c r882 ; 


IV. JftnmmU Cometic<e Synopfis, Jut-ore Edmunda 
Halieio apud Oxonienfes- GeometrU (Profeffore Sa- 
viliano, 6c Xeg. Soc. S. 

V Etercs JEgyptii 8c ChalcLei, fiqua tides Diodora Sicuto y 
longa oblervationum ferie inftru&i, Cometarum 
ivi-roilf prtenuntiare valuerunt. Cum autem iifdem ar- 
tibus etiam Terrae-motus ac tempeftates prasyidifle dican- 
tur, extra dubium eft: Aftrologia? potius calculo fatidico, 
quam Aftronomids motuum Theoriis eorum de his rebus 
fcientiam referendam efle. Ac vix alia a Graecis utriufque 
popuSi vidoribus reperta eft apud eos do&rina $ adeo ut 
earn , quam nunc eoufque proveximus Aftronomiam , 
Ghecis ipfis, pradertim magno Hipparcho, uti inventoribus, 
acceptam debenmus. * Apud bos vero Ariftotelfc fententia, 
qui Cometas nihil aliud effe voluit quam Vapores fublu* 
nares vel etiam Meteora aerea, tantum effecit, ut haec 
Aftronomka? fcientia? pars longe fubtiliffima, omnino neg- 
lefta manferit, cum nemini opera? pretiutn vifum fuerit, 
vagas Sc incertas fluitantium in aethere vapprum fernitas 
adnotare fcriptifque mandare 5 unde factum ut ab iiiis 
nihil certi de motu Cometarum ad nos tranfmiftum repe* 
riatur, 

Seneca autem Philofophus, perpenfis duorum infignium 
fui temporis Cometarura Phamomenis, non dubitavit iis 
loca inter corpora ccdeftia atfignare, Sydera elfe cum 
mundo duratura exiftimans, quanquam Motus eorum le- 
gibus nondum compertis regi f ‘catur. -Tandomque Va- 
ticinio non iirtto promittit aliquando future lecula, qui- 
bus hacC tam occulta dies extraheret ac longiertf <evi dil/gen- 

tia : 


The Royal Society is collaborating with JSTOR to digitize, preserve, and extend access to 

Philosophical Transactions (1683-1775). 



www.jstor.org 






( i88$ ) 

tia : quibufque admirationi foret hxc Veteres nefcire po- 
tuifle 3 poftquam Demonjlraverit aliquis Naturae Interpres 
in quibus Cceli partibm Comet & errent , quanti, qualefque fini. 
Ab hac autem Seneca (ententia in diverfas partes abiit 
pene omnis Aftronoinorum Cohors , ac ipfe Seneca , ne* 
que Phenomena Motus quibus opinionem hanc tueretur, 
neque tempora adfcribere dignatus eft, quae pcfteris ad 
h#c definienda ufui forent. Ac evolutis plurimis Come¬ 
tarum Hiftorirs, nihil omnino invenio quod huic negotio 
infervire poftit, ante annum a Chriflo nato 1337. quo 
Nicephorus Gregoras Hiftoricus Aftronomus Conftantino* 
politanm nobis Cometae femitam inter fixas fat is accurate 
defcripfit: tempora astern nimis laxe confignavit, ita ut 
non nifi quod abhinc quadringentis pene Annis apparue- 
rit, lubricus&incertus hie Cometa Catalogo quern damus 
inferi mereatur. Dein Cometa anni 1472 omnium velo- 
ciffimus ac terris proximus Regiomontamm habuit obfer- 
vatorem. Hie magnitudine ac Coma terribilts, unius diei 
(patio 40 gradus fub circulo Cceli maximo emenfus eft, 
ac omnium primus eft de quo obfervata idonea ad nos 
pervenere. Quotquot autem Cometas confiderarunt, uf- 
que ad tempora Tychonis Brahe magni illius Aftronomh-e 
reftauratoris, eos (ublunares efte autumarunt, adeoque 
parvi penderunt, utpote pro Vaporibus habitos. 

Anno autem 1577, ( Tychone jam ftudio aftrorum ferio 
incumbents, comparatifque Machinis ingentibus pro di- 
metiendis cceli arcubus, majori cum cura Sc cerritudine 
quam Veteribus fperare fas erat) Etnerfit Cometa iatis 
confpicuus, cui obfervando ftrenue fefe accinxit Tycho : 
multifque 8c fidis experiment^ deprehendit, riulli qme 
ftntiretur Paraliaxi diurnos obnoxium fuifte, adeoque non 
tantum non fuifte Vaporem aereum, fed 8c edam multo 
fuperiorem extitifle Luna: knmo nihil obftabat quin inter 
ipfos Planetas collocaretur, fruitra interim contra obftre- 
pentibus Scholafticorum nonnulh> 

Linmim .2 2>. 



( 1884 ) 

Tfchonit vero eximiam in obfervando induftriam exce¬ 
pt t Kepleri ftgaciffimum Sc penedivinum ingenium. Hie 
Tychains laboribus fretus Syftema Mundi verum Sc Phyfi. 
cum adinvenit, ac feienriam Aftronomicam in immenfum 
auxit 5 Monftrato fc. Planetas omnes in Planis per Solis 
centrum tranfeuntibus revolvi, Curvafque EUipticas de- 
feribere, ex lege, at Are* Se&orumEllipticorum, ad cen¬ 
trum Solis in Ellipfeos foco conftituti, temporibus, quibus 
deferibanrur arcus, Temper proportionales fint. Invenit 
etiam Diftantias Planetarum a Sole efie in fefquialtera ra- 
tione temporum periodicorum, five Cubos diftantiarum 
efl'e ut Quadrata Temporam. Tantoautem Artifici afful- 
fere duo Comet*, quorum alter maxime illuftris. Ex ho- 
rum oblervatis conclufit Kepler us non uno parallaxis an¬ 
nua? indicio, Cometas inter Orbes planetarum liberrime 
quaquaverfum ferri, motu quidem non multum a re&i- 
lineo diverfo, fed quern nondum definire licuit. Ac He - 
velius , Tychonis remulus, Kepleri veftigiis infiftens, eandem 
Hypothefim Motus redilinei amplexus eft, ipfe plurium 
Cometarum Obfervator perquam fubtilis. Ccelo ramen 
Calculum fuum non penitus confenrire queftus eft, Viain- 
que Cometicam verfus Solem incurvari fuboluit. 

