CORNELL 

UNIVERSITY 
LIBRARY 




TABLES 



OF 



J^ajjles of Melpomene, 




3 1924 012 341 792 





L P 




E N E 




'«^ 



Cornell University 
Library 



The original of this book is in 
the Cornell University Library. 

There are no known copyright restrictions in 
the United States on the use of the text. 



http://www.archive.org/details/cu31924012341792 



TABLE S 



OF 



MELPOMENE, 



BY 



E. SCHUBERT. 



COMPUTED FOR THE 



AMERICAN EPHEMEEIS AND NAUTICAL ALMANAC, 



UKDEK THE SUPERINTENDENCE OF 



COMMANDER CHARLES HENRY DAVIS, U. S. N. 



IttblisfejJr hg ^tt%rilg flf i\i Swrdarg flf % iabg. 



BUREAU OF ORDNANCE AND HYDROGRAPHY, 
WASHINGTON. 

I860. 






t f- — , 



cambkidge: 

electkottfed and feinted by welch, bigelow, & co., 

univeksity press. 



KEPOET 



TO 



COMMANDER C. H. DAVIS, U. S. N. 



I. ON THE COMPUTATION OF THE GENERAL PERTURBATIONS OE MELPOMENE 

BY JUPITER. 

By ERNEST SCHUBERT. 

FOE the computation of these perturbations, Professor Encke's method, published in the Berliner Jakrlmeh 
for 1857, has been used in order to try it by a complete application to a special case. The basis of the 
work are the following elements : — 

Melpomene. Jupiter (from Bouvaed's Tables). 

1854, Jan. 0, Washington Mean Time ; (osculating). 1854, Jan. 0, "Washington Mean Time. 

M= 79 56 36.81 o , , ^ = 269 43 39"l 

71= 15 14 31.52) ,T T? T^ n' = 16 16 53.3-) n = 11 58 43.2) ,. t. t, 

a =. 150 1 8.21 1 ^- ^^- ^P- ^'= 19 16 43.7 I —2 S2 = 98 56 38.7 [ ^^ ^^^ ^'^ 

i = 10 9 4.77 i' = 15 28 17.2) « = 1 18 39.5 

q, = 12 32 46.29 qj — 2 45 55.1 

11 = 1019".96852 11 = 299".12861 

loga= 0.3609465 log a = 0.7162370 

The plane of the orbit of Melpomene has been adopted for the fundamental plane, and the major axis for 
the line of the abscissas. The orbit of Jupiter is referred to this fundamental plane by means of the formulas 
on page 390 {Jahrhueh for 1857). 

Now for the computation of —55- the periphery was divided into 16 parts, so that M and M (the mean 
anomalies of Melpomene and Jupiter) for those 16 points are 0°, 22°.5, 45°, &c. Log m' «^ = 5.5760322 in 
units of the seventh decimal-place, and for the Julian year as the unit of time. Each point of the Melpomene 
orbit is combined with all 16 points of the Jupiter orbit, which gives 16 X 16 = 256 values of — ^. On 
page 354, Professor Enckb says that those values can be checked only by double calculation, since it cannot 
be done by the differences in the series obtained for the different M. But I found that, if we arrange the 
quantities ^^ according to another' principle, they can be tested by differences, which will be shown by the 
following : — 



A. 


1 


M = 


0° 


22°.5 


45° 


67° .5 


90° 


etc, 


1419.6 


2117.7 
2110.9 


3722.0 
3515.1 
3583.5 

etc. 


7454.2 
6636.6 
6418.2 
6753.7 

22°.5 & 0° 
45 & 22.5 
67.5 & 45 

Diff = 22.5 


11776.2 
11195.8 
10851.5 
11154.1 
12234.1 



& 
22.5 & 22.5 
45 & 45 

Diff.= 




11776.2 


9701.8 


M=0° 
5823.7 


3385.1 


2150.3 






7454.2 


11195.8 


M=22°.5 

10838.6 


7038.9 


4099.4 






3722.0 


6636.6 


10851.5 


12032.8 


8415.1 






2117.7 


3515.1 


M= 67° .5 
6418.2 


11154.1 


13455.3 






1419.6 


2110.9 


M=90° 
3583.5 


6753.7 


12234.1 










etc. 









This sketch needs no further explanation ; the principle for the arrangement in B from A is very simple, 
and it is obvious that it is the vertical series in B which can be tested by differences. 

In Table A the values of — ^ are functions of M', and they are developed in series of the form, 

'^ z^ a° -^ a' cos M + J' sin M' 

-f a" cos2M> -\- b" sin 2 M'. 

