  31.  The  late  Lord  Rosso  remarked  (I.e.  p.  704)  that  in  Her- 
schel's  drawing  the  axes  of  the  two  nebulas  are  in  a  line  ;  in  1850 
Mr.  G.  Johnstone  Stoney  found  them  not  to  be  in  a  line;  in  1855 
Mr.  Mitchell  (at  Birr  Castle)  remarked  that  the  axes  were  not 
in  a  line  but  were  parallel ;  while  in  1861  (when  the  drawing  in 
P.T.  1 86 1  was  made)  they  were  neither  in  a  line  nor  parallel,  but 
inclined  at  an  angle  of  160.  Since  then  the  following  observa- 
tions have  been  made : — 

Birr  Castle,  1871.     No  B  of  p  neb  noticed,  the  axis  of  the 
/neb  makes  an  angle  of  about  120  by  a  diagram. 


May  1887.  Variability  or  Proper  Motion.  419 

Birr  Castle,  1872.  The /one  E  i30°"4  (2  meas.),  Pos.  of  line 
joining  centres  ii7°'6  (2).     The  E  neb  [/one]  slightly  cometic. 

Armagh,  1887,  April  27.  p  one  v*l  E,  apparently  towards/ 
one,  the  latter  very  diffused  and  hazy,  Pos.  of  E  i28°*4  (2  meas.), 
therefore  difficult  to  measure;  line  joining  them  i20°*2  (2  meas.). 

The  very  hazy  look  of  the  two  nebulas,  the  small  amount  of 
elongation  of  the  first  one,  and  the  want  of  sharp  condensation 
in  both  of  them  are  more  than  sufficient  to  account  for  the  dis- 
agreement between  the  various  observers. 

M  2o=V  10,  11,  12= h  1991,3718,  the  u  trifid  nebula."   This 
forms  the  subject  of  an  elaborate  monograph  by  Professor  Holden,  * 
in  which  it  is  attempted  to  prove  that  from  1784  to  §833  the 
triple  star  was  centrally  situated  between  the  three  nebulosities, 
but  that  from  1839  to  1877  it  was  involved  in  the  south  follow- 
ing mass  of  nebulosity.     The  latter  proposition  rests  on  a  firm 
basis,  as  the  nebula  has  been  repeatedly  examined  and  drawn 
with  every  care  since  1839;  but  this  cannot  be  said  about,  the 
first  proposition.     At  the  Cape  of  Good  Hope,  Sir  J.  Herschel 
made  a  drawing  in  a  single  night  (August  2835),  which  ex- 
hibits the  triple  star  on  the  very  edge  of  the  sf  nebulosity.     A 
careful  drawing  made  at  Slough  was  lost,  and  that  engraved  in 
P.T.  1883,  fig.  80  (which  Bhows  the  triple  star  in  the  midst  of 
a  vacuity)  was  constructed  from  sketches  "  the  rudest  imagin- 
able aided  by  memory."    The  other  evidence  as  to  the  position 
of  the  star  between  1784  to  1833  consists  in  various  notes  by 
Sir  William  and  Sir  John  Herschel.     But  the  former  never  says 
that  the  double  star  was  in  the  middle  of  the  vacuity,  but  in  1784 
he  describes  the  object  as  "  three  nebulaa  faintly  joined  form 
a  triangle;  in  the  middle  is  a  double  star,"  and  in  1786:  "a 
double   star  with  extensive  nebulosity  of  different  intensity ; 
about  the  double  star  is  a  black  opening."      It  is  quite  true  that 
Sir  John  Herschel  on  three  occasions!  states  that  the  star  is  in 
the  middle  of  the  vacuity.      But  is  it  so  strange  that  at  an  alti- 
tude  of   only    1 50,    and   during   the     strong  twilight  of  our 
Bummer  months  (sweep  30  was  made   on  July   1,    1826),  the 
nebulosity  could  not  be  traced  close  to  a  bright  double  star  of 
the  8*5  and  9th  magnitude  ?      It  is  at  any  rate  curious  that 
the  critical  time  when  the  alleged  motion  of  the  nebula  towards 
the    star  should   have   taken  place  is   precisely  the    moment 
when   we  exchange  strong  twilight,    very  low    altitude,    rude 
sketches  for  little  or  no  twilight,  much  higher  altitude,  and  care- 
ful drawings. 

The  drawings  made  by  Mason,  Lassell,  and  Trouvelot  differ 
in  many  details  just  as  the  various  drawings  of  Orion  do  ;  and 
very  possibly  changes  of  brightness  have  taken  place,  both  near 

*  Am.  Journ.  x\v.  Dec.  1877. 

f  Mem.  B.A.S.  ii.  p.  490,  in  a  footnote  to  a  paper  on  the  Orion  nebula, 
ibid.  iii.  p.  63,  in  his  observations  of  double  stars,  and  in  sweep  30,  Phil.  Tr. 
1833,  p.  460. 


420  Br.  Dreyer,  Nebulce  suspected  etc.  xlyii.  7, 

the  double  star  and  in  the  other  part  of  the  nebula ;  but  that  the 
nebula  should  about  1 835  in  the  course  of  a  few  years  have 
moved  so  as  to  envelop  the  star,  after  which  no  sensible  change 
occurred  again  so  far  as  published  observations  go,  does  not 
seem  sufficiently  well  proved. 

M  1 7= A  2008,  Omega  nebula. — In  the  American  Journal, 
vol.  xi.,  May  1876,  Professor  Holden  published  a  paper  "  On 
Supposed  Changes  in  the  Nebula  If  17,"  in  which  he  endeavours 
to  show  by  a  comparison  of  bis  own  observations  (made  with 
the  Washington  26-inch  refractor)  with  those  of  J.  Herschel, 
Lamont,  Lassell  and  Tronvelot  that  the  western  branch  of  ths 
Q  has  moved  relatively  to  the  little  group  of  stars  10,  3,  11 
(Lassell)  at  the  np  end,  and  particularly  with  regard  to  the  star 
No  1  at  the  sp  side  of  the  O.*  The  nebulosity  is  very  diffused 
at  the  group  of  stars,  vet  there  is  very  little  difference  between 
the  various  drawings,  but  the  star  1,  on  which  reliance  is  chiefly 
placed,  was  by  J.  Herschel  in  1837,  and  Lassell  in  1862,  found 
to  be  on  the  inner  (concave,  north  following)  edge  of  the  carve 
of  the  nebula;  while  Holden  and  Tronvelot  in  1875  placed  it  well 
within  the  nebulosity,  in  fact  preceding  nine-tenths  of  it  A 
drawing  by  Le  Sueur  made  in  1869  (Proe.  R.  S.  vol.  xviii., 
overlooked  by  Professor  Holden)  agrees  with  the  one  made  at 
Washington,  so  that  the  change  should  have  taken  place  between 
1862  and  1869.  But  a  drawing  made  by  M.  Tempel  in  1876 
with  the  1  i-iuch  refractor  at  Arcetri  f  agrees  with  the  earlier 
drawings  in  this  particular,  while  two  sketches  made  at  Birr 
Castle  in  1854  J  Agree  with  the  later  drawings.  There  has  there- 
fore certainly  not  been  any  bodily  shifting  of  the  nebula,  but  the 
possibility  of  changes  of  brightness  are  not  excluded. 

II.  426-427=71  2087-2089. — M.  Flammarion  remarks  that 
there  is  a  great  disagreement  between  J.  Herschel's  and  d'Arreat's 
difference  of  declination,  the  former  observer  making  £.8=82", 
the  latter  61".  It  should  have  been  stated  thut  it  was  only  on 
one  night  that  d' Arrest  found  £8=59"  to. 63",  for  the  mean 
results  of  his  three  nights  give  81".  In  1876  I  found  at  Birr 
Cattle  78//a4  (one  measure  of  pos.  and  distance). 

III.  210-21 1 =/i  2202-2203. — M.  Flammarion  repeats  a  re- 
mark of  d'Arrest'8  that  J.  He^chel  in  1828  Joond  Aa=io'o 
(should  be  9$,o)  and  AS  2=  37",  while  d'Arrest  found  io^s  and  53". 
But  the  mean  of  d'Arrest's  results  gives  8**2  and  62".  This 
faint  pair,  between  which  d'Arrest  found  a  v  F,  v  S  nebula 
(G.C.  61 12),  and  of  which  the  elongation  of  the  preceding  one 
makes  the  measurement  of  £8  difficult,  has  been  frequently 
observed  of  late  years,  showing  no  appreciable  change. 

*  See  Mr.  La* sell's  drawing  (fig.  32)  and  skeleton  chart  (fig.  32  a)  in  Mem. 
E.A.S.  vol.  xxxvi. 

t.  See  Winnecke's  review  in  Vierteljahrtsckrift  d.  a.  G.  xii.  p.  245. 
J  Observations  of  b\bul<s%  1848-78,  pi.  vi. 


May  1887.        Dr.  Dreyer,  Effect  of  Refraction  etc.  421 


D'  Arrest 

1861-64 

s 

A3  =  62" 

3  nights. 

Schonfeld 

1861 

972 

595 

5     » 

bchultz 

1863-65 

905 

6 10 

3     » 

Schonfeld 

1864 

938 

7i'3 

1  night. 

Vogel 

1869 

938 

690 

2  night's. 

Dreyer 

1877 

892 

607* 

1  night. 

Dreyer 

1885 

8-86 

660 

I     .. 

III.  855-856  ==  ft  2294-2295. — These  also  occur  in  M.  Flam- 
inarion's  list,  because  W.  Henschel  in  1790  estimated  the  position- 
al] gle  =  6o°  and  the  distance  60",  while  d'Arrest  found  500  and 
43".  The  objects  are  both  excessively  faint,  and  it  would  be 
easy  to  count  up  hundreds  of  similar  discrepancies.  In  1872 
the  angle  and  distance  were  measured  at  Birr  Castle,  and  found 
=  5i°o  and  6i"'5. 

I  have  spared  no  trouble  in  going  through  these  cases  one 
by  one,  although  in  some  the  evidence  was  of  such  a  character 
as  hardly  to  deserve  a  refutation.  I  would  suggest  to  anybody 
who  in  future  should  feel  inclined  to  lay  a  case  of  proper  motion 
or  variability  of  a  nebula  before  the  public,  first  to  peruse  the 
remarks  of  d'Arrest  in  the  Astr.  Nachr.  vol.  Ivii.  'col.  342.  In 
making  micrometric  observations  of  these  interesting  objects  we 
must  be  content  to  work  for  unborn  generations,  or  at  least  not 
to  expect  immediate  and  startling  results,  which  would  look 
well  in  popular  books. 

Armagh  Observatory : 
1887,  May. 


Note  on  the  Effect  of  Refraction  in  Stellar  Photography. 
By  J.  L.  E.  Dreyer,  Ph.D. 

In  his  paper  read  at  the  April  meeting  of  the  Society,  Mr. 
Grubb  has  'assumed  that  a  displacement  of  o""5  is  the  smallest 
which  would  sensibly  affect  the  symmetry  of  the  image  of  a  star 
on  a  photographic  plate.  It  is  of  interest  to  see  how  soon 
refraction  will  move  the  image  to  this  extent,  assuming  the 
action  of  the  clock  to  be  absolutely  perfect  and  the  instrument 
accurately  adjusted. f 

The  well  known  expressions  for  refraction  in  Right  Ascension 
and  Declination,  first  given  by  Bessel  in  the  Monatliche  Corre- 
8pondenzf  xvii.  p.  214,  are 

57"     T-'8*?*     "d  57"  cot  (*  + »)      • 
cos  9  sin  {$  +  8) 

*  In  the  tingle  measure  of  distance  at  Birr  Castle  on  Oct.  29,  1877,  there 
is  an  obvious  error  of  one  revolution  of  the  screw -65**1. 

f  This  question  is  not  considered  in  Prof.  Pickering's  valuable  paper, 
"  Investigation  in  Sullar  Photography." 


422  Dr.  Dreyer,  Effect  of  Refraction  etc.  xlvii  7, 

where  tfr  is  determined  by  tan  ^r  =  cos  2  cot?),  while  t  is  the  hoar, 
au^le,  8  the  Declination,  and  <f>  the  latitude.  The  rate  of  change 
ol*  refraction  is  found  by  differentiation  with  regard  to  L 

~  =  S7"(.    n°~* \§(i +t*iit>  ImImi) 

j*  "  57      r-  rr-^ )  cot  <p  sin  t 
dt  Vwn  tf  +  8) ) 

The  trail  left  on  the  plate  after  an  exposure  of  n  seconds  of 
time  will  now  be  the  resultant  of  the  displacements  along  the 
parallel  and  the  hour-circle  equal  to 

«5»    <!*^x  .„,*     15*    ** 


—  cos  5  and 


206265  dt  206265  dt 

Assuming  the  latitude  =  500,  the  following  table  shows  the 
values  of  these  quantities  for  various  parts  of  the  sky  for  a  change 
of  4m,  or  i°  in  hour-angle. 


t= 

0* 

da  00s  A     dt 

daoosfi      dt 

2" 

da.  cot  t 

dt 

3* 

da  coe  ft 

dt 

4" 
daooeft      dt 

8=      o° 

099    o*oo 

107     033 

1-33 

0-79 

11 
I  "99 

i:68 

398     4IO 

+  250 

071    000 

073    0-16 

0-81 

036 

096 

064 

1-26      I*  12 

+  50 

0-64    0  00 

064    0  13 

066 

0-28 

069 

045 

072      0*67 

+  75° 

071    000 

070    016 

066 

031 

o*6o 

047 

05I      O-63 

The  value  of  da  cos  8  increases  with  south  declination,  being 
on  the  meridian  and  at  —  io°  =  i"-28,  and  at  —  200  =  i"'8f. 
Reft  action  accelerates  the  rising  of  a  star,  so  that  the  apparent 
place  of  a  star  in  the  east  will  be  in  advance  of  the  true  one,  but 
the  difference  of  hour-angle  gradually  diminishes  as  we  approach 
the  meridian.  After  the  culmination  they  change  places,  the 
apparent  place  now  being  behind  the  true  one.  A  slight  uniform 
retardation  of  the  clock  will  thus  do  away  with  the  greater  part 
of  the  error  in  the  direction  of  the  parallel,  as  the  table  shows 
how  very  slowly  du  cos  5  changes  with  the  hour-angle.  The  case 
is  different  with  regard  to  the  effect  of  refraction  along  the  hour- 
circle,  as  the  full  amount  of  the  change  in  this  will  cause  dis- 
placement of  the  star  on  the  plate,  and  it  seems  that  a  declina- 
tion clock  will  ultimately  become  desirable,  though  the  mechanical 
arrangements  would  be  somewhat  complicated  if  the  instrument 
were  to  be  available  for  lengthened  exposures  on  any  part  of 
the  sky.  But  this  would  be  unnecessary  in  the  case  of  system- 
atic work,  such  as  star-charting,  as  this  could  always  be  carried 
on  close  to  the  meridian,  where  the  refraction  in  declination 
changes  very  slowly.  Thus,  for  the  latitude  of  500  an  equatoreal 
star  will  be  27™  past  the  meridian,  and  a  star  of  +250  Decli- 
nation 39m  past  the  meridian,  before  a  displacement  of  o'"5 
occurs. 


May  1887.    Mr,  Lefavour,  R.  A.  nf  Stars  near  the  Pole.  423 


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May  1887.      from  Observations  hj'F.  G^  W.  Sfruve. 


425 


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8 

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May  1887.        Mr.  Finlay>  On  Probable  Errors  etc.  427 


On  the  Probable  Errors  of  Transit-observing. 
By  W.  H.  Mnlay,  M.A. 

In  the  winter  months  consecutive  transits  above  and  below 
pole  of  several  stars  are  often  secured  on  the  same  night,  and  a 
question  arises  as  to  how  the  separate  results  for  azimuthal 
error  are  to  be  combined  to  form  the  "  adopted  "  azimuthal  error. 
To  settle  this  question  we  require  to  know  the  probable  errors 
of  observation  at  different  declinations,  and  the  following  deter- 
mination of  the  probable  errors  of  a  single  wire  in  transit-observing 
was  undertaken  for  this  purpose. 

After  my  results  had  been  obtained  I  became  aware  of  the 
formula  given  by  M.  Strove  ("  Sur  1'Emploi  de  l'lnstrument  des 
Passages  "),  but  as  the  latitude  of  the  Gape  is  very  different  from 
that  of  Pulkowa  I  have  thought  it  well  to  give  my  results. 

The  following  is  the  method  I  have  adopted  : — 

Assuming  the  adopted  wire  intervals  to  be  absolutely  correct, 
the  difference  of  the  observed  interval  between  two  wires  from 
the  computed  interval  gives  the  actual  error  made  in  measuring 
a  distance  by  observation  at  two  wires ;  so  that  by  taking  the 
mean  of  a  large  number  of  such  differences  we  get  the  "  average  " 
error  of  a  distance  measured  by  transit  over  two  wires.  If  M 
be  this  "average"  error,  or  mean  of  the  differences  without 
regard  to  sign,  then 

probable  error  of  a  distance  —  M  x  [9*927046] 

and 

M 
probable  error  of  a  transit  at  one  wire-— ^  x  [9*927046]. 

The  differences  for  each  star  were  multiplied  by  cos  (declina- 
tion) to  reduce  to  the  equator,  and  the  stars  were  grouped  in 
zones  according  to  their  North  Polar  distances.  The  observa- 
tions which  I  have  used  were  made  with  the  transit-circle  of 
the  Royal  Observatory,  Cape  of  Good  Hope,  by  the  three  ob- 
servers who  took  the  chief  part  in  the  observations  for  the  Gape 
Catalogue,  1880;  but  the  period  which  I  found  most  convenient 
for  my  purpose  was  18  79-1 881 ;  the  power  of  the  eyepiece  ufeed 
was  180. 

The  following  table  gives  the  probable  errors  for  different 
N.P.D.'s  of  an  observation  at  one  wire  as  observed,  and  also  when 
reduced  to  their  equivalents  at  the  equator : — 


1 1 


428  Mr.  F inlay,  On  the  Probable  Errors  xlvil  7, 


Table  I. 

N.P.D. 
of  Zone. 

Mean 

Z.D.of 

Zone. 

P. 
p.e.at 
Obe. 

No.  of 
Obe. 

M. 

p.e.  at    No.  of 
Obe.       Obe. 

P. 

p.e.  at    No.  of 

Ota.      Obe. 

Reduced  p»e. 
P.            M.            P. 

&>-I0O 

0 
34 

E 
OO49 

208 

B 
OO86 

380 

8 
OO63 

872 

• 
OO49 

e 
0-086 

e 
OO63 

IOO-I23 

13 

0-067 

271 

0094 

362 

0*070 

444 

0063 

OO88 

0066 

124-135 

6 

006l 

163 

OO84 

148 

0078 

I7i 

OO47 

0*064 

O-060 

135-150 

18 

OO67 

239 

0092 

269 

0'080 

221 

O-O4I 

OO57 

0*050 

150-165 

33 

008l 

263 

01 10 

266 

O'lOI 

318 

0031 

OO42 

0040 

166-170 

44 

0203 

159 

0168 

194 

0*042 

0*035 

171-174 

48J 

0278 

155 

0258 

279 

0*036 

O-034 

175-177 

52 

0483 

340 

0410 

626 

OO34 

0*029 

178 

54 

0-891 

120 

0736 

"5 

0031 

0*026 

179 

55 

1-408 

88 

1-129 

125 

O-025 

0*020 

l8l 

57 

1367 

60 

1*229 

97 

0*024 

0*022 

182 

58 

0-789 

26 

0845 

no 

O-028 

0*029 

183-I85 

60 

0553 

443 

0475 

546 

OO39 

0*033 

186-189 

*3i 

0-260 

42 

0302 

200 

OO34 

0*039 

190-194 

68 

0317 

in 

0-227 

216 

0066 

OO47 

There  were  not  sufficient  observations  of  circumpolar  stars 
by  F  in  the  period  1 879-1881  to  give  a  determination  of  his 
probable  errors  beyond  1650  N.P.D.,  and  the  series  for  M  does 
not  rest  on  very  large  numbers  of  observations  except  for  the 
zones  175-177  and  183-185.  I  shall  therefore  take  P  as  the 
average  observer,  and  any  farther  conclusions  will  be  based  on 
the  figures  in  the  last  column  of  Table  I.  It  will  be  seen  that 
the  probable  errors  of  a  single  wire  by  the  different  observers, 
though  differing  in  amount,  follow  the  same  general  law; 
and  that  the  probable  error  of  observing  does  not  by  any  means 
increase  in  an  inverse  ratio  to  the  cosine  of  the  star's  declination. 

If  we  try  to  represent  our  numbers  by  the  formula 

P.E.*  «  a* + b*  sec  e  Bee*  *, 

we  find 

a*  -s  -003978,    6*  -  -000564 , 

and  therefore 

P.E.  -  V(o«-o63)5'  +  (p-024)*  sec  *sec*  5. 

The  representation  of  the  probable  errors  by  this  formula, 
and  some  variations  of  it  which  I  have  tried,  is,  however,  only 
moderately  satisfactory.  The  formulae  all  failed  to  give  the 
rapidly  diminishing  probable  errors  near  the  pole.  Nor  am  I 
surprised  at  this  failure ;  for,  at  a  distance  of  20  or  30  from  the 
pole,  the  star's  disc  is  in  contact  with  the  wire  for  sevoral  seconds, 


1 


May  1887.  of  Transit- observing.  429 

and  the  observer  practically  alters  his  method  of  observing :  he 
fixes  his  attention  on  the  wire  and  waits  till  the  star's  disc  is 
equally  distributed  on  the  two  sides  of  it,  and  this  observation 
can  be  made  with  considerable  certainty  and  accuracy. 

To  find  the  error  in  the  determination  of  the  azimuth  of  the 
instrument  introduced  by  error  in  observing,  divide  these  prob- 
able errors  by  sin  (zenith  distance  of  group),  and  we  get  the 
following  table  of  probable  errors  of  azimuth  reduced  from  a 
single  wire : — 


Table  II. 

N.P.D.  of  Star. 

p.e.  of  azimuth. 

Combination  Weight. 

Approz.  W 

I6# 

g 
0050 

245 

5 

1 72  i 

0-045 

3"l6 

6 

176 

0036 

4*57 

9 

178 

0032 

5*57 

11 

179 

0*024 

1000 

20 

l8l 

0026 

20 

182 

0*035 

11 

184 

0038 

9 

i87i 

0044 

6 

192 

0051 

5 

so  that  four  wires  of  a  star  about  178^°  N.P.D.  are  of  as  much 
value  in  determining  the  azimuthal  error  as  sixteen  of  a  star  at 
1 700  N.P.D. 

We  learn  another  fact  from  the  above  table ;  viz.  that  at  the 
latitude  of  the  Gape  the  probable  error  of  the  deduced  azimuth 
is  the  same  whether  the  star  be  observed  above  or  below  the  pole ; 
that  is  to  say,  the  increase  of  azimuth-factor  for  the  star 
below  pole  is  counterbalanced  by  the  increased  error  of  observa- 
tion due  to  inferior  definition  at  the  greater  zenith-distance. 

The  last  column  in  Table  II.  gives  approximate  weights  for 
combining  azimuthal  errors  determined  from  stars  at  various 
N.P.D.'s. 

Boycd  Observatory,  Cape  of  Good  Hope  : 
1887,  March  31. 


I  I  2 


430  Mr.  Johnson,  Notes  on  a  MS.  Eclipse  Volume,     xlyii.  7, 


Notes  on  a  MS.  Eclipse  Volume.  •  By  the  Bey.  S.  J.  Johnson,  M.A. 

The  accompanying  MS.  volume  *  gives  eclipseB  in  this  country 
for  a  period  of  about  2,000  years,  from  a.d.  538  to  a.d.  2500, 
being  recorded  ones  of  both  luminaries  from  the  date  of  the  first 
in  538  to  1200;  all  solar  eclipses  visible  here  from  a.d.  1200  to 
a.d.  2200,  omitting  a  very  few  in  which  scarcely  a  tenth  of  the 
Sun's  diameter  is  obscured,  including  lnnar  ones  for  a  certain 
period  and  large  solar  eclipses  from  a.d.  2200  to  a.d.  2500. 

It  will  be  seen  that  during  the  1000  years  from  a.d.  1200  to 
a.d.  2200  there  are  only  eight  cases  of  an  interval  so  long  as 
that  through  which  we  are  now  passing  (May  1882  to  June 
1890)  without  a  solar  eclipse  visible  in  England  generally. 

The  only  solar  eclipses  total  at  Greenwich  in  the  period  of 
2000  years  are  those  of  878  and  1715,  as  has  been  before  re- 
marked, unless,  perhaps,  that  of  664  is  an  instance.  Between 
the  eclipse  of  1715  and  the  preceding  one  that  most  nearly 
approached  the  total  phase  at  Greenwich,  viz.  that  of  1140, 
there  is  an  interval  of  575  years  and  a  month.  A  similar 
interval  reckoned  forwards  from  17 15  brings  us  to  a.d.  2290, 
when  there  is  an  eclipse  soon  after  sunrise  that  seems  total  in 
the  extreme  north  of  the  kingdom.  A  similar  interval  reckoned 
previously  to  1140  brings  us  back  to  February  565,  when  the 
Sun  appears  to  have  been  totally  eclipsed  across  this  country 
just  before  setting.  Though  no  ancient  chroniclers  appear  to 
record  this  directly,  yet  Matthew  of  Westminster  says,  "  In  this 
year  there  were  seen  many  signs  in  the  Sun  and  Moon.'1 

Melplash  Vicaraae,  Dorset : 
April  28. 

■       * 

*  This  volume  is  placed  in  the  Library. 


May  1887.     Mr.  Tebbuti,  Obtervatimis  of  Saturn  etc. 
3j 


3  3  a'sV.  5  £  1 .3  3-3.3 


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43 2  Oapt.  Molony,  Sextant  Observations  of  Comet,     ilvu.  7, 

Occultaiion  of  a  Tauri.     1887,  March  2.     By  Gk  L.  Tnpman. 

Notwithstanding  the  daylight,  the  Moon's  dark  limb  was 
plainly  visible.  Aldebaran  was  very  bright  and  flaring,  and  hun<* 
a  long  time  on  the  limb  without  being  projected  on  it  more  than 
half  of  its  apparent  diameter,  which  was  10"  or  15",  the  reddish 
colour  being  very  remarkable.  By  the  click  of  the  armature 
of  the  transit-clock-relay,  at  50s  the  star  suddenly  waned, 
but  remained  conspicuous  until  51',  the  light  lingering,  at  less 
than  one-half  of  its  original  intensity,  for  fully  one  second  of 
time.  The  point  of  disappearance  was  on  the  dark  limb,  well 
clear  of  the  terminator. 

Having  placed  a  wire  tangent  to  the  Moon's  bright  limb  at  the 
calculated  point  of  reappearance,  the  star  was  seen  tore-appear  in- 
stantaneously. It  was  very  much  less  bright  at  the  bright  limb 
than  it  had  before  appeared.  Watched  for  30  seconds  there 
was  no  further  increase  of  its  light.  It  hung  on  the  limb  and 
was  fairly  bisected  by  the  latter  for  a  considerable  time. 

Achromatic  of  4^  inches  aperture,  power  66. 

Local  Sid.  Time.  G.M.T. 

b    m       s  h    m       s 

Disapp.        .        .        4  28  395*  5  49  ir6 

Reapp.         .        .        4  40  33-4  6    1    36 

The  occultation  was  observed  by  Mr*  E.  B.  Knobel  at 
Booking,  who  remarks : — 

"  The  star  glided  out  (at  the  dark  limb  near  the  terminator). 
It  did  not  snap  out  as  usual,  but  there  was  an  appreciable  time 
in  its  disappearance ;  it  was  not  an  instantaneous  phenomenon. 
The  observation  was  good. 

"  The  reappearance  (at  the  bright  limb)  seemed  instantaneous, 
but  the  observation  was  not  quite  so  good  as  the  immersion. 
Time  between  observations  9  minutes  30  seconds." 


Sextant  Observation*  of  Comet  a,  1887,  on  board  the  ship  "British 
Merchant"     By  Captain  E.  J.  Molony. 

(Communicated  by  Captain  H.  Toynbee.) 

1887,  January  21. — Lat.  280  17'  S.    Long.  210  25'  W. 

At  8  p.m.  saw  for  the  first  time  a  comet;  a  long  slightly 
curved  tail,  originating  in  a  point  towards  the  Sun,  and  stretch- 
ing  for  i8£°  towards  the  nearest  (smallest)  Magellan  Cloud, 
from  which  its  visible  termination  is  distant  180.  As  the  comet 
is  very  ill  defined  and  sky  cloudy  the  following  distances  are 
approximate.     G.M.T.  ioh  nm: — 

*  Corresponding  to  the  recorded  50*  by  the  clock. 


May  1887.  Mr.  Monck,  Oometary  Orbits.  433 


o        / 


Canopus  from  head  of  Comet  75  10 

a  Crucis       „  „  „  ...         ...      67  58 

Rigel  „  „  „  104  48 

January  22. — Lat.  270  36'  S.  Long.  210  44'  W.  G.M.T. 
I0h  2ym#  Comet  more  indistinct.  Approximate  distances  of 
point  :— 

Canopus  ...  73  50 

a  Crucis  ...         ...         ...      66  38 

a  Arietis  91  48 

January  25. — Lat.  230  4'  S.  Long.  240  27'  W.  GLM.T. 
ioh  37m.     Comet  visible  but  faint.     Approximate  distances  : — 

From  Canopus      66  10 

„    a  Crucis       ...        66    o 

„    Rigel  ...        90  30 


On  the  Inclinations  of  Oometary  Orbits.    By  W.  H.  S.  Monck. 

Mr.  Chambers  in  bis  Handbook  of  Descriptive  Astronomy  has 
tabulated  the  computed  cometary  orbits  up  to  the  year  1876,  in 
which  year  the  last  edition  of  his  well-known  book  was  published. 
He  arrives  at  the  conclusion  that  there  is  "  a  decided  disposition 
in  the  orbits  to  congregate  in  and  around  a  plane  inclined  500  to 
the  ecliptic."  His  figures,  I  think,  hardly  bear  out  this  result, 
though  on  dividing  the  inclinations  into  intervals  of  io°  the 
largest  number  appears  in  the  interval  between  400  and  500. 
But  the  comets  whose  orbits  are  inclined  at  angles  of  700  to  90° 
amount  to  sixty-seven,  while  those  whose  orbits  are  inclined  at 
angles  of  io°  to  300  number  only  forty- three,  both  being  equally 
removed  from  the  supposed  median  plane  at  500. 

It  occurred  to  me  to  examine  the  orbits  of  comets  which 
appeared  since  the  publication  of  Mr.  Chambers's  List,  and  I 
found  that  the  tendency  towards  orbits  inclined  at  angles  of 
over  50°  became  much  more  marked.  Many  of  the  earlier  orbits 
being  unreliable,  however,  I  thought  it  best,  instead  of  simply 
adding  the  later  comets  to  Mr.  Chambers's  Table,  to  tabulate 
the  inclinations  of  those  which  have  appeared  since  a.d.  1650, 
omitting  all  which  are  known  or  believed  to  be  identical.  Such 
a  table  of  course  involves  some  uncertainties,  but  I  believe  the 
following  will  be  found  substantially  correct : — 


434  Mr.  Bryant,  On  the  Orbit  xlyii.  7, 

Inclinations  of  Cometary  Orbits  to  the  Ecliptic. 
(Containing  only  Comets  which  appeared  since  a..d.  1650.) 


0 

0 

to 

0 
10 

•  •  • 

■•• 

20 

percent. 
77 

10 

»» 

20 

••• 

••■ 

19 

7'3 

20 

ft 

30 

••• 

••• 

»S 

5* 

30 

tl 

40 

♦  •  • 

••• 

30 

US 

40 

II 

So 

••■ 

••• 

37 

142 

50 

II 

60 

•  •  • 

... 

33 

127 

60 

II 

70 

••• 

•  •  • 

32 

12-3 

70 

II 

80 

.<  • 

••• 

37 

I4'2 

80 

ft 

90 

••• 
Total 

«•• 

37 
260 

1 4*2 

99*9 

Here  the  tendency  to  a  maximum  at  500  has  entirely  disappeared 
There  are  in  fact  more  comets  in  the  interval  70°  to  900  than  in  the 
interval  400  to  6o°.  Bat  on  the  other  hand  there  is  a  very  marked 
deficiency  in  inclinations  from  o°  to  300.  In  the  interval  from 
300  to  400  we  first  reach  the  average  number.  From  400  to  900 
the  number  is  invariably  in  excess  of  the  average. 

If  we  were  at  liberty  to  distinguish  comets  of  short  period 
(which  are  now  known  to  be  pretty  numerous)  from  those  which 
move  in  very  elongated  ellipses,  parabolas,  or  hyperbolas,  the 
'results  would  be  more  striking.  Comets  of  short  period  have 
even  a  more  decided  preference  for  small  inclinations  than  the 
other  comets  have  for  large  ones.  And  even  if  we  do  not  adopt 
Mr.  Proctor's  theory,  that  these  comets  of  short  period  have  been 
ejected  from  the  planets  (especially  Jupiter),  or  Professor  Kirk- 
wood's  suggestion  that  some  at  least  of  them  have  a  common 
origin  with  the  asteroids,  I  think  there  is  considerable  reason 
for  regarding  them  as  original  members  of  the  solar  system, 
exhibiting  many  of  the  characteristic  properties  of  that  system. 
If  so,  it  is  only  to  the  other  and  larger  class  of  comets  that  we 
can  look  for  information  as  to  the  prevailing  direction  of  motions 
in  exterior  space ;  for  that  their  high  inclinations  to  the  ecliptic 
is  not  caused  by  anything  in  the  solar  system  is,  I  think,  certain. 
A  comparison  of  the  inclinations  of  their  orbits  with  those 
computed  for  binary  stars  would  be  interesting  from  this  point 
of  view. 


On  the  Orbit  of  Oomet  II.  1883.     By  Robert  Bryant,  B.  A.,  B.Sc. 

In  the  Monthly  Notices  for  last  November  Lieut.- General 
Tennant  gave  parabolic  elements  of  the  orbit  of  this  oomet,  and 
expressed  his  opinion  that  there  is  no  justification  for  assigning 
an  orbit  with  an  eccentricity  different  from  unity. 


May  1887. 


of  Comet  IL  1883. 


435. 


The  elliptic  elements,  which  I  communicated  to  the  Society 
in  June  1885,  depended  upon  three  observations  which  I  con- 
sidered fairly  good  ones,  and  from  these  the  orbit  was  deduced 
with  great  care.  The  difference  between  this  orbit  and  that  of 
Lieut.- General  Tennant  caused  me  to  revise  my  work  and  to 
take  into  consideration  a  larger  number  of  observations.  More- 
over  the  large  residuals  given  in  the  middle  observed  place  by 
Lieut.- General  Tennant's  parabola  seemed  to  me  to  indicate  that 
this  latter  curve  scarcely  sufficed  to  represent  the  observations, 
and  further  investigation  has  confirmed  this  idea. 

As  the  result  of  a  threefold  interpolation  the  residuals  given 

below  were  obtained  by  comparing  the  observations  with  the 

following  approximate  parabolic  elements  referred  to  the  mean 

equator  of  1884*0. 

d 
T         1883,  Dec.  25-30154,  G.M.T. 

»'       113  30  5°'5 
254  33  46:1 
no  37  51-1 

9-490993- 


a' 


log? 


Observation —  Computation. 


RJL 

a 

1884,  Jan.  12 

+  3*17 

—210 

Melbourne 

17 

+  1*2 

+  85-0 

*» 

18 

+  350 

+  10 

11 

19 

+  2'43 

-  r8 

Windsor,  N.S.W. 

21 

+  1-65 

+  4-2 

11 

21 

+  205 

+   ri 

11 

22 

+  1-87 

—  02 

11 

22 

+  2-50 

—   i*i 

Madras. 

23 

+  189 

-  23 

Windsor. 

23 

+2-13 

-186 

Madras. 

24 

+  228 

+  27 

•  Windsor. 

25 

+  176 

-  89 

n 

25 

+  2'06 

+   6-1 

Madras. 

26 

+  2'6l 

+  230 

11 

26 

+  3*55 

-  3"2 

11 

27 

+  1-07 

-  8'3 

Windsor. 

28 

+  2-II 

— 12-4 

Melbourne. 

28 

+  I'96 

-    OI 

Windsor. 

28 

+  2'37 

-   18 

Madras. 

29 

+  I-90 

-147 

Melbourne. 

30 

+  3*26 

+ 190 

Madras. 

31 

+  0*19 

+  28 

11 

Feb.     1 

-0-25 

+   5*1 

Melbourne. 

2 

+2-13 

-  7*8 

Windsor. 

4 

+247 

+  0-3 

Melbourne. 

436  Mr.  Bryant,  Orbit  of  Oomet  II.  1883.  xivii.  7, 

The  observations  of  January  17  and  February  1  were  rejected 
for  discordance.  The  observation  of  January  29  was  rejected  in 
order  to  make  the  time  of  the  second  normal  fell  at  a  suitable 
epoch. 

Taking  the  mean  of  Tebbutt's  observations  on  January  21, 
a  normal  was  formed  from  the  observations  up  to  January  22. 

Taking  the  mean  of  the  observations  on  January  26  and 
January  28,  the  second  normal  was  formed  from  the  observations 
from  January  23  to  January  28. 

Taking  the  mean  of  the  Madras  observations  on  January  30 
and  31,  and  assigning  half  weight  to  the  result,  the  third  normal 
was  formed  from  the  remaining  observations. 

The  resulting  normals  referred  to  the  mean  equinox  of  1884 
January  o*o  are — 

rjl  a 


O         /  //  O         I  II 


(0        343  41    07  —41  47  167       for  1884  Jan.  190 

(2)  350  40  577  -41  59  217  „    25-0 

(3)  357  13    i-3  -4i  44  167  Feb.    2-0 
From  these  normals  the  elements  finally  deduced  are — 

d 
T        1883,  Dec.  25233782 


113  16  4874 


Mean  Equator,  1884*0. 


G'      254  32  1697 
%'        no  31  3408 

«  0*9944387 

log  q  9*4901604 

P  414  years. 

Of  course  any  period  deduced  from  an  arc  of  anomaly  of  only 
1 40  and  from  an  interval  of  only  14  days  is  deserving  of  little 
confidence. 

These  elements  give  the  following  residuals  in  the  three 
normal  places : — 

Observation —  Computation. 

CosftdB.A.  —  6-6  -i*3  +2*8 

d9  00  —0-3  —  O'l 

Referred  to  the  ecliptic  of  1884-0  the  above  elements  be- 
come— 

d 
T        1883,  Dec.  25-233782,  G.M.T. 


Mean  Ecliptic,  18840. 


00 

138  17  5905 

Q 

264  20  1 7 *59 

m 

t 

114  54    0-64, 

6 

09944387 

log  q 

9*4901604. 

May  1887.  Dr.  Morrison,  Orbits  of  Comets.  437 

The  parabolic  elements  given  by  Lieut. -General  Tennant  on 
p.  26,  vol.  xlvii.  of  the  Monthly  Notices,  give  the  following 
residuals  for  the  above  three  normal  places  : — 

Observation —  Computation. 

Cos5<*R.A.  -     4-8  -  857         -141*4 

d&  +6125  +6567         +685-3 

Note. — When  the  above  results  were  communicated  to  the 
Society,  I  was  not  in  possession  of  the  correction  to  the  inclina- 
tion of  Lieut. -General  Tennant's  parabola  given  on  p.  394  of  the 
present  volume.  With  this  correction  the  errors  (observation — 
computation)  of  the  parabolic  elements  are  respectively — 


//  //  _« 


CobWRA.  —17-1  -132  +  182 

d$  -7-3  -  65  -  29 

I  think  the  orbit  is  undoubtedly  elliptic,  but  what  the  eccen- 
tricity is  it  is  impossible  to  state  with  certainty. 

Tne  Melbourne  observations  referred  to  above  are  those  given 
in  the  Astronomische  Nachrichtsn,  and  were  published  after  my 
former  paper  on  this  subject  was  communicated  to  the  Society. 


The  Orbits  of  Comets  Fabry  and  Barnard- Har  twig.  By  J. 
Morrison,  M.D.,  Ph.D.,  Assistant  on  the  American  Ephemeris, 
and  Professor  of  Chemistry  in  the  National  University, 
Washington. 

Comet  Fabry. 

The  observations  upon  which  the  following  hyperbolic  ele- 
ments of  this  comet  are  founded  are  as  follow  : — 

Greenwich  M.T.  Appar.  a  Appar.  ft 

d  h  m       s  o       1      11 

1885,  Dec.    7*536032  o  24  4601  +  20  52  34-9 

1 886,  Mar.    7*316539  23  1942-92  +31  16448* 
„    April  r3397i3                     23  18  30-86                     +38  37  570 
„    June   6-953118                      8  47  5215                     -40  38    0-5 

The  first  is  a  meridian  observation  made  at  Ann  Arbor; 
the  second  results  from  extra  meridian  observations  made  at 
Greenwich  and  Paris,  the  comparison  star  being  the  same  at 
both  places ;  the  third  was  made  at  Bothkamp  and  was  obtained 
from  Astronomische  Nachrichten,  No.  2703 ;  and  the  fourth  was 
made  at  Sydney,  the  comet  being  at  the  time  "  extremely  faint, 
but  in  a  good  position  for  observation  with  Cape  Cat.  (1880) 
4707,"  fifty  comparisons  having  been  made.  (Monthly  Notices, 
vol.  xlvi.  p.  496.)  These  observations  were  corrected  for  aber- 
ration and  parallax  by  means  of  approximate  parabolic  elements. 

*  Geocentric. 


43  8  Dt,  Morrison,  Orbits  of  Comets.  xlvii.  7, 

d 
T  1886,  April  5-9520  Greenwich  H.T. 

«  12?  34  49"'2i5 

Q  36  22  1 1 454  Mean  Equinox,  1 8860 

i  82  37     6012 

6  IOOO47857 

log  a  3- 1278354 

log  g  9*8077809 

The  two  middle  places  are  well  represented. 
The  interval   between  the  extreme   observations  is  181*42 
days,  during  which  the  comet  described  2080  9'  of  its  orbit. 

Oomet  Barnard-Hartwig.     1886. 

From  the  following  observations  the  first  and  third  of  which 
were  made  at  Washington,  D.C.,  and  the  second  at  Kiel  (Astrono- 
mische  Nachrichten,  2753),  an  elliptic  orbit  of  long  period  is 
obtained,  the  elements  of  which  are  given  below  : — 

Greenwich  M.T.  Appar.  a.  Appar.  6. 

d  h     m       6  o      ,     j* 

1886,  Oct.    7*918987  10  42    932  +   1  22    6-3 

„       „    29708660  II  39  2282  +   5  49  19*4 

„    Dec.   2976975  1532    391  +I7  58  55"8 

By  means  of  approximate  parabolic  elements  computed  from 
a  shorter  interval,  the  corrections  for  aberration  and  parallax 
were  obtained  and  applied. 

d 
T  1886,  Dec  16-514158  Greenwich  MX 

«  8(?  21  58-570 

8  137  21  36-163  Mean  Equinox,  18860 

i  78  22  25*525 

e  0*99872521 

log  a  27162151 

log  q  98216538 

Motion  retrograde.  The  middle  place  is  exactly  represented. 
These  elements  give  a  period  of  11,866  years,  which  is  of  course 
very  uncertain,  since  the  interval  between  the  extreme  observa- 
tions is  far  too  short  to  determine  this  element  accurately  in  an 
orbit  snch  as  this  is. 

The  formulae  for  the  equatorial  rectangular  coordinates  are — 

*■  [9*8740086]  r  sin (u+  6  52  45*171) 
y- [98268980]  r sin (v+  198  35  9-651) 
*- [9*9977333] rsin(v+  102    5  28657) 


May  1887.  Dr.  Morrison^  Satellites  of  Mars* 


439 


Ephemerides  of  the  Satellites  of  Mars  during  the  Oppositions  of 
1888  and  1890.  By  J.  Morrison,  M.D.,  M.A.,  Ph.D., 
Assistant  on  the  American  Ephemeris,  and  Professor  of 
Chemistry,  National  University,  Washington. 

These  ephemerides  have  been  computed  from  the  following 
elements  of  the  orbits  of  the  satellites,  referred  to  the  equator 
and  equinox  of  the  respective  epochs : — 

Phoboi. 


Epochs 

1888,  April  no 

1890,  May  2; 

Period 

d 
0-3189113  (mean  solar) 

M 

1 1 288405 

a 

12953  (at  distance  unity) 

i 

$8  44*6 

1      ' 
36  44  0 

N 

47  182 

47  I9'0 

u 

17  40 

Deimos. 

117  53*5 

Epochs 

1888,  April  no 

1890,  Hay  27 

Period 

d 

1-262435  (mean  solar) 

M 

285*16322 

a 

32*354  (at  distance  unity) 

• 

t 

35°  3^ 

35°  35  5 

N 

48  10-66 

48  1 1-5 

u 

225  41 

172  21*5 

Greenwich  Mean  Time  of  Greatest  Elongation. 

Phobos. 


1888. 


G.M.T. 

p 

a 

b 

d       h    m 

21    7  535  W 

3064. 

191 

A 

22  10  40-4  E 

23  13  273  W 

24  16  14-2  E 

25  19    i"i  w 

26  21  480  E 

126-2 

196 

6-4 

28    0  348  W 

29    3  217  E 

// 


ojr.T.  p 

1888.    d     h     m  Q 

Mar.  30    6    85  W 

31     8  553  E 
Apr.    1  n  42*1  W   3058    205 

2  14  29*0  E 

3  17  I5"8  W 

4  20    26  E 

5  22  494  W 

7     1  36-1 E     125-3    210 


b 


6-8 


7*3 


44© 


Dr.  Morrison,  Ephemerides  of  the 


xlvti.  7, 


» 


// 


7-6 


G.M.T.  p 

1888.    d      h       m  o 

Apr.    8     4  22-8  W 

9  7     96  E 

10  9  56  3  W 

11  12  431  £ 

12  15  29-8  W   304*9    2i*3 

13  18  166E 

14  21     33  w 

15  23  5°'  E 

17  2  36*9  W 

18  5  237  E 

19  8  io*5  W 

20  10  572  E 

21  13  440  W 

22  16  30*8  E 

23  19  17-6 W  3037    21'2     80 


124*4    2i'4     7'8 


123-3    21-0     So 


G.M.T.  p 

1888.    d    h        m  0 

Apr.  24  22    4*4  E 

26  o  51*3  W 

27  3  38  2  E 

28  6  25-1  W 

29  9  11-9E 

30  II  588  W 
May    1  14  458  E 

2  17  327  W 

3  20  197  E 

4  23    67  W   3027    20*5     8-i 

6  1  538  E 

7  4  409  W 

8  7  280  E 

9  10  17-1  W 

10  13    4*3  E    I23t)    200    8-2 


Deimo8. 


u 


u 


G.M.T.  p 

1888.    d     h     m  0 

Mar.  20  15  43*4  E     1251    478    155 

22  13    7*9  W 

24  10  323  E 

26  7  565  W 

28  5  205  E 

30  2  44-4  W    3046     50*4    16  8 

Apr.    1  o    8*1  E 

2  21  31*6  W 

4  18  54-9  E 

6  16  182  W 

8  13  41*4  E     124*0    52*6    18*4 

10  II     4*5  W 

12  8  276  E 

14  5  50  7  W 

16  3  138  E 

18  o  370  W   3029    53  5    196 

19  22    0-3  £ 
21  19  236  W 


G.M.T.  pah 

1888.   d     h      m  0  „ 

Apr.  23  16  470  E 

25  14  107  W 

27  11  34*4  E     I22-I     526   20*1 
29    8  583  W 
May    1     6  22*4  E 
3    3  469  W 

5  1  ii*9  E 

6  22  372  W   301*4    51*2  201 
8  20    28  E 

10  17  286  W 

12  14  54-6  E 

14  12  20*8  W 

16    9  47*1  E    121  *o    50*6   200 

18    7  I3'4  W 

20    4  39*8  E 

22  2    6*4  W 

23  23  33*1  E 

25  21    00  W   300*2    488   197 


May  1887.         Satellites  of  Mars,  1888  and  1890. 


441 


G.M.T.  p  a 

1800.     d     h    m  e  „ 

May   8    o  44-8  £    123*6    23-5 

9    3  318  W 

10  6  18-8  £ 

11  9    5'8W 

12  11  528  E 

'3  '4  39*8 W  304-1    250 

14  17  268  £ 

15  20  138  W 

16  23    o*8  E 

18  1  478  W 

19  4  347  E    1245    25*4 

20  7  217  W 

21  10    8*6  E 

22  12  556  W 

23  15  425  E 

24  18  295  W   305*0    26 o 

25  21  164  £ 

27  o    33  W 

28  2  502  £ 

29  5  37-0  W 

30  8  239  E    1256    263 

31  11  108  W 
Jane    1  13  57*6  E 

2  16  44-6  W 

3  19  31*4  E 

4  22  18-4  W   3061     267 
6    1    52  E 


Phobos. 
b 


23 


3-0 


3'3 


38 


43 


48 


// 


1267    265     53 


G.M.T. 
1890.    d     h     m 
June   7    3  521  W 

8  6  390  E 

9  9  26*0  W 

10  12  129  E 

11  14  599 W 

12  17  468 E 

13  20  338  W 

14  23  208E 

16  2    77  W   3071    260 

17  4  54'8E 

18  7  417  W 

19  10  289  E 

20  13  16*0  W 

21  16    32  E 

22  18  502  W 

23  21  374 E 

25  o  246  W 

26  3  11-9E 

27  5  59'2  W   3075    249 

28  8  46-4  E 

29  1 1  33  7  W 

30  14  210  E 
July    1  17    8-3  W 

2  19  556  E 

3  22  42*9  W 

5  1  302  E 

6  4  176  W 


Deimos. 


b 


QM.T.  p  a 

X890.    d     h     m  0  „ 

Apr.  30  22  40*9  E    1225    55' x     5  6 

May   2  20    69  W 

4  17  327  E 
6  14  583  W 

8  12  236  E 

10    9  489 W   303-1     59-7     72 
12    7  14-0  E 
14    4  38-9  W 


G.M.T. 
1890.    d     h      m 
May  16    2    36  E 

17  23  280  W 

19  20  52-3  E 

21  18  166  W 


a 


b 
11 


5'6 


1273    255     57 


57 


1277    241     57 


b 
11 


1240    637     94 


23  15  409  E 
25  13    51  W 
27  10  29*1  E 

29    7  531  W  3049    661    n-8 


442  Dr.  Morrison,  Satellites  of  Mars.  xlvii.  7. 


G.M.T. 

P 

a 

b 

6.M.T. 

P 

a         ft 

1800.   d      h      m 

May  31     5  171  E 

0 

1* 

u 

1890.    d     h    m 

JQDV19    3  21*4  E 

0 

n          1 

June  2    2  41*1  "W 

21    0  467  W 

4    0    53  E 

22  22  12*3  E 

* 

5  21  294  W 

24  19  38-1  W 

7  18  53*  E 

125*6 

666 

138 

26  17    41  E 

1265 

62*1     15*2 

9  16  179  W 

28  14  30-3  W 

11  13  424  E 

30  11  56*6  E 

13  11     69  W 

July    2    9  23-1  W 

15    8  315  E 

4    6  49*8  E 

17    5  563  W 

3061 

656 

148 

6    4  168  W 

3066 

57*6    145 

In  these  ephemerides  p  denotes  the  position-angle  of  the 
major  axis  of  the  satellite's  apparent  orbit,  and  is  reckoned  from 
the  north  towards  the  east,  and  from  o°  to  3600 ;  a  and  b  denote  the 
major  and  minor  semi-axes  of  the  apparent  orbit.  During  these 
two  oppositions  of  the  planet  the  satellites  move  in  the  direction 
of  increasing  position-angles,  the  Earth  being  above  the  plane  of 
the  orbits.  The  time  of  greatest  elongation  has  been  given 
to  the  nearest  tenth  of  a  minute  in  order  that  a  sufficiently  accu- 
rate comparison  may  be  had  with  observation. 


MONTHLY   NOTICES 

OF  THE 

ROYAL  ASTRONOMICAL  SOCIETY. 


Vol.  XLVII.  June  io,  1887  No.  8 


J.  W.  L.  Glaishbb,  M.A.,  Sc.D.,  F.R.S.,  President,  in  the 
Chair. 

Lieut.  Arthur  Mostyn  Field,  R.K,  H.M.S.  "  Dart " ; 
Herbert  Ingall,  Champion  Grove,  Champion  Hill,  S.W. ; 
Henry  Addenbrook  uassell,  Addenbrook  Villa,  Love  Lane, 
Stourbridge;  and 

The  Rev.  Charles  John  Young,  Stafford  Place,  Halifax, 

were  balloted  for  and  duly  elected  Fellows  of  the  Society. 

Admiral  E.  Mouchez,  Director  of  the  Observatory,  Paris, 
was  balloted  for  and  duly  elected  an  Associate  of  the  Society. 


Proposed  Index  to  Observations  of  Variable  Stars.     By  Professor 

Edward  C.  Pickering. 

For  the  last  four  years  the  Observatory  of  Harvard  College 
has  published  an  annual  statement  of  the  number  of  observations 
made  during  the  previous  year  upon  each  variable  star.  In  the 
fifth  of  these  publications — to  be  published  during  1S88 — it  is 
proposed  to  give  a  statement  of  the  number  of  dates  of  observa- 
tion of  each  variable  star  during  each  year  since  its  discovery. 
It  is  hoped  that  an  index  of  this  kind  will  be  useful  to  astronomers, 
even  if  it  cannot  be  made  complete ;  but  its  value  will  certainly 
be  much  increased  by  the  addition  of  every  extensive  list  of 
observations  which  can  be  obtained  for  insertion  in  it.  All  who 
are  interested  in  this  department  of  astronomy  are  therefore 
requested  to  send  to  this  observatory  any  information   of  the 

E  K 


444  Prof.  Pritchard,  On  the  Parallax  xlyh.  8, 

kind  above  described  which  they  may  have  at  command.  It  is 
very  desirable  that  the  information  should  be  received  early  in 
1 838,  in  order  that  the  publication  may  not  be  unduly  delayed. 

Harvard  College  Ohstrratory,  Ca.nbridge,  U.8JL. : 

1887,  June  22. 


On  the  Parallax  of  61 ,  and  61,  Cygni,  as  obtained  by  the  aid  of 
Photography.     By  Professor  G.  Pritchard,  D.D.,  F.R.S. 

The  computations  for  the  parallax  of  the  two  components  of 
this  historical  double  star  are  now  completed,  subject  to  some 
possible  slight  revision  of  the  numerical  work. 

Inasmuch  as  the  present  communication  professes  to  be 
nothing  more  than  a  preliminary  and  provisional  announcement, 
perhaps  the  most  interesting  form  of  making  it  may  be  to  give  a 
short  citation  from  the  Report  of  the  astronomical  work  done  at 
the  University  Observatory  in  Oxford  during  the  past  year.  It 
will  be  seen  in  the  sequel  that  it  is  not  without  some  importance 
to  add  that  the  Report  was  approved  and  adopted  by  the  Vice- 
Chancellor  and  other  members  of  the  Board  of  Visitors,  including 
the  Astronomer-Royal. 

The  following  is  the  citation  referred  to  : — 

"  The  somewhat  hazardous  enterprise  of  attempting  for  the 
first  time  in  the  history  of  astronomy  to  obtain  the  distance  of 
fixed  stars  from  our  earth  by  the  aid  of  photography  has  been 
attended  with  success.  The  final  results  of  the  investigation 
have  been  placed  in  my  hands  only  during  the  writing  of  this 
Report.  The  first  observation  was  obtained  on  May  26  of  last 
year,  and  the  last  was  effected  on  May  31  of  the  present  year. 
The  intermediate  computations  were  systematically  continued 
during  the  interval.  They  involved  the  reduction  of  no  less  than 
30,000  bisections  of  star-images,  on  330  photographic  plates, 
procured  on  89  nights.  Eight  independent  determinations  of 
the  parallax  of  the  two  components  of  61  Cygni  resulted  from  all 
this  work,  and  these  happily  indicate  a  substantial  agreement 
between  themselves,  and  afford  other  necessary  proof  of  reli- 
ability. Astronomical  photography  is  hereby  placed  on  a  secure 
basis  as  an  efficient  and  exact  exponent  of  the  highest  form  of 
astronomical  science. 

"  Simultaneously  with  these  observations  similar  work  has 
been  in  progress  for  the  determination  of  the  parallax  of  /x  Cos- 
surpeim  and  Polaris.  These  observations  will  now  be  treated  on 
a  less  laborious  scale.  The  photographic  plates  of  the  Pleiades 
have  also  been  taken  with  the  view  of  obtaining  the  accurate 
relative  positions  of  about  one  hundred  stars  therein.  The 
necessary  triangulations  have  been  commenced. 

"  The  funds  granted  by  the  University  have  been  sufficient 
notwithstanding  the  continuous  activity,  which  requires  a  cor- 


June  1887.  of  61  Cygni.  445 

responding  continuity  of  outlay.  This  grant,  hitherto  triennial, 
expires  in  December  next.  If  the  Board  of  Visitors  see  fit  to 
request  the  University  to  continue  this  grant  for  five  years,  it 
would  assist  in  enabling  me  to  commence  a  valuable  and  extended 
class  of  work,  which  under  other  circumstances  I  should  not  be 
justified  in  attempting." 

This  last  sentence  was  altered  by  the  Board  of  Visitors  into 
"  to  undertake  for  the  University  a  share  in  the  production  of 
a  photographic  map  of  the  heavens." 

The  details  given  above  testify  without  further  words  of 
mine  to  the  unwearied  perseverance  and  intelligence  of  my  two 
able  assistants  Mr.  Plummer  and  Mr.  Jenkins. 

The  following  are  the  particulars  of  the  final  numerical 
results  referred  to  in  the  foregoing  citation : — 

Parallax  of  61 ,  Cygni.  Parallax  of  6it  Cygni. 


u 


Determined  from  star  a  =  0*4294  from  star  a = 0*4250 

b  =  0*4228  b  -04508 

x = 0444 1  x  «  0*4520 

#=04194  y«o*4i35 

Mean    =04289  Mean     =0*4353 

Mean  probable  error  of  a  single  determination  of 


61,  Cygni  =  00136. 
61,  Cygni  =  0*0142. 

Mean  distance  of  star  a  from  b  =*■  2382*20 

x  from  y  »  2066*16 

Distance  a  to  &  fluctuates  from  2380*84  to  2382*89 
x  to  y  2064-80  to  2066-86. 

Oxford  University  Observatory: 
1887,  June  10. 

Postscript  (June  24). — The  very  important  significance  of  the 
above  figures  is  twofold : 

1.  That  in  order  to  arrive  at  exactness  of  angular  measure 
in  a  photograph,  and  especially  in  a  series  of  photographs  carried 
through  considerable  periods  of  time,  it  is  absolutely  necessary 
that  each  plate  should  be  considered  as  carrying  with  it  its  own 
scale,  which  scale  may  be  slightly  variable  from  night  to  night, 
or  even  during  the  same  night.  This  fact  is  indicated  by  the 
small  variations  in  the  distances  of  the  comparison  stars  a,  6, 
and  x,  y  from  each  other.  This  fact,  however,  is  not  peculiar  to 
photographic  plates,  but  exists  (to  a  less  extent)  even  in 
measures  taken  with  the  heliometer. 

KK2 


446  Mr.  Downing,  Star-Places  of  the  xlvii.  8, 

2.  That  if  dae  regard  be  had  to  this  slight  variation  of  scale,, 
photography,  properly  handled,  gives  reliable  results,  eqnal  in- 
accnracy  and  delicacy  to  those  obtainable  by  any  other  known 
astronomical  methods. 

Since  the  writing  of  the  foregoing  very  succinct  and  pro- 
visional account  of  work  recently  completed  at  the  University 
Observatory,  Dr.  De  la  Rue,  with  that  munificent  generosity 
which  he  has  so  often  exercised  for  the  promotion  of  knowledge, 
has  promised  the  pecuniary  means  of  adding  a  photographic 
telescope  or  camera  to  the  large  Refractor  in  that  institution. 
The  condition  attached  to  this  gift  is  the  compliance  of  the 
University  with  the  request  made,  as  above  stated,  by  the  Board 
of  Visitors.  Oxford,  therefore,  may  now  be  expected  to  be 
associated  with  Greenwich  in  the  production  of  the  great  inter- 
national  photographic  chart  of  the  heavens  projected  at  the 
Paris  Conference. 


A  Comparison  of  the  Star-Places  of  the  Argentine  General  Catalogue 
for  1875  with  those  of  the  Cape  Catalogue  for  1880,  and  with 
those  of  other  Southern  Star  Catalogues.  By  A.  M.  W. 
Downing,  M.A. 

In  making  this  comparison  the  places  of  those  stars  which 
are  common  to  the  Argentine  General  Catalogno  and  the  Cape 
Catalogue  for  1880,  as  given  in  the  former,  have  been  brought 
tip  from  1875  to  1880,  and  the  differences,  Cordoba — Cape,  taken. 
Proper  motion  has  been  applied  in  forming  both  the  Cordoba 
mean  places  for  1875  and  the  annual  variations  in  all  those  capes 
in  which  a  proper  motion  is  given  in  the  Capo  Catalogue,  the 
quantity  of  proper,  motion  being  taken  from  the  latter.  The 
mean  epochs  of  the  two  Catalogues  are,  however,  so  nearly  iden- 
tical that  this  element  can  have  no  sensible  effect  on  the  result 
deduced  from  such  a  large  number  of  stars  as  is  the  present.  In 
combining  the  separate  differences,  formed  as  is  explained  above, 
each  hour  of  R.  A.  has  been  taken  by  itself,  and  the  stars  occurring 
in  each  hour  arranged  in  order  of  N.P.D.,  and  then  the  means 
taken  over  zones  io°  wide  for  the  extremes,  900 — ioo°,  ioo° — 
no°,  and  1700 — 1800,  and  50  wide  for  intermediate  N.P.D.S: 
In  this  manner  the  table  (Table  I.)  has  been  formed,  exhibiting 
the  values  of  Cordoba — Cape,  both  for  R.A.  and  N.P.D.,  corre- 
sponding to  each  hour  of  R.A.  and  to  each  zone  of  N.P.D.,  and 
the  number  of  stars  (always  the  same  for  Aa  and  AS)  in  each 
group.  It  will  of  course  be  understood  that  the  R.A.s  of  these 
two  Catalogues  depend  on  different  systems  of  time-stars.  In 
the  formation  of  the  Argentine  Catalogue  the  star-places  of  the 
American  Ephemeris  for  the  different  years  were  used  ;  the  Cape 
R.A.s  depend  on  the  annual  lists  of  fundamental  stars  issued  from 
the  Greenwich  Observatory. 


•Jane  1887.        Argentine  General  Catalogue  etc.  447 

The  noxt  table  (Table  II.)  is  formed  by  taking  the  means  of 
the  differences  occurring  in  each  horizontal  line  of  Table  I.,  and 
thus  forming  the  mean  difference  in  R.A.  and  N.P.D.  over  the 
whole  range  of  N.P.D.  corresponding  to  each  hour  of  R.A. 

The  next  table  (Table  III.)  is  formed  from  the  means  of 
vertical  columns  in  Table  I.,  and  exhibits  the  mean  differences 
In  R.A.  and  N.P.D.  over  the  whole  range  of  R.A.  corresponding  to 
the  different  zones  in  which  the  N.P.D. s  have  been  combined. 
To  enable  the  reader  better  to  estimate  the  range  of  the  dis- 
cordances in  R.A.  the  differences  corresponding  to  each  zone  of 
N.P.D.  are  given  reduced  to  the  equator,  as  well  as  the  actual 
mean  discordances  at  the  different  N.P.D.S. 

It  will  be  noticed  that  there  is  a  remarkable  break  of  conti- 
nuity in  the  value  of  A8  (as  exhibited  in  Table  III.)  corresponding 
to  the  zone  1400 — 1450,  and  in  that  corresponding  to  1450 — 150°, 
the  value  being  +  o8,o88  for  the  former,  and  -f  o"*oo6  for  the  latter, 
or  +o8*o54and  +os'003  respectively,  expressed  in  equatorial  in- 
terval. As  the  former  of  these  mean  differences  depends  on  1,229 
stars,  and  the  latter  on  1,179  stars,  this  break  cannot  be  con- 
sidered accidental,  and  the  general  agreement  is  so  good  (except 
for  stars  in  the  immediate  neighbourhood  of  the  pole)  that,  though 
the  actual  quantities  are  small,  the  attention  is  arrested  by  the 
abrupt  change. 

The  negative  differences  in  N.P.D.  appear  to  increase  in 
magnitude  as  the  northern  limit  is  approached,  being  — o"*73 
for  the  zone  90°-—  ioo°.  The  difference  for  the  zone  1650 — 1700 
is  also  abnormally  large,  though  depending  on  a  considerable 
number  of  stars. 

It  will  be  remarked  that  the  mean  discordance  in  R.A.  is 
+  o*"047  ( +  o8*o36  reduced  to  the  equator),  and  in  N.P.D  — o"\4o, 
and  that  the  total  number  of  stars  used  in  the  comparison  is 

The  next  step  has  been  to  obtain  the  values  of  Aa  and  AS 
for  the  beginning  of  each  hour  of  R.A.  and  for  each  50  of  N.P.D. 
by  means  of  a  graphical  representation  of  the  changes  of  these 
values  taken  from  Tables  II.  and  III.,  it  being  assumed  that  the 
mean  value  corresponding  to  a  certain  hour  of  R.A.  or  to  a 
certain  zone  of  N.P.D.  refers  to  the  middle  of  the  hour  or  of  the 
zone.  The  Aas  aud  ASs  read  off  from  their  appropriate  curves  for 
the  beginning  of  each  hour  of  R.A.  have  been  respectively 
corrected  by  the  quantities  — 0^047  an(*  +o"*4o  (the  means, 
with  reversed  signs,  of  the  Aas  and  A$s  taken  throughout),  so 
that  the  difference  Cordoba — Gape  for  any  given  R.A.  and  N.P.D. 
ib  the  sum  of  the  quantities  corresponding  to  that  R.A.  and 
N.P.D.  as  given  in  the  tables  (Tables  IV.  and  V.).  From  the 
comparisons  published  in  Monthly  Notices,  vol.  xlii.  pp.  22,  23, 
vol.  xlv.  pp.  298-301,  and  vol.  xlvi.  pp.  366-379,  in  connection 
with  the  comparison  of  the  Argentine  General  Catalogue  and 
the  Cape  Catalogue  for  1880,  forming  the  first  parts  of  Tables 
IV.  and  Y.,  the  remaining  portions  have  been  formed,  and  these 


443  Mr.  Downing,  Star-Places  of  the  XLvn.  8, 

tables  therefore  give  the  corrections  applicable  to  the  Cape 
Catalogue  for  1880,  the  Melbourne  Catalogue  for  1870,  and  the 
Cape  Catalogues  for  i860,  1850,  and  1840,  to  reduce  them 
respectively  to  the  system  of  the  Argentine  General  Catalogue 
for  1875. 