Tandem de fummo Coelo lapfus eft prodigiofus ille Co- 
meta Anni 1680. quafiCafu perpendiculari Solem petens, 
6c exinde pari velocitate allurgem : Hie per quatuor 
Menfes cominuos vifus, infigni ac peculiar! Curvitate Or¬ 
bit* ad inveftigationem Motus Theori* pr* c*teris ido^ 
neus erat: Inftrudtis autem jampridem Regiis Obfervato- 
riis, Vsrifienfi Sc Gretiovicenji, ac Aftronomorum Clarifli- 
morum curs commifiis, accidit ut hujus Comet* Motus 
apparens, quantum forfan mortalibus fas eft, accuratiffime 
a Cajfwo Sc irUtnfledio obfervaretur. 

Non multo poft, dum Geotnetrarum Princeps iiluftrifii- 
mus Newtonus operam dabat Vrincipiis PhilofophU Mathe¬ 
matics 5 non folum invema Kepleri in $y<‘tm;ne Planeta- 
xio necefiario locum habere demonltravit. vtrum etiam 

Co- 



( * 88 $ ) 

Cometarnm .Phenomena omnia ex iifdem Principib evi* 
denter con’- qui. Id quod exemplo prasdi&i Comets an. 
ni 163o, ah unde iliultravii.modurnque docuit Geometrice 
conftrut'udi Orhitas Cometarum $ Problemaque arduutn 
ac tanto Oedipo dignum fumma cum omnium admirati- 
one relolvit, Cometam autem hunc in orbe parabolico So- 
lem circumiifle probat, ita utAreae ad Centrum Solis sfti- 
mat* Temporibus proportionales fuerint. 

Tanti viri veftigia infecutus eandem methodum calculo 
Arithmetico accommodare aggrefius fum, nec irrito Co- 
namine. Undique enim conquifitis Coraetarum Obferva- 
tionibus, Tabellam hanc, immenfi pene Calculi frudtum, 
obtinui, exiguum quidem fed non ingratum Aftronomis 
munus. Hi etenim numeri vim habent omnia qua* de mo- 
tu Cometarura ha&enus obfervata fnnt accuratillime re- 
praefentandi, ope folius Tabulae Generalis infequentis, cui 
adornands nullis lane peperci laboribus, ut perfeda pro- 
diret, utpote Pofteritati confecrata ac cum Scientia Aftro- 
nomica duratura. 


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H<cc Tabula vix indiget explications, cum ex titulis fatis pateat quid fibi velint Numeri. 
Diftanti# autem perihelia fftimantur in ejufmodi partibus quales media dijlantia Terr « * 
Sole habit catties ntillenas. Tabula 





(i88 7 ) 

Tabula Getter alls pro Supputando Motu 
Cometarum in Orbe Tarabolko. 


Medius 

>Angulm a 
peribelio. 

Logarithmus 

Medius 

yingulut d 

Logarkhmus 

mom. 

pro diftantid 
d Sole, 

morns . 

peribelio, 

pro diflantid 
a Sole, 

o 

gr. ' " 

0 

g r * ' " 

I 

1.31.40 

O. 000077 

3 1 

42. ??. 07 

0. 062400 

2 

3 - 3 -iy 

O.OOO3C9 

3 2 

44 - 3. id 

0.od?8j5 

3 

4 - 34-43 

0. ooodp4 

33 

4?. IO. 2d 

O.O 69316 

4 

6. < 5 . 0 

0.001231 

34 

46. l6. ^ J 

O. O72835? |l 

5 

7,17. I 

6. OOI92I 

35 

47 . 21. 3d 

0,076396 \ 

6 

9 . 7-44 

O. 00275 ' 5 > 

3 * 

48.25. 33 

0.079984 

7 

IO. 38, 2 

0.00374? 

37 

49 -28.29 

0.083804 

8 

12. 7*^3 

O. 004876 

38 

5O.3O.23 

0.087249 

9 

13. 37 -17 

O.OOdl?I 

39 

*i- 3 1 -11 

O.090912 

io 

iy. 6. 6 

0. 007^64 

40 

52.30.54 

0.0945-94 

II 

16. 34.20 

0. 009115 

41 

53. 29. 42 

0. 098298 

12 

x8. 1. 54 

0. 010798 

42 

54. 27. 32 

O .102019 

*3 

rp. 28. 47 

0. 012609 

43 

55. 24. 22 

O. I0f7f2, 

14 

20. * 4 -*3 

0. 014550 

44 

5*6. 20 11 

0.109490 

.*5 

22. 20. 14 

0. 016607 

_45_ 

57 . 15 . ? 

0.113240 

1 6 \ 

i 

23.44.43 

0.018783 

4 d 

?8.9. 2 

0. nd 995 

17 

25. 8. 22 

0.02x072 

47 ! 

59 . 2. 5! 

0.1207 ? <5 

18 

2d. 31. 7 

0.023470 

48 

59 - 54 -13 

0.124518 

19 

27. 52. 55 

0. C 2 ?pdp 

49 

60. 4 y. 2.6 

0.128278 

20 

2P. 13.52 

O. 028??! 

?o 

<Sl - 35 - 45 

0 ^ 3^35 | 

21 

3 °- 33 - 39 

0.0312d3 

r 1 

d2. 25. 14 

o.l^ 79 'i 

22 

3 M 2 3* 

0.03404? 