It is evident that now in these series the coefficients are functions of M, and they must be developed in series 
of the same form, that is, for instance, 

a° = a° + «' cos Jf -f /S' sin M 

+ a" COS 2 M-\- /S" sin 2 M. 

Each of the latter series must be multiplied with the cos «' M or sin i' M belonging to it, and. then, finally, 

by resolving the products of two cosines or sines into sums and differences, we obtain — ^ developed in series 

of the general form 

af cos {i M — i' M) + 6f sin {i M — i' M). 

In order to have throughout — i' M we only have to change the sign of i' and that of the coefficient of 
the sine. 

The formulas for the components of the disturbing force (page 392) are : — 

Therefore, after having developed —^^ according to the above precepts, we subtract from it 

^ = 2684.3 + 388.2 cos M 

+ 28.1 cos 2 M 

+ 2.0 cos 3 M 

' + 0.1 cos 4 M 



and get thus m' *^ l\ — isY This periodical series is to be multiplied successively with x\, y\, and z\ j 
developed also in periodical series they are : — 

y:\ = —0.37409 + 5.16475 cos M' + 0.25210 sin M' 
-f 0.12450 cos 2M' -\- 0.00608 sin 2 M' 

. -I- 0.00450 cos 3 iJf' 4- 0.00022 sin 3 M' 

-f 0.00019 cos 4 M' 

yi^ = +0.02313 — 0.31933 cos M' + 5.14340 sin M' 

— 0.00770 cos 2M' -\- 0.12401 sin 2 M' 

— 0.00028 cos 3 ilf' -j- 0.00446 sin 3 M' 

4- 0.00019 sm 4 M' 



a'j = —0.03518 4- 0.49693 cos M' + 0.68709 sin M' 
-j- 0.01336 cos 2 ilf' -)- 0.01657 sin 2 JIf' 
-|- 0.00185 cos 3 i(f' -|- 0.00060 sin 3 Tif' 

I- 0.00144 cos 4 ilf' 
-f 0.00142 cos 5 7(f' 
4- 0.00142 cos 6 M< 
4- 0.00142 cos 7 J!f' 
-1-0.00071 cos 8 ilf' 

ikfler that, the periodical series — ^ must be multiplied with — x^ and y^. 



We have —x^ — -f 0.74808 — 2.25537 cos ilf 

— 0.24159 cos 2 ilf 

— 0.03886 cos 3 ilf 

— 0.00741 cos 4 ilf 

— 0.00155 cos 5 ilf 

— 0.00035 cos 6 ilf 



—v, = — 2.22785 sin ilf 



-yi 



— 0.23961 sin 2 ilf 

— 0.03861 sin 3 ilf 

— 0.00737 sin 4 ilf 

— 0.00155 sin 5 ilf 

— 0.00035 sin 6 ilf 



Finally, after these five multiplications, by forming the sums, we obtain the series for Xj, Yi, Zj. 

I subjoin here now the terms of ^ and of to' x^ (4 — ^) retained for multiplication, the terms smaller 



than 0.5 having been omitted. 



i— 


— 








^^ 




m>^ 
































p"- 


















i. 


ii 


coa 


sin 


«, 


V 


COS 


sin 


t, 


V 


cos 


sin 


i, 


i' 


cos 


sin 










+4348.2 


0.0 


-4 


_1 


- 7.3 


0.0 


6 


-1 


+ 


5.6 


- 


5.8 


-2 


-2 


- 1.1 


+ 0.5 




1 


n 


- 602.6 


+25.8 


-3 


_1 


+ 6.3 


- 1.6 


7 


-1 


- 


2.7 


+ 


6.6 


-1 


-2 


- 14.0 


- 8.8 




2 


n 


+ 19.8 


-60.9 


-2 


_1 


- 6.0 


+ 2.8 


8 


-1 




0.0 


- 


3.7 





-2 


+ 195.3 


+ 33.7 




3 





+ 1.3 


- 5.1 


-1 


_j 


+ 109.0 


+ 64.1 














1 


-2 


-1174.9 


+156.8 




4 







- 1.6 





1 


-1384.0 


+ 90.2 


-8 


-2 




0.0 


+ 


0.5 


2 


-2 


+2618.4 


-301.3 










1 


_1 • 


+5208.0 


-305.3 


-7 


-2 


+ 


0.5 


- 


1.1 


3 


-2 


+ 350.1 


- 13.4 




-8 


-1 


0.0 


- 3.7 


2 


_2 


+ 185.2 


+ 26.4 


-6 


-2 


- 


0.8 


+ 


0.7 


4 


-2 


+ 77.3 


- 27.7 




_7 


-1 


+ 2.9 


+ 6.7 


3 


_;! 