It  is  remarkable  that  the  differences  in  B.A.  depending  on 
N.P.D.  of  the  Cordoba  and  Cape  7880  Catalogues  at  about 
1300 — 1400  are  very  nearly  equal  in  magnitude,  but  of  opposite 
sign,  to  those  of  the  Cordoba  and  Cape  1850  Catalogues  at  the  * 
same  N.P.D. ,  the  discordances  of  which  at  about  this  place  have 
been  the  subject  of  considerable  discussion  (Introduction  to 
Cape  Catalogue  for  1850,  p.  xi.,  Monthly  Notices,  vol.  xlv.  p.  2^)* 

I  should  add  that  the  expenses  of  the  computations,  the 
results  of  which  are  embodied  in  this  paper,  have  been  defrayed 
by  a  grant  from  the  Government  Grant  Committee  of  the  Royal 
Society,  to  whom  my  thanks  are  due. 


Table  I. 

N.P.D. 

90' 

'-100° 

xoo 

°-no° 

no' 

>_xl5o 

RJL 
h     h 

O-I 

Aa 

8 
—  •002 

AS 
11 

— 066 

No. 
*9 

Aa 

8 
+  -0O4 

AS 

11 
+  OQ3 

No. 
H 

Aa 

8 
+    015 

AS 

n 
-O44 

So. 
21 

1-2 

+  •003 

-034 

17 

—  •020 

—029 

12 

+  "Oo8 

-0'33 

18 

2-3 

+  •007 

—0-56 

23 

+  •040 

-0*32 

6 

-r"007 

-071 

27 

3-4 

+   OI4 

—  I'OI 

18 

+  ■050 

-087 

6 

+  017 

-074 

15 

4-5 

+  •026 

—0*69 

20 

+  OI9 

-O36 

9 

+  '020 

—  0*09 

13 

5-6 

+   037 

-o-86 

45 

+  069 

-0*65 

15 

+  •072 

+  O08 

13 

6-7 

+  •043 

-0-63 

12 

+  O93 

-084 

19 

+  079 

-030 

33 

7-8 

+  •090 

—  1  07 

'3 

+  •049 

—  I  27 

17 

+  •098 

-028 

26 

8-9 

+  *03I 

—096 

13 

+  090 

—  122 

12 

+  O93 

-OI7 

10 

9-10 

+  *080 

-.114 

28 

+  '06l 

—  I'OI 

11 

+  •002 

+  055 

9 

10-11 

+  •030 

—072 

27 

+  •078 

—  1-26 

10 

+  •057 

+  0-I9 

7 

11-12 

+  •026 

-068 

15 

+  O36 

—  071 

12 

+  •072 

+  Ol8 

10 

12-13 

+  *083 

+  0-43 

3 

—  *OIO 

-0-95 

2 

+  •0/3 

+  OII 

16 

13-H 

+  •070 

—091 

4 

—  ■004 

-O'8o 

5 

+  •082 

+  O4O 

9 

14-15 

+    O48 

-034 

4 

+  048 

—  024 

4 

+  -OI9 

+  027 

16 

15-16 

-OI5 

-068 

2 

-.•O30 

-o-35 

5 

+  •043 

+  0*23 

27 

16^-17 

+   OIO 

—016 

4 

+  -OOS 

+  023 

4 

v  O32 

+  0*50 

23 

17-18 

—  •040 

—  1  00 

3 

+  OI7 

-185 

3 

+  •050 

+  OI8 

22 

18-19 

+  -005 

-159 

4 

•OOO 

—072 

1 

+  •028 

-OI3 

21 

19-20 

-OI5 

-078 

2 

—  •OI4 

+  0'2I 

5 

+  ■075 

—  0'20 

17 

20.21 

—  ■020 

-0-48 

5 

+  •008 

—  O42 

5 

+  •058 

-0'37 

18 

21-22 

+  •040 

—017 

3 

+  •005 

-O36 

6 

+  •007 

-O52 

17 

22-23 

—  OO4 

— 019 

7 

+  "Ol6 

-078 

10 

+  *Ol8 

—  O76 

21 

23-24 

—  •029 

-023 

10 

+  •039 

-082 

17 

+  O32 

-0'59 

19 

Jane  1887.        Argentine  General  Catalogue  etc. 


449 


N.P.D. 

R.A. 
h     h 

O-I 

"5< 
Aa 

8 
+  •075 

»-T20° 
A* 
II 
—  O64 

No. 
28 

X20 

Aa 

8 
+    I0O 

°-I25° 

AS 
11 
-103 

No. 
32 

Aa 
8 
+  •024 

AS 

No. 
44 

1-2 

+  •077 

-0-45 

23 

+  •074 

-O76 

36 

+  •017 

-056 

38 

2-3 

+  012 

-o*53 

34 

+  •059 

-083 

40 

+  023 

-o*43 

42 

3-4 

+  •016 

-048 

41 

+  •047 

-055 

39 

+  O36 

-025 

46 

4-5 

+  •017 

-032 

36 

+  •078 

—  0*40 

4i 

+  034 

—  0-12 

60 

5-6 

+  •096 

-0-28 

4i 

+  •122 

—  0*46 

50 

+  •088 

+  OI7 

57 

6-7 

+  •093 

—022 

76 

+   128 

—  0"26 

64 

+  "I08 

+  OO9 

55 

7-8 

+  108 

-008 

62 

+  ■135 

-OI7 

57 

+  -IIO 

+  o-i8 

89 

8-9 

+  •058 

—007 

52 

+  •093 

-OI3 

62 

+  •094 

+  012 

68 

9-10 

+  •056 

—014 

59 

+  082 

-0-25 

49 

+  063 

—001 

48 

IO-II 

+  •017 

—007 

33 

+  •064 

-Ol8 

38 

+  •057 

-013 

44 

11-12 

+  •079 

O'OO 

45 

+  O95 

—  O29 

46 

+  •073 

-003 

47 

12-13 

+  •086 

+  008 

34 

+  082 

-037 

41 

+  *II2 

-017 

33 

13-H 

+  073 

+015 

38 

+  O57 

-O25 

46 

+  *III 

-030 

42 

14-15 

+  •039 

+036 

53 

+  •083 

—  OIO 

5i 

+  •085 

—  Oil 

43 

15-16 

+  •028 

+014 

49 

+  •082 

—  Ol6 

48 

+  •055 

-008 

63 

16-17 

+  •048 

+  016 

50 

+  O49 

-0-30 

70 

+  '06l 

-033 

5o 

17-18 

-•013 

—  012 

49 

+  •040 

-O27 

70 

+  020 

—021 

76 

18-19 

+  •025 

-0-24 

56 

+  '03I 

—  070 

70 

+  •046 

-049 

62 

19-20 

+  •034 

-0-05 

38 

+  •065 

—  066 

37 

+  *020 

-038 

5i 

20-21 

+  •043 

-0"43 

5i 

+  •067 

-I08 

42 

+  -OOI 

—067 

34 

21-22 

+  •028 

-o-68 

48 

+  •096 

—  0"6o 

25 

+  035 

-059 

39 

22-23 

+  •054 

-0-65 

42 

+  •072 

—  roi 

27 

+  •027 

-053 

35 

23-24 

+  •060 

-052 

34 

+  052 

-065 

33 

+  'OI7 

-0-58 

33 

N.P.D. 

RJL 
h     h 

O-I 

1300 

Aa 

8 
+  •037 

-135° 
AS 
11 
—  046 

No. 
43 

i35c 
Aa 
s 

+  •075 

'-i4o° 
Ad 

-065 

No. 
26 

140* 
Aa 

8 

+   OO5 

>-i45° 

AS 

ii 
-O73 

No, 
48 

1-2 

+  •055 

—  040 

34 

+  098 

-0'55 

30 

+   O43 

-086 

47 

2-3 

+   Ol6 

-O32 

42 

+  06l 

-081 

23 

+  *035 

-0'52 

44 

3-4 

+  •033 

+  0*06 

46 

+  •028 

—  022 

38 

+  •044 

—  0*40 

42 

4-5 

+  -049 

-OI3 

47 

+  •047 

^012 

30 

+  •041 

-O38 

46 

5-6 

+  •088 

+  020 

5o 

+  •066 

-O45 

41 

+  •107 

-O47 

52 

6-7 

+  •084 

+  O49 

67 

+  -II8 

-O25 

48 

+    125 

-c-28 

64 

7-8 

+  'I08 

+  CI2 

69 

+   Il8 

—  0*12 

64 

+    139 

—027 

85 

8-9 

+  •071 

—  0'04 

76 

+  "I06 

-0-24 

108 

+  •103 

—0-29 

93 

9-10 

+  •059 

OOO 

42 

+  •138 

-0-26 

64 

+    131 

-050 

70 

IO-II 

+   039 

+  0-08 

55 

+  •095 

-O45 

56 

+   O8O 

—0-17 

74 

11-12 

+  *06l 

+  015 

34 

+  •124 

-03I 

56 

+   077 

— 016 

51 

12-13 

+    114 

—0-07 

36 

+  'l8o 

—  0'60 

44 

+  •159 

-0'49 

45 

45° 


Mr.  Downing,  Star-Places  of  tlte 


xlvii.  8, 


N.P.D. 

ILA. 

h     h 
13-14 

130' 

Aa 
s 
+  092 

A3 

tt 
—  0-09 

Ko. 

57 

135 

Aa 
+  •137 

0-i4O° 
A3 

—  062 

Ko. 
56 

I4©f 
Aa 

8 
+    142 

'-145° 
A3 

n 
-O47 

55 

I4-IS 

+  •119 

—  0*22 

47 

+   I48 

-O44 

54 

+  'l6l 

-0-48 

36 

I5-I6 

+  •053 

—  0'2I 

70 

+  •119 

-0-53 

49 

+  •134 

-0-39 

49 

16-17 

+  •071 

—0*24 

65 

+  088 

-063 

63 

+  •074 

-0*63 

52 

I7-I8 

+  •047 

—  O24 

54 

+  055 

-O49 

79 

+  •073 

-068 

38 

18-19 

+  ■050 

-O56 

54 

+  087 

-085 

63 

+  •109 

-065 

37 

19-20 

+  •026 

-O54 

36 

+  •108 

—  069 

30 

+  •079 

-084 

39 

20-2I 

+  •048 

-o-68 

55 

+  •043 

-089 

32 

+  •072 

-078 

28 

21-22 

+  •041 

-0-51 

28 

+  ■049 

—  1*21 

?2 

+  *028 

-0*82 

40 

22-23 

+  •085 

-0-51 

38 

+  •038 

-0'8l 

39 

+  X)IO 

-084 

44 

23-24 

+  053 

-0-51 

52 

+  '08l 

-O77 

3i 

+  033 

—070 

50 

K.P.D. 
n,A, 
h     h 
O-I 

«45< 
Aa 
8 
—  *020 

'-150° 

A3 

// 
-O48 

No. 

35 

I** 
Aa 
• 
+  •039 

A3 
—  O24 

No. 
19 

155C 
Aa 

8 
+   O47 

A3 

tt 
-0-34 

No. 
15 

1-2 

+  •001 

-O45 

29 

—  •029 

-0*34 

23 

-•026 

—  0-23 

17 

2-3 

+  036 

-063 

3i 

+  O98 

—  0*26 

33 

—  •024 

—  OXM 

23 

3-4 

+  •061 

—  O-60 

34 

+  •080 

-0*33 

32 

+  •007 

-032 

23 

4-5 

+  039 

-O32 

45 

+  •049 

-O47 

35 

—  •O4O 

—  0*62 

25 

5-6 

-•003 

-O47 

5i 

—  -OI2 

—  C27 

36 

-•019 

—0*40 

31 

6-7 

-•045 

-0-37 

44 

-•018 

-0-03 

35 

+  •055 

—0*69 

27 

7-8 

+  •020 

—  076 

73 

+  •022 

-025 

3i 

+  •056 

-073 

29 

8-9 

+  •003 

-0*50 

60 

+  •051 

—  0*46 

35 

+  •020 

-059 

33 

9-10 

+  018 

-O43 

78 

+  •013 

-0-38 

47 

+  •027 

—0-67 

34 

10-11 

—  •001 

-0-45 

109 

-•018 

-0-48 

79 

+  -0O8 

-044 

27 

11-12 

+  •054 

-052 

72 

+  •017 

-0'33 

86 

+  *066 

—0*64 

28 

12-13 

+  •041 

—0-46 

59 

+  •037 

—  0*20 

44 

+  •083 

-047 

35 

13-14 

+•035 

-047 

48 

+  ■026 

—  0*42 

55 

+  *066 

-052 

37 

14-15 

+  •042 

—0*42 

50 

+  •026 

—  0*46 

32 

+   O54 

-054 

32 

15-16 

-•051 

-058 

47 

+  017 

-O3O 

36 

+  -OI2 

—0-40 

26 

16-17 

-•006 

— 0*2» 

45 

—•002 

—  0"4I 

3i 

+  '072 

-0*45 

25 

17-18 

—  •001 

-063 

45 

—  •016 

—  OT4 

32 

+  •052 

-0-19 

16 

18-19 

-•074 

-078 

40 

+  •020 

—  0"40 

35 

+    O43 

— 0*05 

16 

19-20 

-005 

-0*48 

34 

-•057 

—  0*40 

19 

+  '068 

-044 

32 

20-21 

-•055 

—  0*42 

19 

+  •008 

-055 

29 

+  •071 

-031 

18 

21-22 

-008 

-084 

5i 

+  •010 

-0-50 

24 

+  •074 

-065 

9 

22-23 

—  •005 

-082 

39 

+  039 

-043 

25 

+    H5 

-057 

11 

23-24 

-'027 

-085 

41 

+  •008 

-o*34 

27 

+  •154 

-051 

17 

Jane  1887.  Argentine  General  Catalogue  etc. 


45i 


N.P.D.  i6o°-i6s° 

ILA.  Aa             Ai  No. 

h     h  8                   „ 

O-I  +041  -0-25  22 

1-2  --078  -0-35  18 

2-3  +-078  —0-07  16 

3-4  4*034  +0-09  20 

4-5  +004  -033  16 

5-6  —  *022  — 0-35  20 

6-7  4*048  —  o-66  20 

7-8  4  '067  -074  22 

8-9  4060  —0-50  28 

9-10  too  —0*69  22 

10-11  —  -033  —0-52  19 

11-12  4*123  —0*32  27 

12-13  +'°74  —  0#44  24 

13-14  4*056  —0*64  17 

14-15  —'041  —  0*54  20 

15-16  —  '043  40*19  27 

16-17  4*032  4  0*01  20 

17-18  4*005   o*oo  16 

18-19  4*080  4  0*  10  18 

19-20  —'063  —0*42  26 

20-21  4*056  —  o*ii  25 

21-22  —'Oil  —0*24  26 

22-23  4*024  —0*20  15 

23-24  4*070  —0*56  20 


x65°-x7o° 

Aa             A6  Ko. 

—  •068  —097  25 

-•023  -073  23 

4*184  —067  16 

—  •O3O  —0*62  21 

—  *I02  -0*52  14 

—•067  -o*86  15 

—  •109  —0*64  14 

-050  -1-34  15 

—  •090  —1*26  23 

—  •076  —1*90  19 
—•066  —1*13  18 
4*027  —1*42  17 

4*098  —1*12  13 

4*003  —0'86  12 

—  •O48  -I25  20 
4'002  -077  19 

4*106  —0*90  16 

+  *OlO  —0*79  14 

4*055  -o*88  ii 

—  •079  —1*01  16 

—  *I02  —0*62  25 

—  047  —  I*i6  !6 

—  •105  —0*98  17 

4*006  -0-51  8 


i7o0-i3o° 

Aa             Aj  No. 

—  •I69  —0'29  13 

-•O64  —0*32  17 

4-I05  —0-I3  II 

-•on  40*34  15 

-'337  -012  11 

—  •222  —070  9 

—  •261  —0-90  11 

—  •171  -0*96  11 

—  •280  — 1*44  7 

—  •066  -075  20 

—  *i6i  —087  19 

—  •269  —  0*57  11 
-•061  -0-87  11 

—  •103  —098  10 

—  •038  —087  11 
-•525  4043  2 
4*060  40*14  10 
4*043  —0*32  12 

4*100  -074  12 

-•163  -033  3 

-O44  -OI5  17 

-•151  40*11  17 

—  •092  —047  II 

—  •266  —0*5I  19 


R.A. 

h  h 
O-l 

1-2 
2-3 

3-4 
4-5 
5-6 

6-7 
7-8 
8-9 
9-10 
10- 1 1 


Table  II. 

Aa 

AS 

s 
4  0020 

// 
-O56 

*020 

•5* 

•042 

•48 

•O32 

•35 

*022 

•31 

•05I 

34 

•069 

'21 

•088 

*2S 

065 

•30 

•057 

•42 

•024 

•36 

Number  of 
Stars. 

404 
382 
411 

436 
448 
526 

589 
663 

680 

600 

615 


452 


Mr.  Downing,  Star-Places  of  tlie 


xltii.  8, 


RJL 

h   h 

11-12 

' 

A« 

B 
•06 1 

AS 
•31 

Number  of 

6  tars. 

557 

12-13 

+  0098 

-037 

440 

I3-H 

•076 

37 

491        • 

14-15 

•O68 

•29 

473 

I5-I6 

•043 

23 

519 

l6-I7 

•053 

•29 

528 

I7-I8 

•029 

*33 

529 

18-19 

•042 

54 

500 

I9-20 

•028 

•49 

385 

20-2 1 

•027 

59 

403 

21-22 

•Ol6 

•66 

38i 

22-23 

•028 

•68 

38i 

23-24 

+0025 

—061 

411 

O-24 

+  0-047 

—040 

1X752 

Table  IIL 

N.P.D. 

Aa 

Aa  sill  N.P.D. 

AS 

Number  of 
Stars. 

0        0 
9O-IOO 

8 
+  0028 

8 
+  0028 

// 
-073 

301 

IOO-IIO 

•O38 

•037 

70 

2IO 

110-115 

•044 

•04I 

•17 

428 

I 15-120 

•O5I 

•045 

•19 

IO72 

I2C-I25 

■077 

•065 

'43 

III4 

125-130 

•O38 

•O46 

•20 

1199 

130-135 

•O64 

•O47 

•17 

1 197 

135-140 

•097 

•066 

•49 

1156 

140-145 

•088 

•054 

•49 

1229 

145-150 

•OO6 

OO3 

•54 

1179 

150-155 

•OI7 

•OO8 

•36 

880 

155-16© 

#04I 

•Ol6 

•47 

586 

160-165 

+     -024 

+   #oo7 

•32 

504 

165-170 

-     -030 

—  *co6 

•97 

407 

170-180 

-OII3 

—  0010 

-O47 

290 

90-180 

+  0-047 

+  0036 

-O4O 

1 1752 

June  1887.  Argentine  General  Catalogue  etc.  453 

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Mr.  Downing,  Star-Places  etc. 


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2 

«1 


Jane  1887.      Prof.  Auwers,  Catalogue  of  Stars  etc.  455 


A  Catalogue  of  480  Stars  to  be  used  as  Fundamental  Stars  for 
Observations  of  Zones  between  200  and  8o°  South  Declination. 
By  Prof.  A.  Auwers. 

One  of  the  most  important  works  to  be  done  by  the  next 
generation  of  astronomers  will  consist  in  a  new  and  systematic 
determination  of  the  places  of  the  southern  fixed  stars  down  to 
the  9th  magnitude. 

One  object  of  this  determination  will  be  the  completion  of 
the  general  knowledge  of  stellar  proper  motions  by  comparisons 
to  be  made  with  Dr.  Gould's  determinations  for  the  epoch  1875. 
If  this  alone  were  considered,  the  new  observations  might 
advantageously  be  deferred  some  ten  or  twenty  years  more.  But 
the  wants  of  the  great  photographic  survey,  to  be  made  according 
to  the  Paris  programme  with  a  mean  epoch  of  probably  iooo±, 
will  render  it  preferable  to  have  this  new  determination  made 
nearly  for  this  same  epoch. 

The  most  efficient  way  to  secure  homogeneousness  and 
completeness  in  this  determination  will  be  the  arrangement  of 
zone-observations  like  those  of  the  Astronomische  Gesellschaft, 
till  now  made  between  the  declinations  8o°  and  —  20,  and  pre- 
sently to  be  extended  to  —  230,  constructing  the  working  lists 
for  the  zones  from  the  preliminary  photographic  survey  of  the 
southern  heavens  by  which  Dr.  Gill  has  undertaken  to  complete 
the  Bonner  Durchmusterung.  Astronomers  hope  to  have  tho 
results  of  this  survey  within  the  next  few  years,  and  in  order  to 
enable  the  southern  observatories  then  not  only  to  begin  the  zone- 
observations  without  delay,  but  also  to  make  the  reductions 
within  due  time,  it  appears  not  too  early  to  prepare  for  these 
observations  of  southern  zones  by  providing  at  once  for  a 
uniform  and  accurate  determination  of  the  positions  of  a  sufficient 
number  of  stars,  which  ought  to  be  used  as  fundamental  stars  in 
the  reduction  of  the  zones. 

Dr.  Gill  having  expressed  to  me  his  desire  that  I  should 
make  the  selection  of  these  stars,  in  order  that  they  should  be  in* 
eluded  in  the  new  working  list  which  was  to  be  constructed 
about  a  year  ago  for  the  Transit  circle  of  the  Cape  Observatory,. 
I  have  drawn  up  the  following  list,  which  I  now  beg  herewith  to- 
communicate  to  the  astronomers  of  the  southern  hemisphere^ 
expressing,  in  accordance  with  Dr.  Gill,  the  wish  that  a  sufficient 
number  of  them  will  co-operate  towards  the  accurate  determina- 
tion of  these  stars  in  the  same  manner  as  has  been  done  for  the 
fundamental  stars  used  in  the  zone-observations  of  the  Astro* 
nomische  Gesellschaft. 

The  selection  of  the  stars  included  in  the  following  catalogue- 
was  to  be  made  upon  the  following  principles  : — 

1.  The  stars  ought  to  be  distributed,  at  convenient  intervals,, 
as  equally  as  possible  over  the  area  covered  by  the  zones  to  be- 
observed.    This  area  may  be  considered  to  be  conveniently 


456  Prof.  Auwers,  A  Catalogue  of  xxvn.  8, 

filled  with  fundamental  stars,  if  in  each  single  zone  comprising 
io°  of  declination  these  stars  follow  each  other  on  the  average 
within  I5m  to  20™  in  the  lower  declinations,  and  2om  to  25™  in 
the  higher. 

2.  The  stars  onght  to  be  of  such  a  kind  as  will  afford  the 
most  complete  guaranty  for  accurate  and  accordant  observa- 
tion by  different  observers.  The  following  stars  should  be 
avoided : — first,  very  bright  stars,  with  whose  observations  rather 
large  personalities  are  known  occasionally  to  interfere;  and 
second,  doable  stars  in  which  the  companion  might  disturb  the 
observation  of  the  principal  star,  or  possibly  prevent  its  being 
referred  by  different  observers  to  exactly  the  same  point. 

3.  Where  there  is  any  choice  no  star  ought  to  be  admitted 
unless  it  be  sufficiently  observed  in  previous  catalogues  to  allow 
of  a  determination  of  its  proper  motion,  with  an  accuracy 
sufficient  to  allow  the  new  position  to  be  brought  forward  ten  or 
fifteen  years  without  diminishing  its  accuracy  to  an  extent  which 
would  become  appreciable  in  the  reduction  of  the  zone-observa- 
tions. 

The  most  elegant  solution  of  the  problem  with  respect  to 
condition  1,  and  apparently  also  to  condition  2,  might  have  been 
attained  by  the  exclusive  use  of  the  stars  of  one  or  two  middle 
orders  of  magnitude,  the  stars  of  about  6  mag.  and  7  mag.,  as 
fundamental  stars  for  the  zones.  The  number  of  these  stars  is 
sufficiently  great  in  all  regions  to  allow  of  a  very  uniform  distri- 
bution of  the  fundamental  points  throughout,  and,  at  the  same  time, 
the  stars  of  6  mag.  and  7  mag.  most  probably  are  those  objects 
which  with  the  present  meridian  instruments  are  observed  with 
the  highest  degree  of  precision  in  the  single  observation  and 
with  the  least  amount  of  systematic  difference  between  different 
observers.  But  in  the  latter  respect  the  apparent  gain  to  be 
obtained  by  their  use  would  be  quite  illusory,  because  the  places 
of  these  stars  themselves  must  be  determined  by  referring  them 
to  the  brighter  stars,  so  that  it  remains  impossible  to  get  rid  of 
any  kind  of  personality  to  which  the  observations  of  brighter  stars 
are  liable.  On  the  other  hand,  with  the  stars  of  6  mag.  and  7  mag., 
condition  3  could  bo  fulfilled  only  in  such  an  incomplete  and  un- 
satisfactory manner  that  their  choice  could  not  be  recommended. 
The  sacrifice  of  uniformity  of  distribution  unavoidably  connected 
with  the  choice  of  the  stars  of  brighter  magnitudes  than  the  6th, 
because  of  their  varying  frequency  and  comparatively  small 
number,  is  really  much  the  lesser  evil. 

Having,  by  condition  1,  fixed  the  extent  of  the  catalogue  at  a 
number  of  stars  between  400  and  500,  I  have  for  the  above 
reasons  chosen  those  stars  to  form  its  main  body  whose  magni- 
tude, according  to  Gould's  TJranometry,  ranges  between  the 
limits  2*0  and  5*0.  The  limits  of  the  zones,  for  which  the 
fundamental  stars  were  to  be  selected,  were  determined  by  the 
southern  limit  of  the  zones  of  the  Astronomische  Gesellschaf  fc  and 
the  northern  limit  of  the  special  circumpolar  work  already  under- 


Jane  1887.  480  Fundamental  Stars.  457 

taken  by  the  Cape  Observatory,  and  therefore  will  be  —  23°  and 
— 8o°  declination.  For  the  fundamental  catalogue  I  have  ex- 
tended the  northern  limit  to  —  200,  but  generally  retained  the 
southern  limit  of  —  8o°,  because  it  does  not  seem  desirable  to  com- 
bine the  presently  proposed  observations  with  those  of  a  greater 
number  of  stars  within  ten  degrees  of  the  South  Pole.  The  latter 
work  may  be  better  made  the  object  of  other  specially  conducted 
observations  besides  those  of  the  Cape  Observatory  already 
mentioned. 

The  Uranometria  Argentina  contains  between  declinations 
— 200  and  — 8o°  (for  the  Equinox  1875)  380  stars  not  brighter 
than  2'o  mag.  and  not  fainter  than  5*0  mag.,  which  are 
without  companions  such  as  might  interfere  with  the  ac- 
curate and  uniform  observation  of  the  principal  star,  one 
or  two  variable  stars,  however,  being  included  in  this  number, 
which  during  a  part  of  their  period  fall  somewhat  below  5 
mag.  The  exclusion  of  double  stars  has  been  adhered  to  with 
still  greater  rigidity  than  in  the  construction  of  tbe  funda- 
mental list  for  the  southern  zones  (—2°  to— 230)  of  the  As- 
tronomische  Gesellschaft ;  even  the  stars  with  very  faint  or 
distant  companions  have  been  excluded  with  rare  exceptions. 
For  even  where  such  companions  cannot,  by  their  faint  11  ess  or 
their  relative  position,  influence  in  any  degree  the  proper  estimate 
of  the  point  to  be  observed,  or  of  its  correct  position  with  respect 
to  the  wires,  an  observer — and  more  possibly  a  good  observer — 
is  liable  to  be  troubled  to  a  certain  extent  by  their  mere  existence, 
as  they  are  apt  to  detract,  for  a  moment,  part  of  the  attention 
from  what  ought  to  constitute  during  the  transit  of  a  fundamental 
star  the  exclusive  object  of  the  full  attention  of  the  astronomer 
observing  a  zone — viz.  that  he  shall  fix,  with  the  greatest 
possible  accuracy,  a  point  to  which  to  refer  the  zone  under 
observation.  Only  in  some  very  few  cases  I  have  retained  some 
of  those  known  double  stars,  in  which  the  possibility  of  a  disturb- 
ing influence  appears  limited  to  a  very  small  extent — wholly 
excluded  in  one  case — viz.  four  objects  (to  which  afterwards 
€  Cants  maj.  has  been  added  as  a  fifth)  already  occurring  in  the 
Fundamental  Catalogue  of  the  Berliner  Jahrbuch,  and  five  more, 
which  could  not  easily  be  superseded  for  want  of  other  stars  in 
the  same  region.  Possibly  some  more  objects  of  this  kind  will 
be  found  in  the  catalogue  when  the  stars  of  the  southern  heavens 
have  been  examined  more  closely  with  regard  to  their  duplicity 
than  has  yet  been  done,  or  reported  to  have  been  done. 

Out  of  the  380  stars  accordingly  available,  including  the  nine 
known  double  stars,  it  was  not  possible  to  retain  for  the  catalogue 
more  than  280.  The  remaining  100  were  excluded,  part  of  them 
being  wholly  superfluous  in  regions  covered  densely  enough 
without  them ;  part  of  them  because  their  transits  would  take 
place  so  nearly  at  the  same  time  with  those  of  several  other  stars 
in  remoter  declinations  that,  by  retaining  them,  the  time  neces- 
sary for  complete  observation  of  the  catalogue  would  have  been 


45» 


Prof.  Auwers,  A  Catalogue  of 


xltu.  8, 


disproportionally  extended.  The  majority  of  these  excluded  stars 
is  contained  in  the  hoars  6  to  9  and  12  to  15  of  Bight  Ascension, 
in  which  the  brighter  stars  are  most  densely  crowded  together 
in  the  southern  heavens.  To  replace  these  stars  in  more  con- 
venient positions,  where  it  appeared  at  all  necessary  to  replace 
them,  and  to  fill  np  the  greater  gaps,  chiefly  in  the  hours  19  to  2, 
between  the  brighter  stars,  I  had  recourse  to  the  stars  noted  5*1 
mag.  to  60  mag.  in  the  Uranometria Argentina,  in  some  cases, 
for  want  of  such  stars,  to  still  fainter  ones,  adding  in  this  manner 
193  stars  between  the  limits  —  200  and  —  8o°,  sixteen  of  which  are 
of  the  magnitude  6-7,  and  the  four  faintest  of  the  magnitude  7-6  -, 
finally,  two  stars  somewhat  exceeding  the  upper  limit  of  bright- 
ness (c  Cants  maj.  and  fi  Orucis)  were  added,  and,  besides,  five 
stars  situated  a  little  beyond  the  southern  limit  of  — 8o°,  in  regions 
which  could  not  be  provided  for  sufficiently  without  them. 

The  catalogue  accordingly  contains  480  stars,  which  are  dis- 
tributed for  the  Equinox  1875  as  follows : — 


Hour 

contains 

Hour 

contains 

Hour 

contains 

O 

19 

stars 

8 

17  < 

stars 

16 

23  stars 

1 

19 

»» 

9 

19 

it 

17 

23    .. 

2 

18 

tt 

10 

19 

i»  • 

18 

25      n 

3 

19 

it 

11 

19 

11 

19 

21     „ 

4 

*5 

a 

12 

21 

tt 

20 

19    t, 

5 

22 

tt 

13 

20 

>t 

21 

18    „ 

6 

19 

tt 

H 

19 

tt 

22 

26    „ 

7 

21 

tt 

*5 

16 

it 

23 

23    „ 

Zoce 

-20°  tO 

-30° 

contains 

99 

stars 

* 

i» 

-30      ,, 

-40 

ti 

85 

it 

it 

-40       » 

-50 

tt 

89 

11 

1* 

-50       » 

-60 

j* 

77 

tt 

>t 

-60       „ 

-70 

it 

70 

it 

11 

-70       „ 

-80 

it 

54 

it 

11 

-SO       „ 

-825 

tt 

6 

it 

This  distribution  maybe  considered  to  be  sufficiently  uniform, 
and  cannot  be  rendered  more  uniform,  if  conditions  2  and  3 
remain  fulfilled  with  equal  approximation  throughout.  It  has 
not  been  possible,  with  the  available  material,  to  reach  the  average 
number  of  twenty  stars  in  each  single  hour  of  Bight  Ascension, 
while  in  some  hours  it  was  possible  somewhat  to  exceed 
this  number  without  interfering  with  an  equable  facility  of 
getting  through  the  catalogue  in  the  observations  to  be  made* 
for  the  determination  of  the  fundamental  positions.  The  selection 
of  the  stars  has  been  assisted  throughout  by  laying  down  their 
positions,  and  those  of  a  good  many  other  store  of  5  mag.  and  6 
mag.,  besides  those  finally  selected,  in  a  map  drawn  upon  a  large 


»f  fl 


•  •  »l 


Jane  1887.  480  Fundamental  Stars.  459 

scale,  carefully  scrutinising  in  every  single  instance  what  com- 
bination would  afford  the  greatest  advantage  in  the  observations 
and  the  redaction  of  the  zones.  As  to  the  determination  of  the 
fundamental  stars,  care  was  taken  that,  assuming  five  minutes  to 
be  required  for  a  complete  observation  with  a  transit  circle,  in 
no  Bight  Ascension  should  more  stars  interfere  with  each  other 
than  would  allow  of  the  whole  catalogue  being  gone  through  n 
times  completely  in  4»  observing  nights.  This  scrutiny,  how- 
ever, was  made  with  the  catalogue  drawn  up  for  the  year  1875, 
and  has  not  been  repeated  with  the  Bight  Ascensions  as  finally 
brought  forward  to  the  epooh  1900. 

In  what  degree  it  has  been  found  possible  to  adhere  to  condi- 
tion 3,  regarding  the  means  for  determining  the  proper  motions, 
may  be  inferred  from  the  following  statement.  Of  the  480  stars 
there  occur — 

In  the  Catalogue  of  Laotille  (prine.  Ht.)     ...         133 

,,              „            Bradley...         ...         ...  84 

,,              „            Piazzi    ...         ...         ...  221 

Johnson  (St.  Helena) ...  252 

Cape  Catalogue  for  1840      410 

„   1850   452 

tt        it        ft    IoOO    ...     ...     243 

ft  m         tf  IOOO    ...      ...     4*)*) 

„      WiHiamstown  Catalogue      127 

„      First  Melbourne  Catalogue 244 

all  of  them,  of  course,  being  included  in  Gould's  Catalogue 
{Catalogo  General  Argentino). 

Five  stars  were  inserted  into  the  catalogue  which  are  not 
contained  in  any  previous  catalogue  except  Gould's  (three  of 
them,  however,  forming  part  of  the  list  of  fundamental  stars 
recently  determined  for  the  southern  zones  of  the  Astrono- 
mische  Gesellschaft),  and  fonr  others,  which  besides  in  this  cata- 
logue occur  either  in  Stone's  Catalogue,  1880,  or  in  the  Melbourne 
Catalogue.  Two  stars  have  been  observed,  previously  to  Gould 
and  Stone  1880,  only  by  Piazzi.  Further,  fourteen  stars  do  not 
occur  previously  to  the  Cape  Catalogue  for  1850  (except  Taylor's 
Catalogue,  which  contains  some  of  them,  but  scarcely  affords 
positions  fit  for  determining  proper  motions),  and  the  Cape  1850 
Catalogue  gives  only  one  co-ordinate  for  three  of  these  stars. 
Altogether,  therefore,  for  twenty-five  stars  condition  3  is  only 
very  unsatisfactorily  fulfilled;  but  in  all  these  cases  it  proved 
to  be  impossible  to  replace  the  stars  at  convenient  places  by 
other  stars  already  better  determined. 

The  magnitudes  are  given  in  the  following  catalogue  ac- 
cording to  the  determinations  in  the  Uranometria  Argen- 
tina. The  designation  of  the  stars  is,  for  the  great  majority  of 
them,  likewise  that  of  tho  same  work.     In  those  constellations, 

L  L 


460  Prof.  Attwers,  a  Catalogue  of  xlyii.  8, 

however,  which  are  visible  in  middle  Europe  completely,  or  at 
least  to  a  predominant  part  of  their  fall  extent,  and  which  are 
comprised  so  far  in  the  uranometrical  researches  of  Bayer  and 
Argelander,  or  in  Flamsteed's  catalogue  work,  Bayer-Arge- 
lander's  nomenclature  and    Flamsteeds    numbering,   together 
with  limits  of  the  constellations  drawn  accordingly,  ought  to  be 
retained,  in  my  opinion,  without  any  alterations  (except  those, 
of  course,  which  are  necessary  to  correct  for  accidental  errors). 
From  those  constellations,  small  parts  of  which  only  can  be  seen 
in  middle  Europe  and  are  investigated  by  Bayer  and  his  Euro- 
pean successors,   Argo,    Centauries,    Lupus,    Corona   Australis, 
Bayer's  letters  ought  to  be  withdrawn,  being  only  apt  to  inter- 
fere with  the  correct  extension  of  his  own  principle  of  lettering 
over  the  whole  constellation.    In  Argo,  however,  I  do  not  agree 
with  Gould  completely.     It  seems  to  me  impossible  to  supersede 
designations  so  thoroughly  connected  with  the  history  of  astro- 
nomy as  a  Argus  or  17  Argus  by  other  designations,  and  I  consider 
it  necessary,  therefore,  to  retain  the  name  of  the  entire  constel- 
lation Argo  in  the  designation  of  its  brighter  stars.   The  limit  for 
distinguishing  between  this  entire  constellation  and  its  separate 
parts  will  be  drawn  in  the  most  simple  way,  if  all  the  stars 
designated  with  Lacaille's  Greek  letters  are  counted  through 
Argo,  and  the  subdivisions  Carina,  Puppis,  and  Vela  are  in- 
troduced only  to  distinguish  between  the  smaller  stars  designated 
by  a  threefold  repetition  of  the  Latin  alphabet.    According  to 
this  principle  the  names  are  set  down  in  the  catalogue,  with  one 
more  trifling  deviation  from  the   Uranometria  Argentina.     In 
this  work  two  stars  in  Puppis  are  lettered  I  and  J,  a  similarity 
of  designation  too  much  apt  to  produce  confusion,  and  better 
therefore  to  be  avoided.    I  have  suppressed  the  symbol  J  and 
inserted  the  star  which  has  it  appended  in  the  Uranometria 
Argentina  simply  as  Puppis  218  Gould. 

The  last  column  contains  some  remarks  to  note  the  few 
double  stars,  and  to  call  the  attention  to  neighbouring  stars  in 
suoh  cases  when  they  might  give  rise  to  mistakes.  Those 
remarks  would  not  appear  to  be  needed  in  the  determination  of 
the  positions  of  the  stars  of  the  catalogue  with  meridian  instru- 
ments ;  but  it  might  be  inferred  from  experience  that  they  will 
prove  to  be  useful  in  the  zone-observations  themselves  or  in 
some  other  use  of  the  present  catalogue—for  example,  in  field- 
work. 

Catalogue. 

Ko.  Nome:  Hag.       R.A.  1900.    ^JJJJ-    Decl.  1900.     ^JJ*  Remarks, 

h     m    a  8  01  1 

o    4  20  +3-1   -46  17-9  +o«33 
6  30      3-0      28  2 1 -4      0*33 

6  38      30      35  417      <>'33 
14  51   +32      65  278  +035 


I 

c  Phoenicia 

4 

2 

«'  Sculptoris 

5-6 

3 

9  Sculptoris 

5-6 

4 

f  Tucanse 

4 

Jane  1887. 


480  Fundamental  Stars. 


Na 


Name. 


Hag.      H.A.  1900. 


,5    jB  Hydri 

6  a  Phoenici'8 

7  Ceti,  49  G. 

8  A1  Phoenicia 

9  Sculptoris,  77  G. 

10  Phoenicia,  58  G. 

11  Ceti,  59  G. 

12  ft  Phoenicia 

13  if  Phoenicia 

14  X*  Sculptoris 

15  Ceti,  73  G. 

16  xHydri 

17  X*  Tucanae 
iS    a  Sculptoris 

19  Phoenicia,  80  G. 

20  £  Phoenicia 

21  i  Tacanse 

22  Sculptoris,  102  G. 

23  Sculptoris,  109  G. 

24  Hydri,9G. 

25  7  Phoenicia 

26  48  Ceti 

27  8  Phoenicia 

28  Hydri,  14  G. 

29  Sculptoria,  129  G. 

30  c  Sculptoria 

31  t1  Hydri 

32  ^Eridani 

33  *  Phoenicia 

34  X  Eridani 

35  XHydri 

36  59  v  Ceti 

37  a  Hydri 

38  r  Fornacia 

39  P  Fornacia 

40  Phoenicia,  135  G. 

41  *  Eridani 

42  k  Fornacia 


3-2 

2-3 
5-6 

5-4 
6 

6-5 
6 

5-4 

4-5 
6 

5-6 

6-5 
5-6 

4 

6-7 

3-4 

6-5 
6 

6 

6-7 

3-4 

5-* 

4 

6-7 
6 

5 

6-7 
5-6 

5 

4 

5 

4 

3 

5 

5 
6 

3-4 


h     m    ■ 

0  20  30 

21    19 

25  23 

26  35 

28  44 

29  43 
32  12 

36  36 

38  52 

39  21 

39  47 
45    7 

51  16 

53  47 
57  48 

1  1  37 
3  20 

8    9 
18  52 

21  38 

24    1 

24  48 

27  5 
32  59 
37  38 

40  57 

41  16 

42  17 
49  38 

52  4 
52  24 

55  17 

55  37 
o    o 

8  30 

10  29 

12  55 

17  57 


2 


Ann. 
yar. 

+  3'3 
29 
30 
2*9 
30 
2*9 

3*i 
28 

27 
2*9 

30 

2*1 
2'3 

2-9 
2-5 

27 

2*4 

28 

2'8 
2  1 
2*6 

2*9 

2-5 

0'3 

26 

+  2-8 

—  O'l 

+  2*3 

2*4 

23 

28 

1  "9 
27 

2*6 

2*4 

2*1 

+  27 


Decl.  1900. 

-77  49- x 

42  50'9 

24  20*4 

49  214 

30  6*6 

52  55*5 

25  191 

46  380 
58  07 
38  584 
22  334 
75  280 
70    4-0 

29  539 
57  32'4 

47  I5'3 
62  186 

38  232 

31  279 

64  53  4 

43  49'8 
22    8-8 

49  357 
79    07 

37    20'2 

25  33*  1 
79  392 
54  i"6 
46  47*6 
52  6-4 
68    84 

21  337 
62    3-4 

29  46  6 

3i  ""5 
41  37*9 
51  585 
24  1 6*2 


Ann. 
yar. 

+  034 

0*33 

0'33 

0-33 

0'33 

0-33 

0'33 

0*33 

0'33 

0'33 

0'33 

0'33 

0-33 
032 

0-32 

032 

0*32 

032 

031 

0.31 

031 

031 

031 

030 

030 

030 

030 

030 

0*29 

030 

030 

0*29 

029 

0-29 

028 

0'2& 

0-28 

+  0*28 


461 

Remarks. 


9  mag.  5 


tr 


L  L  2 


462 

Prof. 

AuioerSy 

a  Catalogue  of 

to. 

Name. 

Mag. 

BJL.  1900. 

Ann. 
yar. 

Decl.  190a 

Ann. 
yar. 

43 

8  Hydri 

4 

h     m    a 
2   19  58 

8 
+  I"I     « 

-69    6-9 

+  027 

44 

A  Horologii 

6 

22     6 

17 

60  45*5 

0*27 

45 

*  Hydri 

6 

22    16 

0'3 

74    59 

027 

46 

«r  Eridani 

4 

23   19 

2*2 

48   IO'I 

027 

47 

A1  Fornacis 

6 

28  56 

+  2-5 

35    53 

0*27 

4« 

/*  Hydri 

6-5 

33  46 

-i'5 

79  327 

O-26 

49 

if  Horologii 

6-5 

34    6 

+  20 

52  586 

O-26 

50 

i  Eridani 

4 

36  43 

24 

40  17*0 

0'26 

51 

e  Hydri 

4 

38    2 

0-9 

68  41-8 

0*26 

52 

£  Fornacis 

4-5 

44  55 

2'5 

32  49*6 

0*25 

53 

2  rs  Eridani 

5-4 

46  30 

27 

21  25*0 

025 

54 

£  Horologii 

5 

56  54 

i-i 

64  28*  1 

0*24 

55 

1 1  t*  Eridani 

4 

57  59 

26 

24    0*9 

0'24 

56 

Eridani,  58  CK 

6-7 

59  3i 

20 

47  220 

0*24 

57 

/i  Horologii 

5-6 

3    1  15 

1-4 

60    75 

023 

58 

B  Hydri 

6 

2    3 

01 

72  17*6 

023 

59 

12  Eridani 

3-4 

7  48 

2'5 

29  22*9 

024 

60 

Horologii,  38  G. 

6-7 

10    1 

i'5 

57  417 

023 

61 

Fornacis,  79  G. 

7-6 

10  44 

2'4 

35  55'8 

023 

62 

0  Eridani 

4-5 

15  55 

+  24 

43  27*  1 

023 

63 

1  Hydri 

6 

18  26 

-1-6 

77  45'2 

022 

64 

k  Reticuli 

5 

27  36 

+  i*o 

63  1 75 

Oa2I 

65 

19  t*  Eridani 

4 

29  22 

2'6 

21  581 

0'20 

66 

Horologii,  45  G-. 

6 

29  35 

18 

50  43'i 

0'20 

67 

y  Eridani 

5 

33  30 

21 

40  36*  i 

0*20 

68 

8  Fornacis 

5 

38  16 

24 

32  154 

OI9 

69 

27  t*  Eridani 

4 

42  32 

26 

23  327 

OI8 

70 

0  Reticuli 

4 

42  56 

07 

65    73 

CI9 

71 

g  Eridani 

4 

45  43 

+  2*2 

36  302 

Ol8 

72 

7  Hydri 

3 

48  47 

—  TO 

74  327 

Ol8 

73 

Doradus,  1  G. 

7-6 

51  56 

+  r6 

52  58'9 

Ol8 

74 

36  t8  Eridani 

4 

55  40 

25 

24  180 

0'I7 

75 

8  Reticuli 

5-4 

57    9 

0'9 

61  41*0 

OI7 

76 

Eridani,  174  G. 

6 

4    1  29 

2"5 

27  557 

017 

77 

a  Horologii 

4 

10  41 

20 

42  325 

OIS 

78 

a  Reticuli 

3-4 

13    8 

08 

62  434 

OIS 

79 

7  Doradu? 

4-5 

13  24 

16 

51  44*4 

OIS 

So 

Eridani,  212  G. 

5-6 

16  17 

+  2*6 

20  527 

+  OIS 

XLTTI.  8, 
Remarks. 


7-8  mag.  9 


Jane  1887. 


480  Fundamental  Stars. 


463 


Ra.                  Name. 

Mag. 

R>A.  1900. 

DecL  1900. 

*??•          Remarks. 

YlX. 

81    43  d  Eridani 

4 

h    m    s           s 
4   20  l6    +2'2 

0        / 
-34  150 

+  0  14 

82    i»Beticnli 

6 

20  47  +o*6 

63  375 

0*I4 

83    8  Menaa 

6 

24  43  -4-2 

80  27*0 

OI3 

84    SCeli 

5 

27  47   +  1-8 

45  101 

OI3 

85    52  v2  Eridani 

4-3 

31   40       2'3 

30  46*0 

013 

86    a  Dorados 

3 

3i  So      i-3 

55  151 

013 

87    Eridani,  258  G. 

6 

35  57      2'5 

24  407 

OI 2 

88    a  Geli 

5-4 

37  20      1-9 

42    3*3 

OI2 

89    «r  Dorados 

^5 

42  5°  +o*9 

59  55*o 

O'H 

90    p  Mens® 

6-5 

44    3  -06 

71    6-9 

O'H 

91    2  c  Leporia 

3-4 

5    1  13  +25 

22  303 

O-08 

92    11s  Pictoria 

5-6 

2  22      1*5 

49  42*8 

OO8 

93    (  Doradua 

5 

3  48  +ro 

57  36  7 

0'07 

94    jSMensas 

6-5 

4  19  -08 

71  27-1 

OO8 

95    £ Menaee 

6 

10  14  —7-0 

82  36"3 

0*07 

96    0  Doradua 

5 

13  50  —0"I 

67  178 

0-07 

97    0  Columbee 

5 

13  51  +21 

34  594 

0*07 

98    Columbe,  12  G. 

6 

15  26      2-4 

27  283 

006 

99    f  Pictoria 

6 

16  55      1*5 

50  429 

0'06 

100    Columbse,  18  G. 

6 

23  53      i*9 

41     1*3 

O-OS 

101    Pictoria,  20  G. 

6-5 

27  24      1-6 

• 

47    90 

0-04 

102    c  Columbse 

4 

27  39      21 

35  326 

005 

103    j9  Doradua 

4 

32  46  +0-5 

62  33*3 

0*04 

104    7  Mensae 

6-5 

35  5o  -2-4 

76  249 

003 

105    a  Columbee 

2-3 

36      I    +2*2 

34    7'6 

003 

106    13  7  Leporia 

4 

40  18     2-5 

22  287 

0*03  7-8  mag.  pr.i"  b.i' 

•6 

107    8  Doradua 

4-5 

44  35      °i 

65  464 

002 

108    15  9  Leporia 

4 

47     O       2'6 

20  53- 1 

O'OI 

109    IColumba* 

3 

47  26      2*1 

35  48*4 

0-03 

no    7  Pictoria 

5-4 

48    0      i'i 

56  n-5 

0*02 

ui    i)  Columbse 

4 

56    5  +i"8 

42  49*2 

+o*oi 

112    k  Menage 

6 

57    2  -4*1 

79  22-8 

O'OO 

113    Puppia,  1  G. 

6 

6    1  36  +17 

45    2-2 

000  6-7  mag.seq.i2'  a.2' 

♦5 

114    Golombn,  74  G. 

6 

2  15      23 

29  44*8 

O'OO 

115    Hctoris,  47G. 

^-5 

6    8      O'S 

62    81 

—  O'OI 

116    9  Pictoria 

5 

8  21         1*2 

54  56*8 

O'OI 

117    »r  Columbia 

5 

12   59    +21 

35    64 

0*02 

1 18    a  Mensae 

5-6 

13  13  -18 

74  43*o 

—  0'02 

464 

Prof.  Auivers, 

a  Catalogue  of 

No. 

Name. 

Mag. 

&A.  1900. 

Ann. 
rar. 

Decl.  1900. 

Ann. 
var. 

119 

I  C  Canis  mnj. 

3 

h    m    a 

6  16  28 

8 

+  2-3  ■ 

0       / 
-30      12    • 

-0*02 

I20 

A  Canis  maj. 

6-5 

24  27 

+  2*2 

32  3IO 

OO3 

121 

**  Dorados 

6 

26  20 

-0-5 

69  380 

0*04 

122 

5  £*  Canis  maj. 

5 

30  52 

+  25 

22  531 

0'04 

123 

N  Carinae 

5 

32  46 

i*3 

52  535 

OO5 

124 

9  Argus 

3-4 

34  42 

i-8 

43    6-4 

OO5 

125 

13  k  Canis  maj. 

4 

46    6 

2*2 

32  235 

0'06 

126 

a  Pictoris 

3-4 

47  10 

o-6 

61  50*1 

0*06 

127 

t  Argus 

3 

47  27 

+  i-5 

50  297 

007 

128 

f  Mensae 

6 

48  23 

-49 

80  425 

0-07 

129 

1  Volantis 

6-5 

52  35 

-07 

7o  503 

008 

I30 

Canis  maj.,  105  G. 

6 

54  30 

+  25 

25  168 

008 

131 

c  Canis  maj. 

2-1 

54  42 

24 

28  501 

008 

'32 

Carinae,  27  G. 

6-5 

7    2  26 

+  I-I 

56  35'8 

0-09 

133 

0  Mensae 

6-5 

2  55 

-37 

79  166 

009 

'34 

25  ft  Canis  maj. 

2 

4  20 

+  2-4 

26  140 

009 

'35 

/  Puppis 

5 

9  4J 

17 

46  35'6 

O'lO 

136 

x  Argus 

3-2 

'3  37 

2-1 

36  551 

010 

137 

29  Canis  maj. 

5-6 

H  30 

2-5 

24  225 

010 

'38 

&  Volantis 

4 

J6  53 

o-o 

67  464 

on 

139 

31  ri  Canis  maj. 

3-2 

20     8 

2'4 

29    6*4 

O'll 

140 

Puppis,  108  G. 

5-6 

29  46 

• 

2'6 

22    48 

013 

141 

Q  Carinae 

5-6 

33  » 

i'5 

52  186 

013 

142 

/  Puppis 

5 

33  40 

2 '2 

34  44'6 

013 

'43 

I  Puppis 

4-5 

39  47 

24 

28  42*9 

o-i4 

144 

c  Puppis 

4-3 

41  41 

+  2'I 

37  435 

0*14 

'45 

(  Volantis 

4-5 

43    4 

-07 

72  219 

0*14 

146 

7  {Argus 

4-3 

45     5 

+  2-5 

24  365 

015 

147 

P  Puppis 

4-5 

46  12 

i-8 

46    7*2 

015 

148 

a  Puppis 

4 

48  46 

21 

40  191 

015 

149 

Volantis,  19  G. 

6 

49     I 

04 

65  564 

015 

150 

Puppis,  218  G. 

4-5 

50  22 

i-8 

47  5o*5 

015 

IS' 

X  Argus 

4-3 

54  14 

i"5 

52  428 

016 

152 

C  Argus 

2-3 

805 

21 

39  433 

017 

153 

p  Argus 

3 

3  17 

2'5 

24    o*9 

01 7 

154 

7  Argus 

3 

6  27 

i-8 

47    25 

017 

155 

q  Puppis 

5-4 

14  49 

2*2 

36  21  0 

018 

156 

€  Argus 

2 

20  28 

+  1*2 

59  ii'3  • 

-019 

XLVII.  8, 
Remarks. 


IO-II  mag.  8* 


Jane  1887. 

480  Fuuda 

menta 

i  &lare . 

465 

Xa 

Knme. 

Mag. 

h.a.  1900. 

Ann. 
var. 

Decl.  1900. 

^"J"          Remarks. 

^57 

0  Chamseleontis 

5-4 

h    m     8 

8  23  39 

8 
-17 

0         / 
-77    9  7 

—020 

158 

fi  Volantis 

4 

24  39 

+  0*7 

65  481 

020 

159 

e  Velorum 

5-4 

34    8 

21 

42  384 

021 

160 

Pyxidis,  19  0. 

6-5 

34  46 

2*6 

22  19-4 

02I 

161 

0  Pyxidis 

4-5 

36  12 

2'3 

34  571 

0'2I 

162 

d  Carina 

5-4 

38  24 

i*3 

59  24*2 

0'2I 

163 

a  Pyxidis 

4 

39  34 

2'4 

32  49*5 

02I 

164 

3  Argus 

2 

4i  56 

17 

54  205 

0*22 

165 

a  Velorum 

4 

42  38 

+  2*0 

45  40*5 

0'22 

166 

71  Chamseleontis 

6-5 

44  44 

-19 

78  360 

0*22 

167 

7  Pyxidis 

4-5 

46  18 

+  2-5 

27  20-3 

0'22 

168 

c  Carina 

4 

52  47 

i'4 

60  15-8 

0-23 

169 

c  Velorum 

5-4 

9    0  42 

21 

46  419 

0*24 

170 

a  Volantis 

4 

0  52 

10 

65  597 

O24 

171 

A,  Argus 

2-3 

4  19 

2'2 

43     17 

0'24 

172 

G  Carina* 

5 

4  53 

0'2 

72  120 

0*24 

'73 

j8  Argus 

2 

12    6 

07 

69  18  3 

O25 

174 

1  Argus 

2-3 

14  25 

16 

58  51*3 

O25 

*75 

$  Pyxidis 

5-6 

17     4 

26 

25  324 

O25 

176 

k  Argus 

3-2 

19     I 

i'9 

54  35  0 

0-2S 

177 

c  Aotlise 

5 

25     7 

2"5 

35  3o-8 

026 

178 

^  Argus 

4-3 

26  46 

2*4 

40    17 

0-26 

179 

Hydrse,  160  G. 

6 

28  36 

28 

20  40*4 

0  26 

180 

H  Carinse 

6 

30  51 

°'5 

72  382 

0  26 

181 

k  Carinse 

5 

31  32 

17 

58  471 

027 

182 

M  Velorum 

5 

33  15 

2*1 

48  544 

027 

183 

$  Antliae 

5 

39  45 

27 

27  187 

0  27 

1S4 

I  Carinse 

4-5 

42  30 

16 

62    2-8 

0*27 

185 

m  Velorum 

5 

47  49 

23 

46    47 

02S 

186 

«>  Argus 

4 

53  21 

2*1 

54    5  5 

0-28 

187 

17  Antliae 

*-5 

54  35 

2*6 

35  247 

O28 

188 

Hydra,  193  G. 

6 

59  44 

2'8 

23  480 

029 

189 

j  Velorum 

4 

10  10  33 

2*5 

4i  376 

0'29 

190 

»  Argus 

4-3 

11  22 

1*4 

69  32-5 

0*30 

191 

Velorum,  202  G. 

6-7 

16  12 

24 

47  11* 

030 

192 

Antliae,  64  G. 

6-5 

19    7 

2*6 

37  3o- 1 

O3O 

*93 

/Carina) 

4-5 

22  25 

I'2 

73  31*3 

O3O 

194 

a  Antliae 

4-5 

22  34 

+  27 

30  335 

-030 

466 


Prof,  Auwers,  a  Catalogue  of 


xlvii.  8, 


Ko. 

Name. 

Mag. 

R.A.  1900. 

Ann. 
Tar. 

Dec].  1900. 

Ann. 
v^r. 

195 

s  Carina 

5-4 

h     m 
IO  24 

8 

'3 

s 
+  2*2 

0        1 
-58  137 

-030 

196 

p  Carina? 

4-3 

28  28 

2' I 

6l    I02 

031 

'97 

44  Hydra 

6 

29 

15 

2'8 

23  138 

03I 

198 

p  Velorum 

4 

33 

6 

25 

47  42  3 

031 

'99 

7  Chamaleontis 

4-5 

34 

17 

07 

78    54 

031 

200 

m  Velorum 

5 

35 

19 

2*4 

55    49 

03I 

201 

•  Argus 

3 

39  23 

2*1 

63.52-2 

03I 

202 

p  Argus 

3 

42 

28 

2*6 

48  535 

031 

203 

9*  Chamaleontis 

5 

44  51 

06 

80    o-8 

032 

204 

u  Carina 

4 

49  25 

2*4 

58  193 

032 

205 

1  Antliie 

5 

52 

3 

28 

36  35*9 

032 

206 

i  Velorum 

4-5 

55  33 

27 

41  413 

032 

207 

X  Hydrae,  26  Her. 

4-5 

11    0 

3i 

2-9 

26  453 

032 

208 

Carina,  259  G. 

6 

3 

14 

2*1 

70  20"2 

032 

209 

x  Carina 

5-4 

4 

19 

2'5 

58  26-O 

032 

210 

1 1  £  Crateris 

4 

6 

45 

29 

22    l6  8 

0"33 

211 

Carina,  264  G. 

6-5 

8 

37 

2*5 

63  375 

032 

212 

x  Centauri 

4-5 

16 

27 

27 

53  566 

0.33 

213 

Centauri,  29  G. 

6-5 

20 

39 

2*9 

35  308 

0'33 

214 

(Hydrae 

4 

28 

5 

2*9 

31  183 

0'33 

215 

C  Centauri 

5-6 

31 

5 

29 

47    5"2 

o*33 

216 

\  Centauri 

3-4 

31 

9 

27 

62  28*0 

0  33 

217 

x  Chamaleontis 

6 

33 

8 

2'5 

75  20-6 

0'33 

218 

0  Hydra 

5 

35 

14 

3-o 

34  ii-4 

0'33 

219 

xMnsca 

4 

40  53 

2-8 

66  10-4 

0*33 

220 

Centauri,  65  G. 

5-4 

41  41 

2-9 

60  373 

0'33 

221 

Hydra,  298  G. 

6 

43  42 

30 

26  1 1-6 

0'33 

222 

B  Centauri 

5 

46 

9 

30 

44  370 

o-33 

223 

Cruris,  2  G. 

6 

53 

12 

30 

55  45*6 

0'33 

224 

c  Chamaleontis 

5 

54  39 

2-9 

77  39*8 

0'33 

225 

f  >  Cruris 

5-4 

57  56 

30 

62  45*3 

o*33 

226 

Centauri,  88  G. 

6-5 

58 

28 

31 

41  524 

0'33 

227 

8  Centauri 

3 

12    3 

10 

31 

50    99 

0'33 

228 

2  c  Corri 

3 

4  59 

3'i 

22    3-8 

o-33 

229 

8  Crucis 

3-4 

9  5o 

31 

58  1 15 

0'33 

230 

c  Muses? 

5-4 

12 

11 

3*2 

67  24-2 

o*33 

231 

0  Chamaleontis 

5-4 

12 

27 

3*4 

78  45'4 

0'33 

232 

c  Cruets 

4 

15 

58 

+  3*2 

59  50'9 

-0*33 

Remarks. 


6  mag.  pr.32»  b^'$ 


tJ 


Jane  1887. 


No. 


Name. 


233  Centauri,  117  G. 

234  a?1  Centauri 

235  Hydrae,  323  G. 

236  9  Centauri 

237  7  Gratis 

238  7  Muses 

239  9  £  Corvi 

240  7  Centauri 

241  Hydra,  330  G. 

242  IMuscse 

243  $  Cruris 

244  p  Centauri 

245  n  Centauri 

246  8  Mnscse 

247  Is  Centauri 

248  Centauri,  (77  G. 

249  Centauri,  183  G. 

250  if  Musce 

251  r  Centauri 

252  Centauri,  196  G. 

253  46  7  Hydro 

254  1  Centauri 

255  d  Centauri 

256  Hydro,  350  G. 

257  Chamseleontis,  49  G. 

258  e  Centauri 

259  1  i  Centauri 

260  M  Centauri 

261  ft  Centauri 

262  ( Centauri 

263  Centauri,  294  G. 

264  **>  Centauri 

265  47  Hydro 

266  49  ir  Hydro 

267  5  0  Centauri 

268  if  Apodis 

269  <  Lupi 

270  v  Centauri 


4 

80  Jfnnda' 

tnenta 

I  Stars. 

467 

Mag. 

JUL.  1900. 

Ann. 
vftr. 

DecL  1900. 

Ann. 

▼AT. 

-  Remarks. 

h     m    a 

s 

0        / 

z 

7-6 

12   19  51 

+  3*2 

-41  57*5 

-0*33 

6 

20    6 

31 

34  37'9 

0*33 

*-5 

21  36 

31 

32  165 

o-33 

• 

4-5 

22  37 

3*2 

49  40*6 

0'33 

2 

25  37 

33 

56  33  1 

034 

4 

26  y> 

35 

7»  348 

0*33 

2-3 

29    7 

3"i 

22  505 

o*33 

2-3 

36    0 

3'3 

48  246 

0'33 

6 

3841 

3*2 

27  465 

o*33 

3-4 

40    8 

3'6 

67  33*6 

0'33 

2-1 

4i  53 

3*5 

59    8-5 

0  33 

5-6 

45  16 

3*2 

33  272 

o*33 

4-5 

47  53 

3*3 

39  38- 1 

o*33 

4-3 

55  22 

40 

71    0-5 

032 

5 

13    1    5 

35 

49  22*2 

0-32 

6 

1  42 

35 

52  554 

032 

5-6 

6    2 

37 

59  233 

032 

5-6 

8  28 

40 

67  21-8 

032 

6-5 

11  20 

33 

30  585 

032 

6 

11  26 

34 

43  270 

0.32 

3-4 

13  29 

3*2 

22  385 

032 

3 

14  59 

34 

36    I  TO 

0-32 

4-5 

25  14 

35 

38  53*4 

031 

6 

27    2 

3*3 

28  107 

0-31 

6-7 

30  38 

50 

75  iO'4 

031 

3-2 

33  33 

38 

52  57*5 

031 

4-5 

40    1 

34 

32  322 

030 

5 

40  19 

3'8 

50  55*8 

030 

3-4 

43  36 

3*6 

41  585 

030 

3-2 

49  18 

37 

46  47  7 

030 

6-5 

50  25 

43 

63  117 

0.30 

4 

52  11 

3'6 

4i  367 

0-29 

6 

52  55 

3*4 

24  29' 1 

0*29 

4-3 

14    0  40 

34 

26  ii'9 

0-29 

3-2 

0  48 

3*5 

35  526 

030 

11  mag.  3' 

5-6 

5  38 

r« 

80  323 

0*29 

4 

13    0 

3*8 

45  35'8 

028 

5 

13  20 

+  4'i 

55  555 

-028 

468 


Prof.  Auwer8f  a  Catalogue  of 


xltii.  8, 


No.                    Name.  May. 