5 * 

^3.13.5° 

0.139541 

2 3 

33.10.23 

0.03dpid 

53 

<54. I. 38 

Jo. 143288 

24 

34. 27.12 

O. 0398 <54 

54 

< 54 . 48.38 

0.147029 


35 - 4 2 - 59 

O.042892 

55 

<* 5 - 34 » 5 ° 

0. 1507(52 

26 

3^- f7.4i 

O. 045989 

56 

dd. 20. 14 

0.154482 

27 

38. XI. 20 

0.049154 

?7 

d 7 . 04.51 

{ 0. 158192 

28 

39 - ^ 3 - 5 6 

O. 052383 

58 

67. 48. 22 

I o. I dl890 

25> 

40 3 J. 2d 

0. 0??dd8 

59 

d8. 31. 51 

0. Id 5?78 | 

3 ° 

I4I.4?. ?0 

O 

O 

v-o 

\D 

O 

O 

do 

69. 14. id 

jo.Idp2?4 | 
8 


M m 

nimra mm 

til m m m 

) 



(i888) 

Tabula Generalis pro Supputando 


Media* 

[ Singnlut ri 

Logarithms 

mom. 

I perihelia. 

i pro difiantid 

1 d Sole , 

o 

gr. " " 

I.__ 

61 

< 5 ?. yy. 5-8 

0.172914 

62 

70 . 3 6, j6 

0. 176337 

63 

71. 17* I <5 

0.180188 

64 

7 i. c6. c <5 

0. 183803 

61 

72. 33. 37 

0 187404 

66 

73 -14-*5 

0.190978 

6? 

73-yi- yp 

0. i94y+o 

68 

74.29. <5 

0.19808) 

6.9 

7y- °y. 3S 

0. 201 614 

70 

7y-4T- 3y 

0. 20JI22 

7 1 

7 6, 1 6, y6 

0. 208612 

72 

7<y. yi. 43 

0.212080 

7 } 

77. 2J. 57. 

0. 213329 

74 

77- s 9. 41 

0.218963 

75 

78. 32. y4 

0 222378 

76 \ 

79. y. 3y 

0* 2 2> 769 

77 

79.37.4y 

0. 229142 

7 8 

80. 9. 2 3 

0,232488 

79 

80.40. 34 

0 239809 

So 

8r. 11. 16 

0. 239127 

Qt 
■0 * 

8r«4J. 31 

0. 242416 

82 

82.11. 19 

0. 245*684 

8 3 

O 

6 

rt¬ 

f'? 

oc 

0 248933: 

S 4 

83 9 34 

0. 2J21 5*9; 

Jy 

83.38. 4 

°_^l_n 66 \ 

26 

84. <5. 8 

0.258^2! 

87 

84.33. 49 

0 .261720 j 

88 

8y. 1 y 

0. 2648 <5 S' : 

S9 

Sy.27. yS 

O 287989 j 

90 1 

83. y4- 2 7i 

0. 271092,' 


Mediu. 

r singulis d 

Logarhhmm 

motus. 

periheiio. 

pro dijiantid 

0 

' " 

a Sole » 

91 

, 8 < 5 . 20.34 

O. 274176' 

92 

8 < 5 .4<5. 20 

O. 277239 

93 

87- n.43 

0.280284 

94 

87. 3< 5 . 4)- 

0.28330(5 

_?y 

88 . 01 27 

0.28(5308 

' 96 

88. 2y. 49 

0.289293 

97 

88.49.48 

O. 2922 J 2 

98 

89.13.32 

0. 29y2oi 

99 

89. 3 6. 5-4 

0.298122 

100 

90.00.00 

0. 301030 

102 

90. 45-. 14 

0. 30*5782 

104 ; 

91.29 18 

0. 3124(59 

ic 6 

92. 12. 14 

0. 318060 

108 

92. y4. 4 

0. 323 y 87 

110 

93 ; 34 - y 2 

0. 329042 

112 

94 -14- 45 

0.334424 

114 

94 y 3 - 3 ° 

0.339736 

II 6 

93. 31.22 

0.344979 

118 

9< 5 . 8. 22 

0. 33013* 

120 

! 96. 44. 30 

77 y 5 2<5 2 

122 

97 .19 48 

0.360306 

124 

97 . y 4 .17 

0. 363284 

126 

98 28. 00j 

0. 370200 

128 

99■ OO. J 7 : 

0. 37 yoy 2 

* 3 £_ 

99 - 33. It j 

0.37984 2 

132 

TOO. 4.43 | 

0. 384 y 7<5 

T 34 

IC.CX3y.4y! 

0 389 2 y 2 

136 

101. 5748! 0 395868 

138 

101.35722! 

0. 398428 

140 

102, 449' 

0. 402930 







(1889) 


Motu Cometarum in Orle Tarabolko. 


jMediu* 

motus. 

yfngulus a, 
perihelio. 

togarithmm j 
pro dijlantid 


Medius j 
motus. | 

^Jngulus a | 
perihelia . | 

Logarithms 
pro diftantid 

0 

g f - ' " 

a Sole . | 

j 


0 1 

gr. 7 j 

d Sole. 

H 2 

I02.32.4i 

0.407380 


204 

113.37.2jS 

0. j 23 406 

i-M- 

lO3.OO.3i 

0.411784 


208 

114. 9 - 5 2! 

0.J2970J 

146 

I03 27.47 

0.416x32 


212 

114.41.23; 

0.535886 

148 

IO3.y4.3i 

0.420430 


21(5 

II J. 12.02 J 

0.541958 


IO4 20.43 

0.424676 


220 

11 541 ; 51 j 

0.547922 

IJ 2 

104.46.22, 

0.428866 


224 

Il 6 .IO.J 2 

O 

^0 1 

! 