+ 48.1 


- 43.1 


-5 


-2 


+ 


1.0 


- 


0.5 


5 


-2 


+ 16.1 


- 8.6 




-6 


_i 


- 5.2 


- 5.1 


4 


_1 


+ 18.5 


- 7.9 


-4 


-2 


- 


1.2 




0.0 


6 


-2 


+ 4.7 


- 1.5 




-5 


-1 


+ 6.6 


+ 2.9 


5 


-1 


- 4.4 


+ 0.8 


-3 


-2 


+ 


0.9 


+ 


0.5 


7 


-2 


0.0 


- 1.7 





3 

















m' 


jf. 






- 










' - ' -. ' ■ 
















P 


03 


















«. 


i' 


cos 


sin 


«. 


i' 


cos 


sin 


1, 


«•' 


cos 


sin 


i, 


i' 


cos 


sin 


8 


-2 


0.0 


+ 0.5 


-2 


-4 


+ 0.8 


+ 1.1 


6 


-5 


+ 96.3 


- 21.5 


-5 


-7 


t 


5.3 


+ 2.6 










-1 


-4 


- 1.1 


- 1.8 


7 


-5 


+ 38.0 


- 11.8 


-4. 


-7 


- 


7.4 


0.0 


-8 


-3 


+ 0.5 


+ 1.2 





-4 


+ 3.0 


+ 3.7 


8 


-5 


+ 4.5 


- 1.2 


-3 


-7 


+ 


6.8 


- 3.0 


-7 


-3 


- 0.9 


- 2.9 


1 


-4 


- 31.4 


- 5.3 










-2 


-7 


- 


5.3 


+ 5.3 


-6 


-3 


+ 2.0 


+ 2.1 


2 


-4 


+ 158.1 


- 19.3 


-8 


-6 


+ 12.7 


- 1.2 


-1 


-7 


+ 


2.4 


- 6.7 


-5 


-3 


- 2.8 


- 1.2 


3 


-4 


- 447.7 


+120.2 


-7 


-6 


+ 4.4 


- 5.8 





-7 




0.0 


+ 7.4 


-4 


-3 


+ 2.8 


0.0 


4 


-4 


+ 506.8 


-117.6 


-6 


-6 


+ 2.7 


0.0 


1 


-7 


- 


3.1 


- 6.5 


-3 


-3 


- 2.9 


+ 1.1 


6 


-4 


+ 181.6 


- 30.1 


-5 


-6 


+ 1.2 


- 1.0 


2 


-7 


+ 


4.3 


+ 5.1 


-2 


-3 


+ 1.8 


- 2.4 


6 


-4 


+ 52.8 


- 15.4 


-4 


-6 


- 1.0 


0.0 


3 


-7 


- 


2.3 


- 2.7 


-1 


-3 


0.0 


+ 4.8 


7 


-4 


+ 14.7 


- 4.9 


-3 


-6 


+ 0.9 


0.0 


4 


-7 


- 


6.7 


+ 4.7 





-3 


- 27.6 


- 12.0 


8 


-4 


+ 2.2 


- 1.6 


-2 


-6 


- 1.1 


- 0.8 


5 


-7 


+ 


33.9 


- 11.6 


1 


-3 


+ 202.1 


+ 1.6 










-1 


-6 


0.0 


+ 1.0 


6 


-7 


- 


45.4 


+ 23.5 


2 


-3 


- 778.5 


+153.7 


-8 


-5 


+ 4.5 


- 1.2 





-6 


0.0 


- 1.0 


7 


-7 


+ 


23.5 


- 2.9 


3 


-3 


+1199.2 


-205.2 


-7 


-5 


+ 2.8 


- 4.0 


1 


-6 


- 1.2 


+ 0.8 


8 


-7 


+ 


6.9 


- 10.9 


4 


-3 


+ 282.1 


- 30.9 


-6 


-5 


"+ 2.6 


+ 1.5 


2 


-6 


+ 5.7 


0.0 












5 


-3 


+ 73.9 


- 21.2 


-5 


-5 


- 2.5 


- 1.5 


3 


-6 


- 22.5 


+ 4.0 


-8 


-8 


+ 


3.6 


0.0 


6 


-3 


+ 15.1 


- 5.3 


-4 


-5 


+ 2.9 


0.0 


4 


-6 


+ 68.9 


- 20.7 


-7 


-8 


- 