271  Circini,  10  G.  6 

272  a  Centanri  5 

273  Librae,  3  G.  6-5 

274  52  Hydro  5-6 

275  1}  Centanri  2-3 

276  a  Lupi  3  -2 

277  a  Apodis  4 

278  Circini,  19  G.  6 

279  cl  Centanri  4-5 

280  b  Lnpi  6 

281  Apodis  18  G.  6 

282  Circini,  29  G.  6 

283  Centanri,  381  G.  6 

284  /BLopi  3 

285  7  Scorpii  1  Hev.  3-4 

286  ir  Lnpi  4-5 

287  CLnpi  4-3 

288  7  Trianguli  austr.  3 

289  £  Circini  5-4 

290  8  Lnpi  4-3 

291  <pl  Lnpi  4-3 

292  a1  Apodis  6 

293  c  Trianguli  austr.  5-4 

294  7  Lupi  3 

295  Scorpii  3  Hev.  4-5 

296  Norms*,  2  G.  6 

297  5  X  I^pi  5-4 

298  £  Trianguli  austr.  3 

299  5  P  Scorpii  5-4 

300  7  8  Scorpii  2-3 

301  8  Norma  5 

302  0  Lupi  5 

303  10  »*  Scorpii  5 

304  k  Normae  5-6 

305  8  Trianguli  austr.  4-5 

306  7*  Normae  5-4 

307  20  <r  Scorpii  3-4 

308  Scorpii,  62  G.  6 


t»  1       Ann. 
*•*•  X900.   w. 

h   m  a     s 
14  16  48  +4'9 

16  53 
19  6 
22  18 


15 


16 


29  10 

35  17 
35  25 
37  21 

37  32 
40  2 

46  28 

47  53 
49  36 
51  58 
58  12 
58  18 

5  7 
9  33 

9  41 

14  48 

15  28 
20  36 

27  33 

28  8 

30  57 
3i  24 
44  36 
46  20 
50  42 
54  25 
59  25 

0  1 

1  33 

5  35 

6  20 

12  21 
15    7 


37 
34 

35 
38 
40 

71 

47 

3*6 

4*2 

6-6 

46 

37 

39 

3*5 

4"i 

4*3 

55 

47 

39 

3*8 

64 

54 
4*o 
36 

4*4 
38 
5'2 
37 
35 
4'2 

39 

3*5 

47 

54 

45 
36 


17  15  +40 


Decl.  1900. 

o        / 

67  444   - 

39    3'2 

24  2I'I 
29     2*5 

4i  43' 1 
46  575 
78  371 
62  269 

34  44'5 
5i  57*6 
76  153 
59  42' 1 
33  270 
42  43*9 

24  533 
46  39-6 

51  431 

68  186 

58  25-6 
40  17-1 

35  53'9 
73  2-5 
65  588 
40  499 

27  48*3 

52  2-6 

33  19*3 
63    73 

28  55*3 
22  20-2 

44  54*i 

36  318 
20  360 

54  22-2 
63  258 

49  54*6 
25  211 

38  57*6 


*n"*  Bemarks. 

▼ar. 

-0-28 
028 
027 
0*27 
0*27 
O-26 
0'26 

0*26  7  mag.  pr.  i"46'  a.5'*4 
0*26 

026  6  mag.  8eq.il*  b.io'6 
025 
025 
025 
025 
0-24 
024 
023 
0-23 
023 

0*22 
0'22 
C22 
0'2I 
0'2I 
CV20 
0'20 
OI9 
019 
Ol8 

0-17 

0*17 
0*I7 

0.I7f9»l4-5mag.pr.34* 

017  J.     b.  i2'o 

016 

016 

015 

015     9  mag.  21" 

-0-15 


June  1887.  480  Fundamental  Stars.  469 

Nc.  Ntina.  Hag.     RA.  1900.     A*£  DecL  1900.  *j£;  Remarks. 

h     m     a  s  o        /  / 

309  f  Triaoguli  austr.  6-5     16  17  41   +6*3  —69  51*6  —0-15 

310  7  Apodis  4  18    6  9-0  78  40-3  0*15 

311  Trianguli  austr.,  33  G.     6  2156  5-3  61247  014 

312  Norma,  59 Gr.  6  2227  43  46     13  014 

313  A'Scorpii  5-4  24  5*  3*9  34  292  014 

314  m  Norma  5-6  26  58  4-2  43  50*0  0*13 

315  £  Apodis  4-5  28  47  84  77  18 4  014 

316  23  t  Scorpii  3-4  29  39  37  28    03  012 

317  a  Trianguli  austr.  2  38    4  63  68506  0*12 

318  ijArae  4  41     9  5*1  58  51*8  oil 

319  26  f  Scorpii  3  43  42  3'9  34    67  01 1 

320  m1  Scorpii  4-3  45     5  40  37  525  on 

321  C2 Scorpii  4-3  47  33  42  42  114  oil 

322  f  At®  3  50  20  49  55  500  010 

323  24  Ophiuchi  6  5046  3*6  22  595  oaio 

324  e1  Ar»  4  51  37  48  53    0-4  010 

325  Scorpii,  117  G.  6-5  5525  39  3*597  009 

326  ri  Scorpii  4-3     17    4  59  43  43    65  0-09 

327  Scorpii,  139  G.  6  10  33  39  32  32*9  007 

328  t  Apodis  6  1056  66  70    ro  0*07  7mag.pr.I,n49,  b.5^4 

329  40 1  Ophiuchi  5  14  59  3-6  21     0-3  0*07 

330  42  6  Ophiuchi  3-4  15  52  37       24  539  006 

331  fi  Arae  3  16  59  50      55  26*1  0-06 

332  44  Ophiuchi  4-5  20  15  37       24     50  006 

333  45 d  Ophiuchi  5  20  57  3*8      29  46*5  006 

334  8  Arse  4-3  22    4  5-4      60  36*0  0*06 

335  o  Arse  3  24     7  46      49  478  005 

336  51  Ophiuchi  5  25  18  37       23  531  005 

337  35 *  Scorpii  2-3  26  49  41       37     18  005 

338  xArse  6  29  53  4-9      54  260  0*05 

339  0  Scorpii  2  30    7  4*3      42  560  004 

340  k  Scorpii  3-2  35  34  41       38  587  004 

341  17 Pavonis  4-3  35  55  5-9      64  405  004 

342  /iAra  6-5  36  12  48      51  467      004 

343  t1  Scorpii  3-4  40  36  4*2      40    52      003 

344  3-*TSagitkmi  4^6  41  15  38      27475      003 

345  G  Scorpii  3-4  43    3  4-1       37    07      003 

346  Apodis,  66  G.  6  57  17  +8*4      75  535  -001 


470 


Prof.  Amoers,  a  Catalogue  of 


xlvii.  &V 


Na 


Name. 


347  t  Pavonis 

348  10  7  Sagittarii 

349  c  Telescopii 

350  13 /t  Sagittarii 

351  Telescopii,  6  G. 

352  i»  Sagittarii 

353  {  Pavonis 

354  19  *  Sagittarii 

355  20  c  Sagittarii 

356  a  Telescopii 

357  Pavonis,  30  G. 

358  22  X  Sagittarii 

359  f  Corona  anstr. 

360  ( Pavonis 

361  Br.  2333 

362  X  Corona  anstr. 

363  Pavonis,  41  G. 

364  ij1  Coronse  anstr. 

365  X  Pavonis 

366  30  Sagittarii 

367  k  Paronis 

368  34  <r  Sagittarii 

369  X  Telescopii 

370  c  Coronse  anstr. 

371  38  C  Sagittarii 

372  p  Telescopii 

373  40  t  Sagittarii 

374  a  Coronse  anstr. 

375  41  ir  Sagittarii 

376  Paronis,  60  G. 

377  Coronse  anstr.,  49  G. 

378  a  Sagittarii 

379  telescopii,  59  G. 

380  Sagittarii,  186  G. 

381  1  Telescopii 

382  52  h  Sagittarii 

383  Pavonis,  70  G. 

384  Sagittarii,  228  G. 


Mag. 

IRJL  1900. 

Ann. 
Tar. 

DecL  1900. 

*"?'          Remarks. 
Tar. 

5-4 

h      ma 

17  5«  57 

+  5*8 

-63  403 

— o-oi 

3 

59  23 

3'8 

30  256 

o-oo 

5 

18    348 

4*4 

45  58  3 

000 

4 

7  46 

36 

21      5*1 

+  o*oi 

6-5 

8  42 

5"" 

56    3'3 

0*01 

3-4 

10  51 

4*i 

36  475 

O'OI 

4-5 

14    0 

55 

61  324 

002 

3 

14  35 

3'8 

29  52-3 

002 

2-3 

17  32 

40 

34  259 

002 

3-4 

19  33 

44 

46    i"5 

002 

6.7 

20    5 

77 

74    17 

002 

3 

21  47 

37 

25  287 

0-02 

5 

26  22 

4*3 

42  23*1 

004 

4 

31  21 

7*0 

71  30*8 

0*04 

6 

32  25 

3*6 

23  354 

0*04 

5-6 

36  55 

4*i 

38  25- 1 

OK>$ 

6 

37  25 

74 

73    62 

0-05 

6-5 

4i  37 

43 

43  47*4 

o*o6 

4-5 

42  57 

5'6 

62  181 

0-06 

6-7 

44  50 

36 

22  16-6 

006 

5 

46  38 

6-2 

67  21*6 

006 

2-3 

49    4 

37 

26  25-2 

0*07 

5 

50  27 

4'8 

53    4'2 

0*07 

5-6 
3 

51  58 
56  14 

4"i 

3'8 

37  143 
30    i"4 

0*07 

6-5 

5825 

4*8 

52  293 

008 

4-3 

19    0  42 

37 

27  490 

008 

4 

2  40 

41 

38    37 

008 

3 

3  49 

3'6 

21  no 

0*09 

6-5 

7    9 

61 

66  50*0 

009 

6-7 

7  23 

4*4 

45  217 

0-09 

4 

16  57 

4*2 

40  48*2 

on 

6 

19  46 

48 

54  31-5 

O'll 

6 

20  37 

3*8 

29  565 

O'll 

5-6 

2748 

4*5 

48  18-8 

012 

5-4 

3i  13 

5i 

25     6*2 

013          11  mag.  3" 

6-5 

37  53 

7-0 

72448 

013 

6-5 

39  39 

+  3*8 

32    91 

+  014 

Jane  1007. 

48 

0  J*undam 

ental 

Stars. 

471 

Ko. 

Name. 

Hag. 

R.A. 1900. 

Ann. 
var. 

Decl.  1900. 

Ann. 
vox. 

Remarks. 

385 

r  Telescopii 

5-6 

h     m    s 

19  39  5i 

8 

+  49  ■ 

-56  36*2 

* 

+  0-I4 

386 

56 /Sagittarii 

5 

40  32 

35 

20     OO 

OI4 

3*7 

Pavonis,  75  G. 

6 

45  57 

53 

6l   257 

OIS 

388 

« Sugittarii 

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472  Prof  Atiwerst  Catalogue  of  Stars,              xlvii.  8, 

No.                    Name.  Mag.      HUA.  1900.  ^j£#  DecL  1900.      *Jj?'          Remarks, 

h      xn    ■  s  e        /  / 

423  r  Octantis  4      21  30  22  +  6*9  -77  489  +0*26 

424  41  Capricorni  6-5  36  18  34  23  429  027 

425  9 1  Piscis  anstr.  5  39    o  3*6  33  29*0  0-27 

426  o  Indi  6-5  42  21  5*2  70    5*6  0*27 

427  7  Grnis  3  47  52  36  37  502  028 

428  « Indi  5  51     7  41  55  281  028 

429  Capricorni,  134  G.  7-6  53    9  33  21  396  028 

430  «Indi  5  5543  4'6"  57  11*  025 

431  X  Grnis  5-4    22    o    6  36  40    1 -5  0-29 

432  a  Grnis  2  I  56  38  47  267  0*29 

433  14  M  Piscis  anstr.  5-4  2  33  35  33  286  0*29 

434  16  X Piscis  anstr.  5  8  38  34  28  157  029 

435  c  Octantis  6-5  8  50  71  80  563  029 

436  ft1  Grnis  5  9  36  3"6  4*  5°7  029 

437  aTucanse  3  II  38  4-2  60455  °'29 

438  Grnis,  37  G.  6-5  11  41  39  54    63  030 

439  rlndi  6-5  15  55  50  72  44-2  030 

440  47Aqnarii  6-5  16    6  33  22     58  030 

441  v  Grnis  6-5  22  47  35  39  382  0-30  7  mag.  pr.  25'  b.  af't 

442  *»  Grnis  4  23  18  3*6  44    04  030  { *£*£*"*  ** 

443  vTxicame  5-6  26  15  41  62  298  030 

444  59  v  Aqnarii  5-6  29  13  33  21  131  031 

445  Piscis  anstr., 49  G.  6  3313  34  33  3$2  °'3* 

446  18  c  Piscis  anstr.  4  35    7  3*3  27  340  031 

447  $  Octantis  4-5  35  53  6-6  81  544  031 

448  0  Grnis  2  36  42  36  47  245  031 

449  t  Grnis  3-4  42  3"  3*6  5*  5°*6  °'3i 

450  Grnis,  69  G.  6  45  21  34  39  412  032 

451  Tncane,  18  G.  6  45  41  39  63  431  032 

452  22  7  Piscis  anstr.  5-4  46  58  3'3  33  244  032        9  mag.  4" 

453  p  Indi  6  47  43  43  7<>  3^5  °'32 

454  f  Grnis  4  54  5*  3*6  53  *7*4  032 

455  Indi,  80  G.  6  58  16  4-0  69  217  032 

456  •  Grnis  4      23     1  15  3-4  44    37  032 

457  86  c1  Aqnarii  4-5  1  19  32  24  170  032 

458  88  c*  Aqnarii  4  4    7  3*2  21  42*9  0*32 

459  1  Grnis  4  4  42  3*4  45  47*3  032        Com.  10 mag. 

460  Tncanse,  25  G.  6-5  1057  +36  62327  +0*33 


June  1887.       Sydney  Observations  of  Double  Stars.  473 

No.  Name.  Mag.     R.A.  190a     *JJ*       DecL  190a    *£*       Remark?. 

h     m    •  ■  0       ,           , 

461  7Tncan»                        4  23  11  36  +35  -58  470  +033 

462  7ScnlptoriB  4-5  13  25  3-2  33    47  032 

463  Scnlptoris,  11  G.             6  15  56  3'2  27  320  0*33 

464  98  &1  Aqnarii  4-5  17  44  31  20  387  033 

465  o  Gnus  6-5  21     1  3-4  53*16-6  033 

466  Tncanse,  33  G.  6  23  14  35  63  39 7  0*33 

467  Octantis,  83  G.  6  26  52  4-0  77  56*3  033 

468  0  Scnlptoris  5  27  37  3*2  38  22*2  0-33 

469  101  6*  Aqnarii  5-4  28    3  31  21  28*0  0*33 

470  <  Phoenicia  4-5  29  42  32  43  100  033 

471  Phoenicia,  11  G.  4-5  32  28  3*2  46    27  033 

472  m  Scnlptoris  5-6  35  23  32  32  376  033 

473  Tncane,  35  G.  6-7  38  41  35  71     29  033 

474  <r  Phoenicia  5  41  57  3*2  50  469  0*33 

475  8  Scnlptoris  5-4  43  43  3'i  28410  033 

476  Aqnarii,  274  G.  6-7  48  1 1  31  24471  033 

477  t  Phoenicia  5  5344  31  53183  033 

478  e  Tncanae  4-5  54  43  3-2  66    80  033 

479  •  Octantis  5-6  56  29  3*2  77  37*0  033 

480  Tncan«,45G.  6  59  37  +31   -71  596  +033 


Measures  of  Southern  Double  Stars,  made  at  the   Observatory, 

Sydney,  New  South  Wales. 

(Communicated  by  R.  C.  Russell,  B.A.,  F.R.S.) 

The  following  are  measures  of  interesting  southern  double 
stars  made  at  Sydney  Observatory  during  1886  with  two  measures 
of  a  Oentauri  in  1884.  With  a  view  of  testing  the  measures  of 
position-angles  several  measures  of  a  Oentauri  have  been  made. 
Taking  A  a  and  A  8,  it  will  be  seen  that  the  results  obtained  in 
this  way  by  Mr.  Pollock  are  rather  less  than  his  direct  measures, 
but  he  thinks  his  direct  measures  are  more  reliable.  There  is  some 
discrepancy  in  the  measures  of  h  5028,  the  large  star  of  which 
Burnham  discovered  to  be  double  (B  759),  and  p  makes  the  dis- 
tance of  the  wide  pair  34//,8i.  Herschel  gives  two  measures 
with  his  reflector  distances,  20"  and  15",  and  the  Sydney  measure 
in  1886  is  I5"'27. 


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in 
in 

!>. 

in 

• 

r>. 

V 

• 

b 

• 

8 

O 

V 

s 

fo 

in 

• 

P 

0 

• 

CO 

b\ 

* 

CO 

O 

vb 

N4 

co 

- 

^ 

O 

0 

m 

0 

CO 

«n 

t?o 

VO 
co 

i        3- 

CO 

CO 

1 

I 

1 

1 

1 

1 

m 

Ov 

00 

o\ 

in 

00 

in 

«*> 

m 

^ 

Ox 

N4 

vO 

tN 

00 

OS 

co 

•-« 

** 

^r 

m 

00 

Cv 

O 

*MI 

»■ 

M 

M 

*m 

CI 

C| 

« 

CI 

3 

VO 

PO 
vO 

vO 
vO 

sg 

IN. 

vO 

tN 

tN, 

Cn 

t>. 

tN, 

»>. 

«Q. 

*Q. 

«Q. 

<5Q. 

OQ. 

03. 

M  M  2 

478  -Mr.  Gore,  On  the  xlvii.  8. 


Observations  of  the  Companion  of  Sirius  made  at  the  Dearborn 
Observatory,    Chicago,   U.S.A.      By   Prof.    G.  W.   Hough, 

Director. 

(Communicated  by  the  Secretaries.) 

Date.  SkLTime.        p.  «.  Remarki. 

h 


o  •/ 


1887  1 18  5.9  247  —  High  winds.    Unsteady. 

148  6-6  244  690  Difficult. 

•186  7*5  237  clouded  Comp.  plain. 

•211  7*2  237  680  Difficult. 

•217  7*5  23*2  677  Comp.  plain.  Vis.  with  925  power. 

'236  80  23*1  6-65  Difficult.    Clouds  passing. 

•249  7*8  23*3  677  Difficult.    Hazy. 

Mean  Results. 
1887195  237  678 

During  the  past  spring  the  weather  here  has  been  very  un- 
favourable. It  is  the  first  year  that  I  have  found  any  difficulty 
in  securing  observations  of  Sirius  on  as  many  nights  as  was 
desirable.  The  decrease  in  the  distance,  however,  makes  the 
observation  of  this  pair  more  difficult  every  year,  and  hence 
requires  better  atmospheric  conditions  than  formerly. 


On  the  Orbit  of  2  1757.     By  J.  E.  Gore. 

A  reference  to  my  paper  on  the  orbit  of  this  binary  star  in 
the  Monthly  Notices  for  November  1886  will  show  that  the  com- 
parison between  the  measures  of  position  angles  in  recent  years 
and  the  angles  computed  from  the  elements  there  given  is  not 
satisfactory.  I  have  re-computed  the  orbit,  using  recent  measures 
kindly  made  for  me  by  Mr.  Tarrant  and  Prof.  Young  (U.S.A.), 
and  now  find  the  following  elements : — 

Second  Elements  of  2  1757. 

P  =  276*92  years  Q  «  870  3^ 

T«  1791*98  a.d.  A  =  185°  23' 

e  m  0*4498  a  «  2*05" 

7-40°  56'  /i=  +  i'3o° 

The  following  is  a  comparison  between  the  observations  and 
the  positions  computed  from  the  above  elements : — 


Jane  1887. 

Epoch. 
182537 

182982 

183239 

183338 

«835'37 
1836*42 

183848 

1841-38 

1842-39 

1842-52 

184345 

184351 
184472 

1845*88 

185038 

185238 

1853-09 

185373 
185437 
i855"3i 
185632 
185642 
1856-88 
185729 
185808 

185837 
185936 
1 860-34 

186035 
1863-32 

1865-97 
1 86601 
1867-27 
186830 
1869-22 
1869-24 
1870-15 
187037 
1871-19 


Orbit  of  S  1757. 


Observer. 
Struve 


»• 


Smyth 
Strare 


»> 


it 


Smyth 
Midler 
Dawes 
Smyth 
Dawes 
Kaiser 

O.  Struve 
Madler 

O.  Struve 
Smyth 
Madler 
Jacob 
Madler 


it 


'i 


Morton 

Seochi 

Morton 

Jacob 

Madler 

ft 
Dawos 

»t 
Dembowski 

fi 
0.  Struve 
Talmage 

Dembowski 
Briinnow 
Talnwge 

Dembowski 
Talmage 

Dembowski 


100 
195 
24*1 

239 
255 

294 

310 

360 

374 

379 
388 

409 

437 
40-8 

488 

517 
52-2 

480 

501 

51*3 
518 

519 

529 
542 
528 

547 

537 

54"3 

534 
590 

60-4 

608 

637 
627 

634 

643 

63*5 
64-1 

634 


Be 
10*47 

1957 
2419 

2583 

2903 

3067 

3362 

37*48 

3872 
3889 
4000 
4007 

4150 
4277 
47*43 
4925 
4998 

50-54 
51-10 

5I-96 
5280 
5289 

53*27 
53-61 
54'24 
5447 
55*24 
5603 
5603 
5823 
6006 
6009 
6100 
6165 
6225 
6225 
6287 
6300 
6352 


Oo-&c 
-047 

-003 

—OO9 

-i-93 

-353 

—  1  27 

—  262 
-148 
-1*32 
-099 

-12 
+  083 
+  220 

-197 

+  1*37 
+  1-45 

+  222 

-2-54 

—  100 
-066 

—  i-oo 

—  I  01 

-037 
+059 

~i*44 
+  023 

-1-54 

-173 
-263 

+  077 

+  034 

+  0-71 

+  270 

+  105 

-t- 115 

+  205 

+  063 

+  I-I0 

—012 


Po 

i-6o 
1  44 

«"5 

i*54 
166 

1-64 

17 

174 

1-67 
17 


189 

2'02 

185 

2'0 

205 

214 

2'  16 

17 

i-5 

2'OI 
184 
200 
1*76 
I-9I 
1-82 
2*31 
208 
2  0I 
2*09 

2'34 
260 

2*04 

259 

203 
200 
213 


Pc 
•26 

•37 

•44 
•46 
•51 

53 
[■58 
•66 
[•69 
1-69 
•70 
71 

177 
•89 
•94 
■96 

[•98 
'99 

2'0I 
2*04 
2*04 
205 

2-06 
207 
2-08 

211 
213 
213 
220 
2'25 
2*25 
228 
2-30 
2*32 
232 

2"34 
2*34 
235 


479 

Po-Pc 

+034 

+  0-07 
+006 
+  0-08 

+015 

+  o-i  I 

+  0-12 

+  0-08 

—  0*02 
+  0-OI 


+015 
+025 

—0-04 
+  0*06 
+  009 
+  o*i6 
+017 
-031 

-0-54 
-003 

—021 
— 0-06 
-0-31 
—017 
—029 
+  018 
+  005 
—019 
— o*i6 
+  009 
+  032 
—026 
+  027 

-031 
-034 
-022 


480  Mr.  Marthy  Formula  for  Correcting  xlvii.  S, 

Epoch.                Observer.                Bc            0c            SQ-Sc  po            pc  Po~pe 

187233  Wilson  &8eabroke  648      6425      +055  230  237  -007 

872-37           Talmag*          673      6427      +303  —  237  — 

1873-23  Wilson  fcSeabroke  640      6480      -080  205  238  -0-3* 

18733S                  „                65-0      6487      +013  200  238  -038 

1874-32                  „                655      65-45      +0-05  2-15  240  -025 

1874*32            Talmage          698      6545      +4  35  Io8?  240  -1-32.! 

1874-41  Wilson  &  Seabroke  64-2      6550      -130  216  240  -024 

1875*31        Schiaparolli         666      6603      +0-57  200  242  -042 

1876-36  Wilson  &  Senbroke  672      6664      +056  215  244  -029. 

1876-41                   „                66*5-     66-67      -0-17  2-21  245  -0-24 

187940              Hall              689      6840      +050  233  250  -017 

1879470      Schiaparolli         6798    6840      -0-42  2462  250  -0*038 

1882467                „                6938    7000     -062  2314  255  -0236 

1883*21         Engelmann          7044    7043      +o*oi  2623  256  +0063 

1887-213         Tarrant            72-44    7252     -008  2-62  262  o*co- 

1887356          Young            7*75    7*59      +°l6  2'79  2'62  +0*1? 

I  have  computed  the  following  abort  ephemera : — 

Date.                Position  Angle.  Distance. 

1890*0                    73'9I°  2*73" 

18950                    76-32  2-78 

19000                    7864  2-83 


On  the  Formula  for  Correcting  Approximate  Element*  of  the  Orbit* 

of  Binary  Stars.    By  A.  Marth. 

The  present  communication,  a  supplement  of  the  paper  in  the 
April  number  of  the  Monthly  Notices,  pp.  333-46,  is  intended  to 
point  out  the  alterations  and  modifications  of  the  formate  there 
given,  which  render  them  applicable  to  the  orbits  of  binary  stars, 
and  to  offer  some  remarks  connected  therewith. 

While  in  the  case  of  the  orbit  of  a  satellite  belonging  to  the 
solar  system  the  apparent  orbit,  or  the  projection  of  the  trne 
orbit  on  a  plane  perpendicular  to  the  line  of  vision,  changes  con* 
tinually  with  the  changing  position  of  the  Earth  relative  to  the 
planet,  in  the  case  of  a  binary  system  the  plane  of  projection 
remains  unaltered,  and  may  therefore  properly  be  adopted  as 
the  plane  to  which  the  plane  of  the  orbit  is  referred. 

Let  80  denote  the  position-angle  of  the  line  of  nodes  of  the 
two  planes,  reckoned  from  the  declination-circle  passing  through 
the  star  at  the  time  f0>  8  the  same  angle  reckoned  from  the 
declination-circle  at  the  time  t,  so  that 

Q  m  0,  +  o°oo557  sin  a .  sec  8 .  (<-<,). 


Jane  1887.    Approximate  Elements  of  Binary  Stars.  481 

Let  i  be  the  inclination  of  the  two  planes,  and  let  it  be  taken 
between  o°  and  900,  if  the  apparent  motion  of  the  comes  is  in 
the  direction  of  increasing  position-angles,  and  between  900  and 
1800,  if  the  motion  is  in  the  direction  of  decreasing  position- 
angles,  so  that  there  may  be  no  need  to  make  a  distinction 
between  direct  and  retrograde  motion  in  the  orbit. 

Farther,  let «  denote  the  angle  between  the  node  and  the 
lower  apsis  in  the  direction  of  the  real  motion  in  the  orbit; 
e  =  sin  <f>  the  eccentricity ;  a  the  major  semi-axis  of  the  orbit, 
expressed  in  seconds  of  arc ;  ap  the  radius  vector,  /*,  c,  v  the 
mean,  eccentric,  and  true  anomaly  of  the  comes  at  the  time  t ; 
fa  its  mean  anomaly  at  the  time  t0 ;  n  its  yearly  mean  orbital 
motion. 

The  trne  anomaly  v  of  the  comes  and  its  radios  vector  p9 
expressed  in  parts  of  a,  being  foand  by  the  usual  formulae 

c-*°.  sin  c-M8* /*•  +  »(<-*•)  «°»570,296.  e, 

psm  v  =  sine.  cosf 

peos0=co8c— «, 

the  values  of  the  position-angle  p  and  of  the  distance  s  of  the 
comes  for  the  time  t  are  foand  by 

sin  <r  sin  ( j>—  Q)  =  sin  (0  +  •)  cos  t 
sin  <r  cos  (p  —  Q)  «=  cos  (v  +  •») 
t =ap.  tin  <r. 

Formula?  for  correcting  the  assumed  elements  by  means  of 
equations  of  condition  between  observed  and  computed  position- 
angles  have  been  published  by  Madler  (Astron.  Nachr.,  vol.  xvi. 
p.  36) ;  also  by  Schur  (Astron.  Nackr.,  vol.  Ixxi.  p.  24),  and  perhaps 
in  other  papers,  not  at  present  within  my  reach.  To  be  really 
efficient,  such  formal©  require  that  the  assumed  elements 
should  be  fairly  approximate,  but  a  rather  wide  field  is  left  for 
their  useful  application.  In  the  case  of  elements  of  question- 
able character,  or  even  of  first  attempts,  the  formation  of  the 
equations  of  condition  ought  not  to  be  neglected,  for  their  mere 
aspect  may  prove  to  the  computer  the  inadequacy  of  the  observa- 
tions at  his  disposal  for  a  fair  determination  of  the  orbit ;  or 
if  it  does  not  prevent  the  publication  of  premature  results  of  very 
doubtful  value,  it  will  at  least  prevent  their  undue  acceptance 
by  readers  competent  to  form  their  own  judgment. 

Introducing  for  greater  simplicity,  as  in  the  case  of  the  orbit 
of  a  satellite  belonging  to  the  solar  system — 

sin  <r  sin  t  =  +  cos  i 
sin  <r  cost**  —  sintcos(t?H*») 
cos  <r  =  +  sin  t  sin  (v  +  »), 


482  Mr.  Marth,  Formula  for  Correcting  xlvil  8, 

the  differentiation  of  the  equations  for  p  and  *  gives 

sin  ffdp  as  sin  t  .  d  (v  +  «)  +  cos  t  .  sin  (0  +  •) .  di + sin  ad  Q 
<£<t  =  co8t  .  <Z(v+»)  — sin  r .  sin  (&  +  ■>). rfi. 

If  e  and  t,  eccentricity  and  inclination,  are  not  of  small  amount* 
the  equations  of  condition  between  the  differences  of  the  ob- 
served and  computed  position-angles  and  distances  and  the 
variations  of  the  assumed  elements  will  be 

p  sin  c .  9p  «  +  sin  t  —  T .  [fyi0  +  (t  -*«)*»] 

P 

+  p  sin  t  .  8« 

+  sin  r  (sin  »  cos  $  +  sin  €) .  l<p 
+  p  cos  r .  sin  (v  +  «) .  8» 
+  psin<r.83 

?':y .  8s  =  +  (cos  <r  cos  t  .  ?2!_T  +  tan  $  sin  a-  sin  v) .  (8/i»  +  (*-  0**) 

+  p  cos  C  cos  t  .  8» 

+  [cos  <r  cos  r  (sin  v  cos  ^  +  sin  •)  —  sin  <r  cos  v  cos  ^) .  ty 

— p  cos  <r  sin  r .  sin  (v  +  •) .  St 

+  psin<r.  ^Z_3jfl. 


In  cases  of  moderate  or  small  eccentricity  it  will  be  safer  to 
substitute 


f>Bin<r.5p=  +  sinr .  (i  +  ecosv) .  [bcc</>  &(m9 +  «)  +  (*  —  *0).sec$.8n] 

—  sin  r .  (cos «  +  cos  c  cos  </>  +  tan  fap)  .  57*3  (tan$  +  8e)sin  8» 
+  sin  t  .  (sin  v  +  sin  €  sec  </>) .  57*3  [(tan  </>  +  8e)  cos  fo — tan  <p] 
+  ^  cos  t  .  sin  (v  +  •) .  8t* 

+  psin  c.  83 

57  3 

-—  .&=  +[cos<rcosT.(i  +  *co8t>)  +  «sin  <rsin  v][sec£  8(/x0+*) 

—  [cos  <r  cos  r  .  cos  v  +  cos  *  cos  ^  +  tan  J^)  +  sin  <r  sin  »] 

.5r3(tan*  +  &)»n8* 
+  [cos  er  cos  t  .  (sin  v  +  sin  e  sec  ^) — sin  <r  cos  t*] 

•  57'3  [(ta»  *  +  **)  cos to-tanf] 
— p  cos  <r  sin  t  .  sin  (t?  +  «)  .  Si 

+  0  sin  0-  .-5Z.3  80. 
a 


June  1887.     Approximate  Elements  of  Binary  Siars.  483 

« 

If  the  assumed  orbit  is  circular  and  the  orbital  longitude  of 
the  comes  from  the  node  is  =  u,  the  equations  become 

sin  ftp  —  +  sin  t  .  [3i/t  +  (t — Q  9n] 

—  suit,  cos  u  .  2<p sin  • 
4-  sin  t  .  sin  u .  2<p  cos  « 
+  cos  t  .  sin  u .  Si 

+  sin<r  .8£ 

57  3  fa  as  +  cos  <r  cos  t  [8h0  +  (2— *0)  **] 

—  (cos  <r  cos  t  .  cos  «  +  i  sin  <r .  sin  u) .  2$  sin  « 
+  (cos er cost. sin «+£ sin <r.  coe u)  .  2<pcos<* 

—  cos  <r .  sin  r .  sin  tf .  8* 

+  sin  <r .  5Zj?  da. 

In  case  the  inclination  of  the  orbit  to  the  plane  of  projection  is 
not  considerable,  the  determination  of  the  line  of  nodes  becomes 
uncertain,  and  this  uncertainty  develops  with  the  decrease  of 
inclination  rapidly  into  indeterminateness.  The  uncertainty  of 
fixing  the  position  of  the  plane  of  the  orbit  may  be  easily  esti- 
mated by  the  reflection  that  in  order  that  the  maximum  effect  of 
the  inclination  upon  the  position-angles  may  reach  the  amonnt 

of 

o°'5  i°o  i°*5  2°o 

the  inclination  must  amount  to 

io°7  i5°i  i8°-4  2i°-2 

the  corresponding  maximum  of  the  foreshortening  of  the  radius 
vector  being 

0*017  *°34  *°5i  0067 

or  1  :  58  29  20  15. 

A  fair  determination  of  S3  and  i  and  consequently  of  a>  being, 
under  such  circumstances,  not  practicable,  they  cannot  serve 
directly  as  elements  of  the  orbit,  but  ought  to  be  supplanted  by 
such  functions  or  such  other  elements  as  will  practically  represent 
whatever  can  be  fairly  established  concerning  the  position  of  the 
orbit,  without  erring  either  on  the  one  side  by  a  display  of  un- 
trustworthy figures,  or,  on  the  other,  by  the  assumption  or  sug- 
gestion of  entire  uncertainty. 

The  proper  selection  of  the  most  suitable  elements  for  the 
purpose  does  not  appear  to  me  doubtful.  The  choice  will  be 
different,  according  as  the  eccentricity  of  the  orbit  is  considerable 
or  not. 

In  case  the  orbit  is  so  eccentric  that  the  place  of  the  chief 
star  in  the  projected  orbit  is  considerably  distant  from  the  centre, 


484  Mr.  Marth,  Formula  for  Correcting  xlyii.  8, 

the  substitution  of  the  position-angle  P  of  the  periastre  for  that 
of  the  line  of  nodes  as  an  element  recommends  itself  at  once,  and 
the  selection  of 

■Snijiintees-  ^  rf  km         cos. 


I  —  sin31  i  sin*  »  1  —  sin*  t  sin* » 

as  the  two  other  new  elements  will  be  found  a  suitable  one  in 
the  course  of  some  simple  considerations. 
If  in  the  equations  for  finding  j9  and  sin  <r 

sin  <r  sin  ( j>—  Q)  =  sin  (0  +  »)  cos  i 
sin<rcos(^-  u)»cos(v  +  ») 

the  true  anomaly  17  is  put  =  o°,  they  supply  the  position-angle  P 
of  the  periastre  and  the  corresponding  value  of  sin  <r,  say  sin  <r0: 

sin  <r,  sin  (P—  Q)— sin  m  cos  i 

sin  0*0  cos  (P  —  8  )  —  cos  » 
and  thereby 

sin'  r,  » 1 — sin*  t  sin'  «. 

The  substitution  of  these  values  in  the  preceding  equations 
gives 

sin  <r„ .  sin  <r  sin  (^>— P)  =  sin  0 . cos  i 

sin  <r0 .  sin  r  cos  {p— P)  —  cos  v .  (1  —sin' t  sin*  •) — sin  v .  sin9  t  sin  «  cos  » 

or  !^.sin(p-P)-sintr.  COBi 


sin  r,  1  —  sin*  t  sin*  » 

"n,r     M./^    t>\    «««•,    «•««  sin*  t  sin*  cos  • 
-s .  cos(p— srjBtQOBV— sin  v. : — . 

sin*,  *        '  1—  sin*  t  sin* » 

By  the  introduction  of  the  position -angle 

P  =  Pt + o°'00557  sin  a .  sec  5 .  {t  — t0)  of  the  periastre, 
and  of 

«•_< =  *  and  ""^'■""^^tanr 

I  —  sin2  i  sin*  »  1  —  sin*  t  sin*  » 

as  the  new  elements,  the  equations  for  finding  p  and  *  become, 
if  (*)  is  written  instead  of 

p  sin  <r 

8111  ff9 

and  (a)  instead  of  a  sin  o-0  or  a*/  \  —sin*  t  sin*~a>, 

(*)sin(p— P)«psinv.£  «=sin  € .  Arcos<£ 

(«)  cos  {p— P)«=pcos  r— p  sin  0 .  tan  ?«  cos  c— sin  t .  tan  v .  cos  f-« 
,-(a).(a) 

If  the  plane  of  the  orbit  coincides  with  the  plane  of  projection, 
the  value  of  tan  v  is  =  o  and  that  of  k  =  + 1  or  —  1  according 
as  the  apparent  motion  of  the  comes  is  in  the  direction  of  t»- 


June  1887.     Approximate  Elements  of  Binary  Stars.  485 

creasing  or  cfacreasing  position-angles.  The  values  of  tan  v  and 
of  the  deviation  of  k  from  ±1,  which  a  careful  discussion  of  the 
observations  furnishes,  represent  fully  whatever  the  observations 
really  indicate  about  the  inclination  of  the  two  planes  and  its 
direction. 

The  differentiation  of  the  last  equations  gives 

(*) Jp--£ .  pdv +p  sin  v . cos  (p- P) .  57-3  dk 

+  p  sin  t; .  sin  (p-T) .  57-3  d (tan  »)  +  (*) d? 

gaj,,^,^^')^^^  p*\nvcc*v  ^      (j)  d 

(«)  \  sin  v.  cost;,  cos**/*        (*)  ^       p    3i  J     r 

+  psiii  v.sinQ?— P).  57*3  dk— p sin  «.  cos  (p— P).  57*3 rf  (tan  v) 
(a) 

The  equations  of  condition  between  variations  of  the  computed 
coordinates  and  the  corresponding  variations  of  the  elements  of 
the  orbit  become  accordingly : 

(,)  Sp-  *    cos  *  [«*,+ (*-«,)  *»] 

+  -£- .  (sin  v  cos  *  +  sin  •) .  ty 

w 

+  p  sin  t; .  cos  (p— P) .  M? 

+  p  sin  v .  sin  (j>— P) .  8  (tan  v) 

+  (*).*P 

(a)  \  sine,  cos  tr.  cos*  r  /        (*)  pJ 

[**  +  ('-'.)*»] 
+  [/^^sin(t>+y)cos(t;+r)\(8b^8^  +  8i.n<)p^ 
\  sin  v .  cos » ,  cos*  v  J  {») 

—  cos  <p .  ^]  cos  t> .  ty 

+  p  sin  & .  sin  (p— P) .  8£ 

— p  sin  t; .  cos  (p— P) .  &  (tan  *) 

(a) 

In  case  the  eccentricity  of  the  orbit  is  not  large  enough  to  allow 
the  position-angle  of  the  periastre  to  be  safely  treated  as  one  of 
the  elements,  the  most  suitable  new  elements  will  be  found  by 
reckoning  the  orbital  longitudes  from  the  point  of  the  orbit,  for 
which  p  =  o°,  or  where  the  orbit  crosses  the  plane  of  the  declina- 
tion circle  to  the  north  of  the  chief  star.  If  a/  is  the  orbital 
longitude  of  the  periastre  reckoned  from  this  point,  or  —  a>'  the 
true  anomaly  of  ibis  point,  the  values  of  a>'  and  of  the  correspond- 


486  Mr.  Marih,  Formula  for  Correcting  xlw.8, 

ing  sin  <r,  saj  sin  cr7,  are  derived  from  the  equations,  which  give 
p  and  sin  <r, 

■in  tf'nn  (p—  fi)  ■  sin  (9  +  »)  cot  t 

sin  a  cos  (p  —  fi  )  «  cos  ( r  +  •») 
by  putting 

p«o°  and  for  v  its  specisl  value—*'. 

Thus  are  found 

■in 0* sin  fi  —  sin (•'—•) cost 

■in  J  cos  fi  =cos  («'  —  ») 

sin*  ^e  1  —sin2 t  sin  (•'—•)  cos  («'—»). 

The  substitution  of  these  values  in  the  preceding  or  their  equi- 
valent equations 

sin  a  sinp = sin  («  +  «•)  cos* cos  fi+  cos(v  +  «)  sin  8 
sin  <rcosj>— cos («  +  •)  cos  fi— sin  (<?+«) cost  sin  fi 

leads  to  the  equations 

sin  a      • •    /    .    f\  cost" 


sin 


-.  sin  jj=>  sin  («+•»') 7-_ -     -_ 

a1  I  -  sin*  1  .  sin*  (•'-») 


Bm<r    ~*.«    ~*-/-^    /\  .    •   /    .    /\  sin*  t .  sin  (•'—«)  cos  («-•») 

^— -^.cospascos^+w'J  +  ^n^  +  w') r-^-T-   .  Vr-A- *—• 

sin*7  '  1— sin*  t.  sin' («'-») 

By  the  introduction  of  <*>'  and  of 

cos»___  _ ^  and sin-i  .  siDfn>-i>)coi(s/-ii)_1a|fl ^ 


1  -sin*  t .  sin*  («'—«)  1  — sin*  * .  sin"  (»'—•) 

as  the  new  elements,  which  supplant  9 ,  <■>,  i,  the  equations  for 
finding  p  and  s  become,  if  (a)  is  written  instead  of 


8in<r 


bin  0^ 

and  a!  instead  of  a  sin  o*7  or  a  -J  1— sin2  t  .  sin8  (<■>'— o»), 

(a)  sin  j»«*  sin  (v  +  «/)  .  # 

(<r) cos p« cos (»  +  «')  +  sin  (»  +  •')  .  tanr'-cos(t;+«'— r')secr' 

The  differentiation  of  these  equations  gives 

p (a)dp=* -— -. p d (t> +  «/)  +  ?  sin (»  +  «') cosp  .  57'3<W 

W 

— p  sin  (0  +  •')  sin^> .  57*3  <Z  (tan  r') 

5^3    <£*  =  ^Jf* — 8*n  (v  +  **  ""  y/)c°B  0^+  *' — "0\     sin  (p + «•)  cos  (v  +  *} 
'    a'    '  \         sin  (v  +  •')  cos  (t;  +  «')  cos*  •  /  *  (a-) 

+  (*)  •  57*3  &P  +  P  sin  («  +  •')  sinp .  573  dK  +  p  sin  (t/  +  «/)cosp .  57'3^ttal1 


Jane  1887.     Approximate  Elements  of  Binary  Stars.  487 

Bat 

pd (v  +  *')=*?21zd(ji  +  **)— (coBv  +  cosecos^  +  tan|^)  .  tamfxJ*' 
P 

+  (sin  t;  +  sin  c  sec  <f>)  .  cos  <pd<p 

and 

57*3  ^p»  tan  ^  sin  vc?(M  +  »r)— sin  v  .  tan  <JkJ«'-cos  t? .  eos^sty. 

Hence  the  equations  of  condition  will  be 

p(<0«*=  +^8  -  •  [*(*  +  «')+('-'.)*»] 
WP 

—  — Xcoe  v  +  cos  c  cos  Q  +  tan  J^) .  57*3  (tan  $  + fc)  sin  to' 
(y) 

+  — (sin  v  +  sin  c  sec  ^)  .  57*3  [(tan  ^  +  8e)  cob  fc/ — tan  ^] 

+  p  sin  (» + 0/)  cos  p  .  57*3  W 

— p  sin  («+  •/)  sin|> .  57*3  3  (tan  •) 

and,  if  A  ib  written  instead  of 

k* sin (*  +  «•)  cos  (»  +  •»') -sin (0  +  «'—•)  cob  (t;  +  •»'-•)  secV, 

5Z^««-  +/r^°^  +  (tr)tan*8iniA  .  [«0*» +  «/)  +  (* -*.)«»] 
«  \  Wp  / 

—  [  — -  (cos  t;  +  cos  c  cos  ^  +  tan  %Q)  +  (<r)  sin  v] 

.  57*3  (tan  <p  +  te)  sin  &V 
+  [  — (sin  v  f  sin  c  sec  Q) — (<r)  cob  v]  .  57*3  [(tan  £  +  9e)  cob  *•'— tan  4] 

+  psin(t/  +  »')sinp  .  57*3  W 

+p  sin  (»+•')  cosp  .  57-3  8  (tan  •) 

+  p(<r).i£3.«a'. 
a 

If  the  assumed  eccentricity  is  o,  and  the  orbital  longitude  of  the 
comes,  reckoned  from  the  point  of  the  orbit,  for  which  p  =  o°, 
is  called  «',  the  equations  for  finding  p  and  s  become 

(*)  sin  p= sin  uf .  V 

(^cofl^p-iCOBtt'+sintt' .  tan  •= cos  («'—•)  .  bbc*' 

««a\  (tr) 

and  the  equations  between  the  variations  of  the  coordinates  and 
the  variations  of  the  elements : 

(<r)  «p  =  +  —  .  \lu\+ [t-U)  tn] 

W 
v 
— .  cob  u' .  20  sin  «/ 

(') 

V 
+  —  .  sin  v!  .  2$  cob  «/ 

+  sin«' .  cos|> .  57*3  W 
—Bin  v? .  sinp  .  57*3  *  (tan  •) 


48S  Mr.  Marih,  Formula  for  Correcting  xltii.  8, 

and,  if  V  is  written  instead  of 

y,__  sin  (•/-•)  cos  (W-fS 
sinn'costi' .  cos*?' 

5ZI?  .  fc.+ *1.  sin  «' cos u\  pa'  ♦(*-*,)*»] 

—  (  , —  .  coe2  k7  +  J  (*)  J  .  sin  v* .  2^  sin «/ 

+  (  — - .  sin*  *'— i(o')  j  .  cos  «/  .  2^  cos  •»' 

+  sin  tf  .  sin  p  .  57*3  W 

+  suitf/ .  cosj> .  57*3  8  (tan  •) 

+  (,).&?.  9a*. 
a 

The  geometrical  meaning  and  the  mutual  relations  of  the  various 
arcs  and  angles  employed  will  be  easily  recognised  with  the  help 
of  a  diagram  constructed  to  indicate  their  significance  on  a  sphere 
which  has  the  chief  star  of  the  binary  system  in  the  centre.  Let 
E  denote  the  astral  position  of  the  Earth  (in  right  ascension 
a+1800  and  declination  —8)  ;  G  tkat  of  the  crossing  point  of 
the  declination  circle  and  of  the  circle  representing  the  plane  of 
projection;  O  that  of  the  (positive)  pole  of  the  orbit,  so  that 
EO  =  i ;  Q '  the  position  of  the  point  of  the  orbit  where  it  crosses 
the  declination  circle ;  Q  that  of  the  point  where  it  crosses  the 
plane  of  projection ;  P  the  position  of  the  periastre  ;  S  that  of 
the  satellite  when  its  true  anomaly  is  v.  Further,  let  P,  be  the 
point  where  the  arc  EP  or  its  prolongation  meets  the  circle  of 
projection ;  and  P'  and  C  the  points  where  the  arcs  OP,  and 
OC  or  their  prolongations  cross  the  orbit. 
The  various  arcs  and  angles  are 


»«E0    «OaE 

P-CE3 

fi«-CQ   =CEQ 

P  =  CEP 

«-ap  -uop 

<r  =  ES 

*-P3    «P03 

<r0«EP 

k-PP  -FOP 

**-£&' 

«'«a'p  -a'op 

r-aSE 

•«a'C'=a'0C' 

0EC  =  9O°-a 

»'-»»a'a»a'Oa 

P0E  =  9O°-« 

The  arcs  between  any  point  of  the  orbit  and  O,  and  between 
any  point  of  the  circle  of  projection  and  E,  are,  of  course, 
all  =  900. 

.  The  values  of  o>.  1,  &> ,  a,  corresponding  to  the  values  of  £, 
tan  v,  P,  (a),  or  of  &',  tan  1/,  0/,  a'  may  be  found  by  means  of 
the  formulae 


Jane  1887.     Approximate  Elements  of  Binary  Stars.  489 


7  sin  2*  =2  tan* 

y 

sin  2  (•'-•»)«  2  tan  • 

7Cos2»-  1—  J^-tanV 

y 

cob  2  (•/-•)-  1  -  A"  -  tan  V 

■in*  t  — 

•  •  •         y 

810*1  — 

1  +  7  bin- « 

I  +  y  sin*  (•'  -  ») 

■in  <r9  sin  (P—  G)  -  sin  »  cos  t 

bid  it'  sin  Q  -  sin  (»'  —  »)  cos  i 

•in  ff9coB  (P—  0)  -»cob • 

sin  </  cos  Q  -  cos  (»'-») 

sin  a". 

a' 

BlUff 

If  k  t  1  and  tan  v  or  A/  ?  1  and  tan  ^  are  of  small  amount, 
small  variations  of  their  values  prod  nee  obviously  large  varia- 
tions in  the  corresponding  values  of  <d,  1,  Q .  The  uncertainty 
in  which  semicircle  a>,  cn\  &  are  to  be  taken  arises,  of  course, 
from  the  uncertainty  which  part  of  the  true  orbit  is  on  the 
positive  side  of  the  plane  of  projection  or  in  front  of  it.  If  the 
apparent  motion  of  the  comes  in  the  direction  of  increasing  or 
decreasing  position-angles  is  to  be  treated  as  analogous  to  direct 
or  retrograde  motion  of  the  bodies  of  our  solar  system  in 
reference  to  the  ecliptic,  the  Earth  is  at  the  positive  pole  of  the 
plane  of  projection,  and  the  ascending  node  &  ought  to  be 
where  the  comes  passes  from  the  further  or  negative  side  of  the 
plane  of  projection  to  the  positive  side  or  to  that  from  which  the 
observations  are  taken.  The  uncertainty  whether  the  position- 
angle  Q  belongs  to  the  ascending  or  descending  node  must  be 
allowed  for  in  transferring  the  position  of  the  orbit  from  the 
plane  of  projection  to  a  plane  parallel  to  the  terrestrial  equator, 
or  to  some  other  fundamental  plane.  If  J  denotes  the  inclina- 
tion of  the  plane  of  the  orbit  to  that  of  the  equator,  N  the 
longitude  or  right  ascension  of  the  ascending  node,  and  Q  the 
orbital  longitude  of  the  periastre  reckoned  from  N,  the  values 
of  J,  N,  Q  are  derived  from  those  of  i,  Q ,  o>,  and  of  a,  8,  the  right 
ascension  and  declination  of  the  star,  by  means  of  the  formni® 

sin  J  sin  (a-  N)  -  ±  sin  G  sin  t  sin  ft  +  cos  t  cos  ft 
sin  J  cob  (a— N)->  ±  cos  fi  cost 
sin  Jsin(Q-»)-  ±  cos G cos  ft 
sin  J  cob  (Q— o»)  *  =FsinQcosftcost  —  sin  5  sin  i 
cos  J  «  ±  sinC cos  8  sin  t— sin  8  cos  i 


or  by  equivalent  formula),  the  upper  or  lower  signs  being  valid 
according  as  the  value  of  "  refers  to  the  ascending  or  descend- 
ing node  of  the  orbit  on  the  plane  of  projection. 

The  apparent  orbit  of  the  comes  may  be  laid  down  in  the 
ordinary  way  by  employing  the  semiaxes  a  and  ft  of  the  apparent 
ellipse  and  their  position. angle  0  deduced  from  the  elements.  If 
II  is  the  position.angle  of  the  centre  of  the  apparent  ellipse  at 


40O  Mr.  Marth,  Formula  for  Correcting  xltii.  8, 

the  place  of  the  chief  star,  and  S  its  distance,  the  values  of 
II,  S,  0,  a,  /?  may  be  found  by  the  formal© 

S  sin  (IT—  Q)=  —  at .  sin  «  cos  t 
Sco8(n— G)=  —  ae  .  cose* 
(a2-/82)  sin  2  (0-  Q)-S2  .  sin  2  (II-  8)  =  fl=e2  .  sin 2 «cos t 
(a*-j3-)cos2(0-a)  =  St.co82(n-a)  +  a*co8*$.  sin*! 

«*  aV  .  cos  2  »  +  a2  sin2 1'  (i  —  e2  cos2  «) 
o2  +  £2 = S2  +  a2  cos2  $  ( i  +  cos*  t)  -  2a* -  o2e2  -  a2  sin2 1  ( I  —  e2  cos2  o»). 

It  will,  however,  be  found  more  instructive  to  compute  the 
apparent  positions  corresponding  to  a  number  of  points  of  the 
true  orbit,  and  to  lay  them  down,  together  with  the  terminal 
points  of  the  axes  of  the  apparent  ellipse,  which  may  serve  in 
drawing  the  latter.  The  eccentric  anomalies  c  in  the  true  orbit 
which  give  the  terminal  points  of  the  axes  of  the  apparent 
orbit  may  be  found  from  the  equation 

.  „  m  -  sin  2«  .  cos  4> 

cos2»  —  c2  cos2  « -r  e*  .  cosec'  i 

or,  in  case  k  and  tan  v  are  the  given  elements,  from 

.  2  tan  v  sec  * 

tan  2f=  T- ^  --  ; 

Ar2  +  tan2v— sec2^ 

or,  if  Id  and  tan  v7  are  given,  from 

(jf  cos  r')2  sin  2«' — sin  2(«/ — vf) 


tan  2€-  —  cos<?>  . 


(*'  cos  y'y  cos  2»'  -  cos  2(«'  -  •)  +  «2[(#  cos  •)*  cos  V  - sinV  -  •)]* 

The  minima  and  maxima  of  the  apparent  distance  of  the  two 
stars,  and  consequently  the  points  of  the  greatest  and  least 
change  of  ppsitaon-angle,  may  be  found  most  conveniently  by 
determining  the  true  anomalies  v,  which  satisfy  the  equation 

ri  n  2(v  +  •)        ,m     .  - .    cos  w 

.      *-\  -  2«  COtg2  *  . , 

8111  (V +  »  —  «,)  COS  CO, 

in  which  tan  o)1=tan  a>.sec2t,  and  which  is  to  be  solved  in- 
directly. 

This  is  a  biquadratic  equation,  and,  when  developed,  takes 
probably  its  simplest  form  if  tan  \  (v  +  w)  is  made  the  unknown 
quantity.     When  written  out  in  full  the  equation  becomes 

tan4 $(»  +  •)+  2coet|.  (<?cos«  +  tan20  .  tan»  £(t>  +  ») 
c  sin  » 

+  i^^.(«cos«-tan2i).Un|(v  +  «)-i«of 
and  the  coefficients  show  that  of  the  four  roots  of  the  equation 


June  1887.      Approximate  Elements  of  Binary  Stars*  491 

two  are  imaginary,  or  else  that  all  four  roots  are  real,  according  as 
the  values  of  the  two  terms 

ccosw  +  tan't*  and  e  cos  a  —  tan1! 

have  the  same  or  opposite  signs. 

This  biquadratic  equation  is  identical  with  the  equation 
which  determines  the  minima  and  maxima  of  the  x  ordinates  of 
those  instructive  carves,  the  a  ecliptioal  intersects  "  of  the  orbits 
of  planets  and  comets,  which,  as  I  have  explained  in  vol.  xlv.  of 
the  Monthly  Notices \  will  be  found  very  serviceable  in  recog- 
nising the  chief  peculiarities  and  mutual  relations  of  the  orbits, 
and  especially  helpful  in  solving  the  problem  of  their  proximities, 
provided,  of  course,  that  they  are  accompanied  by  the  data  neces- 
sary for  the  purpose.  If  there  are  no  imaginary  roots  of  the 
equation,  so  that  there  are  two  minima  and  maxima,  the 
intersects  become  specially  characteristic,  as  is  the  case  with 
those  of  many  cometary  orbits,  a  few  instances  of  which  may  be 
recognised  on  the  reduced  specimen  plates  published  in  vol.  xlv. 

If,  instead  of  o>  and  i,  k  and  tan  v  are  the  given  elements,  the 
equation  for  finding  the  true  anomalies  v,  which  furnish  the 
points  of  min.  and  max.  distance  from  the  chief  star  in  the 
apparent  orbit,  will  be 

o«=  (£*+  tan2  k  —  1)  sin  20— 2  tan  v  cos  2v  +  2e[(&  +  tan*  y)  sin  v  -  tan  v  cos  rj ; 
or,  patting   g  sin  G  —  —  2  tan  r, 

g  cos  G  —  k*  +  tan*  v  —  I, 
AsinH  =  —tan*', 
h  cos  H  ■*  h%  +  tan*  y, 
sin(2«  +  G)  A 

~ — 7 u\    "■'~2S.-t 

sin  (v  +  H)  g 

which  is  to  be  solved  indirectly. 

If  a/,  A/,  tan  V  are  the  given  elements,  the  corresponding 
formulae  are 

g*  sin  G'  -  2  tan  v*, 

0'cosG,->f»+  tanV-i, 

h'  sin  H'  -  -sin  (»'  -  •)  sec  •, 

A'cosH'-^cosw'-sinr'.sin  («'-•), 

sin  1 2f v  +  «*')  +  G'l  ^  _  M    A; 
sin  (r  +  «'  +  H')  "  g1' 

A  special  case  still  requires  to  be  considered — the  case  in 
which  one  of  the  components  of  a  binary  system  is  invisible  or 
unobserved,  so  that  the  orbit  of  the  visible  component  round 
the  centre  of  gravity  of  the  system  has  to  be  determined 
from  its  observed  right  ascensions  and  declinations  referred  to 
those  of  other  stars.  The  prospect  of  a  fair  determination 
must  remain  unpromising  if  the  observations  do  not  extend  at 

«9 


492  Mr.  Marth,  Formula*  for  Correcting  xltii.  8, 

least  over  a  full  revolution,  bo  tbat  an  approximate  value  of  the 
period,  or  of  the  annual  motion  n,  may  be  inferred  with  some 
confidence.  If  n,  e,  /x0,  co',  a',  k't  v'  are  the  seven  elements  of  the 
orbit,  the  rectangular  coordinates  of  the  visible  star  (in  right 
ascension  a  and  declination  8)  referred  to  the  centre  of  gravity 
(in  right  ascension  A  and  declination  D)  and  to  the  circle  of 
declination,  are  given  by  the  equations 

1 5  cos  8  (a  —  A)  *»  8  sin  p  —  a!K ',  p  sin  {v  +  «') 

8  —  D  ««  cos p=*a? sec/,  p cos (»  +  «'  —  r'). 

The  values  of  a  and  3  are  therefore 

o  =  A  + .  p  sin  (i>  +  a/) 

15  cos  8    r        v  ' 

8  =  D  +  a'  gee  •.  p  cos  (v  +  •/—•). 

Introducing  the  eccentric  anomaly  c,  instead  of  the  true  anomaly 
v,  and  putting 

k,  sin  u^a'kf.  sin  «' 

#c,  cos  «,  =  a'A* .  cos  «'  cos  ^ 
*i 


1 5  cos  8 


unci  #c„sin  •j-a'sec/.  sin(«#—  k')cos^> 

ica  cos  <*t »  a'  sec  v* .  cos  (* '  —  *), 

the  values  of  a  and  8  become 

a  =  A  —  e  .  ic"  sin  «,  +  k* .  bio  (c  +  «»,) 
8  =  D*  -  « .  *c,  cos  «2  +  ict .  cos  («  +  «,), 

and  show  that  of  the  seven  elements  or  functions  of  elements  of 
the  orbit  only  five  (71,  /x^,  e;  **  sin  w,,  #cs  cos  wj)  can  be  deter- 
mined from  observed  right  ascensions  alone,  and  five  (ft,  /%  e; 
«c9  sin  o>i,  #cs  cos  ci>s)  from  declinations  alone. 

The  first  approximate  values  of  the  unknown  quantities  may 
be  got  by  deducing  from  the  observations  the  maxima  and 
minima  of  the  rectangular  coordinates,  with  the  times  corre- 
sponding to  them,  and  also  the  times  when  the  coordinates,  in 
reference  to  some  approximate  values  of  A  and  D,  are  o.  If,  in 
the  case  of  observed  right  ascensions,  r  and  r,  are  these  latter 
times,  and  $  and  0}  the  times  of  max.  and  min.  of  a— A,  approxi- 
mate values  of  the  unknown  quantities  are  derived  from 

2«°sin  »,  =  l8o°  — (t,-  r)n 

2e°  cos  «*,  -  (0,  -  0)  »  -  1800 

max.—  min.  =  2k' 

max.  +  min.  ^-  2  (8A  —  e  .  if  sin  »,)  «  2c', 

and  the  mean  anomaly  at  the  time  r  will  be 

b-u,  4-r0  sin  «,. 


Jane  1887.      Approximate  Elements  of  Binary  Star*.  493 

If,  in  the  case  of  observed  declinations,  9  and  6\  are  the 
times  of  the  max.  and  min.  of  8  —  D,  and  r'  and  t\  the  times 
when  the  difference  is  o,  so  that  the  fonr  times  follow  in  the 
order  9t  t',  9lt  t^,  approximate  values  of  the  unknown  quanti- 
ties are  got  from 

2*0sin  «t-  1800 -(*',-*)» 

3*°  cos  •,  -  (t',  -  tO  n  - 1800 
max.'—  min/ =3*, 
max/  +  min/  =  2  (3  D  —  «  .  * ,  cos  »,)  =  2f, 

and  the  mean  anomaly  at  the  time  /  will  be 

»  900  —  «,— «°  cos  «r 

As  the  observed  right  ascensions  alone  leave  it  uncertain 
whether  #  and  consequently  *■  is  positive  or  negative,  proper 
circumspection  must  be  exercised  to  settle  the  point  with  the 
help  of  the  observations  in  declination;  and,  if  required,  1800 
must  be  added  to  the  deduced  value  of  o>,,  so  that  the  longitudes 
in  the  orbit  may  be  reckoned  from  the  point  where  the  orbit 
crosses  the  declination  circle  on  the  north  side  of  the  centre  of 
gravity. 

The  formula?  for  correcting  assumed  approximate  values  of 
the  elements  or  functions  of  elements  are,  if  the  observations  iu 
both  coordinates  are  treated  separately  : 

•  /  *\  CO*  («  +  •,)         «*    r*       .   /j      j  \  •    i 

'  i-ccosf      573 

cosfc  +  dO  • 

+       \ .     i' .  sin  c  .  #r8e 

i—e  cos  c 
+  cos  €  .  8  (*•  sin  «,) 
+  sin  c  .  8  (*•  cos  «,)  +  8r*  .  .  . 

J(5-D)=-BJl^l),A[JMl  +  (/-/>] 
v  '  I -e  cose      573L  J 

_sm(e±«a)     ^ 
I— «  cose 

—  sin  €  ,  8(«.,sin  «,) 

+  cos  e  .  8  («2  cos  «2)  +  8e2 ,  ,  . 

The  two  series  of  results  have  three  unknown  quantities, 
S/io,  8/»,  06,  in  common,  the  most  probable  values  of  which  muat 
be  found  by  properly  combining  the  equations  of  the  two  series. 

From  the  values  of  the  other  quantities  are  found 

a'k?  .  sin  «'=  1 5  cos  3  .  jc*  sin  w, 

a'k  .  cos  »'  =  1 5  cos  8  .  ie*  cos  a,  .  sec  <p 

and  «'  sec  /  .  sin  (»' —  1/)  «  *.,  sin  ut .  sec  ^ 

a'  sec  ►'  .  cos  («'  —  y')  =  «r,  cos  mv 

N  N  2 


494  ^r»  IrthMi  Observations  made  at  xltil  8, 

If  the  eccentricity  of  the  orbit  is  not  large  enough  to  allow  fy^ 
to  be  made  directly  one  of  the  unknown  quantities,  and  it  is 
preferred  to  treat  o>'  a\  k\  tan  J  directly  as  the  elements,  and  to 
determine  the  coordinates  by 

15  cos  I  .  (a-A)-x*-a'k' .  psin(v4-wr) 

8-D=y«a/ .  p cos  (v  +  v')-\  a' .  psin^+o/)  .  tan  • 
««'nec  S  .  pcos(i'  +  »'  —  r7), 

the  equations  of  condition  between  the  differences  of  the  ob- 
served and  computed  coordinates  and  the  corresponding  varia- 
tions of  the  elements  become 

p>«  4  [cos  (»+«')  +  ecog  «'] .  V  .  ^!*  [*(m.  +  "0  +  ('-'.)*«] 

57*3 

—  [cob  ( v  +  «') (cos  t  .  cos  <p  +  tan  \p)  +  cos  «/]  .  ^  .  a'  (tan  ^  +  fc)  sin  8«? 
+  [cos  (v  +  «')  sin  c  -  sin  •'  cos  $]  .  k1  .  a'  [(tan  f  +  8t )  cos  8w'  —  tan  ^] 

+  [sin  (v  +  »'  —  ^(cos  e  .  con  4  +  tan  %<p)  +  sin  (•'  — •)]  .  sec  • 

.  a'  (tan  <f>  +  to)  sin  oV 

—  [sin  («  +  «'—*')  sin  «  +  cos  (»'  —  1^)  cos  ^]  .  sec  *' 

.  a'  [(tan  $  +  fc)  cos  Sw'  —  tan  4>] 
+  p  sin  (0  +  «')  .  a'  8  (tan  •) 

a 

from  which  the  most  probable  values  of  the  corrections  are  to  he 
deduced.  The  elements  q>,  ?',  .  are  then  found  by  the  formulas 
previously  given. 


Observation*  of  Nova  Cygni,  of  some  of  the  Planets^  and  of  Comet 
Barnard,  made  at  Mr.  Wiggleswnrth's  Observatory  with  the 
lyS-vnch  Cooke  Equatorial.     By  J.  G.  Lohse. 

Nova  Cygni. 

1885,  Sept.  1. — Nova  Cygni  is  of  the  same  brightness  as  the 
small  star  of  the  15th  magnitude  north  preceding  of  it.  No 
change  in  the  brightness  of  the  other  stars,  which  were  all  seen, 
could  be  made  out. 

Oct.  3. — Nova  Cygni  was  examined  with  a  magnifying  power 
of  260.     It  has  become  a  little  brighter,  and  is  only  0*3  mag. 


June  1887.  Mr,  WiggleswortWs  Observatory,  495 

fainter  than  the  stars  Nob.  68  *  and  73.  The  star  No.  68  is  a 
li'tle  brighter  than  No.  73,  but  the  difference  is  scarcely  o*i  mag. 
N<*va  Cygni  is  not  so  weil  denned  as  the  comparison  &tars,  and  is 
certainly  surrounded  by  nebulosity.  Attempts  were  made  to  see 
Nova  Cygni  with  a  MeClean  prism  held  in  front  of  the  eyepiece, 
but  no  trace  of  light  conld  be  recognised.  The  spectrum  of  the 
other  three  stars,  forming  with  Nova  a  trapezium,  could  be  seen 
without  much  difficulty,  especially  that  of  the  nth  magnitude 
star  No.  60. 