00 

J 5 + 

ioj.11.33 

0.433012 


228 

116.39. 7! 

0. 559538 

* 5 * 

10?.36 16 

0,437110 


232 

117. 6.38 j 

0. 565199 

xy8 

106.00.32 

0.441164 


236 

11-.33.27 

0.570762 

1 <So 

106.24.23 

0.44J178 


240 

IJ 7 .J 9-35 

0.576233 

162 

106.47.47 

0.449144 


244 

Il 8 . 2 J. j 

0. y8i6i6 

164 

107.10.44 

0.4J3060 


248 

118.49.57 

0,y8^9i2 

166 

107.33.17 

0.4J6936 


2J2 

119.14 14 

0.y92I22 

168 

107.jj.27 

0.460772 


2j<y 

119.37.j6 

0.y 972 y 2 

170 

108.17.14 

0.464208 


2.60 

120. 1. 6 

0. 6 02301 

172 

108.38.37 

0.468318 


264 

i2O.23.44 

0. 607274 

174 

108.j9.3p 

0.472030 


268 

I20.4j.y2 

0.612174 

I 7 <S 

109.20.20 

O. 47 J 70 J 


272 

121. 7.30 

0. 616998 

178 

IO9.40.4C 

O. 479340 


276 

121 . 28.39 

0.62i7yo 

l8o 

IIO.OO.40 

O. 482937 


280 

i2i.49.22 

0. 626438 

182 

HO 20.20 

O. 486498 


284 

122. 9.38 

0 631056 

184 

IIO.39 41 

O.490022 : 

288 

122,29 28 

0. 63 j6o8 

186 

no.y 8*44 

O. 493512 . 

292 

122.48.J4 

0.640098 

188 

111.17.2 

O. 4.9696j‘ 

296 

123. 7.J7 

0. 644525 

ipo 


0. 500384^ 

300 

123.26.36 

0. 648893 

102 

111.y4.0y 

.0. J03769: 

31° 

124.11.40 

0.659559 

iP 4 

112.11.y8 

O. J 07 X 2 I, 

i 20 

I24.j4.36 

0. 669880 

1 96 

112.29 34 

0.J10441I 

33 ° 

I2 5 - 35-34 

0. 679876 

198 

112 46 yy 

0.J13729! 

340 

126.14.44 

0. 68pytf8 

200 

113. 4.00 

0.J16984\ 

35 ° 

126.j2.12 

0. 698970 




(1890) 

Tabula Generalis pro Supputando Motu 
Cometarum in Orbe Varabolico. 


Medius 

motus. 

yfnguius ct 
perihelio. 

Logarithrms 
pro diftantia 
d Sole . 


Medius 
motus . 

* Angulns d 
perihelio . 

Logarithmus 
pro diflantir 
d Sole . 

o 

~ g~ “ 


0 

g£_ ' " 

360 

370 

380 

3P o 

400 

127.28. 6 

128. 2.33 
x28.3j.38 

129. 7 27 
129.38. 4 

0.708104 
0. 714975 
0.723504 
0. 734006 
0. 7421 <35 


820 

840 

860 

880 

poo 

i4i.49.24 
I42.IO.OO 
142.29.36 
142.49,10 
r 43 - 7.48 

0.970836 

0.978397 

0.983771 

0.992970 

1.000000 

410 

420 

430 

440 

4 P 

130. 7.34 
130.34. 2 

P 1 - 5 - 3 ° 
131.30. 2 

0.730150 
0.737930 
0.763315 
0.772918 
0.780148 


920 

940 

960 

980 

1000 

143 23.31 
143.43.21 
144.00.18 
144.16 46 

I ii-J 2 ± 6 

1.00687.1 

1.013384 

1.020193 

1.026983 

1.032876 

460 

470 

480 

490 

5“ 00 

132.20.30 
13 2.44.32 

133 7 -P 
^ 3.30.23 
133.52.20: 

0.787215 

9 - 794 122 1 
0.800882! 
0.807494; 

0..813969 1 

1700 

2000 

25-00 

3000 

350°’ 

149.26. 8 
192.26.13 
194.32.20 
136. 7.27 
197.22 49 

X. 198188 

I. 246038 

I. 313703 
1.368678 

1.414974 

5*20 

740 

5;6o 
y8o 
600 

I54.34.l8 
133.14. 0 
133.31.23 
134.27. 4 
I 37 .«jO.J 7 | 

0.826322; 
0.83 86co 

0. 830187 i 
0.861369 i 
0.872133| 

; 4000 
4)00 
5:000 
J500 
; 6000 

138 24.36 

i r 9 P- Id > 3 d 
160. 1.12 
160.40. 9 
161.14.24 

1.434930 

1. 490129 

1. 921921 
1.349874 

1. 373718 

62 0 
640 
660 
680 
700 

I 37 - 33- I 3 ! 

138. 3.38 

138.33.21 

139. 1.29 
139.28 23 

0.882373 
0.892649 
0.902401 
0. 911866 
0.921012 


6900 

7000 

7900 

8000 

8900 

161.43.00 

162.12.34j 

x62.37.34j 

163.00.23j 

163.21.20j 

1. 399460 

I. 62I4.I7 

I. 64*838 
x.660922 
1-67 834 

720 

740 

760 

780 

800 

139.34.14 
140.19. 3 
140.42.34 
141.03.33 
141.28. 3 ; 

0.929907 
0. 938149 

0.94693 1 / 

op 93124 1 
0.963082 I 


pooo 

97 °° 

: roooo 
5*0000 
100000 

l63.4O.42 
163.38.38 
164.13.20 
170.32. 0; 
172.43.44: 

I. 693708 

I. 711662 

1. 726784 

2 . Ip7p60 

2. 39963 * 

Tabulae 







C 1891 ) 

TabuU Getter alts ConJlruSUo & U/m. 