6.9 


- 8.9 


7 


-3 


+ 5.8 


- 4.7 


-3 


-5 


- 2.8 


+ 1.1 


5 


-6 


- 116.8 


+ 48.6 


-6 


-8 


+ 


13.0 


+ 3.8 


8 


-3 


+ 0.5 


+ 1.2 


-2 


-5 


+ 1.9 


- 2.1 


6 


-6 


+ 75.3 


- 25.2 


-5 


-8 


- 


3.6 


- 2.4 










-1 


-5 


- 1.3 


+ 2.8 


7 


-6 


+ 46.2 


- 18.2 


-4 


-8 


+ 


1.9 


0.0 


-8 


-4 


+ 2.2 


- 1.6 





-5 


- 0.8 


- 3.2 


■8 


-6 


+ 12.7 


- 1.2 


4 


-8 


+ 


1.9 


0.0 


-7 


-4 


0.0 


+ 0.8 


1 


-5 


+ 5.7 


+ 4.3 










5 


-8 


- 


3.6 


+ 2.4 


-6 


-4 


+ 1.3 


- 1.2 


2 


-5 


- 30.7 


- 1.1 


-8 


-7 


+" 6.9 


- 10.9 


6 


-8 


+ 


13.0 


- ;3.8 


—5 


-4 


- 1.4 


+ 0.6 


3 


-5 


+ 111.6 


- 23.4 


-7 


-7 


+ 24.3 


+ 8.4 


7 


-8 


- 


6.9 


+ 8.9 


-4 


-4 


+ 1.5 


0.0 


4 


-5 


- 240.3 


+ 80.8 


-6 


-7 


- 6.4 


- 9.8 


8 


-8 


+ 


3.6 


0.0 


-3 


-4 


- 1.6 


- 0.6 


5 


-5 


+ 204.6 


- 59.9 


































m' «= (- 


L 

33 


^) 
















«■', 


i 


cos 


sin 


i', 


i 


cos 


sin 


i', 


i 


cos 


sin 


i', 


i 


cos 


sin 








+1663.9 


0.0 


6 


-1 


- 1.2 


- 0.8 


-4 


-3 


- 1.6 


- 0.6 


1 


-4 


+ 


18.5 


+ 7.9 


1 





-1772.6 


- 90.2 


7 


-1 


- 3.1 


+ 6.5 


-3 


-3 


- 2.9 


+ 1.1 


2 


-4 


+ 


77.3 


+ 27.7 


2 





+ 167.2 


- 33.7 










-2 


-3 


+ 0.9 


+ 0.5 


3 


-4 


+ 


282.1 


+ 30.9 


3 





- 29.6 


+ 12.0 


-7 


-2 


- 5.3 


+ 5.3 


-1 


-3 


+ 6.3 


- 1.6 


4 


-4 


+ 


506.8 


+117.6 


4 





+ 2.9 


- 3.7 


-6 


-2 


- 1.1 


- 0.8 





-3 


+ 1.3 


+ 5.1 


5 


-4 


- 


240.3 . 


- 80.8 


5 





- 0.8 


+ 3.2 


-5 


-2 


+ 1.9 


- 2.1 


1 


-3 


+ 48.1 


+ 43.1 


6 


-4 


+ 


68.9 


+ 20.7 


6 


"o 


0.0 


+ 1.0 


-4 


-2 


+ 0.8 


+ 1.1 


2 


-.3 


+ 350.1 


+ 13.4 


7 


-4 


- 


6.7 


- 4.7 


7 





0.0 


- 7.4 


-3 
-2 


-2 
-2 


+ 1.8 
- 1.1 


- 2.4 

+ 0.5 


3 

4 


-3 
-3 


+1199.2 
- 447.7 


+205.2 
-120.2 


8 


-4 


+ 


1.9 


0.0 i 


-7 


—1 


+ 2.4 


- 6.7 


-1 


-2 


- 6.0 


+ 2.8 


5 


-3 


+ 111.6 


+ 23.4 


-8 


-5 


_ 


3.6 


- 2.4 


-6 


-1 


0.0 


+ 1.0 





-2 


+ 19.8 


+ 60.9 


6 


-3 


- 22.5 


- 4.0 


-7 


-5 


+ 


5.3 


+ 2.6 


-5 


-1 


- 1.3 


+ 2.8 


1 


-2 


+ 185.2 


- 26.4 


7 


-3 


- 2.3 


+ 2.7. 