Oct.  7. — Nova  Cygni  is  of  a  bluish  colour  and  surrounded  by 
nebulosity.  It  is  more  than  double  as  bright  as  the  star  No  50, 
and  about  of  the  same  brightness  with  Nos.  68  and  73  No.  68 
is  a  little  brighter  than  No.  73. 

Oct.  26. — Nova  Cygni  was  examined  with  magnifying  powers 
of  330  and  130.  It  is  decidedly  surrounded  by  nebulosity,  and 
about  0*3  mag.  fainter  than  the  stars  Nos.  68  and  73.  No.  73  is 
nearly  o*i  mag.  brighter  than  No.  68.  No.  50  was  very  well 
seen,  but  it  has  not  half  the  light  of  Nova  Cygni. 

Dec.  1. — Ni/va  Cygni  is  03  magnitude  smaller  than  stars 
Nos.  68  and  73.     Definition  poor. 

1886,  May  1. — Nova  Cygni  is  of  the  14*5  magnitude.  No 
change  amongst  the  neighbouring  stars  was  noticed. 

July  5. — Nova  Cygni  is  of  the  14th  magnitude,  and  nebulous 
in  appearance. 

July  22  — Nova  Cygni  is  equal  in  brightness  to  star  No.  73, 
and  0*2  mag.  fainter  than  No.  68.  Nova  appears  nebulous.  Tho 
15th  mag.  companion  of  Nova  was  also  seen. 

Aug.  2. — Ntrva  Cygni  is  equal  in  brightness  to  stars  Nos.  68 
and  73.     The  15th  mag.  star  near  it  was  very  well  seen. 

The  estimations  indicate  a  small  increase  in  the  brightness  of 
Nova  during  October,  and  it  seems  that  one  of  the  comparison 
stars  is  variable  to  a  very  small  extent. 

Venus, 

On  January  2  and  February  3,  1 886,  the  dark  part  of  Venus 
was  distinctly  seen  by  Mr.  WiggJeaworth  and  Mr.  Lohse ;  it  is  of 
a  gray  colour,  except  near  the  terminator,  where  the  secondary 
spectrum  causes  it  to  appear  blue,  and  compared  with  the  bright 
part  of  Venus  it  looks  very  much  smaller.  On  January  2,  from 
5h  i5m  to  5h  35m  G.M.T.,  when  the  definition  was  very  good, 
the  upper  or  south  lorn  appeared  rounded  while  the  lower  one 
was  quite  sharp.  In  prolongation  of  the  lower  horn,  but  perfectly 
separated  from  it,  was  a  bright  narrow  line  of  light  about  ^  of 
the  diameter  of  Venus  in  length.  A  similar  phenomenon  is  often 
presented  by  the  mountains  of  the  Moon  near  the  south  horn, 
which  appear  along  the  edge  as  a  detached  irregular  line  of  light 
as  long  as  the  summits  only  ate  illuminated. 

*  Copernicus,  vol.  ii.  p.  118. 


496  Mr.  Lohse,  Observations  made  at  xltii.  S, 


Mars. 

During  the  opposition  of  1886  the  white  spot?  near  the  poles 
of  M'irs  were  vory  small.  On  April  23,  ioh  38m  G.M.T.,  both 
white  spots  were  very  well  seen ;  the  northern  spot  was  brighter 
than  the  southern  one,  but  in  size  they  were  about  equal.  The 
diameter  of  the  spots  was  estimated  to  be  £".  On  April  26,  9* 
G.M.T.,  the  northern  white  spot  was  very  well  seen  ;  it  seemed 
larger  than  on  April  23,  but  the  southern  white  spot  was  certainly 
not  visible  at  the  time. 


Saturn. 

1885,  Nov.  17. — The  globe  extends  attho  top  beyond  Cassini's 
divisiou,  and  encroaches  on  the  outer  ring  to  the  extent  of  a 
quarter  to  one-third  of  the  breadth  of  the  latter.  Encke's  divi- 
sion was  seen  in  the  anasa  four- tenths  of  the  breadth  of  the  outer 
ring  from  Cassini's  division. 

Nov.  18. — Encke's  division  was  seen  in  the  same  position,  and 
the  globe's  shadow  on  the  crape  ring  was  noticed  distinctly. 
Definition  good. 

Dec.  2,  1311  45m  G.M.T. — Mimas  was  seen  distinctly  in  elonga- 
tion on  the  following  side.  Saturn  was  not  artificially  obscured 
at  the  time  nor  moved  out  of  the  field.  Encke's  division  was 
plainly  seen  in  both  ansae  nearly  in  the  middle  of  the  ring. 

Dec.  26. — There  is  a  northern  and  a  southern  belt  and  a  dark 
polar  cap  on  Saturn.  The  brown  copper  colour  of  the  globe  was 
very  strongly  shown.  Encke's  di visum  was  seen,  and  dark  parallel 
lines  on  the  inner  side  of  the  an 8®  of  the  inner  bright  ring. 

1886,  Jan.  2. — The  polar  cap  is  darker  than  the  south  belt. 
Feb.  3. — Encke's  division  was  very  well  seen  by  Mr.  Wiggles- 
worth  and  Mr.  Lohse. 

March  25. — Saturn  was  very  well  seen.  Encke's  division 
could  be  traced  very  nearly  right  round,  when  the  definition  was 
at  its  best.  The  division  is  two-fifths  from  the  outer  edge  and 
three-fifths  from  Cassini's  division.  At  8b  2m  G.M.T.,  Mr. 
Wiggles  worth  saw  Mimas  in  southern' conjunction.  Mr.  Lohse 
tried  to  see  it  as  well,  but  could  not  do  so  with  certainty.  The 
southern  and  northern  dark  belts  showed  very  well,  and  the 
globe  was  plainly  visible  through  the  crape  ring.  Mr.  Wiggles- 
worth  observed  a  faint  narrow  dark  marking  in  the  middle  of 
the  bright  equatorial  zone. 

The  dimensions  of  Saturn  were  measured  1885,  Dec.  26,  and 
1886,  Jan.  2,  and  the  following  are  the  mean  results  reduced  to 
mean  distance  (log  =  0*97950)  : 


June  1887.  Mr.  WiggleewortK  $  Observatory.  497 


Exterior  diameter  of  outer  riog  (A) 

40*95 

Interior          „          „            „ 

35*53 

Exterior  diameter  of  inner  ring  (B) 

34'3« 

Interior          „           „            ft 

25*55 

„                „       of  crape  ring  (C) 

2097 

Equatorial     „       of  globe 

18-57 

Od  Jan.  2  the  following  quantities  were  also  measured,  and 
red  need  to  mean  distance  give 


Polar  diameter  of  outer  ring  (A)  19*06 

Distance  of  south  pole  from  south  limb  i*8i 

„  „       belt    „     north    „  814 

Considering  the  equator  coincident  with  the  plane  of  the 
rings,  the  south  belt  would  be  situated  in  25°'8  south  kronocentrio 
latitude. 

Neptune. 

The  following  observations  of  the  satellite  of  Neptune  were 
made.  The  satellite  was  always  very  faint;  it  was  estimated  to 
be  of  the  14th  magnitude. 


Date. 
1885,  Dec.  2 

Greenwich  M.  T. 

h    m 

12  48 

Position. 

0 
4171 

Distance. 

it 
17-62 

1886,  Nov.  2 

14   195 

4078 

1671 

4 

14  49 

24788 

14  14 

498 


Mr.  Lohse,  Observations  of  Comet. 


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June  1887.  Mr.  Wesley,  The  Solar  Corona.  499 


The  Solar  Corona,  as  sJiovm  in  P/wtographs  taken  during  Total 

Eclipses.     By  W.  H.  Wesley. 

{Communicated  by  the  Secretaries.) 

Having  had  occasion  to  make  a  very  minute  examination  of  the 
negatives  taken  daring  several  of  the  recent  solar  eciipses,  I  have 
thought  that  it  might  be  of  interest  to  give  an  account  of  some 
of  the  prominent  features  of  the  photographic  corona  in  the 
different  years.  I  do  not  attempt  to  propound  any  theories,  and 
shall  only  mention  some  of  the  current  hypotheses  with  a  view 
of  showing  how  far  they  appear  to  be  supported  or  contradicted 
by  the  photographic  records. 

Mr.  Ranyard  in  the  eclipse  volume  of  the  Memoirs  has  so 
fully  discussed  the  photographs  taken  previously  to  1878,  that 
in  most  cases  it  will  only  be  necessary  very  briefly  to  allude  to 
them. 

One  of  the  most  striking  features  in  the  corona  of  almost  all 
the  years  under  examination  is  the  existence  of  a  more  or  less 
well-marked  polar  rift,  roughly,  but  perhaps  never  exactly,  cor- 
responding with  the  Sun's  axis  of  rotatiou,  to  which  it  appears 
.sometimes  inclined  as  much  as  300.  In  most  cases  this  rift  is 
shown  at  both  poles,  but  sometimes  at  one  only  ;  in  1882  it  does 
not  appear  at  all.  The  northern  and  southern  rifts  are  seldom 
strictly  opposite  to  one  another,  so  that  a  line  drawn  through 
them  does  not  pass  through  the  centre  of  the  Sun.  The  polar 
rifts  are  generally  filled  with  shorter,  straighter,  and  more  radial 
rays,  with  a  background  of  less  density  than  in  other  parts  of  the 
corona. 

On  either  side  of  the  polar  rift  there  usually  appears  a  some- 
what conical  mass,  composed  of  rays  curving  towards  each  other, 
forming  groups  of  what  Mr.  Ranyard  has  appropriately  called 
"synclinal  structure,"  which  give  the  quadrilateral  or  cruciform 
appearance  frequently  shown  in  corona  drawings.  They  mostly 
seem  to  be  situated  over  the  zones  of  maximum  sunspot  activity, 
and  have  frequently  greater  extension  than  other  parts  of  the 
corona. 

Eclipse  of  1 85 1,  July  28. 

Dr.  Bnsch's  daguerreotype  is  remarkable  as  the  first  instance 
of  a  successful  photograph  of  the  corona.  It  shows  the  general 
form  to  a  height  nowhere  much  exceeding  \  of  a  solar  diameter. 
The  corona  is  symmetrical  and  of  hexagonal  form,  with  a  well- 
marked  rift  not  far  from  the  north  and  south  poles,  the  southern 
rift  being  much  the  broader.  On  either  side  of  these  rifts  are 
indications  of  synclinal  masses ;  there  are  also  similar  masses  in 
the  equatorial  regions  fairly  corresponding  on  each  side.  The 
orientation  of  the  plate  is  rather  uncertain.  Wolf  gives  64*2  as 
the  relative  number  of  sunspots  for  July  185 1. 


Mr.  Wesley,  The  Solar  Corona 


Eclipse  of  i860,  July  18. 
Ill  the  photographs  taken  at  Desierto  do  las  Palmas,  of  which 
I  have  only  seen  positive  copies,  there  is  shown  a  very  broad 
rift  towards  the  south  pole,  and  a  less  marked  one  on  the  north. 
The  character  of  the  synclinal  groups  is  not  clearly  marked.  The 
corona  is  fairly  symmetrica!  about  a  line  not  much  inclined  from 
the  Sun's  axis.     Wolfs  relative  nnmber  of  sunspots  is  949. 

Eclipse  of  1869,  August  7. 
I  have  not  seen  the  original  negatives  of  tbe  photographs 
taken  at  Shelbyville,  which  are  the  only  ones  which  show  any 
considerable  extent  of  corona.  The  northern  and  southern  polar 
rifts  are  clearly  marked  and  very  broad.  The  bases  of  the  font 
synclinal  groups  can  also  be  clearly  made  out,  especially  that  in 
the  north-west  qaadrant.  The  general  axis  of  symmetry  i* 
slightly  inclined  to  the  north-west  and  south-east  of  the  Son's 
axis.     Wolfs  relative  nnmber  of  sunspots  is  776. 


Eclipse  of  1870,  Sec.  21. 
Mr.  Brothers's  negative,  taken  at  Syracuse,  shows  a  ^reat 
extent  of  corona,  reaching  in  some  parts  qui'e  40'  from  ihe  li"ib. 


Jane  1887.  as  shown  in  Photographs.  501 

The  general  outline  is  somewhat,  circular,  with  a  quadrilateral 
ana  of  grenter  brightness,  brighter  on  the  western  aide.  The 
northern  polar  rift  is  broad  and  ill-defined  ;  to  the  en  at  of  the 
south  pole  ia  a  much  narrower  and  more  sharply  defined  rift, 
easily  traceable  to  the  limb.  To  the  east  and  west  of  this  are 
other  rifts,  and  there  is  structure  evidently  synclinal  to  the 
north-west  ;  otherwise  the  photograph  shows  but  little  detail. 
The  general  axis  of  symmetry  appears  inclined  to  the  north-west 
and  south-east  of  the  Sun's  axis  a*  much  an  20°,  but  the  orienta- 
tion is  not  verv  certiiin.  The  eclipw  occurred  at  a  period  of 
great  solar  activity,  Wolf's  relative  monthly  number  being  1354 


Eclipse  0/187 1,  Dec.  12. 

Lord  Lindsay's  and  Col.  Tennant's  excellent  series  of  nega- 
tives show  a  corona  remarkably  symmetrical,  about  a  line 
inclined  about  10°  to  the  north- went  and  south-east  of  the  Sun's 
axis.  The  northern  and  southern  polar  rifts  are  well  defined, 
nearly  opposite  to  one  another,  and  very  similar  in  character. 
The  four  synclinal  groups  are  well  marked,  appearing  to  indicate' 
zones  of  synclinal  structure  extending  nearly  from  the  pole  to 
abont  40°  north  and  south  latitude.  These  groups  are  generally 
separated  from  the  equatorial  portions  hy  narrow  definite  rifts. 
The  western  margin  of  the  south-east  synclinal  croup  shows  s> 
distinct  tendency  to  double  curvature — a  form  which  reappears 
in  1883  and  1885.  The  extension  is  greatest  in  the  equatorial 
regions,  giving  a  somewhat  hexagonal  form  to  the  corona.  The 
great  polar  rifts  are  filled  with  short  straight  rays. 

The  greatest  extent  of  the  photographic  corona  does  not 
exceed  27',  but  the  minuteness  of  the  detail  near  the  limb, 'which 


502  Mr.  Wesley,  The  Solar  0-tuna  XLTII.  8, 

with  a  Btroug  transmitted  light  can  be  seen  through  the  densest 
part  of  film,  has  never  been  equalled  in  any  subsequent  eclipse 
photograph.  The  remarkable  feature  of  the  lower  structure  is 
the  prevalence  of  rays  completely  curving  over,  and  of  branching 
rays,  somewhat  resembling  a  frequent  form  of  solar  prominence. 
Few  of  these  reach  a  height  of  more  than  5'  from  the  limb;  above 
this  height  the  rays  are  generally  straight  or  more  slightly  curved. 

It  is  impossible  to  be  certain  whether  these  lower  details  are 
really  near  the  limb,  or  whether  they  are  rays  on  the  nearer  or 
further  parts  of  the  corona,  seen  foreshortened.  In  the  latter 
case,  they  could  hardly  be  the  extreme  ends  of  coronal  rays,  as 
these  invariably  fade  away  so  much  towards  their  extremities 
that  they  would  certainly  be  lost  on  the  dense  background.  On 
the  whole,  the  difference  of  character  between  the  higher  and 
the  lower  details  lends  great  probability  to  the  view  that  the 
latter  are  really  near  the  limb.  Mr.  Ran  yard  considers  that  ihe 
more  contorted  character  of  these  lower  structures  indicates  the 
existence  of  a  resis'ing  atmosphere  in  the  lower  part  of  the 
corona.  It  seems  evident,  at  least,  that  many  nf  the  curvatures 
of  the  coronal  ravs  conld  not  be  caut-cri  by  g-avity  alone.  Still 
when  we  consider  what  an  intricate  mass  <>f  crossing  and  inter- 
lacing rays  must  be  produced  by  perspective  as  we  approach 
the  limb,  we  must  feel  that  the  question  cannot  be  decided  with 
certainty. 

The  eclipse  occurred  at  a  time  of  somewhat  less  solar  activity 
than  that  of  the  previous  year.  Wolf's  relative  monthly  number 
being  980. 


Eclipse  of  1875,  April  6. 

The  small  size  of  the  photographs  taken  by  Dr.  Schuster 
renders  it  impossible  to  make  out  more  than  the  general 
character  of  the  corona,  and  from  the  same  cause  the  orientation 
is  not  very  accurately  determined.  The  corona  is  somewhat 
symmetrical  about  a  line  nearly  coinciding  with  the  Snn's  axis, 
the  northern  and  southern  polar  rifts  being  very  broad  and  well 
marked.  Fonr  synclinal  groups  are  plainly  seen,  their  axes 
making  angles  of  more  than  45°  with  the  Sun's  axis.  The  polar 
rifts  are  filled  up,  but  not  to  a  great  height,  the  polar  exten- 
sion of  the  corona  being  only  about  half  the  equatorial,  where 


June  1887.  an  ihown  in  Photograph*.  503 

the  greatest  height  is  nearly  a  Folar  diameter  The  half  of 
the  corona  lying  to  the  east  of  the  axis  is  decidedly  larger 
than  that  to  the  west,  so  that  the  nearly  straight  lines  which 
hound  the  corona  north  and  south  converge  towards  the  west. 
Dr.  Schaster  draws  attention  to  the  remarkable  similarity 
between  this  corona  and  that  of  1874,  of  which  no  photographs 
were  taken.  He  thinks  this  similarity  extends  to  the  irregularity 
in  the  symmetry  just  mentioned;  bat  the  want  of  accordance 
between  the  drawings  made  in  1874  renders  this  uncertain. 

Notwithstanding  this  general  resemblance,  the  solar  activity, 
br  indicated  by  the  sunspotn,  was  less  than  half  as  great  as  in 
the  previous  year,  Wolfs  relative  number  for  April  1874  being 
491,  and  for  April  1875,  105. 


Eclipie  of  1878,  July  29. 
The  photographs  which  I  have  examined  are  two  negatives 
by  Mr.  Ranyard,  mnde  at  Denver,  and  a  series  of  9  positive 
copies  on  glass  of  the  photographs  taken  by  Professor  Harkness 
and  Mr.  Rogers  at  Creston  and  La  Junta.  The  exposures  of  Mr. 
Ranyard'B  plates  were  so  short  that  tbey  show  but  a  small 
extent  of  corona.  A  drawing  combining  the  detail  of  the 
Creston  and  La  Junta  negatives,  and  showing  a  further  extension 
of  the  equatorial  rays,  from  a  smaller  photograph  by  Mr.  Peers, 
is  given  in  the  "  Appendix  to  the  Washington  Observations  "  for 
1876.  On  comparing  this  drawing  with  the  positives,  it  does 
not  seem  very  satisfactory.  I  can  make  out  as  much  or  more 
detail  on  the  positives  as  on  the  drawing  (except  the  equatorial 
extension),  and  no  doubt  much  more  would  be  seen  on  the 
original  negatives. 

The  corona  belongs  to  the  same  type  as  those  of  1874  and 
187S-  The  equatorial  extension  greatly  exceeds  the  polar,  and 
both  the  northern  and  southern  rifts  are  widely  opened,  so  that 
their  eastern  and  western  boundaries  form  nearly  straight  lines 
tangential  to  the  limb.  The  northern  and  southern  synclinal 
groups  are  so  much  depressed  towards  the  equator  that  they 
appear  to  coalesce  into  one  great  mass,  occupying  the  whole 
equatorial  region.  The  rifts  are  filled  with  fine  rays,  straight, 
and  nearly  radial  in  the  centre  of  the  rift,  and  becoming  more 
and  more  curved  towards  its  boundaries.  In  one  rift  there  are 
as  many  as  20  separate  rays,  remarkably  uniform  in  length  and 


504  Mr.  Wptley,  The  Solar  Corona  I  LTD,  8, 

distance  apart,  never  branching  or  crossing.  The  two  rifts  ire 
almost  identical  in  character,  but  are  not  opposite  each  other; 
the  northern  rift  having  ite  general  axis  inclined  about  15° 
towards  the  east  from  the  Sane  axis,  and  the  southern  being 
more  symmetrical  with  it. 

The  great  equatorial  extensions,  of  which  the  bases  only  in 
visible  in  the  positives,  are  very  symmetrical  in  detail,  but  the 
western  mass  is  the  broader,  reaching  farther  both  to  the  north 
and  south.  These  great  masses  are  broadest  near  the  limb,  and 
gradually  become  narrower,  so  that  their  northern  and  southern 
boundaries  would  meet  in  a  point  about  2  diameters  from  the 
limb  on  the  western  side,  and  rather  less  on  the  eastern.  Those 
equatorial  extensions  were,  however,  observed  by  Newcomb, 
Langley,  and  others,  to  reach  to  a  distance  of  at  least  11 
diameters.  They  mast  have  been  very  faint,  as  in  the  American 
drawing,  combined  from  various  negatives,  they  do  not  extend 
more  than  a  diameter. 

It  is  a  remarkable  peculiarity,  which  I  have  observed  in  no 
other  corona,  that  while  at  the  poles  it  is  split  up  into  a  great 
number  of  fine  rays,  the  equatorial  extensions  are  broad  smooth 
masses,    showing   scarcely   any  detail,  even  at    their  extreme 

The  eclipse  occurred  at  a  time  of  decidedly  low  solar 
activity,  Wolf's  relative  number  being  only  3-3. 


Eclipse  of  188: 


The  negatives  taken  by  Dr.  Schuster  show  a  large  extent  of 
corona,  reaching  in  several  places  a  height  of  a  solar  diameter, 
one  straight  ray  in  the  south-west  extending  as  far  as  ii 
diameter.  The  corona  presents  none  of  the  features  which 
characterised  those  of  1874,  1875,  and  1878.  Although  very 
irregular  in  detail,  it  is  approximately  circular  in  form,  and  » 
entirely  without  that  great  difference  between  the  polar  sua 
equatorial   extensions   which  had   be^n  so   striking  in  the  three 


June  t 


i  1'hotograplus. 


5°5 


last  eclipses.  At  the  same  time  it  shows  none  of  that  symmetry 
about  a  line  not  very  far  from  the  Sun's  axis  that  had  been 
more  or  leas  apparent  in  most  previously  photographed  coronas, 
and  es[>ecially  in  that  of  1871.  This  absence  of  an  axis  of 
symmetry  and  of  polar  rifts  is  its  most  striking  feature.  There 
are  groups  of  synclinal  structure,  but  they  are  not  of  a  very 
definite  character,  and  are  quite  irregularly  placed.  The  solar 
axis  does  not  pass  through  the  line  of  least  extension,  as  is 
almost  always  the  case.  The  only  approach  to  an  axis  of 
symmetry  seems  to  be  about  a  line  nearly  at  right  angles  with 
the  Sun's  axis.  The  orientation  was,  however,  very  carefully 
made,  and  in  Dr.  Schuster's  opinion  is  not  more  than  half  & 
degree  in  error :  it  nearly  agrees  with  that  adopted  by  Professor 
Tacchini. 

The  rays  are  rather  more  frequently  straight  than  carved, 
and  there  is  only  one  instance  of  a  ray  completely  curving  over  : 
this  is  in  the  south-east;  it  reaches  a  height  of  about  12'  from 
the  limb.  Beneath  it  are  two  rays — the  only  ones  showing  any 
traces  of  a  branching  structure.  There  are  distinct  rifts  on  the 
western  side,  reaching  to  the  limb ;  but  they  are  more  filled  up 
with  coronal  matter  than  those  of  1871.  The  rays  are  in  all 
directions,  from  radial  to  tangential,  and  there  are  several  cases 
of  rays  crossing  each  other,  but  no  clear  case  of  a  ray  of  double 
curvature.  The  lower  details  of  the  corona  are  less  distinct 
thau  in  1871  ;  but  this  may  be  dne  to  the  great  density  of  the 
film  near  the  limb,  which  is  common  to  all  dry-plate  negatives. 
The  definition  of  the  outer  portions  is  extremely  fine.  I  caunot 
see  any  evidence  of  the  distinction  between  an  outer  and  inner 
corona,  which  Dr.  Schuster  thinks  the  photographs  show. 
Wolfs  relative  monthly  number  of  sunspots  is  64*5  ;  a  remark, 
able  outburst  had  occurred  during  the  preceding  month,  for 
which  the  number  was  958. 


So6  Mr.  Wesley,  The  Solar  Corona  xlvii.  8, 

Eclipse  of  1883,  M«y  6. 

Successful  photographs  wore  taken  by  M.  Janssen,  and  also 
bj  Messrs.  Lawrance  and  Woods.  The  most  prominent  feature 
is  an  unusually  well-marked  rift,  partly  filled  with  short  straight 
rays,  near  the  north  pole  of  the  Snn's  axis,  from  which  the 
general  axis  of  the  rift  in  inclined  at  an  angle  of  about  30°  to 
t>he  east.  On  each  side  of  this  rift  are  most  characteristic 
groups  of  synclinal  structure,  whose  bases  meet  at  the  limb:  the 
easternmost  shows  a  double  curvature  on  both  sides,  bat  on  the 
western  edge  this  appearance  seems  caused  by  the  superposition 
of  different  raya.  There  seems  no  regularity  in  the  arrangement 
of  the  rays  in  the  rest  of  the  corona,  nor  any  rill  in  the  south, 
corresponding  to  that  in  the  north.  The  general  outline  of  the 
corona  is  somewhat  circular,  but  the  two  synclinal  groups  extend 
farther  than  any  other  part.  In  M.  Janssen's  long- exposed 
plate,  one  of  these  groups  extends  nearly  as  far  as  two  solar 
diameters,  which  is  the  greatest  extension  shown  by  any  corona 
photograph.  Indeed,  M.  Janssen  says  that  it  is  much  greater 
than  it  appeared  to  the  eye  in  his  telescope. 

The  solar  activity  was  rapidly  decreasing,  Wolfs  relative 
monthly  number  of  sunspots  being  321. 


Eclipse  of  1885,  September  8. 

Several  photographs  were  taken  of  this  eclipse,  bat  the 
weather  was  generally  unfavourable,  and  few  show  much  detail. 
The  most  marked  feature  is  the  southern  rift,  which  is  broad  and 
well  marked,  with  clear  indications  of  straight  raya  filling  it. 
The  only  distinctly  synclinal  group  is  to  the  south-east;  its 
axis  makes  an  angle  of  about  45°  with  the  Sun's  axis,  and  its 
extension  is  greater  than  any  other  part  of  the  corona.  The 
western  edge  of  this  group  presents  a  double  curvature.  The 
other  parts  of  the  corona  are  very  irregular,  and  there  does  not 
appear  to  be  any  distinct  rift  on  the  north  corresponding  with 
the  southern  rift.  There  is  a  marked  broad  depression  in  the 
corona,  about  350  to  the  east  of  the  north  point  of  the  axis. 
This  depression,  and  the  southern  rift,  appear  to  divide  the 
corona  into  two  very  unequal  parts,  the  western  one  being  much 
the  greater. 

The  solar  activity,  as  shown  by  the  sunspots,  was  diminish- 


June  1887. 


at  ihmon  in  Photograph*. 


5°7 


iag  ;  Wolfa  relative  monthly  number  being  83  7  for  ihe  month 
of  June,  and  39*6  for  September. 

The  results  of  the  observations  of  the  eclipses  of  1883  and 
1886  are  in  coarse  of  publication  by  tbe  Royal  Society,  and  I 
have  not  their  permission  to  describe  the  details  of  the  corona  of 
these  years. 

Since  the  corona  entirely  surrounds  the  Son,  and  is  not  a 
mere  fringe  as  it  necessarily  seems  to  the  eye,  its  appearance  is 
greatly  modified  by  perspective.  The  groups  of  synclinal 
structure,  when  they  occur  somewhat  symmetrically  on  opposite 
sides  of  the  Son,  most  evidently  be  regarded  as  zones  of  curving 
rays,  the  shorter  and  straighter  rays  filling  the  polar  rifts,  being 
probably  the  rays  on  the  nearer  or  further  parts  of  the  synclinal 
zone  seen  foreshortened.  A  curved  tangential  ray,  if  curved  or 
inclined  in  the  line  of  sight,  will  appear  straight  and  radial  bat 
shortened.  On  tbe  other  hand,  foreshortening  may  greatly 
increase  the  apparent  curvature  of  a  ray.  The  true  point  on  the 
Sun  from  which  a  ray  springs  is  not  seen  unless  it  springs  from 
the  limb.  The  polar  rifts  must  be  greatly  modified  in  appear- 
ance if  they  are  inclined  in  the  line  of  sight.  It  is  obvious  that 
a  rift  which  would  resemble  a  if  actually  on  the  limb  would  be 
more  like  b  if  its  axis  were  directed  towards  or  from  the  Earth. 


Tbe  greater  apparent  density  of  the  corona  near  the  limb 
must,  of  course,  be  largely  due  to  its  greater  thickness.  It  is 
only  at  the  extreme  outer  limits  of  the  corona  that  we  can  see 
the  true  character  of  its  rays,  as  it  is  only  there  that  they  are 
unaffected  by  perspective  or  superposition. 

A  large  proportion  of  the  coronal  rays  are  carved,  the  curves 
being  of  various  kinds.  It  frequently  occurs,  at  the  edges  of 
the  synclinal  groups,  that  a  ray  which  appears  to  spring1  from 
the  limb  in  a  nearly  radial  direction  is  abruptly  curved,  and  then 
straightened,  so  as  to  become  almost  tangential :  this  is  a  most 
characteristic  form  of  coronal  ray.  Sometimes  after  it  has 
attained  a  considerable  height  it  is  slightly  curved  in  a  contrary 
direction,  as  is  welt  seen  in  1871,    ""  '     "" 


508  Mr.  Wesley,  The  Solar  Corona  xlvii.  8, . 

Rajs  completely  curving  over  and  branching  rays  have  been 
mentioned  in  the  description  of  the  corona  of  187 1,  in  which, 
they  are  very  numerous  ;  but  they  are  scarcely  seen  in  any  other 
eclipse.  Possibly  they  occur  as  a  rale  only  near  the  limb,  which 
portion  has  never  been  so  clearly  shown  as  in  the  photographs 
of  1871. 

Dr.  Hoggins  suggests  that  the  curved  rays  may  be  caused  by 
matter  blown  upwards,  rising  with  the  smaller  rotational  Telocity 
of  the  photosphere  from  which  it  started,  and  appearing  to  lag 
behind  in  its  ascent.*  But  in  this  case  we  should  expect  the 
curves  to  be  similar  in  direction  and  character  in  any  part  of  the 
corona,  while  in  fact  there  is  no  such  regularity,  which  seems  to 
show  that  the  curvature  cannot  be  the  result  of  this  cause  alone. 
The  coronal  rays  are  invariably  brighter  near  the  limb,  and 
fade  gradually  away  towards  their  extremities,  where  they  are 
sometimes  pointed  and  sometimes  spreading.  Sometimes  they 
rise  from  a  broad  extended  base,  which  character  may  be  more 
frequent  in  reality,  as  the  base  would  be  hidden  if  the  ray  is  not 
upon  or  near  the  limb. 

The  absolute  brightness  and  extension  of  the  corona  during 
different  eclipses  cannot  be  ascertained  from  the  photographs,  as 
they  have  been  taken  with  various  instruments  and  exposures, 
and  on  plates  of  different  degrees  of  sensitiveness.  The  earlier 
collodion  photographs  probably  never  showed  half  the  visible 
corona,  while  the  recent  negatives  taken  on  dry  plates  with  long 
exposures  may  show  more  than  is  visible  to  the  eye. 

The  coronal  matter  is  very  transparent,  many  rays  crossing 
others  which  are  seen  through  them. 

Nothing  that  I  have  seen  on  the  eclipse  photographs  seems  to 
give  the  least  countenance  to  any  of  the  meteoric  theories  of  the 
corona.  Drawings  such  as  that  of  Liais  in  1858,  representing 
the  synclinal  groups  as  symmetrical  cones,  would  be  readily 
interpreted  as  streams  of  meteors  passing  round  the  sun ;  and 
drawings  like  Gillman's  in  1869,  giving  innumerable  rays  all 
truly  radial,  might  indicate  matter  falling  into  the  Sun.  In  the 
photographs,  however,  the  cones  are  never  symmetrical,  and  are 
shown  to  consist  of  many  rays  of  various  curvatures,  while  rays 
that  are  truly  radial  are  quite  exceptional.  If  the  rays  were 
meteor  streams  sweeping  past  the  Sun  we  should  expect  to  trace 
the  same  streams  at  opposite  sides,  while  in  fact  there  is  no  such 
exact  correspondence,  even  in  the  most  symmetrical  corona  of 
1878. 

The  detailed  structure  of  the  corona  seems  quite  conclusive 
evidence  against  Professor  Hastings's  theory  that  it  is  a  diffrac- 
tion phenomenon. 

Whatever  may  be  the  true  cause  of  the  corona,  it  is  impos- 
sible for  one  who  has  examined  the  photographs  to  resist  the 
conclusion  that  in  some  way  it  proceeds  from  the  Sun.  The 
character  of  the  curved  rays— especially  those  which  curve  com* 

*  Baksrian  Lecture/  Froe.  Roy.  8oc.t  vol.  zxxix.  p.  127. 


Jane  1887.  as  shown  in  Photographs.  509 

pletely  oyer — the  invariably  greater  brightness  of  the  corona  as 
it  approaches  the  limb,  the  broad  base  from  which  the  rays 
sometimes  spring,  all  seem  capable  of  no  other  explanation. 

Although  many  observers  have  spoken  of  movement  of  the 
coronal  rays,  and  have  recorded  changes  of  form  daring  totality, 
there  is  nothing  in  the  photographs  to  show  that  changes  of  such 
magnitude  as  to  be  visible  have  taken  place  in  so  short  a  time. 
Photographs  taken  an  hoar  apart  in  187 1  show  no  visible  change, 
while  the  clearness  of  the  details  proves  the  appearance  of  move- 
ment to  have  been  an  illusion. 

I  am  unable  to  see  in  the  eclipse  photographs  any  ground  for 
the  distinction  often  drawn  between  an  "inner"  and  "  outer" 
corona.  The  principal  details  can  generally  be  traced  down  to 
the  limb,  and  there  does  not  seem  any  sudden  falling-off  of  the 
light  (except  what  is  caused  by  occasional  strongly  curved  or 
foreshortened  rays),  nor  other  indication  of  a  want  of  continuity. 
It  seems  to  be  of  the  same  character  throughout.  At  the  same 
time,  it  may  be  true  that  the  lower  structures  are  more  frequently 
of  a  strongly  curved  or  branching  character. 

There  is  no  sign  of  any  connection  between  the  coronal  rays 
and  the  solar  prominences. 

The  only  generalisation  with  regard  to  the  form  of  the  corona 
which  has  seemed  well  supported  by  the  photographic  evidence 
is  that  of  Mr.  Ranyard,  that  there  is  a  connection  between  the 
general  form  of  the  corona  and  the  solar  activity  as  shown  by  the 
number  of  sunspots.  The  corona  of  a  sunspot  maximum  has 
generally  been  somewhat  symmetrical,  with  synclinal  groups 
making  angles  of  450  or  less  with  its  general  axis.  The  sunspot 
minimum  coronas  show  polar  rifts  much  more  widely  open,  syn- 
clinal zones  making  larger  angles  with  the  axis,  and  being  there- 
fore more  depressed  toward  the  equatorial  regions,  in  which  there 
is  usually  greater  extension.  This  generalisation  is  well  borne 
out  by  the  maximum  coronas  of  1870  and  187 1  and  the  mini, 
mum  coronas  of  1867, 1874,  1875,  and  1878.  On  the  other  hand, 
the  eclipses  of  1883,  1885,  and  1886,  do  not  strikingly  confirm 
the  theory.  The  eclipse  of  1883,  at  a  time  of  rapidly  decreasing 
solar  activity,  shows  all  the  characters  of  a  sunspot  maximum 
corona;  the  same  in  a  somewhat  less  degree  may  be  said  of  1885 
and  1886,  at  both  of  which  times  the  solar  activity  was  decreas- 
ing. Although  the  polar  rifts  were  wide  in  1886,  there  was  no 
marked  depression  of  the  synclinal  groups  towards  the  equator, 
nor  any  great  equatorial  extension,  although  the  relative  number 
of  sunspots  for  August  1886  was  only  i6ao.  Striking,  there- 
fore, as  the  evidence  in  favour  of  the  generalisation  has  been  in 
many  years,  it  still  seems  probable  that  the  form  of  the  corona 
is  modified  by  other  causes  at  present  unknown  to  us. 

It  may  be  that  the  coronal  axis  (to  use  a  convenient  term)  is 
always  inclined  at  the  same  angle  to  the  Sun's  axis  of  rotation, 
and  that  the  apparent  changes  in  its  inclination  are  caused  by  its 
being  seen  from  different  points  of  view.     Before  this  question 

002 


510  Mr.  Wesley,  The  Solar  Corona.  xlyil  8, 

can  be  answered,  photographs  must  be  taken  at  every  total 
eclipse  for  many  years  to  come.  It  will,  above  all,  be  necessary, 
however,  that  the  utmost  care  be  taken  in  the  orientation  of  the 
plates,  that  there  may  not  be  the  slightest  doubt  as  to  the  posi- 
tion of  the  Sun's  axis.  Unfortunately,  on  several  of  the  eclipse 
photographs  there  is  great  uncertainty  on  this  most  important 
point.  It  is  preferable  to  take  a  series  of  photographs  of  the 
solar  crescent  (by  stopping  the  clockwork  in  the  usual  way) 
both  before  and  after  totality,  so  as  to  guard  against  the  danger 
of  any  slight  shift  of  the  instrument. 

Sometimes  a  wire  has  been  placed  in  the  instrument  for  the 
purpose  of  orientation ;  but  wherever  this  crosses  the  corona  it 
interferes  with  the  details,  and  is  on  that  account  a  disadvantage. 
In  1886  two  pointers  were  used,  one  on  either  side,  beyond  the 
limits  of  the  corona;  but  there  is  a  risk  of  these  not  being  visible 
on  the  plates.  If  the  plate  perfectly  fit  the  plate-holder  there 
hardly  seems  any  necessity  for  a  wire. 

To  prevent  mistakes  in  orientation  the  plan  adopted  by 
Mr.  Davis  in  187 1  was  an  excellent  one.  Each  of  his  plates  had 
one  corner  cut  off,  corresponding  with  a  small  fixed  block  in  one 
corner  of  the  exposing  frame,  so  that  no  doubt  could  afterwards 
arise  as  to  the  position  of  each  plate  when  exposed. 

In  the  reports  of  the  observations  it  need  hardly  be  said  that 
the  data  from  which  the  orientation  is  obtained  should  always  be 
fully  stated. 

It  is  much  to  be  wished  that  in  future  eclipses  photographs 
could  be  taken  which  would  show  the  lower  details  as  clearly  as 
the  negatives  of  187 1 ;  I  am  almost  inclined  to  recommend  col- 
lodion plates,  such  as  were  then  employed.  The  excessive 
density  of  the  corona  near  the  limb  in  all  the  dry-plate  negatives 
obscures  the  lower  details,  while  the  greater  coarseness  of  the 
grain  makes  it  impossible  to  use  much  magnifying  power  in 
their  examination.  At  the  same  time,  we  ought  not  to  forego 
the  great  advantage  of  the  gelatine  film  in  giving  the  full  ex- 
tension of  the  corona.  It  is  to  be  hoped  that  by  some  improve- 
ment in  the  preparation  of  plates  both  these  advantages  may  be 
combined. 

In  the  meantime  careful  drawings  would  be  of  great  utility 
if  observers  would,  instead  of  vainly  trying  to  give  a  general 
view  of  the  entire  corona,  which  is  quite  impossible  in  the  short 
time  at  their  disposal,  restrict  themselves  to  making  as  exact 
delineations  as  possible  of  the  details  in  some  portion  only.  The 
general  appearance  of  the  corona  is  admirably  given  in  a  good 
photograph  ;  but  this  would  be  most  usefully  supplemented  by 
detailed  drawings  of  selected  portions,  especially  of  the  structure 
near  the  limb,  in  which  the  photograph  most  frequently  fails. 

1887,  June  9. 


June  1887.         M.  Elger,  Observations  of  Saturn.  511 

Physical  Observations  of  Saturn  in  1887. 
By  Thomas  Gwyn  Elger. 

The  following  observations  of  the  planet  were  made  with  an 
8^-in.  silver-on-glass  reflector  by  Calver  during  the  months  of 
February,  March,  and  April. 

1 2th  February,  o*  to  1  oh.  Good  definition ;  East  wind.  Planet 
beautifully  defined  with  a  power  of  350.  Rings. — A.  No  trace 
of  any  division  ;  outer  border  slightly  darker  than  the  remainder. 
B.  Inner  edge  very  dark.  King  gradually  increasing  in  bright- 
ness to  about  midway  between  the  interior  and  exterior  borders. 
Outer  half  uniformly  bright.  G.  Both  ans»  extremely  dark, 
hardly  distinguishable  except  where  it  crosses  the  ball ;  here  it 
is  sufficiently  transparent  to  allow  the  latter  to  be  seen  through  it. 
Belts. — The  broad  equatorial  belt  is  orange-yellow  in  colour,  and 
sharply  defined  on  its  northern  edge  by  a  darker  band  of  vary- 
ing width.  Its  southern  limits  are  marked  by  a  much  fainter 
band,  the  intervening  space  exhibiting  a  mottled  appearance — due 
to  the  presence  of  light  spots  and  markings.  About  midway 
between  the  bluish- grey  polar  cap  and  the  equatorial  zone  there 
is  a  faint  belt,  but  this  region  is  very  indistinct.  Shadow  of  ball. 
— The  /  side  of  the  sharply-defined  shadow  on  B  appears  to  be 
concave  up  to  Cassini's  division,  where  there  is  a  well-marked 
notch,  apparently  coincident  with  the  latter.  South  of  this,  on 
ring  A,  the  shadow  follows  the  curvature  of  the  ball,  and  seems 
to  be  somewhat  narrower  than  any  portion  of  the  shadow  on 
ring  B.  The  south  limb  of  the  ball  is  slightly  within  the  outer 
edge  of  A. 

16th  February ,  8h  to  o*.  Frosty;  wind  N.E.  Definition 
variable — not  so  good  as  on  the  12th.  Powers  used,  284,  350. 
Rings. — A.  Is  similar  in  colour  to  the  polar  cap — viz.  greyish- 
blue.  There  is  an  evident  though  faint  light  line  concentric 
with  the  ring  about  midway  between  the  outer  and  inner  edge, 
but  rather  nearer  the  former.  It  can  be  traced  for  some  distance 
on  both  ansae,  but  is  more  easily  seen  on  the  p  side.  B.  The 
shading  on  this  ring  becomes  gradually  lighter  from  the  inner 
edge  to  a  point  about  £th  the  apparent  width  of  the  belt  from 
the  outer  edge,  where  it  suddenly  ceases,  the  remainder  of  the 
ring  being  uniformly  bright.  C.  Dark,  but  distinct  on  p  side. 
/  ansa  nearly  indistinguishable.  Belts  less  favourably  seen  than 
on  the  1 2th. 

21st  February,  9*  to  9*  3om.  Definition  variable.  Power 
used,  350.  Rings. — A.  No  trace  of  any  detail.  B.  The  bright 
outer  edge  appears  to  be  of  the  same  tone,  but  slightly  more 
brilliant  than  the  central  portion  of  the  ball  immediately  north 
of  the  equatorial  belt.  C.  Both  ansre  very  dusky — scarcely 
distinguishable,  except  here  and  there.  Belts. — North  border  of 
-equatorial  belt  sharply  defined.  Mottled  surface  evident.  Polar 
and  intermediate  zone  indistinct.  Shadow  of  ball. — As  on  the 
12th 


5 1 2  Mr.  Elger,  Physical  Observations  xxvn.  8, 

2$th  February,  gh  to  9h  30™.  Definition  on  the  whole 
favourable.  Power  used,  350.  Rings. — A.  No  detail  seen; 
innor  edge,  adjoining  Cassini's  division,  on  p  ansa  somewhat 
darker  than  the  general  surface.  B.  As  on  the  21  at.  C.  p 
ansa  very  obscure,  in  places  as  dark  as  the  space  between  the 
ball  and  the  ring  system.  Nothing  abnormal  was  noted  in 
connection  with  the  /ansa,  though  at  times  the  nf  part  of  the 
ring  seemed  to  be  lighter  than  the  remainder.  Belts. — All  badly 
defined. 

26th  February,  8h  30™  to  9*  30™,  Clear  frosty  night 
with  good  definition.  Powers  used,  284,  350.  Rings. — 
A.  No  detail  visible.  B.  Gradually  increasing  in  brightness 
from  the  inner  to  the  outer  edge,  which  is  bounded  by  a 
narrow  zone  of  uniform  brilliancy  about  equal  in  width  to 
Cassini's  division.  C.  With  both  eyepieces  the  p  ansa  exhibits 
on  its  inner  border  three  or  four  large  re-entering  angles  like 
the  teeth  of  a  saw,  the  intervening  spaces  being  apparently  as 
dark  as  that  between  the  ball  and  the  ring,  and  extending  nearly 
to  the  outer  edge  of  the  ring.  This  appearance  is  confined  to  the 
western  section  of  the  ansa,  there  being  nothing  abnormal  as  re- 
gards the  sp  and  np  portion  of  it.  The  /  ansa  is  dark  but 
traceable.    Belts. — Details  well  seen. 

27th  February,  9h  to  9h  30™.  Definition  variable.  Powers 
used,  284,  350.  .Rings. — A.  Light  line  visible  for  some  distance 
on  both  ansae,  as  on  the  16th  inst.  Inner  edge  slightly  darker 
than  the  rest  of  the  surface.  B.  As  on  the  previous  evening. 
C.  The  indented  edge  of  the  p  ansa  cannot  be  made  out,  but  the 
surface  of  the  ring  is  unequally  dark.  At  times  of  best 
definition  two  or  three  dark  areas  are  noted  upon  it  with  both 
eyepieces. 

28th  February,  gh  to  9h  30™.  Sky  hazy.  Good  definition, 
affording  some  exquisite  glimpses  of  the  planet.  Power  used, 
350.  Rings. — A.  Light  streak  seen  on  both  ansae,  as  on  the  16th 
and  27th.  C.  Very  dusky,  only  isolated  areas  of  the  p  ansa 
visible.  Belts. — Equatorial  belt  covered  with  ill-defined  detail, 
and  bounded  on  the  north  by  a  wide  band,  much  darker  than  any 
other  portion  of  the  ruddy  zone.  Faint  belt  on  the  northern 
hemisphere  visible  near  the  east  and  west  limb.  The  greater 
portion  of  it  is  hidden  by  the  ring  C,  to  which  it  is  about  equal 
in  tone. 

12th  March,  8h  3om  to  9h  30™  Definition  variable.  WindE. 
Powers  used,  284,  350.  Rings. — A.  No  detail  visible.  C.  p 
ansa  is  very  evidently  broken  up  into  several  areas  of  different 
degrees  of  darkness,  so  that,  except  a  short  section  of  it,  np,  it 
is  impossible  to  recognise  it  as  a  ring  surrounding  the  planet. 
The /ansa,  on  the  contrary,  is  easily  visible.  Belts. — All  fairly 
distinct.  Shadow  of  ball. — The  southern  limb  and  outer  edge  of 
A  are  apparently  coincident,  and  the  shadow  south  of  the  well- 
marked  notch  at  Cassini's  division  becomes  gradually  wider  as  it 
approaches  the  boundary  of  the  ring. 


June  1887.  of  Saturn  in  1887.  513 

i$th  March,  8h  30™  to  9h  ism.  Frosty;  E.  wind.  Definition 
variable.  Powers  used,  284,  350.  Rings. — A.  A  faint  dark  line, 
presumably  Encke's  division,  seen  on  the  widest  part  of  both 
ansaB.  B.  Inner  edge  very  obscure,  ring  gradually  increases  in 
brilliancy  to  a  point  about  £rd  its  apparent  width  from  its  outer 
edge,  where  it  becomes  suddenly  bright.  C.  At  times  it  is 
impossible  to  recognise  any  traces  of  this  ring  on  the  p  side, 
though  the/  ansa  is  obvious  enough.  During  the  best  definition, 
however,  three  or  four  large  dusky  areas  are  just  distinguish- 
able amid  the  general  blackness  of  the  space  between  the  ball 
and  the  p  ansa  of  B.  /  ansa  very  dark,  but  traceable.  Belts. — 
Details  well  seen.  Shadow  of  ball. — Extremely  sharp;  notch 
very  evident ;  shadow  falling  on  B  slightly  concave  towards  the 
east,  becoming  gradually  wider  from  the  notch  to  the  outer  edge 
of  A. 

16th  March,  8h  i5m  to  9*  15™.  Frosty;  E.  wind.  Definition 
variable,  but  at  times  excellent,  affording  superb  views  of  the 
planet  Powers  used,  284,  350.  Rings. — A.  When  seen  to  the 
greatest  perfection  it  seems  to  be  of  a  lavender-grey  hue,  the  p 
ansa  being  slightly  darker  and  the  /ansa  much  darker  than  the 
dusky  northern  edge  of  the  equatorial  belt.  Encke's  division  is 
seen  on  the  p  side  only ;  here  it  is  an  easy  object,  and  can  be 
followed  for  some  distance  round  the  ansa.  During  the  most 
favourable  glimpses  both  ansa?  appear  to  be  striated  with  faint 
concentric  markings.  B.  The  brilliant  outer  edge  of  this  ring 
causes  it  apparently  to  stand  up  like  a  step  in  front  of  Gassini's 
division.  The  graduated  shading  is  not  so  evident  to-night.  It 
seems  to  occupy  about  $rds  of  the  width  of  the  ring.  G.  The 
anomalous  appearance  of  the  p  ansa  again  observed  with  both 
eyepieces.  /  ansa  dark,  but  easily  seen.  Belts. — Equatorial 
zone  covered  with  minute  white  spots  on  an  orange-yellow  back- 
ground, and  exhibiting  much  ill-defined  detail.  Its  northern 
boundary  consists  of  a  dark  band  of  irregular  width,  with  a 
sharply-defined  edge  towards  the  north.  The  southern  limit  of 
the  zone  is  marked  by  a  similar  but  much  fainter  band.  Polar 
cap,  bluish-grey.  A  suspicion  of  two  or  three  finer  belts  between 
this  and  the  equatorial  zone.  About  midway  between  the  latter 
and  the  most  northerly  belt  (which  is  partially  hidden  by  G) 
there  is  a  faint  band,  which  at  9h  extended  from  the  eastern  limb 
across  nearly  three-fourths  of  the  visible  disc.  That  portion  of 
the  ball  between  the  equatorial  zone  and  G  is  much  brighter  and 
more  decidedly  yellow  than  the  brightest  part  of  the  ring-system, 
viz.  the  outer  portion  of  B. 

iSth  March,  8h  to  9h.  Wind  E.  Definition  excellent. 
Powers  used,  284,  350.  Rings. — A.  Encke's  division  steadily 
seen  on  both  ansa?,  and  occasionally  glimpsed  all  round  the  ring, 
though  it  is  more  distinct  on  the  p  ansa  than  elsewhere ;  here  it 
is  bordered  on  the  inner  side  by  a  faint  narrow  light  edge.  B. 
As  on  March  16th.  C.  The  anomalous  condition  of  the  p  ansa 
very  evident  with  both  eyepieces;    as  on  February   26th,  it 


514  -Mr-  -E^w,  Observations  of  Saturn.  nvn.  8, 

exhibits  a  deeply  jagged  or  indented  edge,  while  there  is  a  wide 
black  space  on  the  s  p  side  concentric  with  B  and  adjoining  it* 
/  ansa  very  obscure,  bnt  visible.  Belts.-  -All  the  detail  seen  on 
the  1 6th  met.  observed  to  great  perfection.  Faint  band  north  of 
equatorial  zone  again  visible,  bnt  it  could  only  be  clearly  traced 
from  the  east  limb  to  the  centre. 


Saturn,  IS  Mutch,  I5fi7,  S*  u>  9".     TLuo.  Gwjn  Elger. 


24th  March,  gb  to  ioh.  Definition  not  good.  Power  need, 
350.  Rings. — A.  No  detail  visible.  G.  Irregular  ontline  of 
inner  border  in  p  ansa  traceable,  but  ring  very  dark  and  in- 
distinct,   /ansa  apparently  normal,  bnt  very  obscure. 

•jfh  April,  9h  to  9h  30"™.  Definition  variable — very  good  at 
times.  Powers  used,  284,  350.  Rings. — A.  No  detail  visible. 
C.  The  unsym metrical  inner  border  of  the  p  ansa  very  con- 
spicuous and  remarkable  as  exhibiting  a  scalloped  edge.  The 
boundary  between  this  ansa  and  B  very  ill-defined — so  much  so 
that  it  is  difficult,  as  regards  the  »p  portion,  to  trace  any  definite 
line  of  demarcation.  /  ansa  very  dark,  hardly  distinguishable 
from  the  space  between  ball  and  ring.  Belts. — All  well  seen. 
Faint  belt  north  of  equatorial  zone  glimpsed  once  or  twice  on 
the/side  of  the  centre.  Shadow  of  ball. — Notch  at  Cassini's 
division  seems  decidedly  blonter  than  it  did  a  fortnight  ago. 
The  outer  border  of  the  shadow  on  A  now  runs  up  to  the 
extreme  point  of  the  notch.  The  outline  of  the  shadow  both  on 
A  and  B  is  evidently  concave  towards  the  east. 

10th  April,  8h  20™  to  oh  10™.  Wind  E.  Definition  variable, 
but  at  times  excellent.  Powers  used,  284,  350,  and  420.  Rings, 
— A.  No  detail  seen.  B.  As  on  16th  March.  0.  Irregular  inner 
border  of  p  ansa  evident  with  all  the  eyepieces  used,  and  a 
dark  interval  between  C  and  B  extending  for  some  distance  on 
either  side  the  apparent  major  axis  of  the  ring.  Three  or  four 
dusky  spots  noticed  on  the  surface  of/  ansa.  These  features 
satisfactorily  seen  with  all  powers.     Belts. — Details  finely  seen, 

*  Sob  Accompunjing  drawing. 


June  1887.    Copt.  Noble,  An  old  Engraving  of  Jupiter.  515 

bat  no  trace  of  delicate  belt  north  of  equatorial  zone,  observed 
on  March  16th  and  18th  and  on  7th  April.  Shadow  of  ball, — 
As  the  notch  now  projects  very  little  beyond  the  outline  of  the 
shadow,  it  is  Terr  difficult  to  make  out. 

11th  April,  8h  30m  to  8h  5Sm.  Definition  variable.  Fine 
clear  night;  wind  E.  Powers  need,  284,  350.  Rings. — A.  No 
detail  seen.  G.  Irregular  border  glimpsed  several  times  on  p 
ansa.    /  ansa  very  obscure. 

14th  April,  8h  30m  to  9h  om.  Definition  excellent.  Wind 
N.E.  Powers  used,  284,  350,  420.  Rings. — A.  Encke's 
division  steadily  seen  on  both  ansse.  B.  As  on  16th  March. 
C.  With  all  the  eyepieces  the  inner  edge  of  the  p  ansa  is  clearly 
serrated.  Dark  spots  again  visible  on  /ansa.  Belts. — Beauti- 
fully distinct ;  faint  belt  north  of  equatorial  zone,  first  seen  on 
1 6th  March,  traced  from  limb  to  limb. 

20th  April,  8h  2om  to  9b  o™.  Definition  pretty  good. 
Powers  used,  284,  350.  Rings. — A.  No  detail  visible.  G.  Both 
ansre  very  dark.  Irregular  border  of  p  ansa  evident.  The 
surface  of  ring  in /ansa  is  manifestly  irregular  in  tone,  though 
no  definite  spots  can  be  distinguished. — Belts  not  favourably 
seen.  Shadow  of  ball. — It  requires  some  attention  to  see  the 
notch  this  evening ;  even  at  times  of  best  definition  there  is 
hardly  a  recognisable  projection  at  the  Gassini  division. 

After  this  date,  though  several  observations  were  attempted, 
the  increasing  duration  of  twilight  and  unfavourable  weather 
prevented  the  details  of  the  planet  from  being  seen  to  advantage. 

Kempston,  Beds : 

1887,  June  6. 


On  an  old  Engraving  of  Jupiter.    By  Captain  W.  Noble. 

The  other  day,  in  the  valuable  library  of  old  astronomical 
works  belonging  to  my  friend  Mr.  G.  Leeson  Prince,  F.B.A.S.,  I 
came  across  a  curious  little  volume,  described  on  its  title-page  as 
"  Atlas  Ccslestis,  containing  the  Systems  and  Theoryes  of  the 
Planets,  the  Constellations  of  the  Starrs.  Sold  by  Ben  Bragg 
in  Paternoster  Bow."  Neither  the  author's  name  nor  the  date 
of  publication  is  appended ;  but  the  name  of  "  John  Seller  " 
appears  in  the  corner  of  one  of  the  plates,  and,  from  a  note  in  the 
body  of  the  work  with  reference  to  an  eclipse,  it  must  have  been 
published  in  1680.  Presumably  this  is  the  same  John  Seller 
who  was  the  author  of  a  quarto  treatise  on  navigation  which 
appears  in  the  catalogue  of  our  own  library,  and  who  produced 
a  variety  of  books  on  arithmetic,  astronomy,  and  navigation 
between  the  years  1671  and  1711.  My  immediate  object,  how- 
ever, is  to  invite  attention  to  one  of  Mr.  Seller's  engravings, 
which,  through  the  kindness  of  Mr.  Prince,  I  am  able  to  repro- 
duce in  fac-simile. 


5x6  .Capt.  Noble,  An  old  Engraving  of  Jupiter.       ram.  8, 

The  interest  which  I  conceive  to  attach  to  this  resides  in  the 
fact  that  the  "  movable  spot  inherent  in  Jupiter  "  shown  in  this 
old  engraving  is  situated  in  precisely  the  same  part  of  the 
planet's  disc  as  the  familiar  red  spot  which  has  been  watched 
of  late  years  by  so  many  scores — not  to  say  hundreds— of  ob- 
aervers.  I  have  no  means  of  access  to  Anzout's  observations ; 
but  the  early  volumes  of  the  Philosophical  Transactions  contain 
several  notices  of  those  of  Gassini ;  and  I  have  little  donbt  that 
one  in  the  first  volume  (January  8,  1666),  p.  143 — "  Of  a  perma- 
nent spot  in  Jupiter,  by  which  is  manifested  the  conversion  of 
Jupiter  about  his  own  axis  " — has  reference  to  the  very  marking 
which  Sellers  draws.  The  words  are  these :  "  Besides  that  tran- 
sient shadow  "  (of  a  satellite)  "  last  mentioned  *  there  hath  been 
observed  by  Mods.  Cassini  a  permanent  spot  in  the  disque  of 

to  Mr  * 


Jupiter ;  by  the  help  whereof  he  hath  been  able  to  observe  not 
onely  that  Jupiter  turns  about  upon  his  own  axis,  but  also  the 
time  of  such  conversion,  which  he  estimates  to  be  9h  56™." 
Again,  on  p.  172  of  the  same  volume  (February  1666),  after 
speaking  of  changes  in  "  the  three  obscure  belts  "  of  Jupiter  de- 
tected by  Gassini,  the  account  goes  on  to  say  that  he  (Gassini) 
"  hath  at  length  discovered  a  permanent  spot  in  the  northern 
part  of  the  most  southern  belt,  by  the  means  whereof  he  hath 
concluded  that  Jupiter  turns  about  his  axis  in  9  dayes "  (an 
obvious  lapsus  for  hours)  "  56  minutes."  This  is  followed  by  a 
somewhat  elaborate  argument  to  show  that  the  spot  is  actually 
attached  to  the  surface  of  the  planet,  from  the  different  manner 
in  which  it  and  the  shadow  of  a  satellite  behave  in  traversing 
Jupiter's  disc ;  and  then  the  account  goes  on  to  say  that  Gassini 
"  hath  calculated  many  tables  whereof  he  gives  the  explication 
and  use  in  the  letters  by  him  addressed  to  the  Abbot  Falconiere. 
By  the  means  of  them  one  may  know  when  this  spot  may  be 
seen  by  us  .  .  .  and  shews  by  his  tables  what  is  to  be  added  or 

*  This  is,  I  suspect,  the  «  Glassing  Shadow  of  a  Satilite  "  of  the  en- 
graving.—W.  N. 


Jane  1887.         Mr.  Neison,  On  Prof.  Hills  Paper.  517 

substracted  to  know  at  what  time  the  said  spot  is  to  come  into 
the  middle  of  Jupiter's  diske."  In  all  of  which.  Gassini  only 
anticipated  Mr.  Marth  by  two  hundred  years  or  so.  In  connec- 
tion with  this  it  is  noteworthy  that  in  the  year  1858  a  remarkable 
dark  spot  appeared  upon  the  face  of  Jupiter,  in  the  same  part  of 
his  disc.  My  first  intention  was  to  have  copied  a  drawing  of  my 
own,  made  at  this  date,  to  illustrate  this,  but  I  find  one  by  Mr. 
Lassell  on  p.  52  of  vol.  xix.  of  the  Monthly  Notices,  in  which  the 
spot  is  depicted.  Putting  all  this  together,  it  would  appear  that 
a  permanent  source  of  disturbance  exists  in  a  very  circumscribed 
region  to  the  south  of  Jupiter's  equator,  and  that  in  observing 
the  red  spot  we  are  probably  only  watching  the  marking  by 
which  the  first  determination  of  Jupiter's  period  of  rotation  was 
ever  made. 


On  Prof.  Q.  W.  Hill's  Paper  on  Delaunay's  Method. 

By  Edmund  Neison. 

It  had  been  my  intention  to  have  passed  over  in  silence 
Prof.  Hill's  paper  in  the  November  number  of  the  Monthly 
Notices,  entitled,  "A  Reply  to  Mr.  Neison's  Strictures  on 
Delaunay's  Method  of  Determining  the  Planetary  Perturbations 
of  the  Moon;"  but  it  has  been  pointed  out  to  me  that,  as  the 
question  involved  is  one  which  cannot  readily  be  followed  by 
most  astronomers,  it  is  proper  that  I  should  make  known  my 
dissent  from  the  superficial  criticisms  urged  by  Prof.  Hill, 
based  as  they  are  on  so  much  misconception,  betraying  as  they 
do  such  imperfect  acquaintance  with  the  previous  history  of  the 
question,  and  supported  as  they  are  by  no  evidence  beyond 
strong  unsupported  assertion.  The  whole  paper  is  unjustifiable, 
unless  we  accept  as  incontrovertible  the  point  of  view  from 
which  the  whole  is  written — namely  that,  because  I  differ  from 
Delaunay,  I  must  have  a  confused,  erroneous  conception  of  his 
method,  and  must  be  entirely  in  the  wrong!  The  veiy  key- 
note to  the  tone  of  the  paper  is  given  in  almost  the  opening 
paragraph,  that  "If  we  were  obliged  to  admit  the  validity  of 
all  the  statements  in  this  article,  an  easy  corollary  from  them 
would  be  that  Lagrange's  general  method  of  the  variation  of 
arbitrary  constants  in  the  problems  of  mechanics  was  a  blunder. 
Now,  I  think  that  no  one  acquainted  with  this  method  could, 
for  a  moment  even,  entertain  such  a  proposition.  Hence,  we 
may  conclude  there  is  some  flaw  in  the  reasoning  of  this  paper." 
As  a  simple  assertion  this  is  strong  enough  and,  polemically, 
may  be  good,  but  if  Prof.  Hill  undertakes  to  substantiate  his 
assertion  it  will  be  he  who  will  have  made  the  blunder. 

I  do  not  wish  even  to  seem  wanting  in  courtesy  to  Prof. 
Hill,  whose  valuable  contributions  to  the  Lunar  Theory  have 
always  commanded  my  warmest  admiration ;  but  I  cannot  admit 
that  the  objections  raised  by  him  in  this  paper  are  such  as  to 
call  for  any  serious  reply. 

Perhaps  there  are  two  points  which  might  be  noticed. 


518  Mr.  Neison,  On  Prof.  Hill's  Paper.  xivn.  8, 

i.  Prof.  Hill's  justification  of  Delaunay  is  singularly  enough 
the  simple  reiteration  of  the  unquestionable  error  dealt  with 
in  my  very  paper,  where  I  clearly  showed  that  it  was  no 
justification  of  Delaunay  to  say  that  he  neglected  these  quan- 
tities depending  on  m4,  m5,  m6,  m7  .  .  . .,  because  they  were  be- 
yond the  order  of  approximation  fixed  by  him,  and  seemed 
obviously  to  be  very  small,  because  in  the  face  of  Hansen's 
explicit  statement  that,  according  to  his  calculations,  it  was  these 
terms  and  these  only  which  yielded  the  large  values  found  by 
him,  Delaunay  was  bound  to  so  fix  the  order  of  his  approxima- 
tions that  these  terms  were  included.  For  remember  that 
Delaunay  was  verifying  Hansen's  results ;  he  was  bound  to 
include  all  included  by  Hansen,  and  in  interpreting  Hansen's 
statements  was  bound  to  assign  Hansen's  meaning  to  Hansen's 
words;  so  it  is  useless  to  try  to  evade  the  difficulty,  as 
Prof.  Hill  does  on  p.  2,  by  assigning  to  Hansen's  words  a  new 
and  forced  meaning  that  was  never  employed  by  Hansen  or  any 
of  his  contemporaries. 

2.  Prof.  Hill  points  out  how  amusing  it  would  be  if  it 
should  "  turn  out  that  the  set  of  values  withheld  from  pub- 
lication by  Hansen  were  identical  with  those  of  Delaunay." 
Amusing !  Very  !  in  the  face  of  Hansen's  letter  to  Leverrier 
shortly  before  his  death,  in  which  he  again  expresses  his  complete 
disagreement  with  Delaunay's  results,  and  his  conviction  from 
his  calculations  that,  despite  Delaunay,  both  ttfe  terms  in  ques- 
tion had  sensible  coefficients. 

The  question  at  issue  may  be  stated  thus : 

By  the  ordinary  direct  methods  of  dealing  with  this  problem, 
methods  whose  soundness,  simplicity,  and  adequacy  is  unques- 
tionable, there  are  obtained  in  the  value  of  these  coefficients 
certain  quantities  of  the  order  m6,  m7  .  .  .  .  depending  on  the 
higher  powers  of  the  disturbing  force,  which  give  rise  to  sensible 
values  to  these  terms  of  long  period.  By  the  use  of  Delaunay's 
complex  method  neither  he  nor  his  followers  have  been  able  to 
obtain  these  terms.  They  argue — We  do  not  obtain  them, 
therefore  they  cannot  exist.  Hence,  you  ought  not  to  get  them 
by  the  ordinary  direct  methods,  consequently  those  you  do  get 
must  really  disappear  in  some  unexplained  manner.  The  reply 
is — No ;  the  onus  of  proving  this  disappearance  lies  with  you ;  if 
you  cannot  derive  them  from  your  special  method,  the  presumption 
is  that  you  are  not  properly  using  your  special  method,  so  it  is 
yielding  you  imperfect  results. 