Ut Planet# in Orbibus Ellipticis, ita Comet* in Para- 
bolicis Solera in Foco corarauni fit urn ambiunt 5 ea lege ut 
Areaeaequales a?qualibus temporibus defcribantur. Quoni- 
am vero Parabolas oranes inter fefimiles funt, fi determi- 
nata aliqua pars Area* dats Parabola dividatur in partes 
quotlibet 5 in omnibus Parabolis fiet fimilis divifio fub 
iifdetn angulis, atque diftantite erunt proportionates: 
ideoejue una noftra Tabula pro Coraetis omnibus fufficiet. 
Calculi autem hujus Tabulae ha?c eft ratio. In Schemate 
fit S Sol, P O C orbita Corneta?, P Perihelion. O Lo¬ 
cus ubi Cometa quad rante diftat a Perihelio, G Locus 
quivis alius, 
junge C P> 

C S. ac fiant 
St, SR z- 
qualcs ipfi 
CSfac dud- 
is rcti'iis C R, 

C T (quarnm haecCurva: Tangens eft, ilia perpendicularis) 
in axem P SR demute normalera CQ^ Jam data quAvis 
Area COPS, oportet anguium CSP, fkdiftantiamC S 
inqutrere, Quoniarn ob naturam Parabola: refta RQ_ 
ubique asqualis eft femilateri refto, ponatur latus redunr 
— 2, adeoque R CL — 1: ac fit recla CQ_ = z .* erit itaque 
P CL” i z z>,acSegraentumparabolicumCOP = ,’jzz.z,. 
Triangulum autem CSP erit — ' n z: adeoque Area tnix- 
tilinea COPS erit % * + -4 z. = ac s 3 -4 3 & ~ 
12 a. Qua re refolud hac sequatione CubkA, a foe 
ordinatim applicata CO innotelcet. Proponatur jam Area 
OPS in partes cemems dividenda; hxc Area duodecima 
pars eft quadrati lateris r :<fti, adeoque 12: a xquantur 
Quadrato illo — 4 : Si itaque fucceffive extrahantur ra¬ 
dices aequationum 5$ 3 4 - 3 & = 0,04: 0,08 : o v i ai 0,16 




( l8p2 ) 

&c. habebuntur totidem % five ordtnatim applicatas C Q_ 
refpecrive $ ac divifa erit areaSOP in partes centenas. 
Eodemque modo ultra locum O continuandus eft calculus. 
Radix a mem hujus squationis, cum RQ^fit = i, Tan- 
gens eft Tabular** anguli CRQ., five dimidii anguli 
CS P, adeoque angnlus CS P datur. 'Ejufdemque anguli 
CRQTecans RC, Media proportionaiis eft inter R Q. 
five Unitatem Sc R T, quae dupla eft ipfius SC, ut ex 
Conicis notifiimum eft. Quod fi S P ponatur r, adeoque 
Litas reftum —4 ( ut in Tabula noftni) ipta RT erit di- 
ftantia quaefita , duplum lcilicet ipfius SC in priore Para¬ 
bola. Ad hunc modum itaque prscedentem Tabulam 
elaboravi repraTentandis omnium Cometarum motibus 
infervientem: haftenu^ enim nullusex obfervatis Parabolse 
leges refpuit. 

Reftat jam prscepta Calculi tradere, modumque fup- 
putandi locum Cometae vifum ex his Numeris exhibere. 
Cometae autem in Parabola moventis Velocitas ubique eft 
ad velocitatem Planets gyrantis in Circulo eirca Solem, 
ad eandem a Sole diftantiam, ut V 2 ad 1 : ut conftat ex 
Primipiis Phil. Nat « Math. Lib. I. Prop. 16. Corol . 7, Si 
itaque Cometa in perihelio ad diftantiam aequalem di- 
ftantis Terrs a Sole fupponatur, erit area diurna, 
quam deferiberet Cometa, ad aream quam defcribit 
Terra, ur/2 ad 1. ac proinde tempus annuum, ad tern- 
pus quo Cometa tabs deferiberet Quadrantem Orbitae 
i'ux a Perihelio ut 3. 14159 8cc. (hoc eft ut area circuli) 
ad V Cometa igitur deferiberet Quadrantem ilium 
diebus 109. 14*. 4 6'. adeoque area ilia Parabplica areae 
POS analoga in centum particulas diftributa, fingulisdie¬ 
bus competunt particular 0,912280. Cujus Logarithmus 
nempe 9,960128 in perpetuum ufum fervandus eft. Tem- 
pora autem, quibus Cometa in diftantia majore vel minore 
Quadrantes fimiles deferiberet, funt ut Revolutiones in 
Circulis * hoc eft in fefquiplicata ratione diftantiarum: 
adeoque ares diurnx in partibus centefimis Quadrantis 

aefti- 



( i) 

#ftimat# (quas medii Motus menfuras, inftar Graduum, 
ponimus) flint in fingulis in fubfefquialtera ratione diftan- 
tiae Perihelia a Sole. 

His neceffario pr#miflis proponatur alicujus e Cometis 
noftris Locum vifum ad datum tempus fupputare. Pri- 
mum itaque *Solis Locus ab iEquino&io in promptu He, 
ejufdemque diftanti# a Terra Logarithmus. a 0 . Capiatur 
intervallum Temporis inter Tempus Perihelii 8c Tempus 
datum, in diebus partibulque diei decimalibus. Hu- 
jus numeri Logarithmo addatur Logarithmus conftans 
9,960128 ac complementum Arithmeticum fefquiaherius 
Logarithm! diftanti# Periheli# a Sole: fumma Logarith¬ 
mus erit Motus medii in prima Columns Tabul# Generalis 
quarrendi. 3 0 . Cum motu medio capiatur in Tabuli cor- 
refpondens angulus a Perihelio, 8c Logarithmus pro diftan¬ 
tia a Sole: ac in Cometis Di raft is adde, in Retrogradis Cub. 
duc, fi fuerit Tempus poft Perihelium 5 vel in Dire&is 
fubduc 8c in Retrogradis adde, fi fuerit ante Perihelium, 
angulum fic inventum a loco vel ad locum Perihelii. Et 
habebitur Locus Comets in orbits propria : Et ad Loga¬ 
rithm!! m pro Diftantia ibidem inventum addatur loga¬ 
rithmus diftantise Perihelia, fumma erit Logarithmus 
diftanti# ver# Comet# a Sole. 4 0 . Cum Loco Comets 
in Orbit,dato Loco Nodi, capiatur diftantia Comet# a 
Nodo : ac data Inclinatione plani, dabnntur, Notitfimis 
Trigonometric praeceptis. Locus Comet# ad Eclipticam 
reduftus, cum Inclinatione five Latitudine Heliocentrica, 
ac Diftantiae Curtat# Logarithmus. $°. Ex his datis, iif- 
dem omnino regulis quibus loca Planetarum, ex dato Lo¬ 
co 8c Diftantia Soli?* ot tmebitur Locus Vifus feu Geocen- 
tricus cum Latitudine vi£a. Id quod exemplo uno vel 
altero operas: pretium erit illuftrare. 


Ex- 


Mmmmmmmmm 



( 1894 ) 


Exemp. I. Quzritur Locus Cometae Anni 166* Martil r°.7 h . oo'. 

P. M. LonUni. Hoc eft $6 ( ', j f. 8'. poft Perihelion 
ejus Novemb. 24°. Ceiebracum. 

Lag dtfl PerihsL o. 011C44 Perthet. SI ro. 41, 55 Leg, fro dtfl. o. a 5 5369 

Leg. $ej\malt. 0 0 16566 Ang. Correfy. 83 . 38, of-— s Log. PerihsL o. 011044 

C Arith • 9 * 9^3 in Orb . b x 7 * 3 * 20 C0 - fin . Incl* 9, 990754. 

9. 960I28 U 21* *4* 00 log. *#/?. Curt . o. 257167 

Ltg'Tmp. i« 985862 Cow. £ 7 «fo 34* so. 40 £<?£. dift, © 9. 997918 

Mo/. * 9*94*4 R^. adEcl:P' 3 2 *9* o? © X 2 *. 44* 4$ 

Me dm Motus 85. oqj Cow* Hp/ioc 18. 54. 55 Cow. ^ 7 /a* T 29. 18. 30. 

lnclBor.il. 46* 50. Lap. J/ifn 8 . 36. if. Ben 

Exemp.IE Quseritur LocusCometas Anni 1683 Julii 23°. i ] h . if, 

P. M. Loniini. Vel 13b. 40'. T. tequat. hoc eft 
2i d . ro h , jo’, poft Perihelion. 

Log dift Perihel. 9. 74§343 Peribel H 25. 20. 30 Log. pro dift. o. 111336 
Log Sefquialt. 9. 622514 Ang. Correfp. 56.47. zo Log. Peribel. 9. 748343 

Comp. Arith. O. 377486 Cwi. tnOrh. T 2,8.41. IO Co - fm■ lad. 9; 913187 

9, 960128 y K 13. 23. oO Log. dift. Cart. 9. 772866 

Log. Temp. 1. 310 723 Com. <3 y 35. 19. 10 Log-dift. ® O. 006104 

Leg. Med.Mot. 1. 648337 Red. ad Eclip • 4. 48. 30 ® Isom it Jto. 41. 25 

Mediae Mctus. 44. 498 Com. Helioc.^ 28.11.30 Com-Vifttt S 5. I i • 59 

lml. Bor. 35 - 2 . 00 Lat.Bor.1'6. 52 , 00 

Memento autem primi Exempli, Londini obfervatum eft 
Cometam applicari ad Stellam fecundaru Arietk ; ita ut 
novem minutis ilia borealior repertus fit, ac tribus minutis 
orientalior : Obfervante D no Roberto Hoo^io. In fecundo 
autem Exemplo ipfe, in vicinia Londini , inftrumentis qui- 
bus olim Stellas Auftrales obfervaveram, Comerse locum 
deprehendi s. 5 0 . n'. cum Latitudine Boreali, 2352*, 
confentiente ad amuflim obfervatione Grenovkenfi eodem 
pene momento fafta. 

Cometa antem Anni 1680, qui pene Solem attigit, (non 
enim triente femidiametri corporis Solaris a fuperficre ejus 
diftabat in Perihelio) cum Lacus redum exiguum > 
dum fit, Tabula Generali baud coerced potu.it, ob ima.;» 

necn 



( 1895 ) 

nem Motus medii velocitatem: praeftat itaque in hoc, 
poftquam inventus fuerit Motus medius, ex eodem, ope 
precedents squation is zzzAr 3 z — T-53 Mat. med . Tan* 
gentem dimidii anguli a Perihelio elicere, una cum Loga- 
ritlamo pro diftantia a Sole. Quibus datis iifdem omnino 
regulis ac in csteris procedendum eft. 