Having  now  explicitly  expressed  my  dissent  from  Prof.  Hill's 
criticisms,  I  shall  defer  all  further  remarks  to  my  Memoir  on  this 
subject,  when  I  will  show  still  more  explicitly  than  I  have  yet 
done  how  Delaunay's  application  of  his  method  to  the  computa- 
tion of  these  terms  is  vitiated  by  an  implicit  assumption  analogous 
in  principle  to  that  which  would  be  made  by  assuming 

/(R.R'  +  R")-/(R.R')+/(R.R"). 
Natal  Observatory; 

1M7,  April  11. 


Jane  1887.       Mr.  Buckney,  Tlie  Westminster  Clock.  519 

Note  on  the  Performance  of  the  Westminster  Clock. 
By  Thomas  Buckney. 

The  reputation  of  the  great  clock  of  the  Houses  of  Parliament 
is  so  well  established  that  some  adequate  reason  must  be  given 
to  justify  any  further  reference  to  its  performance  here.  This 
will,  I  think,  be  furnished  by  an  inspection  of  its  error  from 
Greenwich  time  on  each  day  of  the  period  nnder  review,  viz., 
from  March  29  last  until  June  9.  The  clock,  as  is  well  under- 
stood, is  not  allowed  to  run  for  an  indefinite  time  with  an  accu- 
mulated error  like  an  astronomical  clock,  but  is  kept  as  close  to 
Greenwich  time  as  possible,  the  necessary  correction  being  made 
as  soon  as  the  error  reaches  2  seconds  either  fast  or  slow.  The 
pendulum  is  never  stopped  for  this  purpose,  but  alterations  of 
rate  are  effected  by  the  addition  or  removal  of  small  weights  in 
such  a  way  as  practically  to  shorten  or  lengthen  the  pendulum, 
whilst  errors  of  4  seconds  or  more  are  corrected  by  stopping  the 
train  of  wheels  or  allowing  them  to  run  on  for  a  few  seconds  as 
may  be  necessary.  Four  seconds  is,  however,  the  smallest  altera- 
tion that  can  be  made  in  this  way.  Now  the  clock,  which,  in 
common  with  most  others  in  the  country,  was  stopped  by  the 
snowstorm  of  Dec.  26  last  (the  snow  having  blocked  tne  path  of 
the  hands),  had  since  been  going  very  well,  requiring,  however, 
small  corrections  from  time  to  time.  The  last  of  these  was  made 
on  March  29,  and  since  that  day  no  alteration  or  correction  what- 
ever has  been  made. 

The  following  table  shows  the  daily  error  of  the  clock  since 
that  time,  and  the  figures,  which  have  been  kindly  furnished  by 
the  Astronomer  Royal  from  the  records  of  the  Royal  Observatory, 
may  be  taken  as  authentic.  It  should  be  mentioned  that  the 
clock  automatically  reports  itself  by  electric  current  to  the  Royal 
Observatory  twice  daily : 

1887.  aces.  1887.  sees.  1887.        socs.  1887.  sees. 

March    29     —00      April  9     —20        April  20     —10        May    I     —  ro 

30      —OO  10      — *  21      —20  2      —  2X> 

31—10  II  —10  22  — 2-o  3  —  ro 

April       1  —  ix>  12  —10  23  —  ix>  4  —  ro 

2  —  ro  13  —  ro  24  —i*5  5  —  ix> 

3  —  3X)  14  —  ro  25  —20  6  —  ro 

4  —20  15  -ro  26  —ix)  7  —ix) 

5  —  2-o  16  —ix)  27  — 1-5  8  —  ro 

6  — 2X)  17  —ro  28  —  2X>  9  —IX) 

7  —20  18  -ro  29  — 1-5  10  —  ro 

8  — *  19  —ro  30  —15  11  —  2x> 

*  No  observation  taken  on  tfrese  days. 


520  Lieut.-Qen.  Tennant,  Orbit  of  Comet  Boss.        xlyii.  8. 


1887.  sees.  1887.  sees.  1887.  sees.  1887. 

May  12     —  2*0        May  20     —  2*0        May  27     —  2*o  Jane  3    —  ro 

13  — 2*o  21  —20  28  —20  4  -ro 

14  -20  22  — 2*0  29  —  ro  5  -co 

15  -2*o  23  —20  30  —1*0  6  -0*0 

16  —20  24  — 2*0  31  —20  7  -0*0 

17  -20  25  —  2*0        June  1  —  ro  8  +it> 

18  —20  26  -*  2  —  ro  9  +07 

19  —20 

An  inspection  of  these  figures  will  show  that  on  March  29  the 
clock  was  exactly  to  Greenwich  time,  and  again  on  June  5,  6, 
and  7.  In  the  meantime  it  had  made  small  variations,  its 
greatest  error  having  been  3  seconds  on  April  3.  The  most  re- 
markable part  of  the  table  is  the  period  comprised  between  May 
1 1  and  May  28,  the  clock  having  maintained  an  error  of  2  seconds 
without  any  variation  whatever,  and  on  30  ont  of  the  72  days  its 
error  was  exactly  1  second — but  these  were  not  consecutive  days 
— one  group,  however,  of  10  days  in  succession  being  noted. 

I  believe  this  performance  is  unprecedented,  so  it  may  deserve 
to  be  placed  on  record. 

1887,  June  9. 

P.S. — The  clock  is  still  2  sees,  slow,  no  correction  having  been 
required  np  to  the  present  time,  July  6th. 


Note  on  the  Orbit  of  Comet  Boss  (1883  H-)     By  Lieut-General 

J.  F.  Tennant,  R.E.,  F.R.S. 

Mr.  Bryant  has  pointed  out  two  errors  in  the  "  Comparisons 
of  the  Observations  of  Mr.  Ross's  Comet  (II.  of  1883)  "  w^  mv 
ephemeris,  which  would  considerably  affect  the  last  normal 
place,  and  which,  moreover,  render  the  observations  so  much 
more  accordant  that  it  would  now  be  worthwhile  to  get  normals 
with  more  trouble.  The  gross  result  would  possibly  be  to 
approximate  to  his  orbit,  and  I  hasten  to  recognise  the  defect  of 
that  I  proposed. 

*  No  observation  taken  on  this  day. 


MONTHLY    NOTICES 

OF  THE 

ROYAL  ASTRONOMICAL  SOCIETY. 

Vol.  XL VII.        Supplementary  Number.  No.  9 

The  Sidereal  System,  Revised  in  1887.     By  Maxwell  Hall. 

Ten  years  have  now  elapsed  since  my  article  on  "  The  Sidereal 
System"  appeared  in  vol.  zliii.  of  the  Memoirs  of  the  Royal 
Astronomical  Society,  and  during  this  time  much  work  has  been 
done  in  sidereal  astronomy :  the  annual  parallaxes  of  several 
more  stars  have  been  ascertained  by  different  observers  and 
computers ;  the  velocities  of  stars  along  the  line  of  sight  have 
formed  a  special  branch  of  investigation  at  the  Royal  Observa- 
tory, Greenwich ;  Dr.  Gill,  at  the  Royal  Observatory,  Cape  of 
Good  Hope,  has  found  that  the  parallax  of  about  o"'936  ascribed 
to  the  star  a  Centauri*  by  his  predecessors  Henderson  and 
Maclear  is  a  little  too  large,  and  has  thereby  confirmed  the 
researches  of  Dr.  Elkin  ;  and,  lastly,  the  Greenwich  observations 
show  that  the  radial  velocity  of  Sirius  is  variable, t  and  the  curve 
of  variation  indicates  that  any  constant  part  will  prove  to  be 
small,  so  that  theory  and  observation  agree  in  the  case  of  this 
important  star. 

These  considerations  render  a  revision  of  that  article  highly 
advisable;  and  we  feel  encouraged  to  take  a  somewhat  wider 
view  of  the  system  than  was  possible  in  our  first  attempt ;  for 
we  had  then  but  few  stars  to  deal  with,  and  the  general  assump- 

*  One  of  the  three  stars  employed  in  the  former  determination  of  the 
constants  of  the  system. 

t  Reference  was  made  in  the  first  article  to  an  assumed  variation  in  con- 
sequence of  the  orbital  motion  of  Sirius  as  a  binary  star,  and  the  connection 
requires  special  investigation.  A  note  will  be  found  at  the  end  of  this  article 
respecting  the  curve  of  variation. 

P  P 


5" 


Mr.  Ball,  The  Sidereal  System, 


1LT1I.  9, 


tion  of  circular  motion  round  the  centre  was  absolutely  necessary ; 
but  now  we  may  discriminate,  and  say  that  among  the  elliptic 
orbits  of  the  stare  there  must  be  several  nearly  circular,  so  dot 
by  assuming  them  to  be  truly  circular  the  constants  of  the 
system  may  be  accordingly  determined. 

This  wider  and  doubtless  more  correct  view  of  tbe  sidereal 
system  requires  but  little  change  among  our  former  equations; 
by  means  of  proper  motions  we  mnst  compute  parallaxes  and 
radial  velocities  as  before ;  and  if  in  the  case  of  any  star  the 
difference  between  observation  and  computation  be  large,  or  if 
the  computation  breaks  down  by  assigning  a  negative  parallax, 
the  orbit  cannot  be  circular  and  the  star  cannot  assist  na  hi  the 
determination  of  the  constants  of  the  system. 

But  before  dismissing  such  a  star  we  may  first  ascertain 
whether  its  orbit  be  slightly  or  highly  elliptic,  for  while  we  are 
prepared  to  admit  into  the  sidereal  system  a  large  proportion  of 
moderately  elliptic  orbits,  a  preponderance  of  highly  elliptic 
orbits  would  throw  great  doubt  upon  our  investigations. 

There  will,  therefore,  be  three  classes  of  orbits :  those  which 
are  either  circular  or  nearly  so,  those  which  are  moderately 
elliptic,  and  those  which  are  highly  elliptic. 

Stars  which  move  in  the  last  class  of  orbits  will  generally 
have  large  proper  motions ;  and  that  such  stars  should  have  been 
selected  for  observation  of  annual  parallax  may  be  regarded  as 
unfortunate  for  our  problem,  for  we  have  thus  forced  upon  us,  as 
it  were,  an  undue  proportion  of  stars  whose  abnormal  velocities 
and  orbits  must  always  distract  our  attention. 

Let  us  now  consider  the  motion  of  a  star  in  the  plane  of  its 
elliptic  orbit  about  the  centre,  C. 


Let  at,'  and  V  *  be  the  semi-major  and  semi-minor  axes  C  A 
and  C  B ;  and  taking  these  rectangular  axes  as  the  axes  of 
Cartesian  co-ordinates,  we  have : 


of  epice  in  quantities  marked  with  these  suffixes  U  ttas  dii- 
whono  parallax  is  l";  in  all  other  quantities  the  unit  is  the 


•  The  unit 
tanee  of  a  star  whose  paralh 
mssn  distance  of  the  Earth  from  the  Sun. 


Sup.  1887.  Revised  in  1887.  523 

(ft)'-w-i/>; 

and 

■^-FC^  +  ^-r,") .    (V). 

where  F,  v,  and  r0  have  the  same  significance  as  in  the  original 
article. 

Again,  let  ty  be  the  angle  AGS,   or  the  eccentric  anomaly; 
then 

—  --^.a/sin*;  ^=^F.  b.'cos*; 

so  that  if  h  be  twice  the  area  swept  over  by  the  radius  vector  in 
the  unit  of  time, 


and  the  period  of  revolution  is 

SF .  sin  i"' 

Now  let  t  be  the  angle  between  .the  radius  SC  and  the 
direction  of  motion  of  the  star ;  then 

vcoai=~ (VI) 

at 

and 

h  =  vrB)U  i, 

so  that 

vr98mi=a9'b9'SF (VH) 

Equation  (V)  can  be  rendered  more  convenient  for  our 
present  purposes.     Let 

then 

t*«Fra2  +  A»* (i3) 

and  in  the  case  of  the  solar  orbit, 

V*  =  FR#t+AV«. 

Bnt  we  shall  still  consider  the  solar  orbit  to  be  circular,  as  in 
the  former  article,  although  indeed  we  recognise  the  necessity  of 
determining  its  ellipticity  at  some  future  time;  therefore  we 
shall  put  A=o. 

p  p  2 


524  %£r.  Hall,  The  Sidereal  System,  xlyii.  9, 

Substituting  for  the  equations  (I)  and  (II)  in  the  former 
article  in  (13),  we  have 

^*Y  +  2aV^  +  (c«-ir\r«)p0»  +  2V(ft-HnV)p0=A««     .    .    .    (14) 

Again,  for  elliptic  orbits,  equation  (III)  in  the  former  article 
becomes 

|(H+iv0)+p#(K+anV)  +  rv=nr0g; 
and  remembering  that 


rv=^=o, 

dt 


we  have 


J(H  +  Ilpb)  +  p0(K+anV)  =  nreg (15) 

Now  when  both  p0  and  -f  are  known,  of  course  At;*  becomes 

dt 

known  from  (14),  and  -^  from   (15).      When  only  p0  or  -jt 

dt  dt 

is  known,  At>*  is  indeterminate;  but  in  many  cases  we  may 
assign  to  Av2  its  lowest  value,  so  that  the  quadratic  equation  may 
have  possible  and  equal  roots,  or  so  that  the  resulting  value  of 

S-  from  (15)  may  be  fairly  in  accordance. 

Thus  no  value  of  Av2  can  be  assumed  in  (14)  which  would 
make  cos  t  in  (VI)  greater  than  unity ;  and  no  value  of  Av* 
should  be  assumed  in  (14)  which  would  make  cos  i  unnecessarily 
large. 

Again,  when  Av2  and  —  are  known,  or  roughly  approximated, 

ALL 

the  corresponding  values  of  r0,  v,  and  i  become  known ;  also 

(<*o'2  +  &o,s)  an(*  ao'W  I  80  *na^  ao  and  W  are  known;  and 
finally  we  have  the  ellipticity  of  the  orbit,  which  is    ■ 


< 


Let  us  take  as  an  example  the  star  17,415  Oeltzen  ;  *  it  was 
shown  that  when  the  proper  motions  of  this  star  are  employed  in 
the  general  formulae,  p.  186  of  the  original  article,  the  result- 
ing parallax  has  a  negative  sign ;  consequently  the  orbit  of  this 
star  cannot  be  circular. 

The-  observed-  parallax  is  o''*247 »  therefore  p0  is  4*05,  and 
equation  (14)  becomes 


so  that 


(g)\  .6-3^-847. 

(g  +  8IS)5=AB.-,8-3. 
*  No.  67  in  the  following  tables. 


Sup.  1887.  Revised  in  1887.  525 

Consequently  the  least  possible  value  of  At'2  is  +18*3 ;  and 

then  _£  becomes  —8*15. 

dt  ° 


Substituting  these  values  of  p0  and  -£  in  equation  (15),  we 

CLv 


Bnt  r0  =149  from  (I)  ;  so  that 

nrt  =  0  99, 
and 

,    m  +  6O. 

<Lt 

Again,  from  (II)  or  (13),  t,=  io*7;  so  that  from  (VI), 
cos  t  =  0*56 ;  consequently  while  Av2  indicates  a  very  small 
ellipticity,  cos  i  indicates  a  much  larger  one. 

Let  us  therefore  assume 

At*=  + 1 18-3; 
then 

g~  +  r85,    J-«7.    t-147. 

and 

cos  i  =  o  18, 

so  that 

•  -8o'. 

Now,  while  we  cannot  say  which  of  these  two  solutions  is  the 
more  correct,  we  prefer  the  latter,  and  place  the  star  17*415 
Oeltzen  among  those  of  the  second  class  whose  orbits  are 
moderately  elliptic. 

.    Proceeding   with  the  latter  solution,  (a</*  +  W2)  =  71 461, 
aQ'b0'  =.  32623  ;  a0'  =  224,  b0'  =  146 ;  and  the  ellipticity  =  0*35. 

Let  us  take  as  another  example  the  star  1830  Groombridge* ; 
when  the  proper  motions  of  this  star  are  employed  in  the  general 
formulae,  the  resulting  parallax  becomes  far  too  large,  and  there- 
fore the  orbit  of  this  star  cannot  be  circular. 

The  observed  parallax  may  be  taken  as  o"*i45  ;  therefore  p0 
is  6*90;  and  equation  (14)  becomes 

so  that 

Ai^-2459. 


(*♦*»)' 


Consequently  the  least  possible  value  of  Av3  is  +  2459  ;  and 

then 

dp 

*  No.  62  in  the  following  tables. 


526  Mr.  Hall,  The  Sidereal  System,  XLyu.  9, 

Substituting  these  values  of  p0  and  ?/   in  equation  (15)  we 

at 

bo  that 

and  as  v  =  51,  cos  t  =  0*76,  and  t  =  40°*5. 

The  orbit  of  the  star  1850  Groombridge  is  therefore  highly 
elliptic  ;  and  proceeding  numerically ,  a0'  =  774,  60'  =  98,  and  the 
ellipticity  =  ©'87. 

Remembering  that  the  radius  of  the  solar  orbit  was  found  to 
be  150,  it  appears  that  the  semi-major  axis  of  this  star  is  about 
five  times  as  large;  and  in  the  solar  system  we  are  well 
acquainted  with  such  relations  between  planetary  and  cometary 
orbits. 

The  following  table  requires  but  little  explanation ;  the  stars 
are  arranged  according  to  magnitude  ;  the  magnitudes  given  are 
for  the  most  part  the  means  of  the  results  found  by  Professors 
Pritchard  and  Pickering ;  the  Bight  Ascensions  are  given  in  time 
to  the  nearest  second,  but  in  the  calculations  they  were  previously 
expressed  in  arc  to  the  nearest  minute ;  the  columns  "  P.M.  in 
R.A.  "  and  "  P.M.  in  N.P.D."  give  the  proper  motions  in  Right 
Ascension  and  North  Polar  Distance  respectively,  and  the  latter 
have  been  taken,  when  possible,  from  the  papers  of  Professors 
Main  and  Stone  in  vols,  xix.,  xxviii.,  and  xzxiii.,  of  the  Memoirs  of 
the  Royal  Astronomical  Society  ;  and  a  list  of  the  proper  motions 
taken  from  other  authorities  will  be  found  at  the  end  of  this  article, 
together  with  notes  on  the  annual  parallaxes  and  radial  velocities 
which  have  been  adopted. 

It  will  be  noticed  that  instead  of  merely  indicating  to  which 
class  the  orbit  of  any  star  belongs,  the  adopted  values  of  Av8  and 

flr0    ~  have  been  tabulated  ;  when  an  orbit  is  assumed  to  be  cir- 
dt 

cular,  these  values  are  of  course  zero ;  when  an  orbit  is  assumed 

to  be  elliptic  the  values  given  are  those  which  were  roughly 

adopted  as  previously  explained.  • 

It  will  be  convenient  to  reproduce  the  formulas  given  in  the 

first  article,*  p.  186,  and  to  add  those  required  for  elliptic  orbits. 

Formulas. 

B    -North  Polar  Distance) 

_.  ,  .  f  of  a  star,  Jan.  ro,  1850 ; 

<p  »  Right  Ascension         ; 

80  —  Annual  proper  motion  in  $  \ 

I  in  seconds  of  arc ; 
ty— Annual  proper  motion  in  <p  J 

*  A  small  list  of  errata  in  that  article  will  be  found  in  the  Monthly  Notice*, 
vol.  zxxix.  p.  133. 


Sap.  1887.  Revised  in  1887.  5*7 

v  =  Annual  parallax,  in  seconds  of  arc ; 
f%  a  Distance  in  sidereal  units  -  - ; 

*£- = Annual  change  in  distance,  taking  the  radius  of  the  Earth's  orbit  as  the 
at 

unit  of  space. 

/  aginlcos^,        Bl  =nWcos<?>— raty, 
t»  -  sin  0  sin  <?>,        Zm  =  nt$B\n<p  +  l$<p, 
ft  — cos  0,  &»  =  — sin0M. 

a  =  Ja  +  m/i  +  nv,  log  X  =  —9*16642, 

6-xW  +  /*5m  +  y8»,       log  m*  -Q'^SS0- 
e*»«2  +  O0i2  +  o,»,f  log  r-  +  9743&X 

log  L=  -9"946oi, 
logM  =  -915806,   . 
log  N  =  -964992. 

^br  Circular  Orbits. 

K  +  aTlV , 
w« ; 

logn   =  782282, 
e»+tt*_n*V2      lognV=  882034, 


2  V(au- 6 +  HnV)'  log  2V  =1129855, 

n*v*=  0004. 

dp u 

di~     w 

Far  Elliptic  Orbits. 

(*tY + 2dV  *£ + (c*-  n2V)p0« + 2V(6HnV)Po  -  At-» 
g  (H  +  nP.)  +  ,.(K  +  anv)  =  nr.  * ; 

or  more  simply 

log  2R0=  12-47821, 
t/cos»=~.  log   F  =   764068; 


dt 


Re*  =  22613, 
Vs  =  98-9. 


5*8 


Mr.  Hall,  The  Sidereal  System, 


xlvil  9, 


No. 

Star 

M 

R.A.  : 

[850 

P.M.  in  R.A. 

N.P.D.  1850 

P.M.  in 
NJJ) 

I 

a  Canis  Maj.  (Sirius) 

—  1-2 

h    m 

6  38 

6 

32 

8 
-0035 

0        / 

106  31 

+  1*24 

2 

a  Argus  (Canopus) 

-0-4 

6  20 

37 

—  0  002 

H2  37 

-0-03 

3 

a  Centauri 

oo 

14  29  27 

—  0*484 

150  13 

-075 

4 

a  Bootis  (Arcturus) 

o*o 

14    8 

49 

—  0-079 

70    2 

+  T93 

5 

a  Aurigae  (Capella) 

O  I 

5    5  37 

+  0008 

44  10 

♦0-43 

6 

a  Lyra  (Vega) 

0'2 

18  31 

51 

+  0*017 

51   21 

-0-28 

7 

0  Ononis  (Eiffel) 

0*2 

5    7 

20 

—  OOOI 

98  23 

+0*02 

8 

a  Canis  Min.  (Procyon) 

o-5 

7  3i 

27 

—  0-048 

84  24 

+it>8 

9 

a  Orionis 

0*9 

5  47 

3 

+  0*001 

82  38 

0*00 

10 

a  Aquilse  (Altair) 

10 

19  43 

28 

+  0-036 

81  32 

-0-38 

ii 

0  Centaari 

IO 

13  53 

17 

— o-oio 

149  39 

+0-05 

12 

a  Tauri  (Aldebaran) 

II 

4  27 

19 

+  0-004 

73  48 

+017 

»3 

a  Virginia  (Spica) 

VI 

13  17 

18 

-0005 

100  23 

+0*04 

14 

8  Gemin.  {Pollux) 

12 

7  36 

8 

—0049 

61  37 

+0-06 

15 

a  Leonis  (Regulus) 

i  "3 

10    0 

23 

—0019 

77  18 

-o*oi 

16 

a  Cygni               • 

»"4 

20  36 

19 

—0002 

45  15 

coo 

17 

a  Gemin.  (Castor) 

""5 

7  25 

1 

—0013 

57  47 

+0*08 

18 

«  Unse  Majoris 

1-8 

12  47  25 

+0013 

33  14 

+0-05 

19 

a  Persei 

i-9 

3  13 

38 

+  0-002 

40  41 

+0-05 

20 

/3  Tauri 

i  "9 

5  16 

49 

+  OOO3 

61  31 

+  0'20 

21 

a  Andromedse 

2*1 

0    0 

39 

+  0009 

61  44 

+  015 

22 

0Ceti 

2"I 

0  36 

3 

*  0*013 

108  49 

-002 

23 

a  Ursse  Min.  (Polaris) 

2  1 

1     5 

1 

+  0065 

1  29 

o-oo 

24 

a  Arietis 

21 

1  58 

44 

+  0012 

67  15 

+0*15 

25 

7  Cassiopese 

2'2 

0  47  42 

—  o-oo8 

30    6 

-0*02 

26 

y  Leonis 

2*2 

10  11 

42 

+  0019 

69  24 

+0-15 

27 

(  Ursae  Majoris 

2*2 

13  17  53 

+  0017 

34  17 

+  0*04 

28 

a  Ophiuchi 

2'2 

17  27 

58 

+  0004 

77  20 

+  0-20 

29 

a  Corona 

2*3 

15  28 

20 

+  0-009 

62  47 

+0-07 

30 

7  Cygni 

23 

20  16 

51 

o-ooo 

50  13 

-002 

3i 

£  Cassiopese 

2'4 

0    1 

12 

+  0*063 

3i  4i 

+019 

32 

/3  Urese  Majoris 

2'4 

10  52  45 

+  o-oio 

32  49 

-ot>3 

33 

>  Ursae  Majoris 

24 

11  45 

55 

+  001 1 

35  28 

0*00 

34 

7  Draconis 

24 

17  53 

8 

ocoo 

38  29 

+0*04 

Sup.  1887.  Bevised  in  1887.  539 


Observed 

l 

Aaramed 

Computed 

» 

Po 

4      • 

dt 

Av 

nr»5? 

w 

p. 

dp 
dt 

Aw 

dt 

u 

// 

It 

0268 

373 

-  21? 

O 

0 

0'2I0 

476 

-    0'5 

+0058 

-1*6 

0-028 

357 

•  •  • 

-    125 

+ 

75 

■  •  • 

■  •  • 

+  19*2 

•  •  • 

•  •  • 

0765 

i-3" 

•  •  ■ 

0 

0 

O-909 

I'lO 

-    2*6 

-0144 

•  •  • 

0132 

7-52 

-15-9 

O 

0 

OI88 

533 

-145 

—0056 

-1*4 

0-046 

21-7 

+  90 

0 

0 

0'029 

34'4 

+  87 

+  0*017 

*-o*3 

0128 

781 

—  124 

0 

0 

0*069 

145 

-18-7 

+  0-059 

+  6*3 

•  •• 

•  •  • 

+  6*6 

-  75 

— 

3"i 

OOI5 

66-7 

•  •  • 

B   ■    • 

••• 

0123 

813 

+  53 

0 

0 

OO74 

135 

+   8-6 

+  0-049 

-33 

•  •  • 

•  •  • 

+   9*3 

0 

0 

0:017 

600 

•H4"4 

•  •  • 

-51 

0*181 

5*53 

-  8-6 

6 

0 

0*146 

687 

-141 

+  0035 

+  55 

00? 

large 

••  • 

0 

0 

OOOI 

701 

+   22 

00? 

•  •  • 

•  •■ 

•  • 

+  II'O 

0 

0 

OOl8 

568 

+  142 

B   •    • 

-32 

•  •  ■ 

•  •  • 

-  41 

0 

0 

OOOI 

948 

-  56 

•  •  • 

+  i*5 

•  f  • 

■  •  ■ 

—  II'O 

+  196    ■ 

-  103 

0-060 

166 

•  •  • 

•  •  • 

■  •  • 

•  »• 

•  *  • 

+  3*5 

0 

0 

0020 

50-4 

+  96 

•  *  ft 

-61 

00? 

large 

— 117 

0 

0 

0-004 

282 

-149 

o*o? 

+  3*2 

0198 

505 

+  6*i 

-   128 

— 

0*9 

•  •  • 

B   •  • 

*  •  • 

•  •• 

•  •  • 

•  ■  • 

•  •• 

+   4'l 

+  168 

+ 

6-4 

0019 

SIS 

•  •  • 

•  •  • 

•  •  • 

•  •  • 

•  •  • 

—  96 

♦   5o-3 

— 

62 

o-ooj 

2O4 

•  •  • 

•  •  • 

•  •  • 

•  •  • 

•  •• 

-  4*9 

+   148 

+ 

30 

0026 

380 

•  •• 

•  •  * 

•  •  • 

•  •  • 

•  •  • 

-  97 

+  49"  1 

+ 

5'i 

0017 

59*0 

•  *  • 

•  •  • 

•  •  ■ 

•  •  • 

•  •  ■ 

-ii-5 

+  206 

+ 

45 

0034 

295 

•  •• 

•  *  • 

•  •  • 

0-043 

233 

•  •  • 

0 

0 

0068 

133 

—  126 

+0035 

•  •  ■ 

■  •  • 

•  »  • 

-  4'9 

+     i*5 

+ 

5"i 

0030 

330 

•  •  • 

•  •  • 

■  •  • 

•  •  • 

•  •  • 

-  67 

+ 100 

+ 

50 

0022 

43'6 

•  •  • 

•  •  • 

•  •  • 

•  •  • 

•  •  • 

• 

—  90 

+  185 

+ 

o*6 

0034 

290 

•  •• 

•  •  • 

•  •• 

tW 

•  *• 

+   67 

+  200 

+ 

36 

0-038 

26*0 

•  •  • 

•  •  • 

•  •  • 

•  •• 

•  •• 

-  3  8 

+ 100 

+ 

91 

0012 

870 

•  •  • 

•  ■  ■ 

•  •  • 

■  •  ■ 

•  «  • 

+   7*2 

+  260 

+ 

5"  1 

0-036 

28'I 

•  •• 

•  •  • 

•  •  • 

•  •  • 

•  «• 

-  46 

-  154 

+ 

47 

0010 

970 

•  •  • 

•  •  ■ 

•  •  • 

•  •  ■ 

•  •« 

-  0*4 

-     69 

— 

1-9 

0065 

154 

■  •  • 

•  *  • 

•  •  » 

•  •  • 

•  •• 

+   79 

+  230 

+ 

55 

0-017 

6o-o 

•  •  • 

•  •  • 

m  •  • 

•  •  • 

•  •  ■ 

+  6*o 

+  200 

+ 

*5 

0016 

61 '0 

•  •  ■ 

•  •  « 

■  •  • 

0092 

io*9 

-  *"5 

—     o*6 

+ 

0'5 

0150 

667 

o*o 

■  •  • 

•  •• 

53<> 


Mr.  Hall,  The  Sidereal  System, 


xlvil  9, 


No.  Star 

35  c  Pegasi 

36  a  Pegasi 

37  a  Gephei 

38  TPegaai 

39  y  Virginia 

40  y  Aqoilse 

41  8  Cygni 

42  jB  Cygni 

43  C  Aqnil® 

44  1  Ursa  Majoris 

45  &  Androned© 

46  i»  Casaiopefe 

47  7°  P*  Ophiuchi 

48  e  Eridani 

49  0*  Eridani 

50  9  Una  Minoria 

51  <r  Draconis 

52  ( Toucani 

53  6l  Cjfi^i 

54  m  Cassiopese 

55  « IQdi 

56  Cephei  51  (He v.) 

57  85  Pegasi 

58  3077  Bradley 

59  6  B.  Cygni 

60  Piazzi  III.  242 

61  16 1 8  Groombridge 

62  1830  Groombridge 

63  21,185  Lalande 

64  9352  Lacaille 

65  34  Groombridge 

66  21258  Lalande 

67  1 74 1 5  Oeltzen 

68  1 1677  Geltzen 


If 

BJL  1850 

PJtlnBJL. 

NJ»J).  1850 

PJLU 
KJJ). 

24 

h    m 
21   36 

s 
49 

8 
+  0003 

8049 

(TOO 

2-4 

22  57 

18 

+  0-003 

75  36 

+0*02 

2*6 

21    15 

0 

+  0-02I 

28    3 

-o-oi 

2*8 

0    5  31 

O'OOO 

75  39 

+0-02 

28 

12  34 

4 

-0-037 

90  38 

+Ot>5 

28 

19  39 

8 

+  0'OOI 

79  45 

0t)0 

2'9 

19  40  17 

+0*006 

45  14 

0*00 

30 

19  24  40 

— 0*002 

62  21 

0*00 

3"  1 

18  $8 

31 

—0*006 

76  21 

+<ro7 

32 

848  55 

—0*047 

41   22 

+  0-28 

33 

0  31 

19 

+0-009 

59  58 

+  0*10 

3*5 

0  40 

3 

+0132 

32  59 

+0-49 

43 

17  57  53 

+0-015 

87  28 

+  1-12 

4*4 

3  13  55 

+0-270 

133  39 

-0-75 

44 

4    8 

22 

— 0148 

97  53 

+  346 

44 

|8  20 

44 

+  0*048 

3  24 

-0-03 

47 

19  32 

38 

+0*096 

20  36 

+  179 

50 

0  12 

12 

+0*273 

155  45 

-116 

50 

21    0 

II 

+  0*342 

5i  59 

-311 

52 

0  58 

19 

+  0386 

35  49 

+  1-56 

52 

21  51 

51 

+  0-480 

147  24 

+2*60 

5*3 

6  28 

33 

—0*027 

2  45 

+0*08 

5-8 

23  54 

21 

+  0*067 

63  43 

+o?5 

59 

23    6 

4 

+  0250 

33  40 

-0-27 

60 

19    8 

12 

-0015 

40  25 

-0-62 

6'5 

3  57 

35 

+  0-017 

52  20 

+0-15 

65 

10    2 

6 

-0*139 

39  48 

+050 

6'5 

11  44 

19 

+  0344 

51  12 

+  570 

75 

10  55 

8 

—0*044 

53    2 

+4-66 

7*5 

22  56 

10 

+0567 

126  43 

-1*3* 

80 

0    9  52 

+  0*255 

46  50 

-o-37 

8'5 

10  58 

0 

-0386 

45  42 

-136 

9-0 

17  37 

17 

—0-070 

21  33 

+  1-20 

9*5 

11  12 

0 

-0507 

23  20 

.0*21 

Compute 

d0 

Aw 

dp 

dt 

dt 

•  •  •  ••  • 


•*•  • • • 


Sup.  1887.  Revised  in  1887.  S31 

Obeerred  Assumed 

P»  £  At;  Tlrodt  vr  pe 

—  49  o  o  0009  106  —  8-2  ...        +3*3 

—  8*8  o  -  0*9  0006  155 

—  U*4  o  o  0*016    637  —142  ...         — 0'2 

—  8*i  + 136  +    i-2  0008  129 
+  8-6  +  31*3  +  93  0*060     167 

—  8-4  o  o  0-013    75°  ""I55  •■•         +  7'1 

—  5*1  —  60-9         o-o  0012    8o*o 

—  4-9  +105  +  77  0008  119 

—  7'9  —  37"6  +  7°  0*020    500 

0133      7-52        ...  o  —  0-9  +  70 

— 14*0  +143  +  97  0023    43-2 

0*154      6-49        ...  o  o  0*065    T5"3  ~"  4*4       +0-089 

o-i6o      625        ...  o  o  01 1 1      900  -171       +0049 

°"I36      7'35        ...  o  o  0328      305  +17-6      —0-192 

0-194      5'i6        •••  +4*4  —  28  +  86 

0-034    29-4  ...  o  o  0015    657  — 12*4       +0019 

0-255      3-92        ...  +  43-6  +    17     .       —  7*6 

0-057     17-5  ...  +795  -22-8  +  58 

0*441      2-27        ...  o  o  0-422      237  —105       +0019 

0*342      2-92        ...  o  q  0199      502  —  25       +0143 

0-215.    4"^5        •••  +100  -  0-5  ...  ...  +108 

0-027    37'Q  •••  o  o  0-037    270  +16      —0010 

0*050    20-0  ...  o  o  0071     140  —  20      —0021 

0-185      5*4°        •••  o  o  0126      7-91  —  5-8       +0-059 

0*482      2*07        ...  o  +  01  00 

0*016    625  ...  o  o  0028    35*0  +  89      —0012 

0-322      3-11        ...  o  -  0*3  +  58 

0-145      6-90        ...  +2459  +392  -  42 

0-501        2-00  ...  +       70  +    2'7  —12*2 

0*285      351        •••  +1000  —  6-i  —i9'5 

0*307      3-26        ...  o  o  0195      514  —  10       +0112 

0"26l        383  ...  +    800  —    4*0  +  22*1 

0-247      4-05        ...  +   118  +  27  +   r8 

0*256      3-91        ...  + 1600  —  2-o  -45*9 


532  Mr.  Hall,  The  Sidereal  System,  ilvil  9, 

This  table  contains  the  computations  for  all  stars  whose  an- 
nual parallaxes  have  been  ascertained,  and  Of  all  stars  whose  radial 
velocities  have  been  determined  at  Greenwich  with  a  moderate 
degree  of  certainty. 

With  regard  to  the  Greenwich  observations  of  radial  velocities 
pnblished  in  the  Monthly  Notices  of  the  Royal  Astronomical  Society, 
vols,  xxxvi.,  xxxvii.,xxxviii.,  xli.,  xlii.,xliii.,xliv.,  and  xlv.,  the  stars 
were  divided  into  three  classes :  ( 1 )  those  whose  radial  velocities  can 
be  depended  on  in  consequence  of  the  number  and  the  agreement  of 
the  observations ;  (2)  those  whose  radial  velocities  are  less  certain ; 
and  (3)  those  whose  radial  velocities  cannot  be  depended  on  in 
consequence  of  the  Bmall  number  of  the  observations  or  of  want 
of  agreement  among  them. 

Stars  of  the  third  class  have  not  been  considered  in  the 
above  table;  and  indeed  many  stars  of  the  second  class  have 
radial  velocities  assigned  to  them  which  are  far  from  reliable. 

Let  us  take  as  an  example  the  star  c  Ursce  Majoris,  and  collect 
all  the  observations  of  its  radial  velocity  published  in  the  volumes 
referred  to  above : 

Date. 
1877,  May    2 

1879,  May  21 
„     June    9 

1880,  May  22 
„    June   4 

1883,  July  13 
„    Aug.  21 

Mean 

And  dividing  by  2*9  we  have  J-  =  +4'i  as  adopted  in  the 

at 

table  ;  and  consequently  we  have  an  elliptic  orbit  for  the  star. 

But  iu  vol.  xlvi.  of  the  Monthly  Notices,  published  after  the 
commencement  of  the  present  revision,  we  find  that  on  Aug.  10, 
1885,  a  radial  velocity  of  —41*7  miles  per  second  was  observed 
at  Greenwich ;  so  that  e  Ursce  Majoris  should  be  placed  in  the 
third  class  at  present,  and  rejected. 

This  latter  radial  velocity  has,  however,  been  confirmed  by 
Mr.    G.   M.   Seabroke  at    Rugby,  who  found  —32  miles  per 

second  (Monthly  Notices,  vol.  xxxix.,  p.  453)  ;  so  that  j£  may  be 

about   —8  instead  of  +4*1.     Now  if  the  orbit  of  «  Ursce  Majoris 
be   assumed   circular,   we   would   have  «r=o//,o44,  p0=22*8, 

and  ??  =  —  7*4 ;  and  it  thus  appears  that  the  orbit  of  this  star 
at 

is  most  probably  circular,  although  our  systematic  computations 

require  us  to  assume  it  to  be  elliptic. 


Miles  per  sec 

+   59 

+  24*4 

+   9*8 

+    0*2 

+  154 

+    21 

+  24*8 

+  118 

Sup.  1887.  Revised  in  1887.  533 

This  example  has  been  given,  not  to  detract  from  the  value 
of  the  Greenwich  observations  of  radial  velocity,  bat  to  point  ont 
as  clearly  as  possible  that  most  of  the  res  alts  which  have  been 
obtained  up  to  the  present  time  cannot  be  regarded  as  even  ap- 
proximately final,  and  must  therefore  be  accepted  with  great 
caution. 

There  is  therefore  no  reason  to  be  dissatisfied  with  the  results 
of  oar  systematic  computations  given  in  the  table  above ;  in  the 
case  of  37  stars  observed  for  annual  parallax,  21  have  circular, 
1 1  have  moderately  elliptic,  and  5  have  highly  elliptic  orbits  ;* 
in  the  case  of  40  stars,  including  Sirius>  observed  for  radial 
velocity,  14  have  circular,  24  have  moderately  elliptic,  and  2  have 
Highly  elliptic  orbits.f 

It  will  be  noticed  that  stars  observed  for  radial  velocity  do 
not,  on  the  whole,  give  such  good  results  as  stars  observed  for 
annual  parallax ;  one  reason,  that  of  uncertainty  of  observation, 
has  just  been  discussed ;  another  reason  will,  perhaps,  be  found  in 
the  uncertainty  attending  the  very  small  proper  motions  attri- 
buted to  many  of  these  stars.  In  the  first  article  it  was  considered 
right  to  omit  all  stars  which  have  very  small  proper  motions ; 
but  this  restriction  was  removed  in  the  computations  above,  and 
the  results  apparently  justify  its  removal,  as  we  cannot  attribute 
to  chance  the  circularity  of  the  orbits  of  a  Orionisy  a  Cygni, 
t  Pegasi,  and  y  Aquilce.  The  uncertainty,  however,  may  exist, 
although  we  are  not  at  present  entitled  to  reject  stars. however 
small  their  proper  motions.  And  a  third  reason  will  probably 
be  found  by  combining  the  enormous  distances  of  many  of  these 
stars  with  our  present  imperfect  knowledge  of  the  sidereal  sys- 
tem. Therefore,  by  taking  into  consideration  all  the  sources  of 
error,  we  have  no  reason  to  be  dissatisfied,  as  already  said,  with 
the  general  results  we  have  obtained. 

In  an  article  "  On  the  Theory  of  the  Sidereal  System,"  which 
was  written  by  Mr.  W.  £.  Plummer,  and  which  appeared  in  Coper- 
nicus, No.  15,  March  1882,  we  find  that  the  formula  of  the  original 
article  were  applied  to  stars  whose  radial  velocities  had  been  ob- 
served at  Greenwich  between  the  years  1875  an0-  1880.  There 
were  90  of  these  stars,  but  the  greater  portion  were  rejected  on 
account  of  their  small  proper  motions,  and  a  few  were  omitted 
as  having  been  already  examined  in  the  original  article,  so  that 
but  40  remained  for  computation. 

Now  of  these  40  stars,  26  still  belong  to  what  we  have  termed 
the  third  class,  1 1  belong  to  the  second  class,  and  only  3  to  the  first 
class ;  and,  rejecting  the  third  class  altogether,  we  find  consider- 
able differences  between  the  remaining  radial  velocities  obtained 

at  that  and  the  present  time.     For  instance,  -?  for  /3  Cassiopece 

was  then  +128;    it  is  now  —0*4 ;   and  ??  for  a  Persei  was  then 

at 

*  Nob.  2,  52,  62,  64,  and  68.  f  No«.  39  and  43. 


534  Jtfr-  2fatf,  The  Sidereal  System,  xlvii.  9, 

+  7*9;  it  is  now  —96.  In  short,  the  data  were  not  reliable, 
and  disappointment  was  the  consequence. 

But,  on  the  other  hand,  I  have  to  thank  Mr.  Plummer  for 
pointing  out  an  error  in  the  computation  of  21 185  Lalande 
given  in  the  Monthly  Notices,  vol.xxxix.  p.  132,  which  has  of  coarse 
been  corrected  in  the  table  above,  and  for  calling  attention  to 
the  proper  motions  of  the  stars  generally.  As  already  stated, 
Mr.  Main's  proper  motions  have  been  systematically  employed  in 
the  original  and  present  articles ;  bnt  Mr.  Plnmmer  used  proper 
motions,  or  the  means  of  proper  motions,  given'  by  various 
authorities.  By  such  procedure  we  might  easily  have  found 
proper  motions  to  suit  such  stars  as  y  Draconis,  1  Ursae  Majorit, 
6  B.  Cygni,  16 18  Oroombridge,  and  others,  whose  orbits  are  now 
very  slightly  elliptic,  and  thus  have  largely  increased  the  nnm. 
ber  of  circular  orbits.  What  we  really  require  is  a  careful 
determination  of  the  proper  motions  of  all  stars  whose  annual 
parallaxes  and  radial  velocities  have  been  observed ;  and  until 
this  be  done  we  shall  adopt  Mr.  Main's  proper  motions  as  here- 
tofore. 

We  have  now  passed  through  our  tentative  stage,  and  found 
a  system  which  satisfies  our  principal  stars,  Sirius,  Arcturus, 
Capella,  Vega,  Procyon,  and  Altair  in  both  distant  and  radial 
velocity ;  which  satisfies  a  number  of  stars  in  either  distance  or 
radial  velocity ;  and  which,  upon  the  assumption  of  moderately 
elliptic  orbits,  satisfies  the  rest  of  the  stars  subjected  to  computa- 
tion with  but  few  exceptions. 

It  still  remains  to  form  equations  of  condition  in  order  to 
find  corrections  to  the  adopted  values  of  L,  M,  N,  n,  and  V ; 
there  will  be  twenty-one  such  equations  depending  upon  annual 
parallax,  and  there  will  be  fourteen  depending  upon  radial 
velocity. 

In  the  original  article  the  formation  of  such  equations 
depending  upon  annual  parallax  was  folly  discussed,  and  we 
need  only  reproduce  the  formulas. 

Let 

H  +  Ity,      * 

HS«;k,"~-,orw6s 

U  -  Bl  +pBm  +  qBn — u(l + jm  +  j») ; 
^«V(a«-6  +  HnV)  +  «p0«n; 

^  =  w(a«-6  +  HriV)  +  «Sn+Vn«+wHllV; 

CL  V 


Sup.  1887.  Revised  in  1887.  535 

*£-8(aV+£)+wVt(H+n*): 


d< 

cU 

d* 

A: 

dh 

=3T; 

C 

ax 

E- 

dn 

wd*  • 

dw 

dm 

dvr 

then 


A  .  AL  +  C.  AV+E.  aii  +  Aw-o, 


is  the  equation  for  the  determination  of  AL,  AY,  and  All,  the 
corrections  which  must  be  added  to  the  adopted  values  of  L,  V, 
and  II,  where  Aw  is  the  difference  between  the  observed  and  the 
computed  parallax.     And  lastly  AM==p  .  AL,  AN=g  •  AL. 

In  order  to  form  similar  equations  depending  on   A-A  the 

dt 

difference  between  the  observed  and  the  computed  radial  velocity, 

since 

do 

— !-mt  —  1 


dt       "*• 


we  have 


but 


solthat 


or 


dp     Aw/  Au\ 

dt      w*  \  Aw/  ' 

A«  __  <?«__  t/p0*n  *. 

Atr     rfw      H  +  npf  ' 
.dp  __  Aw         ttH 

<fc  ~  w2  '  ff+n^' 

«fc «H 

If,  therefore,  in  the  case  of  any  star  we  multiply  A^  by  the 
factor 

w»(H  +  Tip,) 
«H 

we  have  the  equation 

A.AL  +  C.AV  +  E.An  +  A^.'^^l^^o, 

where  A,  C,  and  E  are  to  be  computed  as  before.  This  arrange- 
ment will  permit  the  equations  depending  on  annual  parallax 
and  radial  velocity  to  be  very  simply  treated  together  according 
to  the  method  of  least  squares ;  and  it  will  save  very  much  labour 
when  many  stars  are  employed  which  may  have  been  observed 
for  both  annual  parallax  and  radial  velocity. 

We    thus    obtain    the    following  equations  depending   on 
parallax : — 

*  S«e  original  article,  p.  178. 


536  Mr.  Hall,  The  Sidereal  System,  xlyil  9, 


No. 
1 

-8540 

first  Series. 
AL  +  0*041       AV  +  29*  140 

An  « -0*058 

Wdgl 

3 

3 

+  4747 

+  0-097 

+  8940 

-  +0-144 

3 

4 

-0196 

+  0*019 

+  0873 

■■  +  0*056 

3 

5 

+  0036 

+  O*0O2 

—  0-921 

-  —0*017 

3 

6 

-0063 

+  0006 

-  1796 

«— 0059 

3 

8 

+  0*030 

+  0008 

+  0*240 

-  —0*049 

3 

10 

-0615 

+  0*014 

-  1525 

«  -0*035 

3 

11 

+  0001 

0000 

+  0550 

t-     0000 

1 

16 

0000 

O'OOO 

—  0*842 

-      O'OOO 

1 

23 

+  0021 

0000 

-   11 86 

=  -0*035 

3 

46 

— 0*008 

+  0006 

-  0444 

-  —0*089 

2 

47 

+  0054 

+  0013 

+   2712 

-  —0049 

2 

48 

+  0  106 

+  0032 

—  2120 

=  +0192 

2 

50 

+  0051 

+  0001 

—   1  170 

=  —0-019 

2 

53 

-0345 

+  0042 

—  0*646 

-i  —0019 

3 

54 

-0005 

+  0  020 

~  0471 

=  -0143 

2 

56 

+  0356 

—001 1 

- 19  560 

«  +OOIO 

2 

57 

+  0002 

+  0007 

—  0-520 

»  +0*021 

2 

58 

—0020 

+  0012 

-  0505 

-  -OO59 

2 

60 

+  0053 

+  0002 

—  1-192 

-  +OOI2 

2 

65 

+  0062 

AL  +  0019 

AV-  0890 

An  » -01 12 

2 

And  similarly  we  obtain  the  following  equations  depending 
on  radial  velocity : — 


No. 

Second  Series. 

Weight. 

I 

-8540 

AL  +  0*041 

AV  +  29T40 

An=  +0768 

I 

4 

—0-196 

+  0019 

+  0873 

-  +  0-019 

3 

5 

+  0036 

+  0'002 

—  0921 

-  +0001 

3 

6 

-0063 

+  0-006 

—  1796 

=  -0015 

3 

8 

+  0.030 

+  0*008 

+  0*240 

=  —0044 

3 

9 

+  o*ioo 

+  0001 

—  2000 

•=•  +0-004 

2 

10 

-0*615 

+  0*014 

-  1-525 

«— 0048 

3 

12 

+  0-014 

+  o-ooi 

-  0936 

•=  —  O'OOI 

2 

13 

o-ooo 

0000 

+  0536 

==  —  O'O02 

1 

15 

—  0051 

+  0003 

+   1*450 

«  — 0'020 

1 

16 

O'OOO 

O'OOO 

—  0842 

•=  +0002 

2 

35 

—  0*021 

+0001 

—  0666 

as        O'OOO 

1 

37 

+  0007 

+  0001 

—  0770 

=    0*000 

1 

40 

—0052 

AL     O'OOO 

AV-  1-585 

All  =  +  OOO4 

1 

Sup,  1887. 


Revised  in  1887. 


537 


With  reference  to  the  weights  adopted,  a  weight  of  3  has 
been  given  to  each  star  whose  parallax  is  well  known,  or  whose 
parallax  is  confirmed  by  its  radial  velocity,*  and  to  each  star 
whose  radial  velocity  of  the  first  class  is  confirmed  by  ittf  parallax* 
Again,  a  weight  of  2  has  been  given  to  each  star  whose  uncon- 
firmed parallax  is  less  certain,  and  to  each  star  whose  uncon- 
firmed radial,  velocity  is  of  the  first  class.  And,  lastly,  a  weight 
of  1  has  been  given  to  each  star  whose  parallax  or  radial  velocity 
must  be  considered  uncertain  at  present. 

The  following  table  has  been  drawn  up  according  to  this 
system:— 


/Sirina 
a  CentAuri 
ArcturctB 


Parallax. 


\ 


Capella 

Vega 

Procyon 

Altair 

Polaris 

61  Cygni 


\ 

/Arctium* 
I  Capella 

I  Vega 

Velocity,     j  Procyon 

Altair 


Radial 


Weights, 
2 
V  Cauiopen 

70  p.  Ophiuchi 

e  Eridani 

ft  Vnm  Minoris 

/i  Caasiopeffi 

Gephei  51  (Hev.) 

85Pega«i 

3077  Bradley 

Piani  III.  242 

34  Groombridge 

a  Ononis 
Aldebaran 
a  Cygni 


jB  Centauri 
o  Cygni 


Sirina 

Spica 
Regnlus 
c  Pegasi 
a  Cephei 
7  Aqnilse 


Proceeding  by  the  method  of  least  squares,  the  first  series 
of  equations  are  reduced  to  the  following : — 


+  8629       aL+  0797       AV-1872 
+0*797       AL+  0-1309     AV  + 18*62 

- 1872  AL  +  1862  AV  +  IOOI5 


Alia  +10*81, 

An  =  +  0-093, 
An--  32; 


whence 


aL=»  +0*0158, 
AV-+0380, 
Ana  +000165. 

Substituting  these  values  of  the  corrections  in   the   first 

*  Aa  in  the  case  of  Capella,  where  the  agreement  of  O.  and  C.  in  parallax 
may  be  aaid  to  be  confirmed  by  the  agreement  of  0.  and  C.  in  radial  velocity. 

QQ 


/ 


538  Mr.  Hall,  The  Sidereal  System,  xlvii.  9, 

series  of  equations,  the  sum  of  the  squares  of  the  errors  is 
reduced  from  0*12 1  to  0099. 

Again,  proceeding  by  the  method  of  least  squares,  the  second 
series  of  equations  are  reduced  to  the  following : 

+  767  aL-o'457         AV-242        An-— 632, 

-  0*457       AL+ 00076       AV+ro5       An- +0025, 
—242  aL+i-05  AV+941        An* +232; 

whence 

aL-  -00431, 

AV--1378, 
An-  +001507. 

Substituting  these  values  of  the  corrections  in  the  second 
series  of  equations,  the  sum  of  the  squares  of  the  errors  is 
reduced  from  o  595  to  0*008. 

But  it  is  to  be  remarked  that  the  results  of  the  second  series 
depend  chiefly  on  Sirius;  and  when  —  2*1  was  assumed  as  the 
mean  radial  velocity  of  that  star,  it  was  not  intended  that  the 
assumption  should  have  any  great  weight  in  the  final  equations, 
much  less  that  it  should  greatly  influence  them. 

It  therefore  becomes  necessary  to  remove  Sirius  from  the 
second  series,  when  the  remaining  equations  give  the  fol- 
lowing : 

+  38       aL-oiio     aV+7        An- +0-23, 
— 0110    aL  +  o*oo59    aV— 0*14    An«—  0006, 
+  7  AL-014       AV  +  93       An- +0*9; 

whence 

aL«  +0051, 

AV -+0-063, 

An-  +0-006. 

Substituting  these  values  of  the  corrections  in  the  second 
series  of  equations,  No.  1  being  omitted,  the  sum  of  the  squares 
of  the  errors  are  reduced  from  0*005  *°  °'°°4- 

Lastly,  combining  both  series,  No.  1  being  omitted  from  the 
second  series,  we  have  the  equations 

+  8667    aL  +  0687     aV  - 1865      An  -  + 1 104, 
+0687    aL+  01368    AV+ 18-48     An=+  0087, 
-1865     AL+1848       AV+10108     An--  23; 


whence 


AL-  +0*0194, 
aV-  +0113, 
An-  +0*00315. 


Sap.  1887.  Bevised  in  1887.  539 

Now  the  quantities  to  be  corrected  are:  * 

L-  -08831 
M- -01439 
N-  —0*4466 

V«+9943 

n  «■  +  0*00665 

and  applying  the  corrections  next  above  to  L,  V,  and  II,  and 
determining  the  new  values  of  M  and  N  as  in  the  original 
article,  p.  184,  we  have  as  the  corrected  quantities : 

L--  0*8637,  log  L--  9"93*536 

M-—  0*1670,  log  M-  —  9*22262 

Ke—  0*4756,  log  N-  —  9*67720 

V ■  + 10056,  log  Vs  + 1 1*00243 

n-+  0*00980,      log  n-+  7*99123 

The  centre,  therefore,  lies  in  the  direction  of  the  point  whose 
co-ordinates  for  the  year  1850  are 

e        / 

R.A.        10  56 
N.P.D.        61  36 

This,  point  is  very  near  the  firBt  point  adopted  in  the  original 
article ;  and  it  may  be  said  that  all  the  work  expended  on  the 
system  since  it  was  first  sketched  oat  was  required  for  the 
determination  of  n,  the  annual  parallax  of  the  centre. 

Now  IlV  is  the  angular  motion  of  the  Sun  round  the  centre 
during  one  year,  expressed  in  seconds  of  arc ;  and  as  the  new 
value  of  11 V  is  o" '0985  5,  the  new  length  of  the  Annus  Magnus, 
or  period  of  general  revolution,  is  13,150,000  years. 

Here  we  must  rest  awhile;  annual  parallaxes  and  radial 
velocities  have  agreed  in  giving  almost  the  same  corrections  to 
the  former  values  of  the  constants ;  and  the  question  now  arises 
as  to  whether  the  position  of  the  centre  has  not  been  determined 
with  greater  accuracy  than  the  direction  of  the  Sun's  motion. f 
Of  course  the  time  will  come  when  the  two  problems  must  be 
combined,  and  when  the  assumption  of  the  circularity  of  the 
solar  orbit  must  be  removed  ;  but  as  the  combined  problem  will 
contain  seven  unknown  corrections,  namely  AL,  AM,  AY,  AA, 
All,  AA,  and  Aft,  a  large  number  of  stars  must  be  employed. 

Lastly,  putting  perturbations  aside,  it  cannot  be  assumed 
that  the  law  of  force  holds  good  beyond  a  certain  distance  from 
the  centre ;  the  star-density  on  either  side  of  a  certain  radius 
may  vary  as  much  as  the  star-density  on  either  side  of  the  galactic 

*  Original  article,  p.  185. 

f  The  recent  researches  of  Mr.  Plummer  (Memoir*,  vol.  xlvii.  p.  327)  on  the 
motions  of  southern  stars  have  at  least  removed  the  certainty  assumed  in  the 
original  article. 

QQ2 


54© 


Mr.  Hall,  The  Sidereal  System, 


XLYII,  9, 


plane ;  and,  indeed,  considering  the  complexity  of  the  general 
problem,  we  may  be  well  satisfied  with  the  definite  results  we 
nave  so  easily  obtained. 

Note  I. 

The  proper  motions  employed  in r  this  article  were  taken  from 
the  lists  of  Professors  Main  and  Ston  e  in  the  Memoirs  of  the  R.A.S., 
vols.  19,  28,  and  33,  excepting:— 

No.  Star. 

2  a  Argus 

3  a  Centauri 


Authority. 
Stone,  Mem.,  yoL  42,  p.  135. 


Elkin 

11  $  Centauri  Stone 

48  e  Eridani  Elkin 

49  o«  Eridani  GUI 
52  CTcrocani  Elkin 

55  «Indi 

56  Cephei  51  (Hey.)       B.A.C. 

57  85Pegasi 

58  3077  Bradley 

59  6  B.  Cygni 

60  Piazri  III.  242 


»t 


11 


t> 


it 


11 


11 


48,  p.  14. 
4*i  P.  139. 
48,  p.  175. 

156. 

168. 

119. 


t> 


»i 


»i 


Copernicus,  No.  22,  p.  201. 

Argelander,  Dunsink  Obs.,  Part  V.,  p.  232. 

0.  Strove,  M.  N.%  yol.  41,  p.  36. 

61  1618  Groombridge     Argelander,  Duneink  Obs.,  Part  V.,  p.  187. 

62  1830  Groombridge     Argelander,  B.A.C. 

Lynn. 

Gould,  Mem.,  vol.  48,  p.  140. 
Nature  „        43,  p.  172. 

Lynn,  M.  N.t  vol.  33,  p.  102. 

1*  ii         31*  P*  4*. 

Geelmnyden,  Mtr.  Notch.,  No.  2287. 

Note  IL 

The  following  parallaxes  were  employed  in  the  above  article, 
the  means  of  different  results  being  taken  when  possible : 

Parallax  and  Authority. 

0*23,    Henderson,  Mem.,  vol.  11,  p.  239. 

0*27,   Abbe,  M.  N.t  yol.  28,  p.  6. 

0*193,  Von  Gylden. 

0*381,  Gill  and  Elkin,  Mem.,  yol.  48,  p.  187. 


63  21 185  Lalande 

64  9352  Laoaille 

65  34  Groombridge 

66  21258  Lalande 

67  1 741 5  Oeltten 

68  11677  Oeltzen 


No.  Star. 

I    Sirius 


0*268,  Mean. 


2  Canopus 

3  a  Centauri 


0-028,  Elkin,  Mem.,  vol.  48,  p.  183. 

0*913,  Henderson  and  Maclear,  Mem.,  yoL  12,  p.  37a 

0*919,  Maclear,  Mem.,  yol.  20,  p.  98.  . 

0*916,  Mean  from  senith  distances. 


Sup.  1 887. 


Bevised  in  1887. 


S4i 


No. 


liter. 


5    oCentauri 


4    Arcturus 


5  Capella 

6  Vega 


8  Procyon 

10  Altair 

17  Castor 

23  Polaxia 


34  7  Draconis 

44  <  Urne  Maj. 

46  if  Cassiopea     . 

47  70  p.  Ophinchi 

48  e  Eridani 

49  os  Eridan 


50  SUrsceMin. 

51  tr  Draconis 

52  ( Toucani 

53  61  Cygni 


Parallax  and  Authority. 

0880,  Moeeta  (at  Santiago). 

0512,  Elkin,  M.  N.,  toI.  41,  p.  223. 

Q'753.  Gill  and  Elkin,  Mem.,  vol.  48,  p.  186. 

0765,  Mean. 

0*127,  Peters. 

01 38,  Johnson,  M.  N.,  rol.  17,  p.  271. 

0*132.  Mean. 

0046,  Peters. 

006,    ?  Airy,  Mem.,  rol.  10,  p.  265. 

0*155,  W.  Strove,  Peters,  and  0.  Strove,  Af.  N., 
vol.  13,  p.  74. 

0*103,  Petexs,  Cosmo*,  vol.  III.,  p.  261. 

0-13,    Briinnow. 

0*141,  Johnson,  M.  N.,  vol.  17,  p.  271. 

o*i8o»,  A.  Hall,  „     .43,  p.  222. 

0*128  Mean. 


0-123,  Auwers. 

0181,  Strove,  Menu,  vol.  12,  p.  29. 

0*198,  Johnson,  M.  N.,  vol.  17,  p.  271. 

0067,  Peters. 

0-046,  Nature,  vol.  18,  p  669. 

0*015,  I*"-  de  Ball,  Observatory,  No.  101,  p.  314. 

0043,  Mean. 

0*092,  Nature,  vol.  18,  p.  669. 

0*133,  P^ers. 

0*154,  Nature. 

.01 6,   Xrnger. 

0*136,  Elkin,  Mem.,  vol.  48,  p.  178. 

0166,  Gill,  Mem.,  vol.  48,  p.  160. 

0*223,  A.  Hall,  Observatory,  October  1885. 

0*194,  Mean. 

0*034,  L.  de  Ball,  Observatory,  No.  ioi,  p.  314 

0255,  Briinnow. 

0*057,  Elkin,  Mem.,  vol.  48,  p.  171. 

0*374,  Bessel  corrected  by  Peters. 

0-349,  Peters,  Cosmos,  vol.  IIL,  p.  260. 

0553,  Anwers,  M.  N.,  vol.  23,  p.  74. 


*  Corrected  to  o"*i34  (Nature,  -vol.  35,  p.  258). 


54* 


Mr.  Hall,  The  Sidereal  System, 


XLYIL  9, 


No.  Star. 

53    6*  Cygni 


54  /*  Cassiopese 

55  * Indi 

56  Cephei  51  (Her.) 

57  85PegMi 

58  3077  Bradley 


59  6BCygni 

60  Piasri  III.  242 

61  1 61 8  Groombridge 

62  1830  Groombridge 


Parallax  and  Authority. 

0*402,  Johnson,  Main's  Practical  and  Spk.  Astronomy, 
p.  378. 

0*465,  Ball,  M.  N.t  toI.  40,  p.  250. 
0-468     „  „        41,  p.  164. 

0-478*  A.  Hall     „        43,  p.  222. 

0-441,  Mean. 

By  the  application  of  photography  to  the  determin- 
ation of  parallax,  Professor  rritchard  has  jut 
found  o"-440,  Af.  N.,  voL  47,  p.  87. 

0*342,  0.  Strove. 

0-215,  Gill  and  Elkin,  Mom.,  vol.  48,  p.  187. 

0*027,  k  <*•  Ball,  Observatory,  No.  101,  p.  314. 

0*05,    Briinnow. 

0*205,  Backlund,  M.  N„  vol.  43,  p.  223. 

0*28,    Von  Gylden  .    „  „ 

0*07,   Briinnow. 

0*185,  Mean. 

0*482,  Ball,  M.  N.t  toI.  43,  p.  222. 

0*016,  Ball  (from  distances),  M.  2VL,  vol.  41,  p.  4a 

0-322,  Ball,  M.  K,  vol.  45,  p.  254. 

0*034,  0.  Strove,  M.  iV.f  vol.  10,  p.  124. 

0-226,  Peters  „        14,  p.  138. 

0*141,  Peters  and  Wichmann,  M.  N.,  vol.  14,  p.  138. 


13.  P-  13* 


63  2ii85Lalande 

64  9352  Lacaille 

65  34  Groombridge 

66  21258  Lalande 


67  1 741 5  Oeltsen 

68  1 1677  Oeltsen 


11    $  Centanri 
16    a  Cygni 


o*i8,    Wichmann  and  Schlnter,     „ 
0*145,  Mean. 
0*501,  Winnecke. 
0*285,  Gill»  Mem.,  roL  48,  p.  154. 
0*307,  Auwers,  M.  N„  toL  28,  p.  97. 
0*262,  Anwers  „         23,  p.  74. 

0*260,  Kriiger  „  „   p.  172. 

0*261,  Mean. 

0*247,  Kriiger.  M.  N.,  vol.  23,  p.  172. 
0*270,  Geelmnyden  from  B.A. 
0*242  „  „    DscL 

0*256,  Mean,  Astr.  Nock.,  No.  2287. 

Gill  found  a  small  negative  parallax;   hence  the 
parallax  must  be  very  small. 

In  Herschel's  Outlines  of  Astronomy  ("sixth  edition) 
p.  593,  the  parallax  is  similarly  taken  to  be 
very  small. 


*  Corrected  to  o"*27o  (Nature,  vol.  35,  p.  258). 


Sup.  1887. 


Revised  in  1887. 


543 


Note  III 

The  following  radial  velocities  were  adopted  from  the  ob- 
servations made  at  Greenwich : — 


FlB0X 
Ha          Star. 
4       aBootiB 

Culm. 

Miles  per  See. 
—46*0 

No. 
13 

8ncoio>  CuLsa. 

Star.                   Miles  per  Seo. 
a  Virginia                    —11*9 

5      a  Aurigse 

+  260 

15 

aLeonie 

+  io-i 

6      oLyrse 

-361 

18 

e  UrsseMaj. 