Ad hunc itaque modurn Aftronomico Lectori examinare 
licet numeros a me pofitos, quos fumma cura ex oblervari* 
onibus qus fuppetebant exantlavi ^ neque enim, antequam 
probe ad incudem red aft i fuerint, ac multorum annorum 
ftudio quantum fieri poffit poll'd, in publicum prodeunt. 
Hoc autem fpecimen Aftronomis Cometics, futuri open's 
Prodromum, editum efle volui 5 ne forte fupcrveniente 
fato perirent lucubrationes noftre, ob Calculi diiiicukatem 
non cuivis homini denuo fufcipiends. Monendus autem 
eft Leftor, quinque priores ordine Cometas, quorum tertius 
& quartus eft a Petra Apiano obfervatus, quintus vero a 
Paulo Pabricioy uti & decimus a M<cfilino (ni fallor) anno 
1596 confpeftus, non eundem certitudinis gradum cum re- 
liquis pre fe ferre. Neque enim debiris organis nec cura 
ad hoc requifita obfervationes ipfe perafts funt 5 adeoqae 
inter fe diffiduntes nullo modo cum compute regukri con- 
ciliari poflunt. Cometam Anni 1684 unus viditPlkaacbi- 
vrn obfervator Ror/tanm: ultimum vero Annf.fc. 1698 
Parifietifet foli confpexerunt, ejufque curfum infohco modo 
defignarunt. -jfcurus hie admodum, etiamfi velox ac 
terris fatis vicinus, noftros fane oculos alioquin non irtcu- 
riofos effugit. Infignes autem duos hac noftra state Ca¬ 
meras, alterum Anno 1689 Menfe Novembri ortum, akerum 
Menfe Febrmrio Anni 1702, Catalogo fabjungere non li- 
cuit, propter defeftum obfervationum. Etenim verfus 
mundi plagas Auftrales curfum dirlgehtes,' ac .in Europe vix 
confpicui, contemplatores non habuere negotio pares. 
Quod fi forfan ex partibus Lndicfa adveftse faerint accurate 
obfervationum feries ad hoc necefiaris 5 lubens cakuium 
Mmramrammmrnrani 2 re* 



(is?<5; 

repetere, horumque Orbitas, reliquorum ad modum, Nu- 
tneris dcfignandi laborera lufcipere non gravabor. 

Anguftia autem paginae 1886, fadum eft, ut omifta fit 
necellaria ilia Columella quae oftendat an direde vel retro¬ 
grade mod fuerint Cometse. Sciat ifaq^ Aftronomus unde- 
cim e noftris Cometis dire&o curfu fecundum ftriem figno- 
rum proceffifle, nempe illos annorum 1532, 155< 5 , 1580, 
1585, 1618, 1650, 1661, 1672, 1680, 1684 8c 1 686. 
Reliquos vero tredecim motu, retrogrado contra feriem 
fignorum curfum tenuifle. Quibus perpenfis, ac collatis in¬ 
ter fe caeteris boram Cometarum motuum Elenientis, videre 
cft^ nullo ordine difpofitos efie Grbitas 3 neqtte ip- 
fos, Planetarum more, Zodiaco comprehendi poile, qua- 
quaverfsm tarn Retrograde quam direde indifterenter la- 
tos ^ unde manifeftum eft eos motu vorticali nullo modo 
circumagi. Quinetiam diftantise Perihelia nunc majures 
nunc minores reperiuntur^ unde pronum eft fufpicari eti- 
am multo plures efie Cometas, qui in partibus a Sole remo- 
tioribus, obfcuri caudaque deftituti, adeoque nobis incon- 
fpicui, praeterlabi poflunfv 

Ha&enus Cometarum Orbes confideravimus ut perfede 
Parabplicos •, quo fuppofito confequeretur Cometas, vi 
Centripeta verfus Solera impulfos, a fpatiis infinite diftan- 
tibus defcendere, cafuque fuo velocitatem tantamacquirere, 
ut iterum in fpatia Mundi remorifljriia f-fe abdere poffint, 
perpetuo nifu furfum tendentes, ac ad Solem nunquam re- 
verfuri. Cum autem fat is frequentes fine Cometarum ad¬ 
vent us $ ac eorum nullus reperiarur motu terri Hyperbo- 
lico, feu velociore quara cadendo ad Solem acquirere de¬ 
beat, credibile eft potius in Orbibus valde Excenirlcis re- 
volvi eos circa Solem, ac poft longidimas ptriodos reverti. 
Sicenim Numerus eorum praefinirus c-fiet, ac fort die non 
ufque adeo magnus. Spatia autem inter Solem v ixafque 
tanta funt, ut Comet* revolventi cum Pe;.udo qua unvfs 
longa fatis loci fit. Latus auterri rectum EUipfis et* 1 La- 
tus redara Parabolae eandem Periheham diftanwam : alvn- 



( l-8<?7 ) 

tfs, ut diftantia,.Aphe’b m Ulij ii ;ft ad Axem totum EF* 
lipfis 5 Veloa cates autem funt m dimtdiata ratione eorun* 
dem : quapropter in Orbibus valde Excentricis ratio baec 
accedit proxime ad ration cm squaiitatis. Tandlla autetn 
differentia, quae intercede ratione raajoris in Parabola ve- 
locitaris, facillime in fitu Orbis determinando compenfatur. 
Htijns itaque Tabulae Elementorum Motuum ufus prscipuus 
eft, atque etiam propter quern illam conftruere operae pre- 
tium duxi, ut,fi quando novusCometa emerferit, poffimus 
collatis elementis dignofcere an poterit efle aliquis ex anti- 
quis, necne 5 ac proinde Periodum Orbitsque Axem deter- 
minare, redirumque prsdicere. Ac fane raulta me fuadent 
ut credam Cometam anni 1531 ab Apiano obfervatum, 
eundem fuiffe cum illo qui anno 1607 defcriptus eft a 
Keplero 8c Longomontano , quemque ipfe iterum reverfum 
vidi ac obfervavi anno 1682. Quadrant Elementa omnia, 
ac fola inaequalitas periodorum adverfari videtur: hsc au- 
rem tanta non eft ut caufis Phyficis non poffit attribui. 
Saturni enim motus a caeteris, prsfertim Jove, ita intertur- 
batur, ut per aliquot dies integros incertum fit hujus Pla¬ 
nets tempus Periodicum. Quanto tnagis talibus erroribus 
obnoxius erit Cometa, qui quatuor pene vicibus altius ex- 
currit Saturno, cujufque velocitas, vel tantillum aufta, 
Orbem ab Elliptico in Parabolicum poftit immutare > 
Confirmatur etiam eundem effe potuifie ex eo, quod anni 
1456 sftate, confpeftus fuerit Cometa eodem- pene modo 
inter Solern & Terram tranfiens retrograde: quern, licet a- 
nemine obfervarus fuerit Aftronomice, ex periodo modo- 
qne tranfitns non diverfnm a prsdiffis extitifle conjicio. 
Unde aufim ejufdem rediium fidenter prsdicere, anno fcil. 
1758. Quod fi hoc evenerit, nulla ampins-erit dubitandi 
caufa, qtiin redire debeant csteri. Habebunt ergo Aftro- 
nomi in hac arena quo fe exerceant per multa Secula, pri- 
ufquam toe tantorumque Corporum circa commune cen¬ 
trum Solis revofvenrium numerus cognofcatur, ac motuum 
fymptomata certis reguiis coerceaatur. Crcdidenm equidem 

Cometa m. 



( » 8<>8 ) 

Cometam etiam anni 1532, eundem fuifle cum illo, quiab 
Hevelio obfervabatur ineunte anno 1661 : fed obfervari¬ 
eties Aplani, quas folas de prime habemus, nimis rudes 
funt, nec quicquam certi in re tam fubtili ex iifdem elici 
poteft, Jufto volumine hsc omnia exequi mihi animus eft, 
nec Aftronotnis promovends bac in re deero, fi Deo O-M. 
vifurn fuerit vitam facultatefque prorogare. Interim qui- 
cunq$ modum Conftruendi Cometarum Orbes per tres ob- 
fervationes accurate babitas addifeere cupir, fub finem 
libri de Syftemate Mundi, five tertii ThilofovhU Nat. prin- 
dp. Math, magni ipfius Inventoris methodum inveniet: 
Quam poftea Dignifbmus CoiSega rneus D. Gregorius, Lib. 
V. pererudirs Aftronotnis fus Pnyfics & Geometries 
plene & luculenter iiluftravit. 

Unicom autem non abs re eric i>ee injucundum, hie loci 
Le&orem monere Aftronomum 3 nempe quod nonnulli ex 
his Cometis Nodes' fuos habeant adeo Orbi Terrs annuo 
videos, ut fi forte accident, tempore reditus Comess, 
Terr am occupare Loca in orbe fno Nodo proxima, dum 
Cometa incrcdibili cum Velocitate prsterierit, Parallaxin 
etiam habiturus fit valde obfervabilem, qusque fuerit 
ad Solis parallaxin in ratione data- Unde occafione talium 
tranfituumobiata eric anfa, rara quidem fed optima, deter- 
ttiinandi Solis a Terra diftantiam 5 quatn hadtenus non nifi 
mediante parallaxi Marti r Acronychii, vel Venerk per'igss, 
triplo quidem folari majore, fedqus vix uliis inftrnmentis 
fentiatur, laxeadmodum concluderelicuit. Ouem Cometa¬ 
rum ufum fuggeflit ClariffimusGeometraD s Nic> Facto. Co¬ 
meta etenim anni 1472 parallaxin habuit pialqcrim vigefies 
Solari majorem. Ac fi Cometa anni 16 s8 apoulilfet, juxea 
medium Menfis Martii , ad Nodum ejus Defcendentem 5 
vel fi Cometa anni 1684 paulo citius ad Nodosa Afcenden- 
tem pervenifiet, profedto Terris admodrm propinqui etiam 
adbuc magis notabiles habuiflent parallaxes : inter omoes 
vero nullus propiore appulfu Terris minatus eft quam ille 
anni 1680 : Hie inito Calculo non amplius ad Boream 

diftabat 



( »8p9 ) 

diftabat ab Orbe noftro annuo, quatn femidiametro folari 
(five Radio Lur-aris Orbits, uti exiftimo) idq. •; Noverab. 
ii°. i h . 6’. P M. Quo tempore, fi Terrs quoad Longitu- 
dinem conjuudtM buffet, parallaxis fane Lunari squalis in 
Comets tiiOJ u obfervati potuiffet. Hsc Aftronomis dida 
funto. Qs vero ab hujufmodi allapfu, vel con tad u vel 
denique coiiifione Corporum coeleftium (qus quidem omni- 
no non impoffibilis eft) confequi debeant, rerum Phyfica- 
rum ftudiofis difcutienda relinquo; 


V. fart of two Lttters from the <ReVerend Dr Rich. 
Wroe, Warden o/Manchefter Colledge , to Dr Hans 
Sloane, $. % S. concerning Horn-like Excrtf- 
cences growing on the Fingers , 8cc. 


Manchefv\ Aug. 2 6. 1704 . 


KJif j 

T Here lives at Bolton ( 8 miles from this Town ) onr. 

Nathaniel Hftlme , aged about 17, who had the 
Small Pox about 8 years of age : Soon after which he had 
a great Itch, almoft to the degree of a Leprofie, with 
whieh his Finger-nails and Thumb-nails began to grow 
thick, and by degrees hardned into Horns 5 which grew 
in 7 or 8 months to the length of an Inch, arid fome al¬ 
moft 2 Inches, and fome much longer; It began in the 
Fore-finger o£his Left Hand, and fo to all the reft of that 
Hand, which had as many Horns as Fingers, and Thumb. 
All which Horns about the end of 12 months fell off by 
degrees 3 that which grew firft falling off firft, without 
any pain, unlefs when cut off, as they were at firft, there 