4-ir8 

7      0  Ononis 

+  191 

19 

aPenei 

-277 

8      a  CanisMin. 

+  I5'5 

20 

0  Tauri 

-i4'3 

9      a  Orionia 

+  269 

22 

/SCeti 

-335 

10      a  Aqnilse 

-249 

24 

a  Arietia 

—  142 

12      a  Tauri 

+  320 

25 

7  Caesiop. 

-i9'3 

14      0  Gemin. 

-31-8 

26 

7  Leonis 

—  26*2 

16      a  Cygni 

-341 

27 

CUrsaeMaj. 

+  19*3 

17      a  Gemin. 

+  178 

28 

a  Ophiuchi 

— 10-9 

21       a  Androm. 

-282 

30 

7  Cygni 

-135 

29      a  Coronse 

+  207 

31 

0  Caasiop. 

-    1*2 

36      a  Pegaai 

-255 

3* 

0  UrsseMaj, 

+  22*9 

33 

7  Una  Maj. 

•+17-5 

34 

7Draoonia 

—  7-2 

■ 

• 

35 

c  Pegaai 

-14*3 

37 

a  Cephei 

-41-8 

38 

7  Pegaai 

-234 

- 

39 

7  Virginia 

+  250 

• 

1 

40 

7  Aquilae 

-*4*3 

• 

• 

41 

8  Cygni 

-147 

42 

P  Cygni 

-I43 

. 

43 

CAqnilse 

-230 

a 

45 

3  Androm. 

—  406 

p 

Not* 

>  IF. 

The  radial  Telocity  of  Sirius  and  its  cnrve  of  variation  have 
been  deduced  from  the  following  observations  made  at  Green- 
wich, and  given  in  the  Monthly  Notices,  vol.  xlv.9  p.  283 : 

Opposition  of 
1875-76) 

1876-77  J 
1877-78 
1879-80 
1880-81 

Miles  per  Sec. 

+  2I'I 

+  23*0 
+  151 

+  ii*3 

Opposition  of 
1881-82 

1882-83 
1883-84 
1884-85 

Miles  per  Seo, 
4-   2*1 

-  47 
-194 
— ai'5 

Bnt  Dr.  Hoggins  fonnd  +  29*4  for  about  the  opposition  of 
1868,  and  +20  for  about  the  opposition  of  1872,  so  that  we 
have  the  following  curve : 


544  Mr.  Hall,  The  Sidereal  Syi'.em.  XCTIL  9, 


Sap.  1887.     Col.  Tupman,  Observations  of  Oomets  etc.  545 

Assuming  a  mean  value  of  —  6  at  the  opposition  of  1882-83, 
or  early  in  the  year  1883,  and  dividing  by  29,  we  have  —2-1  as 
the  mean  radial  velocity  of  Struts. 

Jamaica :  1 887,  March  26. 


Observations  of  Oomets  and  of  Sappho '(80    [    arrow 

By  G.  L.  Tnpman. 

Revised  Geocentric  places  of  Garnet  1884  III  {Wolf). 
(Monthly  Notices  B.A.8.,  xlv.  403.) 


1884-5. 
Sept.  24 

vnmwiw 

Mean  Time, 
h    m     8 
10  38    0 

<#App.ILA. 

h     m       s 
21    17   23*36 

#App.DecL 

0       1       11 
+  20  36  20'9 

Log.  A. 

99036 

Star. 
I 

25 

9  46     4 

21    17   58*81 

4-20     9  42*6 

99030 

2 

27 

10  45  50 

21    19  22'76 

+  19   12  374 

9-9019 

3 

Oct. 

4' 

9  17  5* 

21'  23   33*82 

+  15  51   520 

99014 . 

.      4 

9  59  47 

21   25  359O 

+  15   51      II 

99014 

4 

10  23  34 

21   25  3689 

+  15  50  35* 

99014 

4 

13 

II  29  16 

21   36  55-31 

+  11  24  1 8*8 

99072 

.5 

22 

9  3°  22 

21   51   21-09 

+  7  12  336 

99200 

6 

26 

* 

10    4  32 

21    58  49*15 

+  5  26  356 

9.9277 

7 

Nov. 

7 

10  27  53 

22  23   57'02 

+  0  49  41-1 

99566 

8 

8 

9  40  20 

22  26     7*26 

+  0  30  21*7 

9*9593 

9 

18 

9  41    0 

22  49  39-28 

—  2  22  34*2 

9*9890 

10 

19 

6  19  34 

22  51   4538 

-  2  35    67 

99918 

10 

20 

9  28  34 

22  54  3177 

-    2  50  554 

9*9954 

11 

* 

21 

5  56  3* 

22  56  37*57- 

•*  -  3    2'3o-8 

99981 

12 

Dec. 

9 

6  34  15 

23  42  2541 

'    -  5  45.275. 

00589 

13 

15 

6    1  59 

23  57  5208 

-  6    9  134 

00796 

14 

Jan. 

7 

6  48  36 

0  56  5632 

-  5  53    82 

01618 

15 

6  48  36 

0  56  5630 

-  5  53  io-6 

01618 

.    16 

Feb. 

5 

6  56  43 

2    8  27-96 

-  3    9  177 

02538 

17 

The  times  have  not  been  corrected  for  aberration. 

*       •  • 

Ccmet  1885  //.  (Brooke). 
(Monthly  Notice*,  xlvi.  123.) 


.2885. 

Sppt. 


> 

6 

Mean  Time, 
h    m     8 

9  54  15 

S>  App.  ILA. 
h     m      s 
»4     3  47'4P 

Lfp. 
+  8719 

f  App.  Deol. 
+  38  24  187 

*Jp. 
+  9*847 

Star. 
18 

9 

9,29.21^ 

14  21  2830 

+  8-730 

+  39  38  44*1 

+  9-808 

.19 

11 

9  28  15 

H  33  55  00 

+  8736 

+  40  23    97 

+  9795 

20 

13 

9  42  43 

»4  46  53*56 

+  8-738 

+  41     3  299 

+  9*jfo6 

21 

9  42  43 

"4  46  53*53 

+  8738 

+  41     3254 

+  9806 

22 

Some  small  errors  were  discovered  in  the  reductions. 


546 


Col.  Tupman,  Observations  of 


ILTII.  9, 


OQ 


W     *     ifl 
M      cl      N 


VQ     N    OQ     »    o      m      m      n    *    «fl  «     N   W     ft    o     *• 
«     MM     M     tOforOfOrotororo«oro***' 


vO  vO  O 

J         r*  r-  00 

^B  •  •  • 

ft     »2i  iSi  i2i 

+  +  + 


ooftooci    p^t-Mpp 


■  •  •  •  B 

*     *    to  00      O 


o    « 

•  • 

+   +   +   +   +   +   +   +   +   +   +   +   +   +   +   + 


00  op  m 

ft  ft  to 

«H  n  •* 

08  8  8 

+  +  + 


CI 

CI      *m 


ro  00     »     O 


w     *•    eo   v©     « 


v» 


u)    N    io    in    ^    d    ft)     ft    to    *2    2*  *° 

M         ^t       lO      1/)       M  CO       ^        *" 


o\    *•     V*  00     t»» 

■  • 

ft    vo 


ro 


+++++++ 


+  +  + 


+  +  +  +  + 


-  $  Jf 

vt    in  \p 

fe,  &  & 

+     +  + 


tm      m     *&      M      8      cf     f?     8*    ^8     ^8      M      f>     fO    JO     tO     tO 

+   +   +   +   +   +   +  +  +   +  +  +  +  +  +   + 


8 

00 


I' 


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ft   t*»  \p 

m   to 

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m     •*  »o 

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to   to   to 

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O       M      00 

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a  o   m 
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+ 


to    ft 
vn    to    ci 


M    in    *   n    P9    y>  cp  op 

■      *      i»    i»   Q   vo    o    o  00 

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to    to 


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7  +  +  i  +  i 


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to 


pvo  »o  t  o  ^  m  m  oo  tovo  !*  f  9*  P  ° 
oo  o  *o^-*vo  »*  O  00  »*  00  ft  -^  — '  - 
ro    «•    •-     «•  cT   To    *    w     ►«     m     ~     ~ 


I    I    + 


O         M 

I    1 


to    *«• 

to   to 
OOmmNmOOOOn 

+    I     I     I    +   +  +    I    +   +   + 


-s, 

M 

a^ 

s 

to 

a* 

m 

7 

*  3 

m 

CO 

*2 

o 

ft 

VO    vo 

VO 

tH 

^ 

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o 

M 

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to 

to 

1886. 

Jan. 

. 

m  vo  r*  to  »n  ^ 

^  w  vo  ^  ^  to 

o  t**  «  o  «  vo 

eo  to  \f%  vn 

NO  N  N  N  O  « 


"  8 

>s     Ih     N     N     N    00 


^    r^    ft    ro 


^*    to    r^ 

M        VO       M 


CI 


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m      MM 


ro  00     ft    m' 


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to 


Sup.  1887.        OomeU  and  of  Sappho,  at  Barrow. 


47 


g 
1 

-8 

a 
8 


£        fl'      to*vn»0*s,qQO*0»*eico    ;•*»/> 


a 


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oo  «  «  mm  co  co  co  00 
d  co  co  co  co  co  co  co  ^ 
+     +     +     ++     +     +     +     + 


Q\  fO  ^  Q\ 

•  •  •  • 

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+  +  +  + 


51    -S> 

+ 


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co    ^*-    *•    O     »•     rococo**     el     co^vO 

mmmNCI       «      «       «      CO     CO     CO     CO     CO 

+      +      +      +      +      +      ♦      +      +      +      +      +      + 


J! 


*»   00     A     On    O      «      W      COW^^O      CO«0     yo. 
ppp~«w«c»«ci«c*c« 

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Bel 

M  CO 


9  *  $  ?  5-  S"  ? 


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tl         M         M 


m  ts.   m   *    *   2   25   2  'S.  ti   1* 


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oQmqqoo    n   n  vo   00    «    n 

V     ^   ^    vt    900     VOCOW00 

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+    1    I    +  +    I    I    I    +    I++I 


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p 

CO      ■* 

w 


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0 


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ts*\o     is.Cs.^ts.ts.ts.ONOO     On  00     On 


ts, 


00 

?j  is  4 


u> 


wM^gcoOOONJ-fO^OOO^yj 


I 


"«1 


546 


Col.  Tupman,  Observations  of 


xlyii.  9, 


w    *    "> 
W      «      « 


SO      N    00      A     O      m      «      <n     *     lO    VO      N    N      a     O      •• 


?f» 


vO    vO      0 
f*    t*»    00 


ti         *"*■     «^    w 

W        i£j   i£j   i2j 
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32 

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34  W.B.  421                23  21  4694  +29  15  530         „      2  -o-8i  -  it 

35  L.L.  45821               23  18  27*22  +29    248-5  Armagh,  5,8  -0*82  -  1*3 

36  L.L.  45839              23  18  5518  +30    5    7-8  Harrow  2  — 081  -  1-9 

37  L.L.  45845              23  19  16-05  +31  45  31-0         „      2  -0-80  -  2*S 

38  L.L.  45857               33  19  44'43  +3«  SO  34*5  Radcliffc  3  -0-79  -  2* 

44*6o  36*0  Armagh  1,  5 

44-41  33-9  Harrow  1 

39  W.B.  346                 23  18  3047  +  3a  37  40-1          „      2  -079  -  31 

40  W.B.  328                 23  17  3m  +38  22  283         „      3,4  -0*68  -  6*3 

41  W.B.  402                23  20  57*38  .  +39  45  526          .,      2  -0-52  -  7«i 

1885*0. 

42  W.B.  344                  3  21  28*21  +  7  20  525  Harrow 3, 4  +401  +  5*4 


1 886*0. 

43 

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1  5*5  4373 

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47 

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48 

L.L.  3715 

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49 

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1  54  4631 

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1  49  1083 

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52 

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1  49  26*10 

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53 

W.B.  1047 

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54 

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+  34  43  295 

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55 

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56 

B.A.C.  482 

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4087 
40*66 

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46'3 
475 

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57 

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59 

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609 

2  33  5973 

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61 

L.L.  5203 

2  43  2952 

+  44  41  513 

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Sap.  1887.  Cambridge  Observations  of  Sappho. 


553 


1 

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Mer.  Obs. 

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!         «3 

DJL  +  90,  3885 

18  44  5159 

+  9  22  59-7 

»        2 

+  0-96  +11-9 

64 

W.B.  1 186 

18  48  4-62 

+  9  31  io-o 

Glasgow  3,  4    +0*96  +  12*2 

472 

97 

Armagh,  7 

65 

L.L.  35624 

18  58  262 

+  87  390 

Harrow  3 

+  1*03  +12-4 

1 

2*53 

40*3 

Glasgow  2,  1 

\ 

66 

WJ.  1474 

18  59    071 

+  87  397 

Harrow  3 

+  1-03  +12-5 

67 

Lamont  4063 

19  11    6-04 

+  6  43  192 

»      2 

+ 1-09  + 12-9 

68 

W.B.  405 

19  26    O'll 

+   4  46  52-2 

»      4 

+  1-17  +13*2 

69 

D.M.+4°,4i68 

19  3'  4061 

+  4  24  U'4 
1887*0. 

M        3 

+  117  +134 

70 

W.B.  1286 

19  53    023 

+   1  21  453 

Glasgow  2,  3 

-175   +  4*1 

7i 

LX.  29697 

16  12  44-19 

-  8  47  360 

Harrow  3 

+  207   +    27 

72 

W.B.  272 

16  16  25*26 

-  6  35  499 

»      3 

+  207   +   3-4 

73 

8J).-6°,  4425 

16  18  19-29 

-  6  27  430 

tt      4 

+  207   +  35 

74 

L.L.  29970 

16  22  4850 

-  5  "  40-9 

»      3 

+  2-07   +   39 

75 

L.L.  301 18 

16  28    i*95 

-  3  33    59 

»      5 

+  2-07  +   3-5 

76 

Lamont  5231 

16  32  4283 

-   1  50    o*5 

»      3 

+  2*07  +   5-2 

77 

Anonymous  92  m 

Observations  of 
vatory  with 
Micrometer. 

ag.  7    9    2*8o 

+  8  55  36-5 

Cambridge  4 

+  0-87  —  9-6 

'  tlie  Planet  Sappho  made  at  the  Cambridge  Obser- 
the  Northumberland  Equatorial  and  Square-Bar 

4 

(Communicated  by  Prof.  J.  C.  Adams.) 

Greenwich 
Mean  Time 
1887. 

BJl. 

Number                Name 
Decl.                     of                       of 

Comparisons.    Comparison  Star. 

, 

Jan.  12-42844 

h     m      b 
7    0  3522 

n       t         it 

8  59  3746 

10          Arg. 

+  £— 1651 

[6  52  3375 

9  17  24*50' 

»! 

+  9—1352 

„     20-40714 

j  6  52  33*89 

9  17  27-27 

■■ 

8 

+  9-1353 

16  52  3397 

9  17  26-24 , 

tt 

+  9-1396 

■ 

Fan.  25-42877 

6  48  10-20 

9  32    i"94 

IO 

+  9—  I3H 

„    2638245 

(6  47  24*51 
16  47  24-38 

9  35    4"io| 
9  35    290) 

-     1" 

x  tt 

+  9— 1314 
+  9—1330 

Jan.  31-36133 

6  43  4978 

9  51  4470 

12 

+  9—1297 

Feb.     1*42203 

6  43    9  62 

9  55  3746 

IO                 ., 

+  9—1276 

Feb.    2-38874 

6  42  3478 

9  59    672 

IO 

+  9 — 1276 

Observations  not  corrected  for  Aberration  and  Parallax. 

B  R 


554  Oen.  Tenncwd,  On  the  Orbit  xlyii.  9, 


Places  of  some  Stars  which  have  been  compared  with  the  Planet  Sappho  at  the 
Cambridge  Observatory  and  elsewhere;  deduced  from  observations  with  the 
Cambridge  Transit  Circle. 


Aig.           No. 

*■* 

Mean 

JLA. 

Jan.  x,  1887. 

Mean 

N.P.D. 
Jan.  x,  1887. 

Number 
of 
Obserrations 

Aig.  +  9 — 1276 

7-5 

h    m       s 
6  39  13*314 

0      /        /» 

80    7    5<>5 

5 

„     +9—1297 

8-5 

6  43  22*912 

80  15    117 

5 

n      +9~  1314 

7-7 

6  45  23784 

80  25  3870 

5 

».       +9—1330 

8-9 

6  48  19*610 

80  22  2573 

5 

»       +9-1352 

9 

6  50  56975 

80  46  1567 

4 

i>       +9—1353 

9 

6  50  58533 

80  50  5487 

3 

»       +9—1394 

7-9 

6  57    2*624 

80  48  3980 

3 

„       +  8—1626 

9A 

6  57    3940 

81    3  5364 

2 

»      +9-1396) 

B.A.C.        2304  / 

6 

6  57    7239 

80  41  5464 

5 

Aig.  +8— 1 65 1 

8-4 

7    0  33209 

81    6  32*65 

5 

„     +9—1447 

8-3 

7    4  27586 

81     1  5656 

3 

„     +8-1697 

8-7 

7    7    8*651 

81  15  1351 

3 

„     +  8—1709 

9-4 

7    9    2798 

81    4  2347 

4 

„     +8—1752 

9 

7  17  30215 

81  12  1988 

3 

,.     +9— 1 541 

8-9 

7  19  20-611 

80  59  3269 

3 

»     +9-1569 

9 

7  22  54*534 

80  59  2445 

3 

t,     +  8— 1801 

8-5 

7  26  38*076 

81    6  1369 

3 

On  the  Orbit  of  Comet  II.    1883.     By  Lieut -Gen.  J.  F.  Tennant, 

rt.E.,  JT.rv.o. 

I  recently  sent  a  note  to  the  Secretaries  acknowledging  that 
Mr.  Bryant  had  pointed  out  two  mistakes  in  the  comparison  of 
the  places  of  this  comet  with  my  Ephemeris.  I  was,  however, 
on  looking  over  his  paper,  very  doubtful  as  to  the  mode  in  which 
his  normal  places  were  obtained,  and  have  examined  and  re- 
peated my  calculations. 

Believing  that  Mr.  Bryant  had  verified  all  my  reductions, 
I  assumed  these,  with  the  corrections  he  pointed  out,  to  be  accu- 
rate, and  proceeded  to  interpolate  the  errors  of  the  Ephemeris  so 
as  to  get  the  most  probable  values  at  the  same  dates  as  before. 
The  errors  changed  a  good  deal,  and  on  proceeding  to  compute 
a  parabolic  orbit  I  found  that  the  following  (which  is  close  to 
Mr.  Tebbutt's)  represented  my  new  places  almost  exactly: — 


Sap.  1887.         of  Oomet  II.  1883.  555 

8 
Perihelion  Passage,  1883,  Dec.  25*30221. 


O  I  II  O  /  II 

*-  43  12  2479  or  *»«  138  45  03*29, 


Equinox  of  Jan.  j,  1884  < 


C-264  27  21*50, 
IL-U4  59  0371, 

log.  2-9*4919541. 


This  result  was  so  different  from  Mr.  Bryant's,  that,  haying 
ascertained  that  he  had  not  verified  all  my  reductions,  I  once  more 
repeated  them,  and  finding  only  one  sensible  change  I  pro- 
ceeded to  deduce  fresh  normal  places.     These  were — 


ILA.  Dec 

II  It  01         II  II 


For  1884,  Jan.    17*0        3404123-07*2*31        -413252-64*1*10, 

23*5   349  09  20-11*1-98    -41  58  18*51*2*34, 
300   355  01  27-03*3-63    -41  51  5578*0*88. 

Longitude. 

or  for  1884,  Jan.    17-0        325  11  34-2*1*89  —30  39  36*5*1*24, 

*3*5        331  36  345*2-05  -33  55  15*3*218, 

300        336  21  03*6  +  1*83  -35  54  41*2*2-31, 

all  being  referred  to  the  equinox  of  Jan.  1,  1884. 

The  corresponding  places,  computed  from  the  elements  I  have 
given  above,  are : — 

For  1884,  Jan.     170        325  11  35'i         -30  39  36^, 

235        33i  36  33'2        -33  55  14" «. 
300        336  21  039        -35  54  41-5; 

that  is,  the  elements  represent  the  normal  places  far  within  their 
probable  errors.  It  would  seem,  then,  that  the  difierenoe  of  the 
results  at  which  Mr.  Bryant  and  I  have  finally  arrived  is  due  to 
the  modes  in  which  we  have  respectively  deduced  our  normal 
places  from  observation. 


R  R  2 


556  Mr.  Marth,  Ephemerides  of  the  xlvii.  9, 

Ephemerides  of  the  Satellites  of  Saturn,  1887-88.     By  A.  Marth. 

In  the  following  ephemerides  the  five  inner  satellites  are  as- 
sumed to  move  in  circular  orbits  in  the  plane  of  the  ring,  the 
ascending  node  N  and  inclination  J  of  which,  in  reference  to  the 
plane  of  the  Earth's  equator,  are  assumed  to  be 

Fop  18880  N  « I26°*6279  J  =  6°*993<>. 

In  the  tables  P  denotes  the  position-angle  of  the  minor  axis 
of  the  ring,  L  +  1800  the  planetocentric  longitude  of  the  Earth 
referred  to  the  plane  of  the  ring,  A+1800  that  of  the  Sun,  or 
A— L  the  difference  between  the  two.  The  apparent  equatorial 
diameter  of  the  ball  and  the  diameter  of  the  outer  rim  of  the  ring 
depend  still  on  Bessel's  determinations.  The  assumed  propor- 
tion of  the  polar  axis  of  the  ball  to  the  equatorial  diameter  is  0*900. 

In  the  tables  for  the  five  satellites  a  and  b  are  the  semi-axes 
of  the  apparent  orbits,  Z-L  the  longitudes  of  the  satellites  in 
their  orbits  reckoned  from  the  points  which  are  in  superior  con- 
junction with  the  planet's  centre  or  in  opposition  to  the  Earth  in 
longitude.  By  adding  to  I  —  L  the  value  of  L  from  the  first  table, 
the  longitudes  I  are  found.  These  longitudes,  which  are  the 
orbital  longitudes  from  the  ascending  node  added  to  the  right 
ascension  N  of  the  ascending  node,  reckoned  from  the  point  of 
the  true  equinox,  are  corrected  for  the  equation  of  light,  and 
depend  on  the  following  assumed  values,  which  refer  to  the  time 
when  the  light  arrives  at  the  distance  [0*950]  : — 


Greenwich 
Noon. 

Mimaa. 

Enceladoi. 

Tethys. 
J. 

Dione. 

Rhea. 

1887,  Oct.  15 

218*950 

190745 

I5&156 

340°497 

o?883 

Nov.  14 

158743 

152699 

117*100 

326*547 

231*586 

Dec.  14 

98538 

1 14-653 

78045 

312597 

102*289 

1888,  Jan.  13 

38-334 

76*607 

38989 

298*647 

332*992 

Feb.  12 

338*131 

38561 

359934 

284697 

203*695 

Mar.  13 

277989 

0515 

320*878 

270747 

74398 

Apr.  12 

217728 

322*468 

281-822 

256796 

305*100 

May  12 

157528 

284*422 

242*767 

242*846 

175803 

The  values  of  P,  a,  b  and  Z  — L  are  to  be  interpolated  directly 
for  the  times  for  which  the  apparent  positions  of  the  satellites 
are  required,  and  the  rectangular  co-ordinates  x  and  y,  reckoned 
parallel  to  the  axes  of  the  ring,  and  expressed  in  seconds  of  arc, 
or,  if  polar  co-ordinates  are  wanted,  the  position-angles  p  and 
distances  0  of  the  satellites  in  reference  to  the  planet's  centre, 
are  then  found  by  means  of  the  formulae  : 

*sin(p—  P)=*  =  aBin(J— L), 
s  cos  {p  -  P)  =y  •=  b  cos  (f-L). 


Sup.  1887. 


Satellites  of  Saturn,  1887-88. 


557 


Greenwich 
Noon. 

1887 
Oct.  15 

20 

25 

30 

Nor.  4 

9 

14 

19 

24 

29 
Dec.  4 

9 

14 

19 

24 

29 

1888 
Jan.  3 

8 

13 
18 

23 

28 

Feb.  2 
7 


352607 
•612 
•616 
•619 

352*622 
'624 
•625 
•625 
•623 
'621 

352618 
'614 
'609 
•604 
•598 

•591 

352584 

'577 
•571 

•564 

•558 

•552 

352546 

•541 


130363 
130*640 

130-875 

131  068 

131*218 

131323 

131*383 
131  397 

131*365 
131  287 

131*164 

130998 

130791 

I30-545 
130262 

129947 

129605 
129239 
128*855 
128458 
128054 
127-649 
127*249 
126859 


Latitude  of 
Earth        |         8nn 
above  plane  of  Ring. 

o 


-18869 
18*776 
18699 
18638 

"  18*593 
18565 

18-554 

l8*562 
18*587 
18*629 
- 18688 
18763 
18854 

i8'959 
19*077 

19*206 

19*344 
19489 

19-640 

19794 
19948 

20102 

-20*252 

20396 


—  21*024 
20970 
20*916 
20-861 

— 20*806 
20751 
20*696 
20-641 
20*585 
20530 

-20474 
20-418 
20361 
20*305 
20248 
20*191 

-20134 
20077 
20020 
19*962 
19*904 
19*846 

- 19788 
19730 


A-L 

o 

—  6099 

6187 
6*234 
6238 

—  6*199 

6*i  16 
5988 
5814 

5*593 

5*327 

-5017 
4*664 

4*269 

3*835 

3365 
2863 

-2*335 

1783 
1212 

0-629 
-0039 
+  0552 
+  1137 

1*712 


log** 

9983285 

•987105 

991009 

•994972 

9998969 

0*002971 

-006949 

•010869 

-014694 

•01 839 I 

0021924 

'025  260 

•028362 

•031 193 

•033720 

•035914 
0037749 

•039204 
•040256 
•040891 
-041 101 

-040886 

0*040250 
•039201 


*Log  v= 0*950— log  A,  the  Naut.  Aim.  values  of  the  distances  A  being 
altered  to  take  the  equation  of  light  into  account. — In  deducing  from  the 
measurements  of  the  satellites'  positions  the  dimensions  of  their  orbits,  and 
consequently  the  mass  of  Saturn,  the  effect  of  the  existing  uncertainty  con* 
ceraing  the  correctness  of  the  planet's  tabular  distances  from  the  Sun  and 
from  the  Earth  must  not  be  lost  6ight  of.  The  difference  between  the 
distances  derived  from  Bouvard's  and  from  Le  Verrier's  tables  of  Saturn  for 
the  opposition  of  1879  (the  only  one,  so  far  as  I  know,  for  which  computations 
from  both  tables  are  available)  corresponds  to  a  difference  of  about  3  units 
in  the  deduced  proportion  of  the  mass  of  the  Sun  to  that  of  Saturn,  and  in 
the  next  preceding  oppositions  the  difference  has  probably  been  larger.  As 
the  observed  positions  of  the  planet  show  that  in  1879  Le  Verrier's  tables  give 
the  heliocentric  longitudes  of  Saturn  about  I2"*7  too  great,  while  Bouvard's 
give  them  about  8"*9  too  small,  the  differences  of  the  tabular  values  of  the 
radius  vector  raise  a  question  at  present  beset  with  doubt.  If  heliocentric 
places  of  Saturn,  computed  accurately  from  Le  Verrier's  tables  for  the  years 
preceding  1879,  exist  anywhere,  the  publication  of  at  least  part  of  them,  be  it 
even  of  only  one  place  for  each  opposition,  would  be  of  service  and  would  be 
appreciated. 


558 


Mr.  Marthy  Ephemerides  of  the 


Green  wloh 
Noon* 

1888 
Feb.  12 

17 
22 

27 
Mar.  3 

8 

*3 
18 

23 
28 

Apr.  2 

7 
12 

17 
22 

«7 
May  2 

7 
12 


Latitude  of 
Bu-th        I        Son 
above  plane  of  Ring. 


Greenwich 
Noon. 

1887. 
Oct.    15 

20 

25 

30 

Nov.    4 

9 
14 
19 
24 
29 
Dec.    4 

9 
14 
19 
24 
29 


537 
533 
•S30 
•527 
352525 
•523 
•522 

•521 
•520 
•520 
352520 
•520 
'521 
•521 
•522 

•524 
352526 

•528 
352531 

Diameter  of  B 
Equat.  I  Phase 
prec.  L 


11 

17*57 
1772 

17-88 

1805 

l8'2I 

1838 
1855 

1872 
18-89 
1905 

19*20 

1935 
1949 

19-62 

1973 
19-83 


0050 

■052 

•053 
•053 
•053 

•052 
•051 
-048 
•045 

-041 

•037 

•032 

■027 
•022 
•017 

•012 


26-485 
26133 
25*808 
25514 

25^55 
25'034 

24854 
24717 

24625 
24579 

24579 
24625 

24'7l6 

24853 

25034 

25'257 
25521 

25824 

26-164 


20^534 
20662 
20-780 
20886 
■  20979 
21058 

21*122 
2I'I72 
21'206 
21*225 
21*228 
2I-2l6 
2I-I88 

2ri45 
2 1  087 
2I'OI5 

-  20929 
20829 

-20715 


19*671 

I96I3 
19554 

19*495 

- 19*435 

19-376 

I9*3l6 
19257 

19-197 

I9-I37 

— 19  076 

19-016 

18955 
18894 

18-833 

18772 

-18711 
18649 

- 18588 


A-L 

o 
2-27I 

2808 
3318 

3797 
+  4*241 

4-646 

5010 

5331 
5607 

5837 
+  6021 

6158 
6-250 
6295 
6-297 
6257 

+  6175 
6054 

+  5879 


XLVII.  9, 
logr* 

•037751 

•035918 

•033728 

•03 1208 

0*028389 

-025301 

•021977 

-018452 

•OI4764 

-OIO947 

OOO7034 

OOO3056 

9-999044 

•995030 

•99IO43 

•987108 

9983248 

979484 
9975837 


II. 
Polar 


11 
600 

6*14 

6-29 

644 

659 

674 

689 

705 
7-20 

735 

7*49 
763 

775 
787 

798 
807 


Axis  of  Ring. 
Major  J  Minor 


11 
4050 

40*86 

4123 

41*60 

4199 

4238 

4277 

4316 

4354 

4391 
4427 

4461 

4493 
45-23 
4549 
4572 


1310 

I3-15 
1322 

1330 
I3-39 
13*49 
1361 

13-74 
1388 

1403 
14-18 

1435 
1452 
1469 

1487 
1504 


« 


27-67 
2791 
28*  1 7 

28-43 
28-69 

28-95 
2922 

2949 

2975 
30*00 

3024 

3048 

3070 
3090 
3108 
31-24 


Mimas, 

-  #95 
899 
903 
908 

-  915 

9*22 
930 

9*39 
948 
958 

-  969 
980 

992 

1004 

10*16 

10*28 


87°-82 
19769 
307*60 

5755 
16755 

27759 

27-67 

137  79 
24796 

358i7 
108-41 

21868 

32899 

7932 
18967 
30004 


1909-87 

•91 
1909-95 

19 1000 

•04 
•08 

•12 

•17 
•21 

•24 
1910*27 

•31 
33 
35 
•37 
39 


Sup.  1887. 


Satellite*  of  Saturn,  1887-88. 


559 


Greenwich 

Noon. 

Diameter  of  Ball 
Eqnat.  |  Phase  |  Polar 
preo.1. 

Axis  of  King. 
Major  |  Minor 

•1 

Mimas 

• 

2888. 

Jan.     3 

// 
19*92 

M 
OOO8 

1&5 

45*91 

11 
1521 

31-37 

- 1039 

5o?43 

0 
1910*39 

8 

1998 

•OO5 

18-22 

46*06 

I5-37 

31*47 

10-50 

160*82 

•40 

13 

20*03 

•002 

1827 

4618 

1552 

31-55 

1000 

271*22 

'39 

18 

2006 

•OOI 

1830 

4624 

1566 

31*59 

10*70 

21  61 

38 

23 

2007 

foil. 

18-31 

4627 

1578 

3I-6I 

10-78 

131*99 

•36 

28 

2006 

limb. 

1830 

46*24 

1589 

31-59 

10*86 

242-35 

•34 

Feb.    2 

2003 

002 

1828 

4618 

1598 

31*55 

—  1092 

35269 

I9IO-3I 

7 

1998 

•005 

1824 

4606 

1605 

31*47 

10*97 

103*00 

•28 

12 

19*92 

008 

18-18 

4591 

16' 10 

31*37 

I  TOO 

213*28 

•24 

17 

1983 

•012 

i8ji 

4572 

1-3*13 

31-24 

1 1  02 

32352 

•20 

22 

1973 

•017 

1802 

4549 

16*14 

3I08 

11  03 

7372 

•15 

27 

19*62 

•022 

1792 

4522 

16*12 

3090 

11*02 

183*87 

'II 

Mar.    3 

19*49 

•027 

1780 

4493 

16-09 

3070 

-10*99 

29398 

•06 

8 

1935 

•032 

1768 

4461 

1603 

3O48 

1095 

4404 

I9I0'00 

13 

18 

1921 
1905 

037 
'041 

I7'55 
17-41 

4427 
43*91 

1595 
1586 

30-25 
3000 

10-90 
10-84 

15404 
26399 

I90995 
•90 

23 

18*89 

045 

1726 

4354 

1575 

2975 

10*76 

1389 

85 

28 

18*72 

048 

17*11 

43i6 

1563 

2949 

1068 

12374 

J 
"79 

Apr.    2 

1856 

051 

16-96 

4278 

15*49 

29-23 

- 1058 

23353 

#    ^ 

'74 

7 

1839 

■053 

1 6- 80 

4239 

I5-34 

2896 

10-48 

343'27 

•70 

12 

l8'22 

054 

1665 

42*00 

15-18 

2869 

1037 

9297 

# 

•65 

"7 

18*05 

•054 

1649 

41-61 

1501 

2843 

1026 

202*62 

•DO 

22 

1788 

•054 

1634 

4123 

1483 

28*17 

10*13 

31222 

56 

27 

1772 

•053 

16-19 

4086 

1465 

27*92 

IO'OI 

6178 

52 

'49 

May    2 

1757 

•051 

1604 

4050 

14-46* 

27*67  - 

-  9*88 

171*30 

7 
12 

1742 
I7*27 

049 
0*046 

1590 
1577 

40*15 
39'8i 

1427 
1408 

27*43 
27*20 

975 
9*62 

28079 
3024 

190945 

Greenwich 
Noon. 

Enceladus. 
a,             6,           /,-L 

Dill 

r. 

«» 

Tethys. 

Dill. 

1887. 

Oct.  15 

20 

25 
30 

35'50 
35-81 

36i3 
3646 

-ir'48 

"•53 
11*58 

11  65 

59?»5 
29336 

16691 

4050 

0 

I313-5I 

•55 

'59 

•6.1 

43"94 
4433 
4473 
45-14 

— 14*21 

1427 
H34 
1443 

25-41 
25871 
132-06 

5*45 

0 
953*30 

•35 
39 

'43 
953*47 

•52 
56 

Kov.    4 
9 

3680 
37'I4 

-1 173 
1 1  83 

27413 
14781 

1313 

•68 
•72 

4556 
4598 

- 1453 
1464 

23888 
11235 

14 

3748 

1193 

2153 

m 

•76 

46*40 

1477 

345-87 

19 

37*82 

12*04 

25529 

•8l 

4682 

14*90 

21043 

61 

560 


Mr,  Marihy  Ephemerides  of  the 


XLY1I.  9, 


Greenwich 
Noon. 

«. 

Encdadus. 

ft.          J.-L 

Dill. 

a, 

Tethyt. 
6.         k-L 

DHL 

1887. 
Nov.  24 

38-16 

1216 

0 
129*10 

0 
'85 

47,*24 

i£'o6 

93°-o4 

0 
•69 

29 

3849 

12*29 

2*95 

•88 

4764 

1522 

326-69 

•65 

Dec.    4 
9 

3880 
39*io 

- 1243 
1258 

23683 
1 1075 

1313-92 
•96 

4803 

48-40 

-15*39 

15*57 

20038 
74*11 

953*73 
76 

14 

3938 

1273 

3447* 

1313*99 

4875 

1575 

30787 

•80 

19 

3964 

12-88 

218-70 

1314*02 

4907 

15*94 

18167 

•83 

24 

3987 

13*03 

92-72 

•04 

49*35 

16*13 

55*50 

•85 

29 

4007 

13*18 

32676 

•05 

49*60 

16-32 

289*35 

•87 

z888. 
Jan.     3 

8 

40-24 
4037 

- 1333 
I3"47 

200*8 1 
74*88 

I31407 
•07 

49*8i 
4998 

-16-50 
1667 

163-22 
37*11 

953*89 
•89 

13 

40-47 

1360 

30895 

# 

•07 

5010 

1684 

271*00 

■90 

18 

40-53 

1373 

183-02 

•07 

5017 

16*99 

14490 

•90 

23 

40-55 

1384 

5709 

9 

06 

50-20 

1713 

18-80 

•89 

28 

40-53 

1393 

291*15 

•04 

50*17 

1724 

252*69 

■88 

Feb.    2 

4047 

— 14-01 

165-19 

1314*02 

5010 

- 17*34 

12657 

95386 

7 

40-37 

14-07 

39*21 

1313*99 

4998 

1742 

o-43 

•83 

12 

4024 

14  11 

273*20 

•96 

49*8i 

17-47 

23426 

•81 

17 
22 

4007 
39'87 

14- 14 
14-14 

M7*i6 
2ro8 

•92 
•88 

49-60 
49*35 

1750 
1751 

10807 
34184 

77 
•73 

27 

3964 

14*13 

25496 

•84 

49*07 

17*49 

215*57 

•69 

Mar.    3 

3938 

-14- 10 

12880 

131379 

4875 

-17*45 

89-26 

953*65 

8 

39*  10 

14*05 

259 

74 

4841 

17*39 

322*91 

•60 

13 
18 

3881 
3849 

1398 
1390 

23633 

1 1002 

•69 
•64 

48*04 
47*65 

1731 
17*21 

19651 
70*06 

*55 
■50 

23 

3817 

"13-81 

343*66 

*59 

47*25 

1709 

303*56 

*45 

28 
Apr.    2 

37-83 
3749 

1370 
- 1358 

21725 
9079 

•54 
13 1  3*49 

46-83 
4641 

1695 
-1680 

177-01 
5o*42 

•41 
953*35 

7 
12 

37'iS 
3681 

1344 
13*30 

32428 
197-72 

•44 
•40 

45*99 
45*57 

16-64 
1647 

28377 
15708 

•31 
•27 

17 

3647 

13*16 

71-12 

"35 

45*15 

16-29 

3o-35 

•22 

22 

36'H 

1300 

304*47 

'31 

4473 

16-09 

263-57 

•17 

27 

35-81 

12-84 

17778 

•27 

44'33 

1590 

13674 

•14 

Hay    2 
7 

35*49 
35'29 

-12-68 
1251 

5 1*05 
28429 

w 

131324 

•20 

43  94 
4356 

-1569 
15*49 

9-88 
24298 

953*10 
•06 

12 

34  89 

1234 

157*49 

43*19 

1528 

1 1604 

Sap.  1887.            Satellites  of  Saturn,  1887-88.  561 

Dione.  Shea. 

1887.  «                   «  o  o  „*  //  00 

Oct    15  5628  -1820  20987  657.46  78'59  -2542  23036  39g.2I 

20  5678           I8-28  147-33  79*29  2552  26857  ^5 

25  5729   1837  8483  8o-oo  2565  30682  ,30 

30  57-81      1848  2237  .59  8074  2580  34512  >34 

Nor.     4  5835  -i860  31996  657.63  8148  -2598  2346  39g.38 

9  5889        1875  25759  .^  8224  2618  6184 

14  5943        18*91  l9S'27  72  8299  2641  10027  #47 

19  5997        1909  13299  77  8375  2666  13874 

24  6050        1928  7076  ,gl  8449  2693  17726  6 

29  61-02        1949  857  .g5  8521  2722  21582  .^ 

Dec      4  61-51  -1971  30642  .g9  8591  -2753  25442  39g.65 

9  6199        1994  244*3*  .92  8657  2785  29307  <69 

14  6243        2018  18223  6srg6  8719  2818  33176  72 

19  6284        2042  120- 19  6  gw  8776  2851  1048  #7S 

24  6321        2066  5819  #02  8827  2885  4923  79 

29  6353        2090  35621  8872  2918  8802  #gl 

1888. 

Jan.      3  6380  -21-13  29425  gjg.^  8909  -2951  126*83  39g.g3 

8  6401        2136  23231  tQ&  8939  2982  16566  .g4 

13  6417        2157  17039  ^  8961  3012  20450  .gs 

18  6426        2176  10847  -og  8974  30-39  24335  .g6 

23  6429        2193  46-55  .Qg  8978  3063  28221  .gs 

28  64-26        2209  34463  8974  3084  32106  .g5 

Feb.     2  6417  -22-21  28270  8961  -3102  35991  39g.g3 

7  6401        2231  22075  .02  8939  3i!5  3874  .g, 

12  6380        2238  15877  ^g-oo  8909  3125  7755  79 

17  6353        2242  9677  6sr97  8872  3131  "6-34  75 

22  6321        2243  3474  .94  88-27  31-32  15509  mJ2 

27  6284        2240  33268  .g9  8776  3129  19381  t69 
Mar.     3  6244  -2235  27057  ,g5  8719  -3122  23250  ^.^ 

8  6200        2228  20842  ,gl  8658  31-11  27115  >6o 

13  6152        2217  14623  6  8592  3096  30975  #55 

18  6103        2204  8399  85-22  3078  34830  >5I 

23  6051        2189  2170  #66  8450  3057  2681  #46 

28  5998        21 71  31936  .62  8376  3033  6527  .42 
Apr.      2  5944  -2152  25698  65rS7  8301  -3006  10369  39g.37 

7  5890        21-32  194*55  .52  8225  2977  14206  .32 

12  5836        2109  13207  7  8150  2946  18038  .37 


5<5* 


Mr.  Marth,  Ephemerides  of  the 


xlvii.  9, 


Greenwich 
Noon. 

1887. 
Apr.     17 

22 

27 

May      2 

7 
12 


Dione. 


J4-L 

5782  2086  69°'S4 

57-29  206 1  6*97 

5678  2036  30436 

5627  -20*10  24171 

5579  1984  17902 

SS'32  l9'S7  1 1630 


Diff. 

o 

'43 

'39 

35 

65731 

•28 


Shea. 

ft. 


Z.-L 


8075 
80OI 

7929 

78'59 

77'9I 
77*26 


2913  21865 

28 79  25688 

2843  29507 

-2807  33322 

2770  1 133 

2733  49'40 


Diff. 

o 
•23 

■19 

'IS 
398TI 

•07 


Approximate  Greenwich  mean  times  of  conjunctions  of  the 
satellites  with  the  centre  of  the  planet  or  of  their  passages  in 
the  direction  of  the  minor  axis  of  the  ring. 

"  n  "  inferior  conjunction,  or  satellite  north,  moving  from  the 
following  to  the  preceding  side. 

"  s  "  superior  conjunction,  or  satellite  south,  moving  from  the 
preceding  to  the  following  side. 

In  the  case  of  Titan  and  Iapetus  the  approximate  distances 
from  the  centre  or  from  the  major  axis  of  the  ring  are  added,  at 
which  they  pass  in  the  direction  of  the  minor  axis. 


i837        h 

Nov.  1  10-7  Rh.  n. 
13-6  Di.  s. 
1 4*  1  En.  s. 
1 6*2  Mi.  8. 

193  Te.  n. 

2  149  Mi.  s. 
17-9  Te.  s. 
22*5  Di.  n. 
23-0  En.  8. 

3  135  Mi.  8. 
15*4  En.  n. 
16-6  Te.  n. 
1 69  Rh.  s. 

4  73  Di-  ■■ 

7*8  En.  8. 

121  Mi.  s. 
15-2  Te.  s. 

5  10  Tit.  s.  61" 
13-9  Te.  n. 
162  Di.  n. 

1 6-7  En.  s. 
23*1  Rh.n. 

6  12-5  Te.  8. 

7  10  Di.  8. 
11*2  Te.  n. 

8  5-4  Rh.  a. 
9*8  Di.  n. 
9-9  Te.  b. 

10-5  En.  s. 

9  8*5  Te.  n. 
16-5  Mi.n. 
187  Di.  8. 

1 94  En.  8. 


Nov.  10  7-2  Te.  8. 
116  Rh.n. 
ii*8  En.n. 
15-1  Mi.  n. 

1 1  3-5  Di.  n. 
5*8  Te.  n. 

137  Mi.  n. 
207  En.n. 

12  4-5  Te.  8. 
12-3  Mi.  n. 
124  Di.  s. 
1 3- 1  En.  s. 
178  Rh.  s. 
202  Tit. n.  58" 

13  31  T*.  n. 
10*9  Mi.  n. 
21*2  Di.  u. 
22-0  En.  s. 

14  i'8  Te.  s. 

87  lap.  8.  52" 
14*5  En.  n. 
20-9  Mi.  s. 

15  o-o  Rh.n. 
0-4  Te.  n. 
6*1  Di.  8. 
6*9  En.  s. 

19*5  Mi.  s. 
23-1  Te.  8. 

16  14-9  Di.  n. 
15-8  En.  s. 
181  Mi.  b. 
217  Te.  n. 

17  62  Rh.  8. 


Nov.  17  8-2  En.  n. 
167  Mi.  8. 
20-4  Te.  s. 

237  Di.  s. 

18  153  Mi.  8. 
17-1  En.n, 
19  o  Te.  n. 

19  8-6  Di.  n. 
9-6  En.  s. 

12-4  Rh.n. 
140  Mi.  s. 
177  Te.  s. 

20  1 2*6  Mi.  s. 
16-3  Te.  n. 
174  Di.  s. 
184  En.  8. 

238  Tit. s.  62* 

21  10*9  En.  n. 
1 1-2  Mi.  s. 
15-0  Te.  s. 
186  Rh.  s. 

22  2*2  Di.  n. 
136  Te.  n. 
19-8  En.  n. 
211  Mi.n. 

23  1 1 'I  Di.  8. 
1 2*2  En.  s. 
123  Te.  s. 
197  Mi.n. 

24  o*8  Rh.  n. 
10-9  Te.  n. 
18-3  Mi.  n. 
19-9  Di.  n. 


Sup.  1887. 


Satellites  of  Saturn,  1887-88. 


563 


1887        h 
Not.  24  2i'i  En.  s. 

25  9*6  Te.  b. 
135  En. n. 
17-0  Mi.  n. 

26  4*8  Di.  s. 
70  Kh.  8. 
8-2  Te.  n. 

1 56  Mi.  n. 
22*4  En.  n. 

27  6-9  Te.  s. 
1 3-6  Di.  n, 
14-2  Mi.  n. 
14-8  En.  s. 

28  55  Te.  n. 
73  En. n. 

12*8  Mi.  n. 
132  Rh.n. 

187  Tit.  n.  60" 
22*4  Di.  8. 

29  42  Te.  8. 
1 1 '4  Mi.  n. 
162  En. n. 
227  Mi.  s. 

30  28  Te.  n. 

7'3  Di.  n. 

8-6  Ec.  s. 
1 00  Mi.  n. 
19*4  Kh.  s. 
Dec.  1  15  Te.  s. 
161  Di.  s. 
175  En.  s. 
20'0  Mi.  8. 

2  01  Te.  n. 
99  En.  n. 

1 8-6  Mi.  s. 
22-8  Te.  s. 

3  09  Di.  n. 
16  Rh.n. 

17-2  Mi.  s. 

188  En.  n. 
2 1  4  Te.  n. 

4  9*8  Di.  b. 
1 1-2  En.  s. 
158  Mi.  s. 
20*i  Te.  8. 

5  78  Kh.  s. 
14*4  Mi.  s. 

186  Di.  n. 

187  Te.  n. 
20' 1  En.  8. 

6  12*6  En.  n. 
13-0  Mi.  s. 
1 7  4  Te.  s. 
22-0  Tit.  s.  64" 

7  34  Di.  a- 
1 1-6  Mi.  s. 

T40  Kh.n. 

1 60  Te.  n. 

2 1 '4  En.  n. 


Dec  8  10-3  Mi.  8. 
1 2*3  Di.  n. 
1 39  En.  8. 

147  Te.  8. 
9  1 33  Te.  n. 

20- 1  Kh.  8. 
20  2  Mi.  n. 
211  Di.  8. 
22-8  En.  s. 

10  120  Te.  a. 
15*2  En.  n. 
18-8  Mi.  n. 

11  5*9  Di.  n. 
7  -6  En.  8. 

io*6  Te.  n. 
17-4  Mi.  n. 

12  2*3  Kh.n. 
9*3  Te.  b. 

148  Di.  8. 
160  Mi.  n. 

16  5  En.  s. 

13  79  Te.  n. 
9-0  En.  n. 

14*6  Mi.  n. 
23-6  Di.  n. 

14  66  Te.  a. 
8-5  Kh.  s. 

133  Mi.n. 
16-9  Tit.  n.  62" 

17  8  En.  n. 

15  52  Te.  n. 
84  Di.  s. 

103  En.  8. 
1 1*9  Mi.  n. 

16  38  Te.  s. 
105  Mi. n. 
14  7  Kh,  n. 
172  Di.  il 
1 9*  1  En.  8. 

J  7  2'5Te.n. 
11*6  En.n. 
20*4  Mi.  s. 

18  vi  Te.  s. 
21  Di.  a. 

190  Mi.  8. 
20*5  En.  n. 
20*8  Kh.  s. 
23-8  Te.  n. 

19  1 09  Di.  n. 
12-9  En.  s. 
176  Mi.  s. 
224  Te.  s. 

20  162  Mi.  s. 
197  Di.  8. 
2i-i  Te.  n. 
2i*8  En.  8. 

21  3oKh.n. 
142  En.  n. 
I4'9  Mi.  s. 


Dec.  21  197  Te.  8. 

22  46  Di.  n. 
67  En.  8. 

13-5  Mi.  8. 
18-4  Te.  a. 
20  o  Tit.  a.  66" 

23  9-2  Kh.  s. 
1 2' 1  Mi.  8. 
13-4  Di.  s. 
155  En. 8. 
17-0  Te.  s. 

24  80  En. n. 
107  Mi.  s. 
157  Te.  n. 
195  lap. n.  58" 
222  Di.  n. 

25  14*3  Te.  8. 
153  Kh.n. 
16  8  En.n. 
206  Mi.n. 

26  70 Di.  8. 
9-3  En.  8. 

12*9  Te.  n. 
19*2  Mi.n. 

27  116  Te.  s. 
15-9  Di.  n. 
178  Mi.  n. 

1 82  En.  s. 
215  Kh.s. 

28  10-2  Te.  n. 
io*6En.n. 
165  Mi.  n. 

29  07  Di.  8. 
89  Te.  s. 

1 5- 1  Mi.n. 
19-5  En.n. 

30  3  7Rh.n. 
7*5  Te.  n. 
9-5  Di.  n. 

11*9  En.  s. 
137  Mi.n. 
14-8  Tit.  n.  64" 

31  62  Te.  8. 
12*3  Mi.n. 

183  Di.  s. 
20  8  En.  8. 

1888       h 

Jan.     1     48  Te.  n. 

98  Kh.  8. 

io*9  Mi.  n. 

13-2  En.n. 

2  3*2  Di.  n. 

3*5  To-  »• 
208  Mi.  8. 

22-1  En.n. 

3  2-1  Te.  n. 
120  Di.  8. 
14*5  En.  s. 
160  Kh.n. 


564                       Mr.  Marth,  Ephemerides  of  the  xlyii.  9, 

1888        huh 
Jan.    3  194  Mi.  8.  Jan.  17     5*8  Te.  s.  Jan.  31  14-5  Mi. n. 

4  08  Te.  8.  7-3  En. 8.  16*5  En. n. 
70  En.n.  1 1*3  Mi. n.  190  lap.  s.  71" 

181  Mi.  s.  18    44  Te.  n.             Feb.    I     5-3  Bl  n. 

20-8  Di.  n.  9-9  Mi.n.  8*1  Te.  8. 

234  Te.  n.  13*0  Di. n.  8*9  En.  s. 

5  15-8  En.n.  1 6* 2  En.  a.  131  Mi.n. 
167  Mi.  s.  19  3*1  Te.  8.  2  00  Rh.  s. 
22*0  Te.  8.  8-6  Mi.  n.  67  Te.  n. 
22- 1  Eh.  8.  86  En.  n.  118  Mi.  n. 

6  5*6  Di.  s.  Hi  Rh.  a.  14*1  Di.  8. 
83  En. s.  21*9  Di.  b.  17*8  En.  s. 

15*3  Mi.  s.  20     17  Te.  n.  3     5-4  Te.  s. 

207  Te.  n.  17-5  En.n.  1 0*2  En.n. 

7  139  Mi.  s.  185  Mi.  s.  iO'4Mi.n. 
14-5  Di.  n.  21  0*3  Te.  8.  22-9  Di.  n. 
17-2  En.  8.  67  Di.  n.  4  4*0  Te.  n. 
174  Tit.  s.  68"  9-9  En.  8.  62  Rh.n. 
19-3  Te.  8.  17-1  Mi.  s.  90 Mi.  n. 

8  4-3  Rh.n.  17-2  Rh.n.  19*1  En.n. 

96  En.n.  23*0  Te.  n.  5  27  Te.  8. 
125  Mi.  8.  22  15-5  Di.  s.  7-6  Mi.n. 
180  Te.  n.  157  Mi.  8.  77  Di.  8. 
23-3  Di.  s.  x8-8  En.  s.  115  En.  8. 

9  Hi  Mi.  s.  21-6  Te.  s.  6  1*3  Te.  n. 
166  Te.  s.  23  1 1-2  En. n.  4*0  En. n. 
185  En.n.             .  14*3  Mi.  8.  6  2  Mi.n. 

10  81  Di.  n.  14-6  Tit.  s.  70"  123  Rh.  s. 

97  Mi.  b.  20-3  Te.  n.  i6'6  Di.  n. 

105  Rh. s.  23*4  Rh. s.  23*9  Te.  a. 
109  En.  s.  24  03  Di.  n.  712*8  En.n. 
153  Te.  n.  129  Mi.  s.  16*1  Mi.  8. 

11  1 39  Te.  b.  189  Te.  s.  22*6  Te.  n. 
169  Di.  8.  20-1  En.n.  8     1*4  Di.  s. 

197  Mi.n.  25     92DU  8.  53  En.  s. 

198  En.  8.  1 1-5  Mi.  s.  i2-o  Tit.  s.  72" 

12  12  2  En.n.  12-5  En.  s.  14*8  Mi.  s. 
12-5  Te.  n.  17-6  Te.  n.  18-5  Rh.n. 
166  Rh.n.  26  5'6Rh.n.  21-2  Te.  s. 
1 83  Mi. n.  10-2  Mi.  s.  9  10 2  Di.  n. 

13  17  Di.  n.  162  Te.  s.  134  Mi.  a. 
1 1-2  Te.  s.  i8*o  Di.  n.  14*2  En.  s. 
169  Mi. n.  214  En.  s.  19*9  Te.  n. 
2ri  En.n.  27  13*8  En.n.  10    66  En.n. 

14  9*8  Te.  n.  14  9  Te.  n.  1 2*0  Mi.  s. 

106  Di.  s.  28  28  Di.  s.  18-5  Te.  s. 
13-5  En.  b.  117  Rh.s.  19-0  Di.  s. 
155  Mi.  n.  13*5  Te.  8.  11  07  Rh.s. 
22*8  Rh.s.  29  1 1 '6  Di.  n.  106  Mi.  s. 

15  60  En.n.  1 2- 1  Te.  n.  15*5  En. n. 
8- 5  Te.  s.  1 5*2  En.  s.  1 72  Te.  n. 

121  Tit.  n.  66"  17-3  Mi.n.  12    39  Di.  n. 

14*  1  Mi.  n.  30    76  En.  n.  7-9  En. b. 

1 94  Di.  n.  1 08  Te.  8.  92  Mi.  b. 

16  7-1  Te.  n.  15-9  Mi.  n.  158  Te.  a. 
127  Mi.  n.  17-9  Rh.n.  13  68  Rh.n. 
14-8  En. n.  20 4  Di.  s.  78  Mi.  6. 

17  4*2  Di.  s.  31     9*4  Te.  n.  127  Di.  8. 
49  Rh.  n.  96  Tit.  n.  67"  145  Te.  n. 


Sap.  1887.             Satellites  of  Saturn,  1887-88.  565 

1888        h  h  h 
Fob.  13  i6*8  E11.  s.            Feb.  28    2*0  En.n.            Mar.  12  14-3  Ml  0. 

14  6-4  Mi.  a.  97  Mi.  s.  189  En. n. 
9-2  En.  n.  138  Di.  n.  21*9  Te.  n. 

131  Te.  b.  168  Te.  n.  13  6*2  *>i.  n. 
215  Di.  n.  29    20  Rh.  8.  1 13 En«  «• 

15  1 1-8  Te.  d.  83  Mi.  8.  129  Mi.  8. 
13  o  Rh.  s.  10-9  En.  n.  I5'i  Rh.  8. 
164  Mi.  n.  155  Te.  8.  206  Te.  s. 
18-1  En. n.  226  Di.  s.  14    37  En. n. 

16  6-3  Di.  8.  Mar.  1  3-4  En.  s.  1 1'6  Mi.  b. 
71  Tit. n.  68"  69  Mi.  8.  150  Di.  8. 

104  Te.  a.  141  Te.  n.  192  Te.  n. 

106  En.  s.  2    5-5  Mi.  s.  15  102  Mi.  8. 

15-0  Mi. n.  7*5  Di.  n.  126  En. n. 

17  90  Te.  n.  82  Rh.n.  17*9  Te-  «• 

136  Mi.  n.  122  En.  b.  21*3  Rh.  n. 
15-2  Di.  n.  128  Te.  8.  238  DL  n. 
192  Rh.n.  3  47En.n.  16  5  1  En.  s. 
194  En.  8.  4-9  Tit. n. 68"  88  Mi.  8. 

18  77  Te.  8.  114  Te. n.  165  Te.  n. 
1  19  En. n.  154  Mi. n.  17  7'4  Mi.  a. 
122  Mi.  n.  163  Di.  8.  87  Di.  b. 

19  00  Di.  8.  4  10-1  Te.  8.  13  9  En-  »• 
43  En.  b.  136  En.n.  152  Te.  8. 
63  Te.  n.  14*1  Mi. n.  18    3-5  Rh. 8. 

io*8  Mi  n.  14-4  Rh.  a.  60  Mi.  s. 

20  1 -3  Rh. s.  5  11  DL  n.  64  En. n. 
50  Te.  8.  60  En.  s.  138  Te.  n. 
8*8  Di.  n.  87  Te.  n.  17*5  Di-  n- 
94  Mi.  n.  127  Mi.  n.  19    29  Tit.  n.  68" 

132  En.  8.  6    74  Te.  8.  125  Te.  b. 

21  3'6Te.n.  100  Di.  8.  15-3  En.  n. 
56  En. n.  1 1 -3  Mi. n.  160  Mi. n. 
8-1  Mi. n.  14*9  En. 8.  20    24  Di.  8. 

177  Di.  8.  20-6  Rh.n.  77  En-  »• 

22  23  Te.  8.  7  6*o  Te.  n.  97  Rh.  n. 
67  Mi.  n.  7*3  En.  n.  1 1  *  1  Te.  n. 
7'SRh.n.  99Mi.n.  21     98  Te.  a. 

14-5  En.n.  188  Di.  n.  112  Di.  n. 

23  09  Te.  n.  8  47  Te.  a.  22  84  Te.  n. 
25  Di.  n.  85  Mi.  n.  159  Rk  «. 
7-0  En.  s.  1 6'2  En. n.  200  Di.  8. 

236  Te.  8.  9    27  Rh.  s.  23     71  Te.  8. 

24  95  Tit. a.  72"  3*3  Te.  n.  24  49  Di.  n. 
113  Di.  a.  3*6  Di.  8-  5'8Te.  n. 

137  Rh.  b.  72  Mi.n.  9*  Mi.  n. 
22-2  Te.  n.  8*6  En.  s.  104  En.  b. 

25  83  En.n.  10    20 Te.  s.  221  Rh.n. 

138  Mi.  b.  12-5  Di.  n.  25  28  En. n. 
201  Di.  n.  171  Mi.  8.  44  Te.  8. 
20  9  Te.  8.  17*5  En.  a.  77  Mi.  n. 

26  12-4  Mi.  s.  II  o-6Te.n.  137  Di.  8. 
171  En.  n.  7'4  Tit.  b.  72"  26  31  Te.  n. 
19-5  Te.  n.  89  Rh.n.  63  Mi. n. 
19-8  Rh. n.  100  En. n.  117  En« n- 

27  5*0  Di.  8.  157  Mi.  8.  226  Di.  n. 
9-6  En.  8.  21-3  Di.  s.  27     17  Te.  8. 

Ill  Mi.  s.  233  Te.  a.  41  En.  a. 

1 8*2  Te.  8.  12     i-o  Iap.n.  74"  4*3  R1*. ■• 


566 


Mr.  Marthy  Ephemerides  of  the 


xlvxi.  9, 


1888        h 
Mar.  27    4*9  Mi.  n. 

57  Tit.  8. 70" 

28  0-3  Te.  n. 
74  Di.  8. 

130  En.  8. 
14-8  Mi.  b. 
23  o  Te.  8. 

29  55  En.  n. 
10-5  Rh.n. 
1 35  ML  8. 
1 6*3  Di.  n. 
217  Te.  n. 

30  121  Mi.  b. 
14*4  En.  n. 
20*3  Te.  b. 

31  i*i  Di.  8. 
6-8  En.  8. 

107  Mi.  8. 
16-8  Rh.  8. 
19-0  Te.  n. 
Apr.  1  9-3  Mi.  8. 
99  Di.  n. 
157  En.  s. 
17*6  Te.  s. 

2  7'9  Mi.  8. 
8*i  En.  n. 

16-3  Te.  n. 
18  8  Di.  8. 
23*0  Rh.n. 

3  66  Mi.  8. 
15-0  Te.  s. 
1 70  En.  n. 

4  v6  Tit.  n.  66" 
3-6  Di.  n. 

9- 5  En.  s. 
13-6  Te.  n. 

5  5-2  Rh.  8. 
1 2*3  Te.  s. 
12*5  Di.  a. 

6  io*8  En.  n. 
10-9  Te.  n. 
13  7  Mi.  n. 
21*3  Di.  n. 

7  33  En.  8. 
9-6  Te.  s. 

1 1 -4  Rh.n. 
12*4  Mi.  n. 


Apr.    8    6*2  Di.  8. 

8*2  Te.  n. 

H'oMt.n. 

1 2*  I  En.  b. 

9    4*6  En.  n. 

69  Te.  8. 

9*6  Mi.  n. 

15-0  Di.  n. 

177  Rh.  8. 

10  k'6  Te.  n. 
8-2  Mi.  n. 

13  5  En.  n. 
23*9  Di.  a. 

1 1  4*2  Te.  8. 
5*9  En.  8. 
6-8  Mi.  n. 

23*9  Rh.n. 

12  29  Te.  n.  68" 
46  Tit 8. 
87  Di.  n. 

14*8  En.  8. 

13  1-5  Te.  8. 
7-3  En.  n. 

176  Di.  s. 

14  0-2  Te.  n. 
6*1  Rh.8. 

14-0  Mi.  8. 
i6'2  En.  n. 
22*9  Te.  s. 

15  2*4  Di.  n. 
8-6  En.  s. 

12-6  Mi.  s. 
215  Te.  n. 

16  ii*3  Mi.  8. 
1 1 '3  Di.  8. 
12*3  Rh.n. 
17*5  En.  s. 
20*2  Te.  8. 

17  9-9  Mi.  8. 
9*9  En.  n. 

188  Te.  n. 
202  Di.  n. 

1 8  14*2  lap.  s.  72" 
17-5  Te.  s. 

1 8-6  Rh.  b. 

19  5-0  Di.  8. 
i6"2  Te.  n. 


Apr.  20    07  Tit.  n.  64" 
13-9  Di.  n. 
14*8  Te.  8. 

21  o*8  Rh.n. 
135  Te.  n. 
227  Di.  b. 

22  12- 1  Te.  b. 

23  7-1  Rh.8. 
7'6  Di.  n. 

108  Te.  n. 

24  9-5  Te.  8. 
16-4  Di.  s. 

25  81  Te.  n. 
13-3  Rh.n. 

26  i*3  Di.  n. 
6-8  Te.  s. 

27  5-4  Te.  n. 
10*2  Di.  8. 
19*6  Rh.  s. 

28  40 Tit 8.  66" 
4*1  Te.  s. 

19-0  Di.  n. 

29  2*8  Te.  n. 

30  1-4  Te.  s. 
18  Rh.n. 
3'9  *>i.  s. 

May  1  01  Te.  n. 
12  7  Di.  n. 
22*8  Te.  b. 

2  81  Rh.s. 
21*4  Te.  n. 
2i-6  Di.  8. 

3  201  Te.  8. 

4  6-5  Di.  n. 
14-3  Rh.n. 
18  7  Te.  n. 

5  15-3  Di.  a. 
IT'4  Te.  s. 

6  16*1  Te.  n. 
20*6  Rh.  b. 

7  0-2  Di.  n. 
0-2  Tit  n.  62" 

147  Te.  8. 

8  90  Di.  8. 
13-4  Te.  n. 

9  28  Rh.n. 


By  means  of  this  list  of  conjunctions  of  the  five  inner  satel- 
lites, approximate  values  of  their  co-ordinates  x  and  y,  expressed 
in  semi-diameters  of  the  planet's  equator,  may  be  easily  found  for 
any  other  time  t  in  the  following  little  table,  the  argument  of 
which  is  the  interval  r  between  the  time  t  and  the  time  of  the 
next  preceding  or  following  conjunction.  The  satellites  are  on 
the  same  side,  north  or  south,  of  the  major  axis  of  the  ring  as  at 
the  time  of  the  next  conjunction,  and  as  they  move  in  the  direc- 
tion of  decreasing  position,  angles,  they  are  in  the  interval  between 


Sup.  1887.  Satellites  of  Saturn,  1887-88.  567 

aN.  and  a  S.  conjunction  on  the  preceding  side,  and  between  a  S. 
and  a  N.  conjunction  on  the  following  side  of  the  direction  of  the 
minor  axis  of  the  ring.  They  are  at  their  greatest  elongations, 
Mi.  57,  En.  8*2,  Te.  11*3,  Di.  16*4,  Rh.  27*1  hours  before  or  after 
the  times  of  conjunction. 


T 

Mimas. 

Enceiadus. 

Tethys. 

Dions. 

Shea. 

h 
O 

0*0 

I'l 

o-o 

y. 

1-4 

O'O 

y, 

17 

00 

?4 

2*2 

00 

y. 

30 

I 

o*9 

VI 

08 

1*4 

07 

17 

o-6 

27 

05 

3-0 

2 

17 

0*9 

1*5 

i'3 

1*4 

17 

1*2 

2'I 

i-o 

30 

3 

2'3 

07 

2*2 

1*2 

20 

1-6 

18 

2*1 

x'5 

30 

4 

28 

0*5 

28 

I'O 

2*6 

i"5 

24 

20 

20 

30 

5 

3i 

0*2 

33 

08 

32 

1  "3 

2-9 

19 

25 

2*9 

6 

3'i 

o-i 

37 

0*6 

37 

i-i 

35 

18 

3*o 

2*9 

7 

2-9 

0-4 

39 

03 

4"i 

0*9 

4-0 

17 

35 

2-8 

8 

2-5 

o-6 

40 

o-i 

45 

08 

44 

16 

40 

27 

9 

i-8 

08 

40 

0*2 

47 

o*6 

48 

i'5 

4*5 

26 

10 

i-i 

I'O 

3-8 

0*5 

4*9 

0-3 

52 

i'3 

49 

2*5 

11 

5-o 

O'l 

56 

i-i 

5*3 

24 

12 

5'8 

0-9 

57 

2*3 

14 

6*2 

o-5 

6'5 

2*1 

16 

64 

01 

71 

18 

20 

8-2 

1*2 

271 

89 

O'O 

Observers  who  are  desirous  to  follow  the  motions  of  the 
satellites  will  find  it  of  service  to  lay  down  the  data  of  the  table 
graphically  on  a  sufficiently  large  scale,  so  that,  by  marking  the 
corresponding  times  for  the  night  of  observing,  they  may  get 
information  about  the  places  of  the  satellites  at  a  glance. 

Careful  observations  of  the  position-angles  of  the  satellites  at 
the  times  of  their  passing  the  direction  of  the  minor  axis  of  the 
ring  afford  the  best  means  for  determining  the  longitudes  of 
the  satellites  in  their  orbits  and  are  least  liable  to  systematic 
errors,  so  that  their  evidence  must  be  of  very  great  weight  in 
settling  any  questions  concerning  the  orbital  longitudes. 

As  the  present  apparition  of  Saturn  is  the  last  one,  for  some 
years  to  come,  which  will  allow  observations  of  the  conjunctions 
of  Mimas  with  the  centre  of  the  ball,  it  is  to  be  hoped  that  the 
opportunities  for  observing  such  conjunctions  with  the  powerful 
telescopes  now  available  will  not  be  neglected. 


568  Mr.  Marth,  Ephemertdes  of  the  xlvii.  9, 

Approximate  Differences  of  Eight  Ascension  and  Declination  between  the  three 

outer  Satellites  and  the  Centre  of  Saturn. 

Titan.  Bypervm.  lapetus. 


Greenwich 
Noon. 
1887. 

Oct.     15 

o«— A* 

8 

-12-34 

—    21 

a,— A. 

-  r68 

+  60-0 

a»— A. 

s 
-2392 

+  16*2 

16 

— 12-97 

-254 

-  656 

+  47*2 

2613 

1 1-5 

17 

-11*71 

-45'° 

- 1073 

+  291 

—  28*19 

-  67 

18 

-  8'79 

-58  3 

-1382 

+  7*9 

3007 

+   1*9 

19 

-  463 

-634 

-1565 

-141 

-3175 

—  2-9 

20 

+    0*20 

-596 

-1618 

-350 

33*23 

77 

21 

+    5'°2 

-473 

-1549 

-53'3 

-34*49 

—  12*4 

22 

+    9*12 

-281 

-1372 

-679 

35*52 

170 

23 

-u-86 

-  46 

-11*05 

-782 

-36*33 

-21-5 

24 

+ 12*76 

+  197 

-  7*67 

-835 

36*90 

25'9 

25 

+  1161 

+  408 

-  380 

-836 

-37'22 

-30-1 

26 

+  8-55 

+  55'2 

+  0*32 

-786 

37*30 

34'i 

27 
28 

+  405 
-  114 

+  605 
+  557 

+  443 
+  825 

-685 
-53*9 

-3714 
3674 

-37"9 
414 

29 

-  616 

+  41*8 

+  ir5° 

-35*4 

-3609 

-447 

30 

— 10-22 

+  2I-I 

+ 1387 

-141 

3521 

477 

31 
Nov.     1 

—  12*72 
-13-33 

—  29 

—  26-6 

+  1504 
+ 1478 

+  8*5 
+  303 

-3410 
3276 

-50'5 
529 

2 
3 

— 12*00 
-    896 

-464 

-598 

+ 12-95 
+  9*60 

+489 
+  6r8 

-31-21 
29-46 

-54*9 
566 

4 

-    464 

-647 

+  S'c6 

+  672 

-2752 

-58^0 

5 

+    0-35 

-6o-6 

—   0*12 

+  64*1 

2539 

591 

6 

7 
8 

+    5'30 

+  9*49 
+ 12*26 

-477 
-278 

-  37 

-  532 

-  9*93 
- 13*52 

+  53"  1 
+  36-0 

+  149 

-23*  10 

20*66 

-1808 

-59'8 

60*1 

— 6o*i 

9 

+  13*12 

+  21*1 

-1585 

—  7*6 

15-38 

597 

10 

+ 1187 

+  42"5 

- 1683 

—29-6 

-1257 

-589 

11 
12 

+  865 
+   397 

+  57'0 
■••  62*0 

-1652 
-1503 

-49*4 
-65-7 

9-67 
—  6-71 

57'8 
-564 

13 

-   138 

+  567 

- 12-53 

-77*8 

369 

54-6 

14 

-  6  54 

+  42*0 

—    9*22 

-850 

—  0*64 

-525 

IS 

— 1067 

+  20*6 

-  5  33 

-869 

+  2-42 

501 

16 

-13*17 

-  41 

—  1*09 

-834 

+   5'49 

-47*4 

17 

-1370 

-283 

+   3*24 

r74  7 

8-53 

44*4 

18 

-1225 

-485 

+  736 

-607 

+  ii'54 

—41-2 

19 

-  904 

— 61*9 

+ 1097 

-427 

1450 

377 

Sup.  1887.  BatdUt*  of  Safer*,  1887-88*  £69 


• 

Gmnwioh 
Koon. 

..-A. 

J.-D. 

.,-A. 

«,-D. 

«•-▲. 

••-D. 

1887. 
Not.   20 

■ 
-  454 

-66-6 

■ 
+ 13  75 

n 
—  21-2 

+ 17*38 

-33* 

21 

+  o-6i 

-618 

+ 15*38 

+    2*1 

2016 

29-9 

22 

+  570 

-48*2 

+ 15*5* 

+  25*2 

+  22*84 

—25*2 

23 

+  996 

-275 

+ 14*12 

+  45*8 

2540 

21*5 

24 

+ 1272 

-  25 

+  11*05 

+  6i*i 

+2783 

—  17-0 

25 

+  13*49 

+  23*0 

+  6-62 

+69*1 

30*1© 

12-4 

1 

I 

26 

+  I2'08 

+  44'8 

+   l'34 

+  68*4 

+  32-20 

+  77 

1 
1 

27 

+  866 

+  593 

-  413 

+  59*1 

34" 

—  2-9 

28 

+  378 

+  63-9 

-  914 

+429 

+  35-85 

+  1-9 

29 

-   176 

+  57*9 

-I3-I9 

+  21*9 

3r38 

6-7 

30 

—  7-02 

+42'3 

-1598 

-  1*4 

+  3869 

+  H-6 

Dee.     1 

+  11*19 

+  19*8 

-17  38 

—24*6 

3978 

164 

2 

-1364 

-  5  8 

-1740 

—46*1 

+40-64 

+  21*1 

3 

-14*05 

-307 

— 16*16 

-643 

41*26 

25-8 

4 

—  12*42 

—51*2 

-13*82 

-782 

+4164 

+  30-3 

5 

—  9-01 

-64-6 

-10*58 

-872 

41-77 

347 

6 

-  4*31 

-68*6 

-  6  67 

-908 

+4165 

+  39*o 

1 

7 

+    I '02 

-°3'3 

-  2*32 

-887 

41-28 

43*0 

8 

+    6*26 

-49-0 

+  218 

-81*0 

+  40-65 

+468 

9 

+  IO-50 

-268 

+  656 

-679 

3977 

50*4 

10 

+  I320 

-  o-8 

+ 10*48 

-5°-o 

+  38-64 

+  537 

•     11 

+  I382 

+  25*5 

+ 1362 

-283 

37*27 

567 

12 

+  1 2*20 

+  477 

+ 15*64 

-  4"  1 

+  35*67 

+  59*3 

13 

+  854 

+  62*1 

+  16*21 

+  205 

33"84 

6i*6 

14 

+  3*44 

+  66*1 

+  15*11 

+  43*0 

+  3178 

+  63*6 

15 

—  2*25 

+  59* 

+ 12-31 

+  60-8 

2951 

651 

16 

—  7-60 

+  42*3 

+  800 

+  712 

+  27-05 

+  663 

17 

—  11  75 

+  187 

+  267 

+  727 

2441 

67-0 

18 

-1409 

-  80 

-  303 

+  651 

+  21-60 

+  67-3 

19 

- 1433 

-33'6 

-  836 

+  497 

1864 

67-2 

20 

- 1247 

-54'5 

— 1280 

+  286 

+ 15  55 

+  66-6 

21 

-  883 

-676 

- 1599 

+  4*6 

1234 

656 

22 

-  3*93 

-7i*3 

-1775 

— 2c-o 

+  904 

+  64*2 

23 

+  i*55 

-648 

— 18*07 

-43-1 

567 

62*2 

24 

+  681 

-49*2 

—  17*06 

-63-2 

+  2*26 

+  599 

25 

+  11-07 

-258 

-14*86 

-79*0 

-  117 

571 

26 

+ 1365 

+   i-4 

—  11-69 

-897 

—  4*61 

+  53*9 

27 

+  14*06 

+  285 

-  777 

-94*8 

803 
8  8 

50-2 

570  Mr,  Marthy  Ephemeride*  of  the  nm.  9, 


Greenwich 
Noon. 
1887. 

Dee.    28 

«.-A. 

■ 
+  12*19 

8,-D. 

// 
-5IO 

•»— A* 

-  335 

H 
-940 

««— A. 

8 

-"39 

8,-D. 

+  48*2 

39 

+  827 

+  65*1 

+  1*29 

-873 

1469 

419 

30 

+  2*96 

+  683 

+  5-85 

-74*8 

-1789 

+  37*2 

31 

-  286 

+  6o-i 

+  10*01 

-57*i 

20*97 

321 

1888. 
Jan.      x 

-  823 

+42*0 

+ 1 3*43 

-351 

-2391 

+  268 

2 

— 12*29 

+  16*9 

+  1575 

—  10*2 

26*69 

21*3 

3 

- 1446 

—  106 

+ 16*65 

+  157 

—29*29 

+  15*5 

4 

-  H'47 

-36*9 

+  15-86 

+  40*1 

3168 

9*6 

5 

-12*37 

-57*9 

+ 1332 

+  6o*i 

-3385 

+  3*5 

6 

-  850 

-70*7 

+  9*17 

+  72*9 

35*79 

-  2-6 

7 

-  341 

-73'5 

+  3*6 

+  76*6 

-37*48 

-  8*8 

8 

+    2*  l8 

-659 

-  i*95 

+  70*6 

38*90 

15*0 

9 

+  7'45 

-487 

-  754 

+  56*1 

-  4005 

—  21*2 

10 

+  1161 

-24*2 

- 12*29 

+  35' 

40*92 

27*2 

11 

+  14*00 

+  4*0 

-15*80 

+   104 

+  4151 

-331 

ia 

+  I4'I7 

+  317 

-1786 

-  154 

41-81 

39*9 

13 

+  12*02 

+  54*3 

- 18*45 

—  40*0 

-4181 

44*4 

14 

+  7*86' 

+  679 

- 1763 

-  617 

4152 

497 

15 

+  2'37 

+  70*1 

- 15-58 

-  792 

-40*95 

-547 

16 

-  3'5i 

+60*6 

-1250 

—  916 

40*09 

59*3 

17 

-  883 

+  4i'i 

-  8  62 

-  981 

-3896 

•763* 

18 

-  "75 

+  14*9 

—    4*20 

-  986 

37*56 

67*5 

19 

-1470 

-13*6 

+  0*50 

-  928 

-35*91 

-70*9 

20 

- 14-46 

-40*3 

+   516 

-  8ro 

34*02 

73*9 

21 

—  12*10 

— 6i*i 

+  9*46 

-  636 

-31*89 

-764 

22 

-  801 

-737 

+  1307 

—  41*6 

29*55 

78*4 

23 

-  279 

-752 

+ 15*63 

—    1 6*2 

-  27*02 

-800 

24 

+  284 

-667 

+  16*80 

+   10*7 

2431 

81-0 

25 

+  805 

-47* 

+ 16*31 

+  36*6 

-21*44 

-81-4 

26 

+  1206 

—  22*2 

+  14*04 

+  584 

18*43 

81*4 

27 

+ 14*21 

+  69 

+  10*11 

+  73'4 

-1530 

-8o*8 

28 

+  14*10 

+  349 

+  4*92 

+  79*2 

12*08 

79*6 

29 

+  11*69 

+  573 

—  0*90 

+  75-o 

-  878 

-78*0 

30 

+  732 

+  70*1 

—  6*62 

+  61*6 

543 

75*8 

3« 

+   1*73 

+  71*2 

-1158 

+  41*0 

—  2*04 

-73-2 

Feb.    1 

—  4*  16 

+  60*4 

-15*33 

+   16*1 

+  i*37 

70*0 

2 

-  9*3*5 

+  39'6 

- 1765 

-  10-4 

+  476 

-66*4 

3 

-1307 

+  12*5 

- 1847 

-  36*  1 

812 

62*3 

Sup.  1887.  Satellites  of  Solum,  1887-88.  571 


QiMnwioh 
Noon. 
1888. 

Feb.      4 

«.— A. 

• 
- 1477 

3.-D. 

-16*6 

«»— A. 

-17-87 

II 

-  592 

«t— A* 

• 
+  11*42 

-578 

5 

— 14*26 

-43'3 

—  i6*oo 

-  780 

1465 

530 

6 

-11  68 

-638 

-1306 

-  917 

+  1779 

-47-8 

7 

-  743 

-75*2 

-  9  29 

-  996 

20*82 

42'3 

8 

-  213 

-75*9 

-  4*94 

- 101*3 

+  2373 

-364 

9 

+   346 

-659 

-  028 

-  966 

2648 

30*3 

10 

+  8-55 

—46-2 

+  439 

-  85  6 

+  29*07 

-239 

11 

+ 12-35 

-197 

+  875 

—  69*0 

3149 

173 

12 

+  1424 

+  98 

+ 1 2-47 

-  47'3 

+  3371 

—  10-7 

13 

+ 1387 

+  37*8 

+ 15-21 

—    22*0 

3572 

-  3*9 

14 

+  11-23 

+  59*6 

+ 16*62 

+     5*2 

+  3752 

+  2-9 

15 

+  672 

+  71*4 

+  16*42 

+  31*9 

3909 

98 

16 

+  o-86 

+  7i'3 

+  14*48 

+   551 

+  40*42 

+  16*6 

17 

-  472 

+  59*3 

+  10*86 

+  719 

4r5I 

233 

18 

-  975 

+  376 

+  5-89 

+   79*8 

+  42-34 

+  29*9 

19 

— 1322 

+  9'9 

+    0*20 

+  77*6 

4291 

36-4 

20 

—  14-66 

-I9'4 

-    5*52 

+  657 

+  43-23 

+  427 

21 

- 13*92 

-45*8 

- 1059 

+  46*2 

43*29 

487 

22 

—  iri6 

-65-5 

-  *4'54 

+    21*8 

+  4308 

+  54'4 

23 

-  681 

—  76*0 

-1708 

-     4*8 

4260 

59*8 

24 

-  i'5i 

-75-5 

-18*15 

-  310 

+  4187 

+  649 

25 

+  399 

-646 

-1779 

-  54'8 

40-89 

696 

26 

+  8-90 

-44*2 

— 16*16 

-  747 

+  39'66 

+  73*8 

27 

+ 1247 

—  17-2 

-1344 

-  895 

3819 

77*6 

28 

+  1411 

+  12-3 

-  986 

-  98-6 

+  3648 

+  81-0 

29 

+ 135° 

+  39*9 

-  568 

-101-5 

34*54 

838 

Mar.    1 

+ 1070 

+  608 

-  115 

-  981 

+  3240 

+  86-0 

2 

+  6-i  1 

+  71-6 

+  3*44 

-  884 

30-06 

877 

3 

+  052 

+  70-4 

+   778 

-  72*9 

+  27'53 

+  88-9 

4 

-  5-15 

+  575 

+  11-56 

-  52*3 

24*82 

895 

5 

—  IO'OI 

+  35*2 

+  1444 

-  277 

+  21-98 

+  89*5 

6 

—  13*20 

+  7*4 

+  16*09 

—    0-7 

19-00 

889 

7 

- 14-41 

—  21*6 

+ 16*23 

+  25-9 

+  I59I 

+  87*8 

8 

-1348 

-473 

+ 1468 

+  5°*o 

12*72 

860 

9 

—  1060 

-662 

+  11-46 

+  68*2 

+    946 

+  837 

10 

-  6-23 

-75'6 

+  685 

+  78*  1 

6-I4 

808 

11 

-  099 

-74*4 

+   1*39 

+  78*  1 

+    280 

+  77*4 

12 

+  4*37 

—62-6 

—   4*22 

+  684 

-  o*55 

8  S  2 

734 

572  Mr.  Marth,  Bphenierides  of  the  xlvii.  gt 


Green  wloh 
Noon. 

•.-A. 

a.-D. 

«,~A. 

«,-D. 

«•-▲. 

3.-D. 

1888. 

Mar.    13 

8 

+  9*08 

-4r8 

• 
-  9*33 

+  5O-0" 

-  3*88 

+  62? 

14 

+ 12*42 

-14-8 

-1342 

+  27*4 

7*18 

64*0 

IS 

+  1384 

+  143 

—  16*19 

+  i-5 

—  10*42 

+  587 

16 

+  13-06 

+  41*1 

-1753 

-245 

'3'57 

52-9 

17 

+ 10*15 

+  6i*i 

-I7-48 

-486 

—  16*62 

+  46-8 

18 

+  557 

+  709 

-16*15 

—69*0 

1955 

404 

19 

+  0*06 

+  68*8 

- 1374 

-847 

-22*33 

+  337 

20 

-  543 

+  553 

-1044 

-950 

2495 

268 

21 

— 10*03 

+  328 

-  651 

-99*3 

-2739 

+  19  7 

22 

-1304 

+  5*3 

-  218 

-974 

2963 

12-5 

23 

- 1405 

-230 

+  2*26 

-89-4 

-31*66 

+  5-2 

24 

—  12*99 

+  47*9 

+  654 

-755 

33*46 

—    2*2 

25 

— 10*03 

-658 

+ 1035 

-565 

-35-03 

-  94 

26 

-  573 

-74*3 

+ 13*37 

-33  4 

36*35 

166 

27 

-  059 

-724 

+  15*28 

-  7*6 

-37*42 

—236 

28 

+  4*60 

— 60*2 

+  1578 

+  i8*8 

3823 

304 

29 

+  911 

-393 

+  14*69 

+  431 

-38*77 

-37*o 

30 

+ 12-25 

—  127 

+ 1196 

+  62*5 

39*05 

434 

3i 

+ 13*49 

+  157 

+  780 

+  74*2 

-39*07 

-494 

April    1 

+ 1259 

+  415 

+  2*69 

+  767 

3882 

55"o 

2 

+  9  65 

+  60*4 

-  274 

+  696 

-3832 

-60-3 

3 

+  5-11 

+  69*2 

-  7-83 

+  54*2 

37*57 

65- 1 

4 

-  025 

+  66*5 

- 1205 

+  329 

-3657 

-69-5 

5 

-  556 

+  528 

-1506 

+  8*3 

35*33 

73*4 

6 

-  90 

+  306 

-1668 

— 16*9 

-  3387 

-76S 

7 

- 1278 

+  3*6 

—  17*01 

-407 

3219 

79*7 

8 

-1364 

-238 

-16*06 

—  61 -4 

-3°'32 

-82-0 

9 

- 1252 

-47'6 

— 14*02 

-779 

2826 

83-S 

10 

—  960 

-64*5 

-1107 

-892 

—26*03 

-851 

11 

-  533 

-72-3 

~  745 

-949 

2365 

858 

12 

-  034 

-69*8 

-  338 

-94*8 

—  21*12 

-86x> 

13 

+  468 

-57*5 

+  0*89 

-887 

I848 

85*7 

14 

+  9*01 

-370 

+  5o7 

-770 

-1574 

-84-S 

15 

+ 1198 

-ii*i 

+  890 

— 6o*o 

12-91 

834 

16 

+  1310 

+  16*4 

+  1206 

-388 

—  IO'OI 

-81- 

17 

+ 12*14 

+  41*1 

+  14*24 

—  146 

7*06 

79-1 

18 

+  921 

+  59*0 

+  I5'i4 

+  108 

-   409 

-76-2 

19 

+  4  77 

+  67*  I 

+ 14'55 

+  349 

+  1*11 

730 

Sap.  1887.  Satellites  of  Saturn,  1887-88.  573 


Greenwich 
Noon. 

a*— A. 

8.-D. 

•i-A. 

«.-D. 

«,— A. 

*.-D. 

1888. 

April  ao 

■ 

-  0-44 

+639 

■ 
+ 12*38 

+  S5-i 

■ 
+    187 

-693 

21 

-  557 

+  50-5 

+   87S 

+  687 

4-83 

65*2 

22 

-  979 

+  28*6 

+    4*06 

+  7^6 

+  774 

-607 

23 

— 12-46 

+  2-5 

-    1*12 

+  694 

1060 

559 

24 

-1325 

-23-8 

-  6- 16 

+  56-8 

1339 

-509 

25 

—  12*09 

-466 

- 1049 

+  380 

16*09 

45*6 

26 

—    9*22 

—  62*6 

- 13  75 

+  153 

+  1868 

—40-1 

27 

-    506 

-697 

-1575 

-  87 

21-16 

344 

28 

—    0*21 

-67*1 

- 16-45 

-3X9 

+  2351 

-285 

29 

+    4'65 

-54-9 

— 15-92 

-52-6 

2571 

22'6 

30 

+    8*82 

-349 

- 1430 

-695 

+2776 

-16*6 

May      1 

+  11-67 

-  9*9 

-1175 

-81-9 

29-65 

10-5 

2 

+  1271 

+  165 

-  848 

-89'! 

+  31-37 

-  44 

3 

+  1174 

+  40*2 

3290 

+   17 

4 

+    887 

+  57'i 

+  34*24 

+  77 

5 

+  4  54 

+  64*6 

3538 

13*6 

6 

-  0-52 

+  613 

+  3632 

+  193 

7 

-  549 

+  479 

37-05 

249 

8 

-  956 

+  26*9 

+  3757 

+  304 

9 

-12-13 

+   18 

37*88 

35'6 

10 

— 12-87 

-234 

+  37*97 

+  405 

11 

-"73 

-451 

3785 

45' 

12 

-  893 

-603 

+  3751 

+  49*5 

574  Mr.  Marth,  Ephemerie  of  the  xlvii.  9, 


Ephemeris  of  the  Satellite  of  Neptune,  1887-88.     By  A.  Marth. 


Greenwich 
Noon. 
1887. 

Oct.    35 

P* 
32270 

a 

» 
829 

16936 

DUE. 
0 
612*32 

u 

13173 

B 
-29-34 

Not.     4 

322-51 

1695 

828 

6168 

•30 

132*00 

29*23 

14 

32230 

97 

'26 

31398 

•28 

132*29 

29*12 

*4 

322*07 

97 

•23 

206-26 

•27 

13258 

29*00 

Dee.     4 

32184 

16-96 

819 

98-53 

•28 

13287 

2888 

14 

321*62 

-92 

•14 

35081 

*20 

13314 

2876 

«4 

321*43 

•87 

•09 

243*10 

0 

•33 

13338 

2865 

1888. 
Jan.      3 

321-27 

16  81 

804 

135*43 

6l2*36 

133-58 

-2856 

13 

3*1*14 

73 

798 

2779 

\0 

'41 

74 

•48 

23 

321-06 

•65 

•02 

280*20 

•46 

•85 

43 

Feb.      2 

321*02 

1656 

787 

17266 

•52 

13390 

2839 

12 

321*02 

•46 

•83 

65-18 

'57 

•89 

•38 

22 

321-07 

•37 

79 

31775 

•64 

•82 

•40 

Mar.     3 

321-17 

16*28 

775 

21039 

•69 

13369 

28*45 

13 

321-31 

•19 

73 

103-08 

74 

.51 

•51 

23 

321*49 

'ii 

71 

35582 

■7       ¥^ 

6l2-80 

•28 

•60 

Apr.      2 

32170 

16-04 

7*70 

248*62 

13301 

-2871 

F  position-angle  of  the  minor  axis  of  the  satellite's  apparent  orbit,  in 
the  direction  of  superior  conjunction. 

a,  b,  major  and  minor  semi-axes  of  the  apparent  orbit. 

«— U,  longitude  of  the  satellite  in  its  orbit,  reckoned  from  the  point  which 
is  in  superior  conjunction  with  the  planet  or  in  opposition  to  the 
earth. 

U  + 1800,  planetocentric  longitude  of  the  earth,  reckoned  in  the  satellite's 
orbit  from  the  ascending  node  on  the  celestial  equator. 

B.  planetocentric  latitude  of  the  earth  above  the  plane  of  the  orbit. 

The  values  of  f*—U,  P',  a,  b  are  to  be  interpolated  directly 
for  the  times  for  which  the  apparent  positions  of  the  satellite 
are  required,  and  the  position-angles  p  and  distances  8  of  the 
satellites  are  then  fonnd  by  means  of  the  formal© 

9  sin  (F—  p)=a  sin  («— IT) 
9  cot  (P'-p)=b  cos  (tt-U). 

The  satellite  moves  in  the  direction  of  decreasing  position- 
angles  and  will  be  at  its  greatest  elongations  (jif  in  pos. 
P'  +900,  */in  pos.  P'— 900  at  dish  a)  and  at  its  nearest  oonjnno- 


Sup.  1887.  Satellite  of  Neptune,  1887-88.  575 

tions  (superior  tup.  in  pos.  P',  inferior  in.  in  pos.  P+  x8o°  at  diet. 
V)  with  the  planet  at  the  following  Greenwich  hours : 


nf. 

sup. 

sp. 

in. 

nf. 

sup. 

sp. 

in. 

n£ 

sup. 

sp. 

in. 

nf. 

sup. 

sp. 

in. 

nf. 

sup. 

sp. 

in. 

nf. 

sup. 

sp. 

in. 

nf. 

sup. 

sp. 

in. 

nf. 

sup. 

sp. 

in. 

nf. 

sup. 

The  only  observations  of  the  satellite  made  during  the  last 
apparition,  which  have  yet  /come  to  my  knowledge,  are  those 
made  by  M.  Perrotin  with  the  great  refractor  of  the  Nice  Obser- 
vatory and  published  in  the  August  number  of  the  Paris 
Bulletin  Astron.  v.  4,  p.  341.  In  the  present  ephemeris  the  plane 
of  the  orbit  is  assumed  in  accordance  with  these  measures,  which 
give  approximately  for  1888  N=i85°.26o  J=i  20*300. 


1887. 

h 

1887. 

h 

1888. 

h 

Oct.   25 

4*2 

in. 

Deo. 

IS 

I49 

•p. 

Feb.     3 

I4a  I 

26 

154 

nf. 

17 

2'2 

in. 

5 

i'4 

28 

27 

sap. 

18 

I3'4 

nf. 

6 

127 

29 

140 

sp. 

20 

0*7 

sap. 

7 

239 

31 

«"3 

in. 

21 

I20 

sp. 

9 

II'2 

Nov.     1 

12*5 

238 

nf. 

22 

23*3 

in. 

10 

22'5 

2 

sup. 

24 

IO*C 
21*8 

nf. 

12 

97 

4 

III 

sp. 

«S 

sap. 

«3 

21 'O 

5 

22-4 

in. 

27 

91 

•p. 

IS 

8'3 

7 

97 

nf. 

28 

20*4 

in. 

16 

195 

8 

20'9 

sap. 

30 

76 

nf. 

18 

68 

10 

82 

sp. 

31 

189 

sap. 

19 

180 

11 

195 

in. 

1888. 

21 

5*3 

13 

68 

nf. 

Jan. 

2 

62 

sp. 

22 

166 

H 

180 

sap. 

3 

175 

in. 

24 

3'8 

16 

5*3 

sp. 

5 

47 

nf. 

25 

151 

17 

166 

in. 

6 

160 

sup. 

27 

2-3 

19 

3*9 

nf. 

8 

3*3 

sp. 

•28 

136 

20 

I5'2 

sup. 

9 

14*6 

in. 

Mar.    1 

o-8 

22 

24 

sp. 

11 

18 

nf. 

2 

I2'I 

23 

137 

in. 

12 

131 

sap. 

3 

233 

25 

I'O 

nf. 

14 

04 

sp. 

5 

I0  6 

26 

12-3 

sup. 

15 

ii*6 

in. 

6 

21*9 

27 

235 

sp. 

16 

22'9 

nf. 

8 

91 

29 

io-8 

in. 

18 

IO'2 

sap. 

9 

20*4 

30 

22*1 

nf. 

19 

21'5 

sp. 

11 

76 

Dec     2 

94 

sap. 

21 

87 

in. 

12 

189 

3 

207 

sp. 

22 

20*0 

nf. 

14 

61 

5 

7*9 

in. 

24 

73 

sap. 

IS 

I7'4 

6 

19*2 

nf. 

25 

185 

sp. 

17 

4-6' 

8 

65 

sup. 

27 

5* 

in. 

18 

15-9 

9 

178 

sp. 

28 

17-1 

nf. 

20 

3'i 

11 

5-0 

in. 

30 

43 

sap. 

21 

144 

12 

16-3 

nf. 

3i 

15-6 

sp. 

23 

16 

14 

36 

sap. 

Feb. 

2 

2-9 

in. 

24 

12-9 

I 

■ 


r 


INDEX. 


PAQB 

Abney,  Cant.  W.  de  W.,  on  the  atmospheric  transmission  of  visual  and 

photographically  actinic  light 260 

Argentine  general  catalogue  of  stars,  note  on  the 178 

comparison  of  the  star-places  of,  with  those  of  the  Cape  and 

other  southern  catalogues,  Mr.  Downing  446 

Armagh,  second  catalogue  of  stars,  note  on  the     181 

Armagh  refractor,  note  on  the  electric  illumination  of.  Dr.  Dreyer  1 17 

Associate  deceased : — Prof.  Th.  von  Oppolzer  145 

Associates  elected 1,  443 

Astronomy,  notes  on  the  progress  of,  during  the  year  1886 : — 

Discovery  of  minor  planets 172 

The  comets  of  1886 ib. 

The  total  solar  eclipse  of  1886,  August  28-29 *75 

Prof.  Hall's  researches  on  the  orbits  of  the  six  inner  satellites  of 

Saturn    177 

The  Argentine  general  catalogue  of  stars  178 

The  Harvard  catalogue  of  1213  stars  for  1875*0 179 

The  Pulkowa  catalogue  of  3542  stars  for  1855-0 1 80 

Prof.  Schonfeld's  extension  of  the  "  Durchmusterung  "    ib. 

The  second  Armagh  catalogue  of  stars  181 

Dr.  Eam's  catalogue  of  C455  small  stars   182 

The  great  comet,  1882,11 ib. 

Prof.  Ball's  determinations  of  stellar  parallax 183 

Stellar  photography 184 

The  Telocity  of  light 190 

The  visual  solar  spectrum  in  1884 191 

Auditors,  report  of  the 125 

Auwers,  Prof.  A.,  a  catalogue  of  480  stars  to  be  used  as  fundamental 
stars  for  observations  of  cones  between  20°  and  8o°  south 

declination 455 

Browne,  Capt.  W.  G.,  sextant  observations  of  Comet  Barnard  (/,  1886).  117 

Bryant,  K.,  on  Kepler's  problem - « 8 

erratum.....'. 78 

,    —  on  the  orbit  of  Comet  II.  1883 434 

Buckney,  T.,  note  on  the  performance  of  the  Westminster  clock 519 

Cambridge  Observatory,  observations  of  the  planet  Sappho,  made  with 

the  Northumberland  Equatorial  and  square-bar  micrometer 553 

Cape' of  Good  Hope,  Boyal  Observatory,  observations  of  comets    277 

Chambers,  G.  P.,  a  working  catalogue  of  "red"  stars 348 

Comets : — 

.1882  U.  (Great  Comet),  note  on  observations  of 182 

1883JLL  (Boss),  the  orbit  of,  Gen.  Tennant    24,  520,  554 

■  ■ the  orbit  of,  Mr.  Bryant 434 

1884  III.  (Wolf),  observed  at  Harrow,  Col.  Tupman   545 

1885  II.  (Brooks),  observed  at  Harrow,  Col.  Tupman 545 

1885  III.  (Barnard),  observed  at  Mr.  Wigglesworth's  Observatory, 

Mr.  Lohse 2S 


578  Index. 

YA.QM 

Comets  (continued) : — 

1886  L  (Fabry),  observed  at  Mr.  Wigglesworth's  Observatory,  Mr. 

Lohse 28 

———————  sextant  observations  of,  Capt.  Randall 117 

— — — —  observed  at  the  Boyal  Observatory,  Gape  of  Good 

Hope — ...  277 

orbit  of,  Dr.  Morrison    437 

— —  observed  at  Harrow,  Ool.  Tupman    546 

1886  II.  (Barnard),  observed  at  Mr.  Wigglesworth's  Observatory, 

Mr.  Lohse 28 

——————  observed  at  the  Boyal  Observatory,  Gape  of 

Good  Hope 281 

— _— _ _  observed  at  Harrow,  Col.  Tupman 547 

1886  V.  (Brooks  I.),  observed  at  the  Boyal  Observatory,  Gape  of 

Good  Hope    284 

— — — - — ^— —  observed  at  Harrow,  Ool.  Tupman 548 

1886  VL  (Winnecke),  observed  at  the  8ydney  Observatory   67 

observed  at  the  Boyal  Observatory,  Cape  of 

Good  Hope 286 

observed  at  Windsor,  New  South  Wales,  Mr. 

Tebbutt 293 

1886  VII.  (FinlayV  observed  at  the  Sydney  Observatory    68 

observed  at  the  Boyal  Observatory,  Gape  of  Good 

Hope  290 

— — observed  at  the  Boyal  Observatory,  Greenwich  ...  275 

■           ■             elements  of,  Mr.  Finlay 302 

1886  IX.  (Barnard- Hartwig),  observed  at  the  Boyal  Observatory, 
Greenwich    27,  65,  116 

— - — sextant  observations  of,  Capt.  Browne  x  1 7 

orbit  of,  Dr.  Morrison   438 

observed  at  Harrow,  Ool.  Tupman  ...  549 

1887  a  (great  southern  comet),  observed  by  Mr.  Finlay  (with 
elements)  303 

— — — ^__  observed  at  Adelaide,  Mr.  Todd  305 

— — ■ sextant  observations  of,    Capt. 

Molony  , 432 

1887  b  (Brooks),  observed  at  the  Boyal  Observatory,  Greenwich  275,  392 

1887  0  (Barnard),  observed  at  the  Boyal  Observatory,  Greenwich...  275 

1887  d  (Barnard),  observed  at  the  Boyal  Observatory,  Greenwich...  ib. 
1887  (Barnard,May  12),  observed  at  Mr.  Wiggles  worth's  Observatory, 

Mr.  Lohse 49$* 

■ observed  at  Harrow,  Col.  Tupman    55° 

Comets  of  1886,  note  on  the 172 

Cometary  orbits,  on  the  inclinations  of,  Mr.  Monck 433 

Copeland,  B.,  on  Hartwig's  Nova  Andromeda  49 

erratum M.M  120 

on  the  variability  of  the  spectrum  of  y  Cassiopeia 92 

Cortie,  Bev.  A.,  bands  observed  in  the  spectra  of  sun-spots  at  Stony- 
hurst  Observatory 19 

Crossley,  £.,  a  centring  tube  for  reflecting  telescopes ~  274 

— — —  description  of  a  new  measuring  rod... 388 

Denning,  W.  F.,  distribution  of  meteor  streams   -...  35 

meteors  with  curved  paths - 119 

Dome,  on  the  best  device  for  revolving,  Mr.  Todd   M  272 

Downing,  A.  M.  W.,  a  comparison  of  the  star-places  of  the  Argentine 
General  Catalogue  for  1875  with  those  of  the  Cape  Catalogue 

for  1880,  and  with  those  of  other  southern  star  catalogues 446 

Dreyer,  J.  L.  K,  note  on  the  electric  illumination  of  the  Armagh  refractor  117 


Index.  579 

PAOS 

Dreyer,  J.  L.  E.,  on  some  nebula  hitherto  suspected  of  variability  or 

proper  motion    412 

— — note  on  the  effect  of  refraction  in  stellar  photography  .  421 

Eclipse,  total  solar,  of  1886,  note  on  the    175 

Eclipse  volume,  notes  on  a  MS.,  Mr.  Johnson  430 

Elger,  T.  G.,  note  on  the  near  approach  of  the  Moon  to  a  Tauri   307 

physical  observations  of  Saturn  in  1887 511 

Fellows  deceased,  list  of 133 

elected i,  49,  79,  309,  395,  443 

Finlay,  W.  H.,  elements  of  Comet  1886  0  (Finlay) 302 

Comet  1887  a 303 

■  ■ on  the  probable  errors  of  transit  observing 427 

Franks,  W.  S.,  a  proposed  nomenclature  for  star  colours    269 

Gore,  J.  E.,  on  the  orbit  of  2  1757 12,  478 

■ formula  for  binary  stars 61 

on  the  orbit  of  14  (t)  Ononis  (0.  Struve  98)  266 

■           observations  of  the  variable  star  S  (10)  Sagittm 267 

on  the  orbit  of  02  400    346 

Greenwich,  Boyal  Observatory,  observations  of  Comet/ 1886  (Barnard) 

27,65,116 

spectroscopic  results  for  the  motions  of  stars  in  the  line  of 

sight,  obtained  in  the  year  1886,  No.  X 101 

observations  of  occultations  of  stars  by  the  Moon,  and  of 

phenomena  of  Jupiter's  satellites,  made  in  the  year  1886    109 

observations  of  Comets  e  1886  (Finlay),  o  1887  (Brooks), 

e  1887  (Barnard),  and  d  1887  (Barnard)    275 

observations  of  Comet  6  1887  (Brooks) 392 


Greenwich  transit  circle,  variations  of  level  and  azimuth  of,  Mr.  Turner  325 

Grubb,  H.,  on  the  choice  of  instruments  for  stellar  photography  309 

Gylden,  Prof.  H.,  on  the  determination  of  the  radius  vector  in  the  abso- 
lute orbits  of  the  planets -  223 

Hall,  A.,  note  on  his  researches  on  the  orbits  of  the  satellites  of  Saturn  177 

note  on  his  determinations  of  stellar  parallax 183 

Hall,  Maxwell,  the  sidereal  system;  revised  in  1887  521 

Harvard  catalogue  of  1213  stars,  note  on  the    179 

Hill,  G.  W.,  a  reply  to  Mr.  Neison's  strictures  on  Delaunay's  method  of 

determining  the  planetary  perturbations  of  the  Moon I 

on  his  paper  on  Delaunay's  method,  Mr.  Neison 5*7 

Hopkins,  B.  J.,  note  on  an  erratic  meteor . 73 

Hough,  G.  W.,  observations  of  the  companion  of  Sirius,  made  at  the 

Dearborn  Observatory,  Chicago 478 

Johnson,  Rev.  S.  J.,  occultation  of  Aldebaran,  Jan.  6,  1887 115 

second  occultation  of  Aldebaran,  1887 308 

notes  on  a  MS.  eclipse  volume 430 

Jupiter,  ephemeris  for  physical  observations  of,  1887,  Mr.  Marth 40 

on  an  old  engraving  of,  Captain  Noble 515 

— —  satellites  of,  observed  at  Windsor,   New  South   Wales,  Mr. 

Tebbutt 30 

__^_^_—  the  Boyal  Observatory,  Greenwich 11 1 

Kam's  catalogue  of  5455  small  stars,  note  on  182 

Kepler's  problem,  Mr.  Bryant 8 

erratum  78 

Knott,  G.,  note  on  the  star  y  Equulei    II 


580  Index. 

PAOB 

Lefavour,  H.,  the  right  ascensions  of  certain  stars  within  ten  degrees  of 

the  pole,  reduced  from  observations  by  F.  G.  W.  Strove 423 

Light,  note  on  determinations  of  the  velocity  of  190 

visual  and  photographically  actinic,  on  the  atmospheric  transmis- 
sion of,  Capt.  Abney 260 

Lohse,  J.  G.,  observations  of  comets  made  at  Mr.  Wigglesworth's  Ob- 
servatory with  the  15*5  in.  Cooke  refractor 28 

■         observations  of  Nova  Cygni,  of  some  of  the  planets,  and  of 
Comet  Barnard,  made  at  Mr.  Wigglesworth's  Observatory  with 

the  15*5  Cooke  refractor  494 

Lunar  theory : — 

A  reply  to  Mr.  Neison's  strictures  on  Delaunay's  method  of  deter- 
mining the  planetary  perturbations  of  the  Moon,  Mr.  Hill I 

On  Prof.  G.  W.  Hill's  paper  on  Delaunay's  method,  Mr.  Neison 517 

Observations  of  the  Moon,  made  at  the  Radcliffe  Observatory,  and 
comparison  of  the  results  from  the  tabular  places  from  Han- 
sen's Tables,  Mr.  Stone 79 

McLaren,  Lord,  on  the  images  formed  by  reflecting  mirrors,  and  their 

aberration 395 

Mart,  ephemerides  of  the  tatellites  of,  during  the  oppositions  of  1888 

and  1890,  Dr.  Morrison   439 

observed  at  Mr.  Wigglesworth's  Observatory,  Mr.  Lohse    496 

Marth,  A.,  ephemeris  for  physical  observations  of  Jupiter,  1887    40 

ephemeris  of  the  satellites  of  Uranus,  1887    75 

on  the  formulae  for  computing  the  apparent  positions  of  a 

satellite,  and  for  correcting  the  assumed  elements  of  its  orbit ...  333 
on  the  formulae  for  correcting  approximate  elements  of  the  or- 
bits of  binary  stars  480 

ephemerides  of  the  satellites  of  Saturn,  1887-88  556 

■ ephemeris  of  the  satellite  of  Neptune,  1 887-88  574 

Maunder,  E.  W.,  Mr.  Sherman's  observations  of  bright  lines  in  stellar 

spectra 63 

Measuring  rod,  description  of  a  new,  Mr.  Crossley 388 

Meteors;  distribution  of  meteor  streams,  Mr.  Denning  35 

On  evidence  with  respect  to  the  form  of  the  area  in  the  heavens 
from  which  the  meteors  of  Nov.  27,  1885,  appeared  to  radiate, 

Mr.  Banyard 69 

Note  on  an  erratic  meteor,  Mr.  Hopkins   73 

Meteors  with  curved  paths,  Mr.  Denning 119 

Minor  planets,  note  on  the  discovery  of 172 

Molony,  Capt.  E.  J.,  sextant  observations  of  Comet  a,  1887 432 

Monck,  W.  H.  8.,  on  the  inclinations  of  cometary  orbits    433 

Morrison,  J.  the  orbits  of  Comets  Fabry  and  Barnard-Hartwig 437 

^—  ephemerides  of  the  satellites  of  Mars  during  the  oppositions 

of  1888  and  r8ox> 439 

Nebulae  in  the  Pleiades,  note  en  photographs  of,  Mr.  Roberts    24 

in  Orion  and  in  the  Pleiades,  photographs  of,  Mr.  Roberts  89 

suspected  of  variability  or  proper  motion,  Dr.  Dreyer    412 

Neison,  £.,  on  Prof.  G.  W.  Hill's  paper  on  Delaunay's  method 517 

— — —   Reply  to  his  strictures  on  Delaunay's  method,  Prof.  Hill 1 

Neptune,  satellite  of,  observed  at  Mr.  Wigglesworth's  Observatory,  Mr, 

"    Lohse 497 

ephemeris  of  the  satellite  of,  1887-88,  Mr.  Marth    574 

Newall,  R.  SM  Newall's  occulter 33 

Noble,  Capt.  W.  on  an  old  engraving  of  Jupiter  515 

Obituary :  List  of  Fellows  and  Associate  deceased 133 

.Doiieau,  jxLaior— V7on.  v.  x.    *.*.*•••.....•..•........<.•...■...............*...  to* 


Index.  581 

PAG1 

Obituary  (continued) : — 

Boreham,  W.  W 135 

Hamilton,  George ib. 

Mann,  B.  J 137 

Pearson,  "Rev.  James 139 

Shadwell,  Sir  C.  F.  A. I40 

Smith,  David 141 

Story,  Edwin 143 

Talmage,  C.  G to. 

Tomlinson,  William,  jnn*. 144 

Oppolzer,  Prof.  Theodor  von  145 

Observatories,  accounts  of  proceedings  of,  during  1886 : — 

Greenwich,  Boyal 14S 

Armagh ici 

Cambridge to. 

Dunsink >.  153 

Edinburgh,  Boyal ib. 

Kew    154 

Liverpool   155 

Oxford,  Badcliffe  ib. 

Oxford,  University   156 

Rugby IS7 

Stonyhurst ib. 

Mr.  Common's,  Ealing 158 

Earl  of  Crawford's,  Dun  Echt tb. 

Mr.  Crossle/s,  Bermerside,  Halifax  160 

Mr.  Peek's,  Lyme  Regis  ib. 

Earl  of  Bosse's,  Birr  Castle ib. 

Coi.  Tomline's,  Orwell  Park    161 

Lieut.-Colonel  Tupman's,  Harrow  ib. 

Mr.  Wigglesworth's,  Scarborough  162 

Cape  of  Good  Hope,  Boyal  164 

Hong  Kong   171 

Penrose,  F.  O,  occultations  of  7  Virginia,  1886  115 

Pickering,  E.  C.,  proposed  index  to  observations  of  variable  stars    443 

Planetary  theory :  on  the  determination  of  the  radius  vector  in  the  ab- 
solute orbits  of  the  planets,  Prof.  Gylden 223 

Prince,  C.  L.,  the  occultation  of  Aldabaran    308 

lunar  occultations  on  March  29,  1887 394 

Pritchard,  Prof.  C,  note  on  the  application  of  photography  to  the  deter- 
mination of  stellar  parallax    87 

— _ —  remarks  on  some  of  the  present  aspects  of  celestial 

photography 322 

________  on  the  parallax  of  6l,  and  6ls  Cygni,  as  obtained  by 

the  aid  of  photography 444 

Probable  errors  of  transit  observing,  Mr.  Finlay 427 

Pulkowa  catalogue  of  3542  stars,  note  on  the 180 

Bandall,  Capt.  W.,  sextant  observations  of  Fabry's  comet 117 

Banyard,  A.  O,  on  evidence  with  respect  to  the  form  of  the  area  in  the 

heavens  from  which  the  meteors  of  Nov.  27,  1885,  appeared  to 

radiate    69 

Reflecting  mirrors,  on  the  images  formed  by,  and  their  aberration,  Lord 

McLaren    395 

Reflecting  telescopes,  notes  on,  Gen.  Tennant 244 

a  centring  tube  for,  Mr.  Grossley  274 

Report  of  the  Council  to  the  Sixty-Seventh  Annual  General  Meeting  of 

the  Society 121 

List  of  papers  read  from  February  1886  to  February  1887     193 


582  Index. 

Report  of  Council  (continued) : —  faob 

List  of  donors  to  the  Library,  &c  198 

President's  address  on  presenting  the  gold  medal  to  Mr.  G.  W.  Hill..  203 

List  of  officers  and  council  221 

Roberts,  I.,  note  on  photographs  of  stars  in  Cygnus  taken  in  August 

1886 22 

— —  note  on  photographs  of  the  nebulae  in  the  Pleiades  taken  in 

October  1886     24 

— — —  photographs  of  nebula?  in  Orion  and  in  the  Pleiades 89 

__—  photographic  search  for  the  minor  planet  Sappho. 265 

Sappho,  photographic  search  for,  Mr.  Roberts 265 

observations  of,  Col.  Tupman 550 

— —   observed  at  the  Cambridge  Observatory 553 

Satellite,  on  the  formulae  for  computing  the  apparent  positions  of,  and 

for  correcting  the  assumed  elements  of  its  orbit,  Mr.  Marth  ...  333 
Saturn,  observations  of,  made  at  Mr.  Wigglesworth's  Observatory,  Mr. 

Lohse . 496 

physical  observations  of,  in  1887,  Mr.Elger 511 

— —  and  9  Geminorum,  observations  of,  Mr.  Tebbutt 431 

ephemerides  of  the  satellites  of,  1887-88,  Mr.  Marth 5  56 

Schonfelas  extension  of  the  "  Durchmusterung,"  note  on  180 

Seabroke,  G.,  spectroscopic  observations  of  the  motion  of  stars  in  the 

line  of  sight,  made  at  the  Temple  Observatory,  Rugby  93 

Sherman,  0.  T.f  reply  to  certain  questions  raised  before  the  Royal  Astro- 
nomical Society  at  the  meeting  on  March  12,  1886,  concerning 
the  matter  detailed  in  a  paper  entitled  "  Bright  lines  in  stel- 
lar spectra"  14 

on  his  observations  of  bright  lines  in  stellar  spectra,  Mr. 

Maunder    63 

Sidereal  system,  the,  revised  in  1887,  Mr.  Hall    521 

Solar  corona,  the,  as  shown  in  photographs  taken  during  total  eclipses, 

Mr.  Wesley  499 

Solar  spectrum,  visual,  in  1884,  note  on  the  191 

Star  colours,  a  proposed  nomenclature  for,  Mr.  Franks    269 

Stars,  fundamental,  a  catalogue  of,  for  observations  of  zones  between  20° 

and  8o°  south  declination,  Prof.  Auwers 455 

Stars,  double: — 

Note  on  the  star  7  Equulei,  Mr.  Knott 11 

On  the  orbit  of  2  1757,  Mr.  Gore    12,  478 

Formulae  for  binary  stars,  Mr.  Gore  61 

On  the  orbit  of  14  (t)  Orients,  Mr.  Gore   266 

On  the  orbit  of  02  400,  Mr.  Gore 346 

Measures  of  southern  double  stars  made  at  the  Sydney  Observatory...  473 
Observations  of  the  companion  of  Sirius,  made  at  the  Dearborn  Ob- 
servatory, Chicago,  Prof.  Hough 478 

On  the  formulae  for  correcting  approximate  elements  of  binary 

stars,  Mr. 'Marth  480 

Stan,  motions  of,  in  the  line  of  sight,  spectroscopic  observations  made  at 

the  Temple  Observatory,  Rugby,  Mr.  Seabroke    93 

__— spectroscopic  results  obtained  at  the  Royal  Observa- 
tory, Greenwich,  in  the  year  1886.    No.  X. 101 

Stars,  parallax  of: — 

Note  on  the  application  of  photography  to  the  determination  of 

stellar  parallax,  Prof.  Pritchard 87 

On  the  parallax  of  61 1  and  62,  Oygni,  as  obtained  by  the  aid  of 

photography,  Professor  Pritchard  444 

Stars,  red,  a  working  catalogue  of,  Mr.  Chambers  348 


Index.  583 

PAGK 

Stan,  right  ascension  of:— 

Mean  right  ascensions  of  Polaris,  Cephei  51  (Hot.),  9  Urea  Minoris, 

and  X  Ursa  Minoris  for  the  year  1887,  Mr.  Stone  85 

The  right  ascensions  of  certain  stars  within  ten  degrees  of  the  pole, 

from  observations  by  F.  G.  W.  Strave,  reduced  by  H.  Lefavour    423 
Stars,  variable: — 

On  Hartwig's  Nova  Andromeda,  Dr.  Oopeland 49 

erratum 120 

A  new  variable  star  in  Puppis,  Mr.  Williams    91 

Observations  of  the  variable  star  S  ( 10)  Sagitta,  Mr.  Gore 267 

Proposed  index  to  observations  of  variable  stars,  Prof.  Pickering  ...    443 
Observations  of  Nova  Cygni  made  at  Mr.  Wigglesworth's  Observa- 
tory, Mr.  Lohse 494 

Stars,  occnltations  of,  by  the  Moon : — 

Observed  at  the  Royal  Observatory,  Greenwich  109 

Occupation  of  7  Virginia  in  1886,  Mr.  Penrose   115 

Occultation  of  Aldeharan,  Jan.  6,  1887,  Mr.  Johnson  ib. 

The  Moon  and  Aldebaran,  March  2,  1887,  as  seen  at  the  Radcliffe 

Observatory,  Oxford,  Mr.  Stone 306 

Note  on  the  near  approach  of  the  Moon  to  a  Tauri,  Mr.  JSlger 307 

{Second  occultation  of  Aldebaran,  1887,  Mr.  Johnson  308 

The  occultation  of  Aldebaran,  Mr.  Prince ib. 

Lunar  occnltations  on  March  29,  1887,  Mr.  Prince 394 

Occultation  of  a  Tauri,  Col.  Tupman 432 

Stellar  photography : — 

Note  on  photographs  of  stars  in  Cygnus,  Mr.  Robert* 22 

Note  on  the  application  of  photography  to  the  determination  of 

stellar  parallax,  Prof.  Fntchard.. 87 

Note  on  stellar  photography 184 

Parallax  of  61  Cygni,  Prof.  Pritchard  444 

Photographic  search  for  the  minor  planet  Sappho,  Mr.  Roberts 265 

On  the  choice  of  instruments  for  stellar  photography,  Mr.  Qrubb  ...     309 
Remarks  on  some  of  the  present  aspects  of  celestial  photography, 

Prol  Pritchard 322 

Note  on  the  effect  of  refraction  in  stellar  photography,  Dr.  Dreyer  .    421 
Stellar  spectra : — 

Reply  to  certain  questions  raised  befere  the  Royal  Astronomical 
Society  concerning  a  paper  entitled  "  Bright  lines  in  stellar 

spectra/'  Mr.  Sherman 14 

Mr.  Sherman's  observations  of  bright  lines  in  stellar  spectra,  Mr. 

Maunder 63 

On  the  variability  of  the  spectrum  of  y  Cassiopeia,  Dr.  Copeland ...      92 
Stone,  £.  J.,  observations  of  the  Moon  made  at  Radcliffe  Observatory, 
Oxford,  during  the  year  1886,  and  a  comparison  of  the  results 
with  the  tabular  places  from  Hansen's  Lunar  Tables 79 

■  mean  right  ascensions  of  Polaris,  Cephei  51  (Hev.),  8  Urea 
Minoris,  and  A  Ursa  Minoris  for  the  year  1887,  from  the 
Radcliffe  Observations  of  the  year  1880  to  1886  85 

the  Moon    and  Aldebaran,  1887,  March  2,  as  seen  at  the 

Radcliffe  Observatory,  Oxford 306 

Strove,  F.  G.  W.,  observations  of  stars  within  ten  degrees  of  the  pole, 

reduced  by  H.  Lefavour  423 

Sun-spots,  bands  in  the  spectra  of,  observed  at  Stonyhurst  Observatory, 

Mr.  Cortie 19 

Sydney  Observatory,  observations  of  Gomet  Winnecke,  1886,  made  with 

the  nj-inch  equatorial  and  filar  micrometer 67 

■  observations  of  comet  discovered  by  Finlay  at  the  Gape,  Sept.  26, 

1886,  made  with  the  nj-inch  equatorial  and  filar  micrometer  .      68 
— —  measures  of  southern  double  stars    473 


584  Index. 

Tebbutt,  J.,  observations  of  phenomena  of  Jupiter  s  satellites  made  at 

Windsor,  New  South  Wales,  in  the  year  1886 30 

___  observations  of  Winneeke's  Comet,  1886,  made  at  Windsor, 

New  Sooth  Wales 293 

observations  of  Saturn  and  8  Geminorum 431 


Tennant,  Gen.  J.  F.,  the  orbit  of  Comet  II.  1883,  discovered  by  Mr. 

Boss 24,520,554 

■  1                                 errata  394 

notes  on  reflecting  telescopes 244 

Todd,  C,  observations  of  Comet  1887  a,  made  at  the  Observatory, 

Adelaide 305 

Todd,  D.  P.,  on  the  best  device  for  revolving  a  dome 272 

Transit  observing,  probable  errors  of  Mr.  Finiay  427 

Tnpman,  G-.  L.f  occultation  of  a  Tauri  432 

observations  of  comets  and  of  Sappho  (80)  at  Harrow ...  545 

Turner,  H.  H.,  on  the  variations  of  level  and  azimuth  of  the  transit 

circle  at  the  Royal  Observatory,  Greenwich 325 

Uranus,  ephemeris  of  the  satellites  of,  1887,  Mr.  Marth  ••  75 

Fmus,  observed  at  Mr.  Wigglesworth's  Observatory,  Mr.  Lohse  •  495 

Wesley,  W.  H.,  the  solar  corona,  as  shown  in  photographs  taken  during 

total  eclipses 499 

Westminster  clock,  note  on  the  performance  of,  Mr.  Buckney 519 

Williams,  A.  8.,  a  new  variable  star  in  Puppit 91 


LIST   OF   PRESENTS 

RECEIVED  DURING   THE   SESSION   OF   1886-87, 

AND  OF 

BOOKS  PURCHASED  WITH  THE  TURNOR  AND 

HORROX  FUNDS 

DURING  THE  SAKE  PERIOD, 

FOBXBfO 

APPENDIX  III. 

To  the  Catalogue  of  the  Library  of  the  Royal  Astronomical  Society, 


Abel,  Sir  F.,  The  work  of  the  Imperial  Institute,  8vo.  The  Author. 

London ,  1887 

Abel,  N.  H.,  (Eavres  completes,  avec  des  notes  et  developpe-      The  Royal 
ments,  redigees  par  B.  Holmboe,  2  vols.,  4to.  Society. 

Christiania,  1839 

Abetti,  A.,  Osservazioni  astronomiche  fatte  all*  Osservatorio     The  Author, 
di  Padova,  nel  1886,  8vo.  Venezia,  1887 

Abney,  W.  de  W.,  Instructions  in  photography,  7  th  edition,  ■ 

8vo.  London,  1886 

Adelaide,  Royal  Society  of  South  Australia,  Transactions  and    The  Society. 
Proceedings  and  Report,  vol.  viii.,  1884-85,  8vo. 

Adelaide,    1886 

Airy,  Sir  G.  B.,  Numerical  Lunar  Theory,  4k).  The  Author. 

London,  1886 

Albategnius,  Mahomet,  de  scientia  stellarum  liber,  cum  aliquot      The  Royal 
additionibus  Joannis  Regiomontani,  4to.     Bononice,  1645        Society. 

All  Past  Time  (new  series),  Nos.  1-4,  4to.     London,  1886-87  c-  A-  Newton, 

Esq. 
American  Academy  of  Arts  and  Sciences,  Memoirs,  vol.  iz.,  The  Academy 

pt.  iv.,  No.  4,  4to.  Cambridge,  1886  * 


48 


Appendix  III. 


Prof.  O.Stone. 


Observatory. 


The  Academy.  American  Academy  of  Arts  and  Sciences,  Proceedings,  new 

series,  vol.  ziii.  (whole  series,  toI.  zzi.),  part  ii.,  1885-86, 
870.  Boston,  1886 

The  Editors.    American  Journal  of  Mathematics,  vol.  viii.  3-ix.  3,  4to, 

Baltimore,  1886-87 
— —        American  Journal  of  Science,  series  III.,  Nos.  187-197,  8vo. 

New  Haven,  1886-87 
The  Academy.   Amsterdam,    Koninklijke    Akademie    van    Wetenschappen, 

Yerhandelingen,  xxv.,  4k).  Amsterdam,  1887 

Verslagen  en  Mededeelingen,    Af  deeling  natuurkunde, 

III.  reeks,  ii.,  8vo.  Amsterdam,  1886 

Jaarboek  voor  1885,  8vo.  Amsterdam 

Annals  of  Mathematics,  vol.  iii.  1,  2,  4 to. 

Okarhtteville,  Va.,  1887 

Armagh  Observatory,  Second  Armagh  Catalogue  of  3,300 
stars  for  the  epoch  1875,  deduced  from  observations  made 
daring  the  years  1859  to  1883,  nnder  the  direction  of 
T.  R.  Robinson ;  prepared  for  publication  by  J.  L.  E. 
Dreyer,  870.  Dublin,  1886 

Association e  Italiana  per  le  OsBervazioni  delle  Meteore  Lumi- 
nose,  Osservazioni  nelP  anni  1886-87,  870.  Torino 

Le  s telle  cadenti  dei  periodi  di  Agosto  1885  e  di  Agosto- 

Novembre  1886,  8vo.  Torino,  1886-87 

Astronomical  Journal,  Nos.  145-156,  4 to.        Boston,  1886-87 

Various  Nos.  to  complete  set.  Boston,  v.d . 

Astronomical  Register,  The,  Nos.  283-288,  8vo. 

London,  1886 

Astronomie,  I/,  Revne  mensnelle  d'astronomie  popnlaire,  de 
m6teorologie  et  de  physique  dn  globe,  pnbliee  par  Camille 
Flammarion,  annees  v.  7-vi.  6,  870.  Paris,  1886-87 

Astronomische  Nachrichten,  Nos.  2734-2787,  4to. 

Kiel,  1886-87 

Athenaeum,  The,  Nos.  3059-31 10,  4to.  London,  1886-87 

Backlnnd,  0.,  Comet  Encke,  I.  1871-85,  870. 

St.  Petersburg,  1886 

Dr.  Harzer's  Untersnchnngen  fiber  einen  speciellen  Fall 

des  Problems  der  drei  Kdrper,  870.    St.  Petersburg,  1886 


Association. 


Dr.  B.  A. 
Gould. 


The  Editor. 


Academy 

of  Sciences,  St. 

Petersburg.- 


Presents,  8fc,  during  the  Session  1886-87.  49 

Ball,  L.  de,  Determination  de  la  parallaxe  relative  de  l'etoile    The  Author, 
prineipale  da  couple  optique  2  1516AB,  a  l'aide  d'ob- 
servations  faites  a   l'lnstitut   Astronomique  annexe1    a 
rUniversite  de  Liege,  4 to.  Bruxelles,  1887 

Sir  R.  S.,  The  story  of  the  heavens.  London,  1885  A.  A.  Common. 

Baltimore,  Johns-Hopkins  University,  Circulars,  Nob.  50-57,  rf^m 

4to.  Baltimore,  1886-87      University. 

Barrow  Isaac,  Lectiones  XVIII.,  Cantabrigi©  in  scholis  pub-      The  Royal 
licis  habit®,  in  quibus  ■  opticorum  phenomenon  genuin©        8ociet*' 
rationes  investigantur  ac  exponuntur,  4to.   Londini,  1669 

Batavia,  Koninklijke  Natuurkundige  Vereeniging  ;  Natuur-     The  Society, 
kundig  Tijdschrifb  voor  Nederlandsch-Indie,  Deel  xlv., 
(Aohtste  serie,  Deel  vi.),  8vo.  Batavia,  1886 

Batavia,  Magnetical  and  Meteorological  Observatory,  Observa-  The 

tions,  vol.  vi  (Supplement),  vol.  vii.,  4to.     Batavia,  1886     Observatory. 

Regenwaarnemingen  in  Nederlandsch-Indie,  Jaargang        

vii.,  1885,  8vo.  Batavia,  1886 

Belfast  Natural  History  and  Philosophical  Society,  Report     The  Society, 
and  Proceedings  for  the  Session  1885-86,  8vo. 

Belfast,  1886 

Berlin,  Astronomisches  Jahrbuch  fur  1888,  mit  Ephemeriden  The 

der  Planeten  (1M247)  fur  1886,  8vo.  Berlin,  1886    0b^^a7, 

Circular,  Nos.  276-298,  8vo.  Berlin,  1886-87        

Berlin,  Konigliche  Akademie  der  Wissenschaften,  Abhand-   The  Academy. 
lungen  aus  dem  Jahre  1885,  4to.  Berlin,  1886 

Sitzungsberichte,  1886,  i.-liii. ;  1887,  i.-xviii.,  8vo.  

Berlin,  1886-87 

Berlin,  K.  preuss.  geodatisches  Institut,  Uebersicht  der  Ar-  The  Institute, 
beiten  des  k.   geodatischen  Instituts  .  .  .  nebst  einem 
allgemeinen  Arbeitsplane  des  Instituts  fur  das  naohste 
Decennium,  4to.  Berlin,  1886 

Lothabweichungen,  Heft  i.,  Formeln  und  Tafeln,    4 to.        

Berlin,  1886 

Berlin,  Physikalische  Gesellschaft,  Die  Fortschritte  der  Physik     The  Society. 
in  den  Jahren  1879-81,  Jahrgang  xxxy.,  xxxvii., 
8vo.  Berlin,  1885-87 

Verhandlungen  im  Jahre  1886,  Jahrgang  v.,  8vo.  _— 

Berlin,  1887 


50  Appendix  III. 

The  Royal     Berthoud,  P.,  Eclaircissemens  sur  l'invention,  la  throne,  la 
S06161**  construction  et  les  ipreuves  des  nouvelles  machines  pro- 

poshes  en  France  pour  la  determination  des  longitudes 
en  mer  par  la  mesnre  da  temps,  4 to.  Paris,  1773 

The  Author.    Biggs,  A.  B.,  Is  Jtipiter  self-luminous  ?   8vo. 

Hobart  Town,  1886 

The  Libraries,  Birmingham  Free  Libraries,  25th  annual  report,  1886,  8vo. 

Birmingham,  1887 

The  Society.    Birmingham   Philosophical  Society,  Proceedings,  vol.  v.,   1, 

8vo.  Birmingham,  1886 

The  Author.     Bisohof,  J.,   Untersuchungen  uber  die  Eigenbewegung  des 

Sonnensystems  aaf  Grund  yon  480  Argelander'schen 
teleskopischen  FLxsternen.    Inangnral-Dissertation,  8vcv 

Bonn,  1884 

H.  J.  Chaney,   Board  of  Trade,  Report  of  proceedings  and  business  nnder 
Ewl-  the  Weights  and  Measures  Act  (1878),  1884-86,  fol. 

London,  1884-86 

The  Aeademy.  Bologna,  Reale  Accademia  delle  Scienze  dell'  Istituto,  Me- 

morie,  serie  IV.,  tomo  yi.,  4 to.  Bologna,  1884 

The  Society.    Bombay  Branch  of  the  Royal  Asiatic  Society,  Index  to  the 

Transactions  of  the  Literary  Society  of  Bombay,  vols, 
i.-iii. ;  and  to  the  Journal  of  the  Bombay  branch  of  the 
Royal  Asiatic  Society,  vols,  i.-xvii.,  with  a  historical 
sketch  of  the  Society,  8vo.  Bombay,  1886 

The  Bonn,  Universitats-Sternwarte,  Astronomische  Beobachtun- 

serva  ry.  ^^  ange8tellt  und  herausgegeben  von  E.  Sohonfeld, 

Band  viii.,  Bonner  Sternverzeichniss,  vierte  Section,  4to. 

Bonn,  1886 

■  Bonner  Sternkarten,  zweite  Serie ;  Atlas  der  Himmel- 

zone  zwischen  i°  und  230  siidlicher  Declination,  fol. 

Bonn,  1886 

The  Libraries.  Bradford  Free  Libraries,  16th  annual  report,  8vo. 

Bradford,  1886 

The  Author.    Bredichin,  Th.,  Sur  les  grandes  cometes  de  1886,  8vo. 

Moscou,  1886 

The  Library.    Bristol  Museum  and  Library,  Report,  1887,  8vo. 

Bristol,  1887 


Presents,  fyc,  during  the  Session  1886-87.  S1 

British  Association  for  the  Advancement  of  Science,  Montreal      Montreal 
meeting,  1884  :  Canadian  Economics,  being  papers  pre-     0f  the  £.A. 
pared  for  reading  before  the  Economical  Section,  8vo. 

Montreal,  1885 

Report  of  the  fifty-fifth  meeting,  held  at  Aberdeen,  1885,  T*?e  . 

8vo.  London,  1886 

Bruxelles,  Observatoire  Royal,  Annnaire,  par  F.  Folie,  54me  The 

annee,  1887,  nmo.  Bruxelles,  1886    obMrvat*ry- 

Bad  a    Pest,     Magyar     Tudomanyos    Akad6mia,   Almanach,   The  Academy. 
1886,  8vo.  Buda  Pest,  1885 

Mathematikai  es  termeszettudomanyi  Ertesitd,  iii.  6-9  ;         ■ 

iv.  1-6,  8vo.  Buda  Pest,  1885-86 

Ertekezesek  a  mathematikai  tudomanyok  Kor^bol,  xi.  - 

10;  xii.  i-ii,  8vo.  Buda  Pest,  1885 

— —  J3rtekez6sek    a  termeszettudomaoyok  KorSbol,  xiv.  9 ;        

xt.  1-18,  870.  Buda  Pest,  1885 

Mathematikai  es  termeszettudomanyi  kozlemenyek,  xx.,        

xxi.  1,  8vo.  Buda  Pest,  1885 

III.  Osztalyanak  Kiilon  Kiadvanya,  1884,  i.,  8vo.  

Buda  Pejt,  1884 

Mathematische  and  natnrwissenschaftliche  Berichte  aus        

Ungarn,  iii.,  8vo.  Buda  Pest  und  Berlin,  1885 

Bulletin  des  Sciences  Mathematiques,  serie  II.,  tomes  x.  7-     xiie  Editors, 
xi.  6,  8vo.  Paris,  1886-87 

Calcutta,  Asiatic  Society  of  Bengal,  Journal,  vol.  Iv.,  part  1,     The  Society. 
Nos.  1-4,  and  part  2,  Nos.  1-4,  8vo.  Calcutta,  1886 

Proceedings,  1886,  i.-x. ;  1887,  i.,  8vo.  ■ 

Calcutta,  1886-87 
California  University  :  Addresses  of  J.  S.  Hager  and  E.  S.      p«>f-  E-  s- 
Holden,  June  30,  1886,  8vo.  Sacramento,  1886 

Cambridge  Philosophical  Society,  Transactions,  vol.  xiv.,  2,     The  Society. 
4to.  Cambridge,  1887 

Proceedings,  vol.  v.  6  ;  vi.  1  Cambridge,  1886-87        ■ 

Camera  Club,  Proceedings,  vol.  i.,  Nos.  1,  5-7,  4to.  The  Club. 

London,  1886-87 
Canada,   Geological  and   Natural  History   Survey,  Annual     The  Survey 
Report  (new  series),  vol.  i.,  1885,  8vo.      Montreal,  1886 


n 


52  Appendix  III. 

The  Cape  of  Good  Hope  Royal    Observatory,  Annals,   vol.  ii. 

***  part  1.     Observations  of  the  great  comet,  1882,  ii.,  4to. 

London,  1886 

Results  of  meridian  observations  made  during  the  years 

1879,  1880,  and  1 88 1,  under  the  direction  of  David  Gill, 
8vo.  London,  1884 

The  Author.    Cellener,  G.,  Etude  numerique  des  ooncours  de  compensation 

de  chronometres  faits  a  l'Observatoire  de  Geneve  en  1884 
et  1886,  4to.  Geneve,  1887 

Gharlier,  0.  V.  L.,    En  metod  att  foroka  konvergensen  hos 

en  trigonometrisk  serie,  8vo.  Stockholm,  1886 

Untersuchung  iiber  die  allgemeinen  Jupiter-Storungen 

des  Planeten  Themis,  4to.  Stockholm,  1887 

The  Library.    Chicago  Public  Library,  14th  Annual  Report  of  the  Board  of 

Directors,  June,  1886,  8vo.  Chicago,  1886 

L.  Clark,  Esq.  Clark,  L.,  Transit  Tables  for  1887,  8vo.  London,  1886 

The  Author.     Clerke,  Agnes  M.,  A  popular  history  of  astronomy  during 

the  nineteenth  century,  second  edition,  8vo. 

Edinburgh,  1887 

The  Academy.  Connecticut  Academy  of  Arts  and  Sciences,  Transactions, 

vol.  vii.  1,  8vo.  New  Haven,  1886 

■  Copenhagen,   Kougelige  Danske    Videnskabernes    Selskabs 

Skrifter,  6te  Rsekke,  naturvidenskabelig  og  mathematisk 
afdeeling,  Bandet  ii.  8-1 1 ;  iii.  2,  4 ;  iv.  2,  3,  4to. 

Kjobenhavn,  1885-87 

Oversigt  over  det  Forhandlinger,  1885,  iii.— 1887,  i.,  8vo. 

Kjobenhavn,  1885-87 

The  Cordoba,  Observatorio  Nacional  Argentino,  Resultados,  vol.  v., 

Observatory.  Observaciones  del  ano  1874,  4to.  Buenos  Aires,  1886 

Resultados,  vol.  xiv.     Catalogo  General,  4to. 

Cordoba,  1886 
The  Office.      Cordoba,  Oficina  meteoroldgica  Argentina,  Anales,  tomo  v., 

4 to.  Buenos  Aires,  1887 

The  Author.    Cornu,  A.,  Etude  des  bandes  telluriques  a,  B  et  A  du  spectre 

solaire,  8vo.  Paris,  1886 

— —        Sur  les  raies  spectrales  spontanement  renversables,  et 

l'analogie  de  leurs  lois  de  reparation  et  d'intensite'  avec 
celles  de  l'bydrogene,  8vo.  Paris,  1886 


Presents,  8fc>  during  the  Session  1886-87.  53 

Delauney,  M.,  Explication  des  taohes  de  Soleil,  8vo.  The  Author. 

Paris,  1886 
Delft,  Ecole  Polytechnique,  Annales,  tome  ii.  1-4 ;  iii.  1,  4to.      taSniaue 

Leide,  1886-87 

Dembowski,  H.  yon,  Misnre  micrometriche  di  stelle  doppie  e  Mile.  M. 

multiple  fatte  negli  anni  1852-78,  vol.  ii.,  4to.  Dembowski. 

Boma,  1884 

De  Moivre,   A.,   Aniraadversiones   in   D.    Georgii    Cheynsi  The  Royal 

tractatum  de  fluxionum  methodo  inversa,  8vo.  Society. 

Londini,  1704 

Depenning,  G.  A.,  A  paper  on  the  nature  of  gravity,  dis-        __. 
closing  that  flotation  necessarily  developes  two  centres 
of  gravity,  8vo.  Calcutta,  1885 

■      A  paper  on  the  effect  of  gravity,  8vo.         Calcutta,  1885  - 

Doberck,  "W.,  The  law  of  storms  in  the  eastern  seas,  8vo.  The  Author. 

Hong  Kong,  1886 
Dollen,  W.,  Zeitstern-Ephemeriden  auf  den  Jahren  1886-87,       Pulkow 

8vo.  St.  Petersburg,  1886  Observatory. 

Dublin,    Royal  Irish  Academy,  Transactions,    Science,  vol.   The  Academy, 
xxviii.,  N08.  21-25,  4to.  Dublin,  1885-86 

Transactions,    Polite   Literature  and  Antiquities,   vol.        

xxvii.  6-8,  4to.  Dublin,  1885-86 

■  Proceedings,  Science,  series  II.,  vol.  iv.  5,  8vo.  ■ 

Dublin,  1886 

■  Proceedings,  Polite  Literature  and  Antiquities,  series        

II.,  vol.ii.  7,  8vo.  Dublin,  1886 

. Cunningham  Memoirs,  Nos.  II.,  III.,  4to.  

Dublin,  1886 

Dan  Echt  CircUar,  Nos.  125-143,  4to.      Dun  Edit,  1886-87     The  Earl  of 

Crawford. 
Dnnkin,  E.,  Note*  on  some  points  connected  with  the  early     The  Author. 

history  of  the  Nautical  Almanac,  8vo.  Truro,  1886 

Earth,  The,  Nos.  S,lt  4to.  London,  1886-87   Jt  Ha 

Edinburgh,  Boyal  Observatory;    Astronomical  observations,  £Jhe 

vol.  xv.,  for  1878-86:  Edinburgh  Star  Catalogue,  R. A.    Observatory. 
4h-23h,  fol.  Edinburgh,  1886 

Ellery,  R.  L.  J.,  H.  C.  lussell,  and  C.  Todd,  Report  on  the      Melbourne 
telegraphic  deterainiiion  of  Australian  longitudes,  4to.        Observatory. 

Melbourne,  1886 


54  Appendix  III. 

The  Author.   Ellis,  W.,  A  brief  historical  account  of  tbe  barometer,  8vo. 

London,  1886 

■  Engelhardt,  B.  d',  Observations  astronomiqaes  faites  par 
B.  d'Engelhardt  dans  son  observatoire  &  Dresde,  ire 
partie,  4to.  Dresde,  1886 

The  Editor.      English  Mechanic,  The,  and  World  of  Science,  Nos.   1108- 

11 59,  fol.  London,  1886-87 

Tbe  Royal      Euclid :  EwcXctSov  SrotxctW  fiifiX.  U  Ik  twv  ©cctwos  Swouauov- 

Eis  rov  avrov  to  icpwrov  'J&frrryrjfiaTitiV  UpotcXov  /?t/&-  8'- 
Adiecta  profatiuncula  [S.  Grynaei]  in  qua  de  disciplinis 
mathematici8  nonnihil,  fol.  Basilece,  1533 

The  Author.    Faye,  H.,  Sur  les  tempetes :  theories  et  discussions  nouvelles, 

8vo.  Paris,  1&Z7 

Fievez,  Ch.,  Essai  sur  l'origine  des  raies  de  Fraunhofer  en 

rapport  avec  la  constitution  du  soleil,  8vo. 

Bruxelles,  1886 

-  Franz,  J.,  Anleitung  zur  Beobachtung  der  totalen  Sonnei- 

finsterniss  in  Ost- und  Westpreusssen  den  19  Aug.  1857, 
4to.  Kbnigsberg,  1S86 

The  Royal      Gazan,  A.,  Constitution  physique  du  Soleil ;  explication  cb  la 
y*  formation  et  de  la  disparition  des  taches,  8vo. 

Antides,  1873 

Dr.  Radford.    Gehler,  J.  S.  T.,  Physikalisches  Worterbuch,  25  vols,  8vo. 

Leipzig  1825-45 

The  Society.    Geological  Society,  Quarterly  Journal,  Ncs.  167-1/0,  8vo. 

Lonlon,  1886-87 

The  Author.    Ginzel,  F.  K.,  Ueber  einige  historische,   bes^ders  in  Alt- 

spanischen  Geschichtsquellen  erwahnte  Sonnenfinster- 
nisse,  8vo.  Berlin,  1886 

The  Society.    Gottingen,    Konigliche     Gesellschaft     de-    Wissenschaften, 

Abhandlnngen,  Band  xxxii.,  xxxiii*  von  den    Jahren 
1885-86,  4to.  Qoltingen,  1886 

Gottingische  Gelehrte  Anzeigen,  1885-86,  8vo. 

Qottingen,  1885-86 

Nachrichten  von  der  Konigl.  Jesellschafc  der  Wissen- 
schaften und  der  Georg-Augists-Universitat,  aus  den 
Jahren  i88«;-86.  8vn,  Qottingen,  1885-86 


Presents,  $c,  during  the  Session  1886-S7. 


55 


Greenwich,  Royal  Observatory,  Astronomical,  magnetical,  and 
meteorological  observations  made  in  the  year  1884,  under 
the  direction  of  W.  H.  M.  Christie,  4to.        London,  1886 

Results  of  the  astronomical  observations,  1884,  4to. 

London,  1886 

Results  of  the  magnetical  and  meteorological  observa- 
tions, 1884,  4to.  London,  1886 

Spectroscopic  and  photographic  observations,  1884,  4U). 

London,  1886 

Rates  of  chronometers  on  trial  for  purchase  by  tho 

Board  of  Admiralty,  1886,  4to.  London,  1886 

Report  of  the  Astronomer  Royal  to  the  Board  of  Visitors, 

June,  1887,  4to.  London,  1887 

Grnbb,  H.,  Description  of  the  great  27-inch  refracting  tele- 
scope and  revolving  dome  for  the  Imperial  and  Royal 
Observatory  of  Vienna,  fol.  London,  1881 

Telescopic  objectives  and  mirrors,  their  preparation  and 

testing,  8vo.  London,  1886 

Gyiden,  H.,  Untersuchungen  fiber  die  Convergenz  der  Reihen 
welche  zur  DarsteUung  der  Coordinaten  der  Flaneten 
angewendet  werden,  4to.  Stockholm,  1887 

Haarlem,  Musee  Teyler,  Archives,  eerie  II.,  vol.  ii.  4,  4to. 

Haarlem,  1886 

Catalogue  de  la  Bibliotheque,  partie  3.     Haarlem,  1886 

Hall,  A.,  Observations  for  stellar  parallax,  4to. 

Washington,  1886 

The  six  inner  satellites  of  Saturn,  4to. 

Washington,  1886 

Halle,  Kaiserliohe  Leopold  inisch-Carolinisohe  Deutsche  Aka- 
demie  der  Naturforscher,  Verhandlungen  (Nova  Acta), 
Band  xlvii.,  xlviii.,  4to.  Halle,  1885-86 

Leopoldina,  Heft  xx.,  xxi.,  4to.  Halle,  1884-85 

Harkness,  W.,  On  the  flexure  of  meridian  instruments,  and 
on  the  means  available  for  eliminating  its  effects  from 
star-places,  4to.  Washington,  1886 

Harley,  Rev.  T.,  Lunar  science,  anoient  and  modern,  8vo. 

London,  1886 


The 
Observatory. 


C.  Thwaites, 
Esq. 


The  Author. 


Musee  Teyler. 


The  Author. 


The  Academy. 


The  Author. 


56  Appendix  III. 

The  Harvard  College  Astronomical  Observatory,  Annals,  vol.  xv. 

Obaervatory.  ^  ^    Catajogue  of  I|2I3  Btarg>    by  W#  j^  Rogers ; 

voL  xvi.,  Observations  of  fundamental  stars ;  vol.  xvii.9 
The  Almucantar,  by  S.  C.  Chandler,  4to. 

Cambridge,  1886-87 

Henry  Draper  Memorial:  First  report  of  the  photo- 
graphic study  of  stellar  spectra,  E.  C.  Pickering,  director, 
4to.  Cambridge,  1887 

Photographs  to  accompany  above. 

41st  annual  report  of  the  director,  E.  C.  Pickering,  8vo. 

Cambridge,  1887 

Finnish  Soc.    Helsingfors,  Exploration  Internationale  des  regions  polaires, 
ofSciences.  1882-84.      Expedition    polaire  Findlandaise,    tome    i., 

M6teorologie,  4to.  Helsingfors,  1886 

Helsingfors,  Society  des  Sciences  de  Finlande,  Ofversigt  a£ 

Finska  Vetenskaps-Societetens  FdrhandliDgar,  xxvii.,  8vo. 

Helsingfors,  1885 

Bidrag  till  kannedom  Finlands  natur  och  folk,  Haftet 

43,  8vo.  Helsingfors,  1886 

■  Observations,  vol.  i.  1,  2  :  Observations  mefceorologiques 

faites  a  Helsingfors  en  1882-83,  4 to.    Helsingfors,  1886 

The  Author.     Hennessy,  H.,  On  the  fluid  bodies  composing  our  planetary 

system,  8vo.  Dublin,  1886 

TJ"^ Royal      Hirsch,  M.,  Integral  tables,  or  collection  of  integral  formulae, 
y'  8vo.  London,  1823 

Holder,  W.,  A  discourse  concerning  time,  8vo. 

London,  1694 

The  Hong  Kong  Observatory,  Observations  and  researches  made 

Observatory.  ^  ^  yearfl  l8g5_86  by  w   Doberck>  ftf. 

Hong  Kong,  1886-87 

Report  on  the  astronomical  instruments  at  the  Observa- 
tory, and  on  the  time  service  of  Hong  Kong  in  1885,  fol. 

Hong  Kong,  1886 

>        Report  on  the  time  service  in  1886,  and  micro  metric 

measures  of  planets,  fol.  Hong  Kong,  1887 

The  Author.    Hoover,  "W.,  Cometary  Perturbations  [Inaugural  Disserta- 
tion], 8vo.  Wooster,  Ohio,  1887 


Presents,  fyc,  during  Hie  Session  1886-87. 


57 


British 

Horological 

Institute. 


The  Author. 


The  Royal 
Society. 


H.  M.'s  Govt, 
in  India. 


Horological  Journal,  The  :  a  monthly  paper  for  the  advance- 
ment of  chronometer,  watch,  and  clock  making,  Nos. 
335-346,  8vo.  London,  1886-87 

Howarth,  E.,  Meteorology  of  Sheffield,  1885,  4to. 

Sheffield,  1886 

Hnet,  J.  M.,  Les  lois  de  la  nature ;  les  causes  materieiles  de 
l'attraction  de*  voices,  12  mo.  Londres,  1801 

Huyghens,  C,  Traite  de  la  lumiere,  ou  sont  expliquees 
les  causes  de  ce  qui  luy  arrive  dans  la  reflexion  &  dans 
la  refraction,  et  particulierement  dans  l'6trange  refrac- 
tion du  oristal  d'Islande ;  aveo  un  discours  de  la  cause 
de  la  pesanteur,  4 to.  Leide,  1690 

Opuscula  posthuma,  2  vols,  in  1,  4to. 

Amstelodami,  1728 

India,  Survey  Department,  General  report,  1884-85,  fol. 

Calcutta,  1886 

Inwards,  R.,  Description  of  a  compensating  pendulum,  with    The  Author, 
some  suggested  improvements,  8vo.  London,  1886 

Jacobi,  C.  G.  J.,  Fundamenta  nova  theoriae  functionum 
ellipticarum,  4to.  llegiomonti,  1829 

Canon  arithmeticus,  sive  tabulre  quibus  exhibentur  pro        

singulis    numeris    primis    vel    primorum    potestatibus 

infra  1000  numeri  ad  datos  indices,  et  indices  ad  datos 
numeros  pertinentes,  4k).  Berolini,  1839 

Japan,  Seismological  Society,  Transactions,  vols,  ix.,  x.,  8vo.       The  Society. 

Yokohama,  1886-87 

Joubert  (le  pere),  Sur  les  Equations  qui  se  rencontrent  dans 
la  theorie  de  la  transformation  des  fonctions  elliptiques, 
4to.  Paris,  1876 

Kaloc8a,Haynald-Observatorium,  Kozlemenyei  a  termeszettu- 
domankyok  s  foleg  a  czillagaszat  korebol,  II.  Macules 
solares,  III.  Meteorologica,  kozli  Hiininger  Adolf,  8vo. 

Buda  Pest  and  Kalocsa,  1886-87 

Kew  Observatory,  Report  of  the  Kew   Committee  for  the        

year  ending  Oct.  31,  1886,  8vo.  London,  1886 

Kleiber,  J.  A.,  Predstojashtcheje  polnoje  solnethoje  fatmenije    The  Author. 
7  Argusta  1887  goda,  8vo.  St.  Petersburg,  1887 


The  Royal 
Society. 


The  Royal 
Society. 


The 
Observatory. 


58  Appendix  III. 

0,  The  K6nig8berg,     Konigliche  Universitats-Sternwarte,   Astrono- 

mische  Beobachtungen  yon  E.  Luther,  Abth.  xxxvii.  i,  2, 
fol.  Konigsberg,  1882-86 

The  Author.     Koerber,  F.,  Ueber  den  Cometen  1865  I.  Inaugural  Disser- 
tation, 8vo.  Breslau,  1887 

Laiigley,  S.  P.,  Sar  les  spectres  invisibles,  8vo.      Paris,  1886 

On  hitherto  unrecognised  wave-lengths,  8vo. 

New  Haven,  1886 
The  Academy.   Laplace,  P.  S.  de,    CEavres,  publiees  sous  les  auspices  de 

1' Academic  des  Sciences,  tome  vii.  1,  2,  4 to. 

Paris,  1886 

Lawrence,  E.,  The  progress  of  a  century,  or  the  age  of  iron 

and  steam,  8vo.  London,  1886 

The  Society.     Leipzig,  Astronomische  Gesellschaft,  Pnblicationen,  No.  xviii. 

(Genaherte  Orter  der  Fixsterne  fur  die  Epoche  1885, 
H.  Romberg),  4to.  Leipzig,  1886 

-  —  Vierteljahrsschrift,  Jahrgangxxi.  1-4,  xxii.  i,8vo. 

Leipzig,  1886-87 

■  ■■        Leipzig,  Koniglich-sachsische  Gesellschaft  der  Wissenschaften, 

Abhandlungen     der     mathematisch-physischen     Classe, 

Band  xiii.  6-7,  4to.  Leipzig,  1886 

Berichte  iiber  die  Verhandlungen ;  mathematisch-phy- 

sische  Classe,  1886,  8vo.  Leipzig,  1886-87 

Royal  Saxon     Leipzig,  Furstlicbe  Jablonowski'sche  Gesellschaft,  Preisschrif- 
Sciences  *eD»  ^°*  xxyi«  (K.  Rohn,  Die  Flachen  vierter  Ordnung), 

8vo.  Leipzig,  1886 

MM.Gauthier-  Lemstrom,  S.,  L'Aurore  Boreale,  etude  generate  des  pbeno- 

1  ars*  menes  produits  par  les  courants  electriques  de  ratmo- 

sphere,  8sro.  Paris,  1886 

The  Royal     Lindenau,  B.  de,  Tables  barom6triques  pour  faciliter  le  calcul 
Society.  ^eg  nivellemente  et  des  mesures   des  hauteurs  par  le 

barometre,  8vo.  Ootha,  1809 

The  Society.    Liverpool  Astronomical  Society,  Journal,  vol.  v.  i~8,  8vo. 

Liverpool,  1886-87 
.  Liverpool  Literary   and   Philosophical  Society,  Proceedings 

during  the  74th  and  75th  sessions,  1884-86,  Nos.  xxrix., 
xl.,  8vo.  Liverpool,  1885-86 


Presents,  §fc,  during  the  Session  1886-87.  59 

Liversidge,  A.,  President's  Address  to  the  Royal  Society  of    The  Author. 
New  South  Wales,  8vo.  Sydney,  1886 

Loewy,  M.,  Ephemerides  des  6toiles  de  culmination  lunaire        

et  de  longitude  pour  Tan  1887,  4to.  Paris,  1886 

Nouvelles  m6thodes  pour  la  determination  complete  de        — — 

la  refraction,  4to.  Paris,  1886 

Rapport  snr  les  observatoires  de  province,  8vo.  

Paris,  1886 

Loomis,  E.,  Contributions  to  meteorology x  revised  edition,        — 
Chapter  II.,  4to.  New  Haven,  1886 

Lynn,  W.  T.,  Celestial  motions :  a  handy-book  of  astronomy,        

5  th  edition,  8vo.  London,  1887 

Madras,  Government  Observatory,  Results  of  observations  of         The 

the  fixed  stars  made  with  the  meridian  circle  in  the  years     Observatory. 
1862,   1863,  and   1864,  under    the  direction   of  K  R. 
Pogson,  4 to.  Madras,  1887 

Madrid,  Institucion  libre  de  ensenanza,  Boletin,  Nos.  222-227,  Tho 

r  *r  j  'i     00*      Institution. 

4to.  Madrid,  1886 

Madrid,  Real  Academia  de  Ciencias  exactas,  fisicas  y  naturales,   The  Academy. 
Memorias,  tomo  xi.,  4to.  Madrid,  1887 

Revista  de  los  progresos  de  las  Ciencias,  tomo  xxi.  7-9  ;        

xxii.  1,  8vo.  Madrid,  1886 

Mairan,  De,  Traits  physiquo  et  historique  de  TAurore  Boreale,      The  Royal 
seconde  edition,  4to.  Paris,  1754        Society- 

Mannheim,  Grossherzogliche  Sternwarte,  Veroffentlichungen,  The 

herausgegeben  von  W.  Valentiner,  Heft  ii.,  4to.  Observatory. 

Karlsruhe,  1886 

Marseilles,  Soci6t6  Scientifique  Flammarion,  Bulletin,   1886,     The  Society. 
4to.  Marseille,  1887 

Matton,  L.  P.,  Appendice  a  la  quadrature  du  cercle,  4to.  The  Royal 

Lyon,  1 88 1        Society. 

Maurolycus,  F.,  Arithmeticorum  libri  duo,  4to.  

Venetijs,  1575 

Melbourne  Observatory,  Monthly  record  of  results  of  observa-  The 

tions  in  meteorology,  terrestrial  magnetism,  <fcc.,  taken    Observatory. 
Jan.-Dec.  1886,  under  the  superintendence  of  R.  L.  J. 
Ellery,  8vo.  Melbourne,  1886 


6o  Appendix  ITT. 

he         Melbourne  Observatory,  Twenty- first  report  of  the  Board  of 
serva   ry.  Visitors,  together  with  the  report  of  the  Government 

Astronomer,  fol.  Melbourne,  1886 

Meteorological  Meteorological  Office,  Report  of  the  Meteorological  Council  of 

the  Royal  Society  for  the  year  ending  Oct.  31,  1886,  8vo. 

London,  1887 

Quarterly  weather  report,  new  series,  parts  1-3,  1878, 

4to.  London,  1886-87 

— —        Monthly  weather  report  for  Feb.-Nov.  1886,  4to. 

London,  1886-87 
1         Weekly  weather  report,  vol.  iv.  i-n. 

■        Hourly  readings,  1883,  iv. ;  1884,  i.-iii.,  4to. 

London,  1886-87 

Meteorological  observations  at  stations  of  the  second 

order  for  the  year  1882,  4to.  London,  1887 

Observations  of  the  International  Polar  Expeditions, 

1882-83  :  Forfc  Ba®*  4to-  London,  1886 

The  Society.    Mexico,     Sociedad   Cientifica    Antonio    Alzate,     Memorias, 

tomo  i.,  1,  2,  8vo.  Mexico,  1887 

0b        to        Milan,  Reale  Osservatorio  di  Brera,  Pubblicazioni,  No.  xxviii. 

(A  Venturi,  di  una  note  vole  semplificazione  nel  calcolo 
dello  perturbazioni  dei  piccoli  pianeti),  4k) .     Milano,  1886 

The  Society.    Montreal,  Royal  Society  of  Canada,  Proceedings  and  Trans- 
actions for  the  year  1885,  vol.  iii.,  4to.       Montreal,  1886 

The  Royal      Morin,  J.  B.,  Astronomia  jam  a  f  undamentis  integre  et  exacte 

restituta ;  complectens  ix  partes,  hactenus  optatra  scientise 
longitudinum  ccelestium  nec-non  terrestrium,  4to. 

Parieiis,  1640 

Morland,  Sir  S.,  The  description  and  use  of  two  arithmetick 

instruments,  8vo.  London,  1673 

The  Society.    Moscow,  Society  Imperial e  des  Naturalistes,  Bulletin,  ann£e 

1885,  iii.,  iv. ;   1886,  i.-iv.;  1887,  i.  Moscou,  1885-87 

Meteorologische  Beobachtungen,  1885-86,  obi.  fol. 

Moskau,  1885-86 
The  Author.    Monchez,  E.,  La  photographic  astronomique  a  l'Observatoire 

de  Paris,  et  la  carte  du  ciel,  12 mo.  Paris,  1887 

Mukhopadhyay,  Asutosh,  Appendix  to  mathematical  questions 

and  solutions  from  the  "  Educational  Times,"  vol.  xliv., 
Solutions  of  some  old  questions,  8vo.  London 


Presents,  jrc,  during  the  Session  1886-87.  61 

Munich,  Koniglich-Bayerische  Akademie  der  Wissenschaften,  The  Academy. 
Abhandlungen  der  mathematisch-physikalischen  Classe, 
Band  xv.  3,  4 to.  Miinchen,  1886 

Gedachtnissrede  auf  C.  T.  von  Siebold,  4to.  

Miinchen,  1886 


Naples,  Accademia  delle  Scienze  Fisiche  et  Matematiche,  Ren-        

diconto,  1882-84;  1885,  L-iii.,  4to.  Napoli,  1883-86 

Natal    Observatory,  Report  of  the  Superintendent  for  the    f^^6 
year  1885,  fol.  Durban,  1886  erv&t0TJ' 

Naturforscher,  Der,  Jahrgang  xix.  25-xx.  24,  4to.  The  Editor. 

Tubingen,  1886-87 
Naturwissenschaftliche  Rundschau,  Jahrgang  i.  i-ii.  24,  4to.         - 

Braunschweig,  1886-87 
Nautical  Almanac  and  Astronomical  Ephemeris  for  the  year  Lords  Commrs. 
1890,  8vo.  London,  1886    of  Admiralty. 

Neison,   Edmund,   Astronomy:    a  simple  introduction  to  a     The  Author, 
noble  science,  8vo.  London,  1886 

New  Princeton  Review,  May  1887,  8vo.  New  York,  1887      2*°*-  C.  A. 

Newton,  H.  A.,  The  meteorites,  the  meteors,  and  the  shooting     The  Author, 
stars,  8vo.  Salem,  1886 

Newton,  Isaac,  Philosophies  naturalis  principia  mathematics,    Dr.  Radford. 
editio  tertia,  4to.  Londinir  1726 

Tractates  de  quadratura  curvarum,  in  usum  studios©      The  Rojal 

juventutis  mathematical,  explicationibus  illustratus,  4to.  Society. 

TTpsalice,  1762 

Newton,  John,  Tabulae  mathematics,  or  tables  of  the  naturall        __ 
sines,  tangents,  and  secants,  with  a  table  of  logarithms, 
i2mo.  London,  1654 

New  York,  Astor  Library,  38th  Annual  Report,  8vo.  The  Library. 

New  lark,  1887 

New  York,  Columbia  College  Library,  Circular  of  Information,    The  College. 
1886-87,  8vo.  New  York,  1886 

■  Second  and  Third  Annual  Reports  of  the  Chief  Libra-        _ 

rian,  1886,  8vo.  New  York,  1886 

Noble,  Capt.  W.,  Hours  with  a  three-inch  telescope,  8vo.  The  Author. 

London,  1886 

Norwegian  North  Atlantic  Expedition,  1876-78 ;  zv.  2,  xvii.  2,  The 

xviii.,  4to.  Christiania,  1886      Norwegian 

Government. 


62  Appendix  III. 

The  Author.     Nursingrow,  A.  V.,   Results  of  meteorological  observations 

made  at  Daba  Gardens,  Vizagapatam,  1885,  8vo. 

Calcutta,  1886 

St.  Petersburg  Nyren,  M.,  Untersuchung  der  Bepsold'schen  Theilung  des 
Academy.  Pulkowaer  Verticalkreises,  4to.  St.  Petersburg,  1886 

The  Editors.    Observatory,  The,  a  monthly  Review  of  Astronomy,  edited 

by  E.  W.  Mannder,  A.  M.  W.  Downing,  and  T.  Lewis, 
Nos.  1 1 2-1 24,  8vo.  London,  1886-87 

Dr.  von  Eon-    O-Gyalla,  Astrophysikaliscbes  Observatorium,  Beobachtungen, 
^oly*  herausgegeben  von  N.  von  Konkoly,  Band  viii.  1,  4to. 

'Halle,  1887 
The  Editor.     Olsen,  0.  T.,  The  Fisherman's  Nautical  Almanac,  1887,  8vo. 

Qrim8by,  1886 
The  Author.    Oppolzer,   Th.   vod,   Bahnbestimmung  des    Planeten   (237) 

Cblestina,  8vo.  Wien,  1886 

■         Ueber  die  astronoraische  Refraction,  4to.       Wien,  1886 

The  Library.    Oxford,  Radcliffe  Library,  Catalogue  of  books  addod  daring 

the  year  1886,  4to.  Oxford,  1887 

The  Oxford,  Radcliffe  Observatory,  Results  of  astronomical  and 

Observatory.  ,•,.••,  ,.  1      .       .*  „« 

meteorological  observations    made   in    the  year   1883, 

nnder  the  superintendence  of  E.  J.  Stone,  8vo. 

Oxford,  1886 
Rev.  A.  Hen-    Paisley  Philosophical   Institution,    Coats  Observatory,  He- 
reon, teorological  observations,  1886,  8vo.  Paisley,  1887 

The  Academy.  Paris,  Academie    des   Sciences,   Comptes-Rendus  hebdoma- 

daires  des  stances,  tome  23-civ.  22,  4to.    Paris,  1886-87 

Bureau  des      Paris,  Bureau   des   Longitudes,    Annuaire  pour   Tan    1887, 
Longitudes.  l2mQ  p^  lg86 

__ ^        Connaissance  des  temps  ou    des  mouvements  celestes 

pour  Tan  1888,  8vo.  Paris,  1886 

The  Paris,  Comite*  International  des  poids  et  mesures,  Travaux 

Committee.  e^  M6moires  du  Bureau  International,  tome  v.,  4to. 

Paris,  1886 

Depot  de  la     Paris,  Depot  gene*  ral  de  IaMarine,  Ann  ales  Hydrographiquep* 

Marino-  serie  II.,  1886,  1,  2,  8vo.  Paris,  1886 

&ole  Poly-     Paris,  Ecole  Poly  technique,  Journal,  Cahier  lvi.,  4to. 
technique.  Paris,  1886 


Presents,  8fc.y  daring  the  Session  1886-87.  63 

Paris,  Observatoire,  Rapport  annuel  pour  l'annee  1886,  par    observatory 
M.  le  Contre-Amiral  Mouchez;  4k).  Paris,  1887 

Paris,  SociSte  Math£matique  de  France,  Bulletin,  tome  xiv.    The  Society. 
3-xv.  4,  8vo.  1886-87 

Paris,  Soci^te*  Philomathique,  Bulletin,  aerie  VII.,  tome  x.  2-        — — — 
xi.  2,  8vo.  Paris,  1886-87 

Philadelphia,  American  Philosophical  Society,  Proceedings,        — 
Nob.  122-124,  8v°*  Philadelphia,  1886 

Philadelphia,  Franklin  Institute,  Journal,  series  III.,  vol.  xcii.   The  Institute, 
i-xciii.  5,  8vo.  Philadelphia,  1886 

Phillips,  W.  H.,  Discovery  and  evidence  of  the  single  ser-    The  Her.  W.J. 
pontine  course  of  the  Moon  round  the  Sun  and  the       "    IC"ard** 
Earth,  8vo.  London,  1883 

Photographic  Society  of  Great  Britain,  Journal  and  Transac-     Tne  Society. 
tions,  new  series,  vol.  x.  9-xi.  8,  8vo.      London,  1886-87 

Physical  Society  of  London,  Proceedings,  vol.  viii.  1-4,  8vo.        

London,  1886-87 
Pickering,  E.  C,  A  plan  for  the  extension  of  astronomical    The  Author. 
research,  870.  Cambridge,  1886 

■  Comparison  of  maps  of  the  ultra-violet  spectrum,  8vo.  — 

New  Haven,  18S6 

Heights  of  the  White  Mountains,  8vo.  ■ 

Pinnington,  G.,  The  distances  of  the  Moon,  the  planets,  and        

the  Sun,  deduced  theoretically,  8vo.  Chester,  1886 

Prague,  K.K.  Sternwarte,  Astronomische  Beobachtungen  im  The 

Jahre  1884,  en  thai  tend  Originalzeichnungen  des  Mondes.  ePTa  ory* 

Herausgegeben  von  L.  Weinek,  4 to.  Prag,  1886 

Magnetische  und  meteorologische  Beobachtungen   im 

Jahre  1885,  4to.  Prag,  1886 

Prince,  C.  L.,  Observations  upon   the  climate  of  Uckfield,    The  Author. 
second  edition,  8vo.  Lewes,  1886 

Summary  of  a  meteorological  Journal,  1886,  fol.  cir-         

cular. 

An  analysis  of  forty  years'  consecutive  observations  of        

storms  in  the  county  of  Sussex,  8vo.  London,  1887 

Proctor,  R.  A.,  Nouvel  atlas  celeste,  comprenant  quatorze  MM.Gauthicr- 
cartes,  precede  d'une  introduction  sur  l'etude  des  con-  * 

stellations.     Traduit  par  P.  Gerigny,  8vo.      Paris,  1886 

9 


64 


Appendix  III. 


The  Author. 


The  Royal 
Society. 


Prof.  Ricco. 


Pulkowa        Palkowa,  Nicolai-Hauptsternwarte,  Jahresbericht,  1886,  8vo. 
Observatory.  gt  Petersburg,  1886 

The  Society.  Queensland  Branch  of  the  Geographical  Society  of  Austra- 
lasia, Report  of  the  second  ordinary  meeting,  March, 
1886,  8vo.  Brisbane,  1886 

■         Proceedings  and  Transactions,  vol.  i.,  vol.  ii.,  8vo. 

Brisbane,  1886 

Rambaut,  A.  A.,  On  the  possibility  of  determining  the  dis- 
tance of  a  double  star  by  measures  of  the  relative 
velocities  of  the  components  in  the  line  of  sight,  8vo. 

Dublin,  1886 

Rayet,  0.,  Notes  sur  l'histoire  de  la  photographic  astrono- 
mique,  8vo.  Paris,  1887 

Recorde,   Robert,    The    Castle  of   Knowledge,    containing 

treatises  on  the  sphere,  and  astronomy,  4to. 

London,  1556 

Rico6,  A.,  Osservazioni  astrofisiche  solari,  1884,  i.,  eseguite 
nel  Regio  Osservatorio  di  Palermo,  4to.  Roma,  1884 

— — —  Risultati  delle  osservazioni  delle  protuberanze  solari 
eseguite  nel  R.  Osservatorio  di  Palermo,  nel  1885,  4to. 

Roma,  1887 

Rigaud,  Rev.  S.  J.,  A  defence  of  Halley  against  the  charge 
of  religious  infidelity,  8vo.  Oxford,  1844 

Rio  de  Janeiro,  Imperial  Observatorio,  Revista  do  Observa- 
torio,  anno  I.  6-11.  3,  4to.  Rio  de  Janeiro,  1886-87 

Rochester,  Warner  Observatory t  History  and  work,  1883-86, 
vol.  i.,  8vo.  Rochester,  N.Y.,  1887 

Rogers,  W.  A.,  and  G.  H.  McLeod,  On  the  longitude  of  the 
McGill  College  Observatory,  8vo.  Montreal,  1886 

Rome,  Accademia  Pontificia  de'  Nuovi  Lincei,  Atti,  anno 
xxzvii.,  sessioni  i.~v.,  4to.  Roma,  1884 

Rome,  Biblioteca  Nazionale,  Bolletino  delle  opere  moderne 
straniere,  Nos.  1-6,  1886,  4to,  Roma,  1886-87 

Rome,  Pontificia  Universita  Gregoriana,  vol.  zzv.  1-12,  4 to. 

Roma,  1886 
Rome,  Reale   Accademia  dei  Lincei,   Atti,  anni  281,  282, 
eerie  III.,  Memorie  della  classe  di  scienze  fisiche,  mate- 
matiche  e  naturali,  vol.  zviii. ;  serie  IV.,  vol.  i.,  ii.,  4to. 

Roma,  1884-85 


The 
Observatory. 

Levis  Swift, 
Esq. 

The 
Observatory. 

The  Academy. 


The  Library. 


Padre  Ferrari. 


The  Academy. 


Presents,  fyc,  during  the  Session  1886-87. 


6S 


The  Academy. 


The  Society. 


C.  E.  Peek, 
Esq. 


The  Society. 


The 
Institution. 

The  Society. 


Borne,  Reale  Accademia  dei  Lincei,  Atti,  anni  283,  284, 
1885-87,  serie  IY.  Rendiconti,  vol.  ii.,  semestre  I.  12-14  5 
vol.  iii.,  semestre  I.,  1-8,  <to.  Roma,  1886-87 

Borne,  Societa  degli  Spettroscopisti  Italiani,  Memorie,  vol.  xv. 
4-xvi.  3,  4to.  Roma,  1886-87 

Rousdon  Observatory,  Devon,  Meteorological  observations 
for  the  year  1886,  made  under  the  superintendence  of 
C.  E.  Peek,  vol.  iii.,  4to.  London,  1S87 

Royal  Asiatic  Society  of  Great  Britain  and  Ireland,  Journal, 
new  series,  vol.  xviii.,  parts  3,  4, 8vo.  London,  1886 

Royal  Geographical  Society,  Proceedings  and  monthly  record 
of  geography,  new  monthly  series,  vol.  viii.  7-ix.  6, 
8vo.  London,  1886-87 

Royal  Institution  of  Great  Britain,  Proceedings,  No.  80,  8vo. 

London,  1887 

Royal  Meteorological  Society,  Quarterly  Journal,  Nos.  59-61, 

8vo.  London,  1886-87 

Meteorological    Record,  by  W.  Marriott,  Nos.   21-23, 

8vo.  London,  1886-87 

Royal  Society  of  London,  Philosophical  Transactions,  vol. 
clxxvi.,  parts  1,  2  ;  vol.  clxxvii.,  parts  1,  2,  4to. 

London,  1886-87 

Proceedings,  Nos.  243-252,  8vo.  London,  1886-87 

Royal  United  Service  Institution,  Journal,  vol.  xxx.,  Nos. 
134-139,  8vo.  London,  1886-87 

Rugby  School  Natural  History  Society,  Report  for  the  years 
1885-86,  8vo.  Rugby,  1886-87 

Russell,  H.  C,  Anniversary  address  to  the  Royal  Society  of 
Now  South  Wales,  8vo.  Sydney,  1885 

Local  variations  and  vibrations  of  the  earth's  surface,        

8vo.  Sydney,  1886 

Results  of  rain  and  river  observations  made  in   New 

South  Wales  during  1885,  8vo.  Sydney,  1886 

St.  Petersburg,  Academic  Imp6riale  des  Sciences,  Bulletin,  The  Academy, 
tome  xxxi.  2,  4to.  St.-Petersbourg,  1886 

San  Fernando,  Institute  j  Observatorio  di  Marina,  Anales, 
seccion  2  ;  observaciones  meteorol<5gicas,  ano  1885,  fol. 

San  Fernando,  1886 

02 


The 
Institution. 

The  Society. 


The  Author. 


The 
Observatory. 


Tbe 
Observatory. 

The  Author. 


Boston 

Scientific 
{Society. 

Meteorological 
Office. 

The  Author. 


•St.  Petersburg 
Academy. 


The  Author. 


The  Editor. 


The  Society. 


66  Appendix  III. 

Santiago,  Observatorio  Astrondmico  ;  Observaciones  meteoro- 
16jicas,  1882-84,  8vo.  Santiago  de  Chile,  1885 

Sawyer,  E.  F.,  Some  account  of  a  new  Catalogue  of  southern 
stars,  8vo.  Salem,  1886 

Scbiaparelli,  Q.  V.,  Osservazioni  astrouomicbe  et  fisicbe  sail* 
asse  di  rotazione  e  sulla  topografia  del  pi  an  eta  Marte. 
Memoria  iii.  (oppozione  1881-82),  4 to.  Roma,  1886 

Schultz,  H.,  Mikrometrische  Bestimmung  einiger  telesko- 
pischen  Sternhaufen,  8 70.  Stockholm,  1886 

Schwedoff,  Th.,  Leg  mouvements  cycloniques,  870. 

Paris,  1887 

Science  Observer,  Nos.  49,  50,  8vo.  Boston,  1886-87 

Scott,  R.  H.,  and  R.  H.  Curtis,  On  the  working  of  the 
Harmonic  Analyser  at  tbe  Meteorological  Office,  8vo. 

London,  1886 

Seeliger,  H.,  Bemerkung  zu  Zollner's  "  Photometriscben 
Untersuchungen,"  8vo.  Karlsruhe,  1886 

Ueber  den  Einfiuss  dioptriscber  Fehler  des  Auges  anf 

das  Resultat  astronomischer  Messungen,  4to. 

Miinchen,  1886 

Ueber  die  Vertbeilung  der  Sterne  auf  der  sudlichen 

Halbkugel,  nach  Schonfeld'a  Durcbmusterung,  8vo. 

Milnchen,  1886 

Shdanow,  A.,  Recbercbes  sur  l'orbite  intermediaire  de  la 
comete  de  Faye  dans  la  proximite  de  Jupiter  en  1841, 
4to.  St.-Petersbourg,  1885 

Recherches  sur  le  mouve'ment  de  la  lune  autour  de  la 

terre  d'apres  la  theorie  de  M.  Gylde*n,  4to. 

Stockholm,  1885 

Sidereal  Messenger,  Tbe,  edited  by  W.  W.  Payne,  Nob.  46- 
55,  8vo.  Northjidd,  Minn.,  1886-87 

Sirius,  Zeitscbrift  fur  populare  Astronomie,  Band  xix.  7- 
xx.  6,  870.  Leipzig,  1886-87 

Societa  Meteorologicaltaliana,  Bollettino  Mensuale,  pubblicato 
per  cura  dell'  Osservatorio  centrale  del  Real  Collegio 
Carlo  Alberto  in  Moncalieri,  serie  II.,  vol.  vi.  3-vii.  4, 
4to.  Torino,  1886-87 


Presents,  8fc,  during  tlie  Session  1886-87. 


67 


Society  Meteorologica  Italiana,  Bolletiino  Decadico,  anno  xiv. 
9-12,  4to.  Torino,  1885 

Society  of  Arts,  Journal,  Nob.  1751-1802,  8vo. 

London,  1886-87 

Stewart,  M.,  Tracts  physical  and  mathematical,  containing 
an  explication  of  several  important  points  in  physical 
astronomy,  8vo.  Edinburgh,  1779 

Stockholm  Observatorium,  Astronomiska  Iakttagelser  och 
TJndersdkningar,  utgivna  af  H.  Gylden,  iii.,  4,  4to. 

Stockholm,  1886 

Stonyhnrst  College  Observatory,  Results  of  meteorological  and 
magnetical  observations,  by  the  Rev.  S.  J.  Perry,  1885, 
8vo.  Roehampion,  1886 

Strove,  H.,  Ueber  die  allgemeine  Beugnngsfigur  in  Fern- 
rohren,  4to.  St.  Petersburg,  1886 

Strove,  0.,  Die  Photographic  im  Dienste  der  Astronomie, 
8vo.  St.  Petersburg,  1886 

Sydney,  Department  of  Mines,  Annual  Report  for  year  1885, 
fol.  Sydney,  1886 

Sydney,  Royal  Society  of  New  South  Wales,  Journal  and 
Proceedings  for  1885,  vol.  xix.,  8vo.  Sydney,  1886 

Tacubaya,  Observatorio  astronomico  nacional,  anuario,  alio 
1887,  i2mo.  Mexico,  1886 

Tasmania,  Royal  Society,  Papers  and  Proceedings  for  1886, 
8vo.  Hobart,  1887 

Tebbntt,  John,  Results  of  meteorological  observations  made 
at  Windsor,  New  South  Wales,  1882-85,  'ol. 

Farramatta  and  Sydney,  1 886 

Results  of  observations  of  Comets  Fabry,  Barnard,  and 

Brooks  (No.  1),  1886,  at  Windsor,  New  South  Wales, 
8vo.  Sydney,  1887 

Tempel,  W.,  Ueber  Nebelflecken ;  nach  Beobachtungen  ange- 
stelltin  den  Jahren  1876-79  auf  der  Eonigl.  S tern w arte 
zu  Arcetri  bei  Florenz,  4to.  Pr&g>  1885 

Tiflis,  Physikalisches  Observatorium,  Meteorologische  Beo- 
bachtungen im  Jahre  1885,  heransgegeben  von  J.  Miel- 
berg,  4to.  Tiflis,  1886 


The  Society. 


The  Royal 
Society. 


The 
Observatory. 


Rev.  S.  J. 
Perry. 


St.  Petersburg 
Academy. 

Pulkowa 
Observatory. 

H.M/8 

Government  in 

N.S.  Wales. 

The  Society. 


The 
Observatory. 

The  Society. 


The  Author. 


The 
Observatory. 


68 


Appendix  III 


The 
Observatory. 


The  Tokyo,  Imperial  University  of  Japan,  Calendar  for  1886-87, 

University.  gy0  To^  l886 

The  Institute.  Toronto,  Canadian  Institute,  Proceedings,  third  series,  vol. 

iii.  4-iv.  2.  Toronto,  1886-87 

The  Academy.  Tonlonse,  Academic  des  sciences,  inscriptions  et  belles-lettres, 

Me"  moires,  serie  YIIL,  tome  viii.,  8vo.        Toulouse,  1886 

Tonlonse,  Observatoire  astronomiqne,  magnetique  et  meteo- 
rologiqne,  Annales,  tome  ii.,  renfermant  nne  partie  des 
travanx  execrates  de  1879  &  1884,  sons  la  direction  de 
M.  Bailland,  4to.  Paris,  1886 

Tnrin,  Osservatorio  della  Regia  Universita,  Bollettino,  anno 

xx.  (1885),  obi.  fol.  Torino,  1886 

The  Academy.  Tnrin,  Reale  Accademia  delle    Scienze,  Memorie,    serie  ii., 

tomo  xxx vii.,  4k).  Torino,  1886 

Atti,  vol.  xxi.  3-xxii.  11,  8vo.  Torino,  1886-87 

Tyerman,  T.  F.,  The  asteroids  and  the  theory  of  their 
formation,  8vo.  Oxford,  1886 

Ulloa,  Antonio  de,  El  eclipse  de  Sol  [1778],  con  en  anillo 
refractorio  de  sns  rayos,  4 to.  Madrid,  1779 

United  States  Coast  and  Geodetic  Survey,  Report  of  the 
Superintendent,  showing  the  progress  of  the  work  during 
the  year  ending  Jnne  1885,  4to.  Washington,  18S6 

University  College,  London,  Calendar,  session  1886-87,  ^v0- 

London,  1886 
Unterweger,  J.,  Znr  Kometenstatistik,  8vo.  Wien,  1886 

Upsala,  Regia  Societas  Scientiarnm,  nova  acta,  series  tertia, 
vol.  xiii.,  1,  1886,  4to.  Upsalice,  1886 

Vienna,  Kaiserliche  Akademie  der  Wissenschaften,  Deuk- 
schriften  der  mathematisch-naturwissenschafilichen 
Classe,  Band  ].,  4to.  Wien,  1885 

Sitznngsberichte  der    inathematisch-iiaturwissenschaft- 

lichen  Classe,  Abtheilnng  II.,  Band  xci.  4,  5  ;  xcii.  1-5 ; 
xciii.  1,  2,  8vo.  Wien,  1885-86 

■         Circular,  Nos.  62-66,  8vo.  Wien,  1886-87 


The  Author. 


The  Royal 
Society. 

The  Survey 
Office. 


The  College. 

The  Author. 
The  Society. 

The 

Academy. 


The 
Observatory. 


Vienna,  K.K..  Universitats-Sternwarte,  Annalen,  Band  ii.-iv., 
Jahrgang  1882-84,  4to.  Wien,  1884-86 

Sternkarten  1-4,  von  J.  Palisa. 


Presents,  <J-c,  during  the  Session  1886-87. 


69 


American 

Ephemeris 

Office. 


Virginia  University,  Publications  of  the  Leander  McCormick  The 

Observatory,  vol.  i.,  part  3  ;  Nebula  of  Orion,  1885,  vol.    O^^toiy. 
i.,  part  2  ;  Tail  of  comet,  1882,  II.,  8vo.  1886 

Washburn  Observatory  of  the  University  of  Wisconsin,  Publi-        

cations,  vol.  iv.,  v.,  8vo.  Madison,  1886-87 

Washington,  Bureau  of  Navigation :  American  Ephemeris 
and  Nautical  Almanac  for  the  year  1889,  8vo. 

Washington,  1886 

Washington,  National  Academy  of  Sciences,  Report  for  the  The  Academy 
year  1885,  8vo-  Washington,  1886 

Washington,  Philosophical  Society,  Bulletin,  vol.  ix.,  8vo. 

Washington,  1887 

Washington,  Smithsonian  Institution,  Annnal  Report  of  the 
Board  of  Regents  for  the  year  1884,  8vo. 

Washington,  1885 

Washington,  United  States  Naval  Observatory :  Astronomical 
and  meteorological  observations  made  during  the  year 
1882, 4to.  Washington,  1885 

Report  of  the  superintendent  for  the  year  ending  June 

30,  1886,  8vo.  Washington,  1886 


The  Society. 


The 

Institution. 


The 
Observatory 


The  Royal 
Society. 


Whewell,  W.,  The  doctrine  of  limits  with  its  applications, 
namely,  conic  sections,  the  first  three  sections  of  Newton, 
the  differential  calculus,  8vo.  Cambridge,  1838 

Williams,  T.,  Method  to  discover  the  difference  of  the  earth's 
diameters  [&c],  8vo.  London,  1788 

Winlock,  W.  C,  An  account  of  the  progress  of  astronomy  in 
the  year  1885,  8vo.  Washington,  1886 

Wolf,  R.,  Astronomische  Mittheilungen,  Nos.  67-69,  8vo. 

Ziirich,  1886-87 

Yale  College  Observatory,  Report  for  the  year  1885-86,  4to. 

New  Haven,  1886 

Young,  C.  A.,  Ten  years'  progress  in  astronomy,   1876-86, 

8vo.  New  York,  1886 

Zoological   Society   of  London,  Transactions,  vol.   xi.    4-6,    The  Society. 
vol.  xii.  3,  4to.  London,  1886-87 

Proceedings  of  the  scientific  meetings  for  the  year  1886,         

i.-iv.,  8vo.  London,  1886-87 


Smithsonian 
Institution. 

The  Author. 


The 
Observatory. 

The  Author. 


70  Appendix  III. 

The  Society.     Zurich,     Naturforschende    Gesellscbaft,  Viertel jahrsschrif t ; 

Jahrgang  xxx.  1-4;  xxzi.  1,  2,  8vo.         Zurich,  1885-86 

The  Institute.   — —  Schweizerisches  meteorologisches  Central- An st alt,  A11- 

nalen,  1885,  4to.  Zurich,  1886 


MSS.y  Photographs,  Sfc^  Presented  to  the  Society. 

The  Author.    Johnson,  Rev.  S.  J.,  Eclipses  visible  in  England  a.d.  538  to 

2500;  all  solar  eclipses  from  a.d.  1200  to  2200;  large 
eclipses  from  a.d.  2200  to  2500  (MS.) 

MM.  Henry.    Two  photographs  of  stars  in  Cassiopeia,  and  photograph  of 

nebula  H.  1180. 

Isaac  Roberts,  Three  photographs  of  stars  in  Cygnus,  three  photographs  of 
***!•  the  Pleiades,  and  photograph  of  the  nebula  in  Orion. 

■  Three  stellar  photographs  showing  the  minor  planet  Sappho. 


Herr  E.  ron     Sixteen  photographs  of   clusters  and  nebulae  made  at   the 
Gothard.  Hereny  Observatory. 

J.  M.  Offord,    Six  stellar  photographs. 
Esq. 

Dr.  R.  Cope-    Three  photographs  of  Barnard's  Comet, 
land. 

Isaac  Roberts,  Photograph  of  telescope  for  stellar  photography. 
Esq. 

E.  Crossley,     Photograph  of  dome  for  3-f t.  reflector. 
Esq. 

A.  Covpcr      Two  photographs  of  M.  Bischoffsheim's  Observatory,  Nice. 
Ranyard,  Esq. 

F.  McClean,     Photographs  of  Mr.  McClean's  Observatory. 

Esq. 

B.  J.  Hopkins,   Drawing  of  a  coloured  solar  spot. 
Esq. 

W.  H.Wesley,   Proof  of  steel  engraving  made  from  photographs  of  the  total 
E8q>  solar  eclipse  of  1882. 


Presents y  jr.,  during  the  Session  1886-87.  71 


Books  Purchased  with  the  Turner  and  Horrox  Funds. 

Albobazen  Haly  filing  Abenragel,  Liber  de  Iudiciis  astrorum, 
fol.  BasiJeae,  1571 

Alembert,  J.  le  Bond  d',  Recberches  snr  la  precession  des 
Equinoxes  et  snr  la  nutation  de  l'axe  de  la  Terre  dans  le 
systeme  Newtonien,  4to.  Paris,  1749 

Balde,  J.,  De  eclipsi  solari,  anno  1654,  12 mo.   Monachii,  1662 

Bayer,  J.,  Uranometria,  omnium  asterismorum  continens 
scbemata,  nova  methodo  delineata,  aereis  laminis  ex- 
pressa,  fol.  Ulmce,  1723 

Bologna,  Epbemerides  Bononienses  Medioeornm  Syderum  ex 
bypotbesibns  et  tabnlis  Jo.  Dominici  Cassini,  4to. 

Bononice,  1668 

Enstacbii  Manfredi  introductio  in  Epbemerides,  cam 

opportnnis  tabnlis  ad  nsnm  Bononiensis  scientiarum 
institnti,  editio  altera  (ad  Epbem.  1 75 1-62  accommodate), 
4to.  Bononice,  1750 

Epbemerides  motnnm  coelestiam  ab  anno  1823  ad 

annnm  1828,  supputato  a  Petro  Catureglio,  4 to. 

Bononice,  1822 
Brabe,  Tycbo,  Epistola,  edidit  F.  B.  Friis,  fasc.  iv.,  4k). 

Havnice,  1886 

Bulletin  Astronomique,  1886-87,  8vo.  Paris,  1886-87 

Calandrelli,  G.,  Eclisse  solare  del  9  Febbrajo  1804,  osservata 

nella  Specola  Astronomica  dell9  Universita  Gregoriana 

nel  Gollegio  Romano,  4to.  Botna 

Carlini,  F.,  Esposizione  di  un  nuovo  metodo  di  costruire  lc 
tavole  astronomicbe,  applicato  alle  tavole  del  sole,  8vo. 

Milano,  1810 

Cellarius,  A.,  Harmonia  macrocosmica,  sen  atlas  universalis 
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Ciel  et  Terre,  1886-87,  8vo.  Bruxelles,  1886-87 


72  Appendix  III. 

Clavius,  Chr.,  Gnomonices  libri  octo,  in  quibus  non  solum 
horologiorum  solarium,  sed  aliaram  quoque  rerum,  qoae 
ex  gnomonis  umbra  oognosci  possunt,  descriptiones  geo- 
metrice  demonstrantur,  fol.  Romas,  1581 

Connaissance  des  temps,  ou  des  mouvements  celestes,  poor 
Tan  1842,  &yo.  Paris,  1839 

Cysat,  J.  B.,  Mathemata  astronomica  de  loco,  motu,  magni- 
tudine,  et  causis  Cometee  qui  sab  finem  anni  1618  et 
initium  anni  161 9  in  coelo  fulsit  [Inangnral  Disserta- 
tion], 4  to.  Ingolstadii,  1619 

Eclipsis  Solaris  Oeniponti,  die  30  Martij  ante  meridiem,  anno 
1 66 1,  fol.  Oeniponti,  1661 

Eger,  G.,  and  O.  Brandes,  Technological  Dictionary  in  the 
English  and  German  languages,  2  vols.  8vo. 

London,  1884 
Ferrall,  J.  S.,  T.  G.  Repp,  and  S.  Rosing,  A  dictionary  of  the 
English  and  Danish  languages,  2  vols.,  8vo. 

Kobenhavn,  1883 

Fixlmillner,  P.,  Meridianus  speculae  astronomicae  Cremifanen- 

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Fontaine  des  Grates,  Traite  complet  sur  l'aberration  des 
6toiles  fixes,  aveo  une  histoire  gen^rale  de  l'astronomie, 
8yo.  Paris,  1744 

Galileo,  Sydereos  nuncius,  4k).  Bononiae,  1655 

Gemeiner,  A.  T.,  Beobachtung  der  am  Junius  1797  Nach- 
mittags  eingetretenen  Sonnenfinsterniss,  8vo. 

Begensbwg,  1798 
Gemma  Frisius,  Arithmetics  practices  methodus  facilis,  8vo. 

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Girault,  Ch.,  Indicatear  plane'taire,  on  recueil  de  tables, 
fournissant  du  1  Jan.  1865,  an  1  Jan.  1900,  la  distance 
angulaire  du  Soleil  aux  planetes  prinoipales,  £valu6e  en 
ascension  droite,  8vo.  Caen,  1867 

s'Grayesande,  G.  J.,  Philosophies  Newtonian©  Institutiones, 
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Habrecht,  J.,  Planiglobium  coeleste  et  terrestre:  Platte 
Stern-  and  Lander-Kugel,  durch  J.  C.  Sturm  verteutschet 
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Presents,  8fc,  during  the  Session  1886-87.  73 

Harfcmaim,   J.  W.,  Dissertationum  physicarum  de    natura 
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Jence,  17 15 

Heinsins,  G.f  De  apparentia  aeqnatoris  lnnaris  in  disco  lunae 
[Inaugural  Dissertation],  4to.  1745 

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4*o.  1745 

De  eclipei  Solis  d.   I.  April   1764,   Lipsiaa   observata 

[Inaugural  Dissertation],  4to.  1765 

Herr,  J.  P.,  Lehrbuch  der  spharischen  Astronomie  in  ihrer 
Anwendung  auf  geographische  Ortsbestimmung  (nach 
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Wien,  1887 

Herscbel,  J.  F.  W.,  The  telescope,  8vo.  Edinburgh,  1861 

Hevelius,  J.,  Machina  coelestis,  pars  prior,  foL    Qedani,  1673 

Hilpert,  J.  L.,  A  dictionary  of  the  English  and  German  and 
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Oarlsruhe,  1857 

Honold,  J.,  Cometographia,  oder  kurtzer  Bericht  von  den 
zweyen  iiingsterschienenen  Cometen,  wie  dieselbe  zu 
Ulm  observirt  worden,  4to.  TJlm,  1665 

Israel-Holtzwart,  K.,  Supplement  zu  den  Elementen  der 
theoretischen  Astronomie,  8vo.  Wiesbaden,  1887 

Jordan,  W.,  Grundziige  der  astronomisohen  Zeit-  nnd  Ortsbes- 
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Junius  (M.),  Nov®  et  accurate  motuum  coelestium  ephemer- 
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Kepler,  J.,  nnd  Herwart  von  Hohenburg,  Ungedruckte 
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Prag,  1886 

Kliigel,  G.  S.,  Commentatio  de  perturbationibns  corporum 
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Le  Boyer,  J.,  Traite  complet  du  calendrier,  8vo. 

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Le  Clerc,  P.,  Beschreibnng  einer  Himmelskarte,  mit  einem 
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74  Appendix  III. 

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Littre,  E.,  Dictionnaire  de  la  langue  francaise,  abregS  par 
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Lobkowitz,  J.  C,  Novem  stelta  circa  Jovem,  circa  Saturnum 
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Lockyer,  J.  N.,  Chemistry  of  the  Sun,  8vo.  London,  1887 

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Meyne,  M.,  Yon  aller  Geschlecht  der  Cometen,  jeder  zeit, 
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Miller,  R.  Kalley,  The  romance  of  astronomy,  third  edition, 
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Nichol,  J.  P.,  The  planet  Neptune  :  an  exposition  and  history, 
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Nolthius,  A.,  Ob3erratio  und  Beschreibung  des  Cometen, 
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Ozanam,  J.,  Dictionnaire  mathlmatique,  ou  idee  generate  des 
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Perlachius,  A.,  Commentaria  ephemeridum,  4 to. 

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Peucer,   G.,  Elementa  doctrinsa  de  circuits  ccelestibus,   efc 

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Presents,  fyz.,  during  the  Session  1886-87.  75 

Rowland,  H.  A.,  Photograph  of  the  normal  solar  spectrum. 
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Schanz,  Die  astronomischen  Anschaoungen  des  Nicolans  von 
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Spiers,   Dictionnaire    general   anglais- francais    et    francais- 

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Winckner,  A.,  Tabnla  ascensionnm  obliquarum,  qu»  locum 
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76  Appendix  III. 

Wochentliche  Unterhalfctmgen  fur "  Dilettanten  and  Freunde 
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Wochenschrift  fur  Astronomie,  Meteorologie  und  Geographic  : 
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Zanotti,  E.,  La  meridiana  del  tempio  di  San  Petronio,  rinno- 

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Zeitschrift  fur  Instrnmentenknnde,  1886-87,  4*°- 

Berlin,  1886-87 

Zeitschrift  fiir  populare  Mittheilnngen  aus  dem  Gebiete  der 
Astronomie  nnd  verwandter  Wissenschaften,  herans- 
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