-« 


-5 


+ 


1.2 


- 1.0 


-4 


-1 


- 1.1 


- 1.8 


2 


-2 


+2618.4 


+301.3 










-5 


-5 


— 


2.5 


- 1.5 


-3 


-1 


0.0 


+ 4.8 


3 


-2 


- 778.5 


-153.7 


-8 


-4 


+ 1.9 


,0.0 


-4 


-5 


- 


1.4 


+ 0.6: 


-2 


-1 


- 14.0 


- 8.8 


4 


-2 


+ 158.1 


+ 19.3 


-7 


-4 


- 7.4 


0.0 


-3 


-5 


- 


2.8 


- 1.2 


-1 


-1 


+ 109.0 


+ 64.1 


5 


-2 


- 30.7 


+ 1.1 


-6 


-4 


- 1.0 


0.0 


-2 


-5 


+ 


1.0 


- 0.5: 





-1 


- 602.6 


- 25.8 


6 


-2 


+ 5.7 


0.0 


-5 


-4 


+ ,2.9 


0.0 


-1 


-5 


+ 


6.6 


+ 2.9 


1 


-1 


+5208.0 


+305.3 


7 


-2 


+ 4.3 


- 54 


-4 


-4 


+ 1.5 


0.0 





-5 




0.0 


0.0 


2 


-1 


-1174.9 


-156.8 










-3 


-4 


+ 2.8 


0.0 


1 


-5 


_ 


4.4 


- .0.8,, 


3 


-1 


+ 202.1 


- 1.6 


-7 


-3 


+ 6.8 


- .3.0 


-2 


-4 


- 1.2 


0.0 


2 


-5 


+ 


16.1 


+ 8.6 


4 


—1 


- 31.4 


+ 5.3 


-6 


-3 


+ 0.9 


0.0 


-1 


-4 


- 7.3 


0.0 


3 


-5 


+ 


73.9 


+ 21.2 


5 


-i 


+ 5.7 


- 4.3 


-5 


-3 


- 2.8 


+ 1.1 





-4 


0.0 


+ 1.6 


4 


-5 


+ 


181.6 


+ 30.3 









-'^^C^»- 


^) 






«•'. 


t 


cos 


sin 


t 


. i 


cos 


sin 


{', i 


cos 


sin 


«•'. i 


cos 


sin 


5 


-5 


+ 204.6 


+ 59.9 


S 


-6 


+ 4.7 


+ 1.5 


-1 


-7 


+ 2.9 


+ 6.7 


-5 -8 


+ 


4.5 


- 1.2 


6 


-5 


- 116.8 


- 48.6 


■ ^ 


-6 


+ 15.1 


+ 5.3 





-7 


0.0 


0.0 


-4 -8 


+ 


2.2 


- 1.6 


7 


-5 


+ 33.9 


+ 11.6 


4 


-6 


+ 52.8 


+ 15.4 


1 


-7 


- 2.7 


- 6.6 


-3 -8 


+ 


0.5 


+ 1.2 


8 


-5 


- 3.6 


- 2.4 


E 


-6 


+ 96.3 


+ 21.5 


2 


-7 


0.0 


+ 1.7 


-2 -8 




0.0 


+ 0.5 










6 


-6 


+ 75.3 


+ 25.2 


3 


-7 


+ 5.8 


+ 4.7 


-1 -8 




0.0 


- 3.7 


-8 


-6 


+ 13.0 


+ 3.8 


7 


-6 


- 45.4 


- 23.5 


4 


-7 


+ 14.7 


+ 4.9 


-8 




0.0 


0.0 


-7 


-6 


- 6.4 


- 9.8 


6 


-6 


+ 13.0 


+ 3.8 


5 


-7 


+ 38.0 


+ 11.8 


1 -8 




0.0 


+ 3.7 


-6 


-6 


+ 2.7 


0.0 










6 


-7 


+ 46.2 


+ 18.2 


2 -8 




0.0 


- 0.5 


-5 


-6 


+ 2.6 


+ 1.5 


-g 


-7 


- 6.9 


- 8.9 


7 


-7 


+ 23.5 


+ 2.9 


3 -8 


+ 


0.5 


- 1.2 


-4 


-6 


+ 1.3 


- 1.2 


-7 


-7 


+ 24.3 


+ 8.4 


6 


-7 


- 6.9 


- 8.9 


4 -8 


+ 


2.2 


+ 1.6 


-3 


-6 


+ 2.0 


+ 2.1 


-€ 


-7 


+ 4.4 


- 5.8 










5 -8 


+ 


4.5 


+ 1.2 


-2 


-6 


- 0.8 


+ 0.7 


-5 


-7 


+ 2.8 


- 4.0 


-8 


-8 


+ 3.6 


0.0 


6 -8 


+ 


12.7 


+ 1.2 


-1 


-6 


- 5.2 


- 5.1 


-4 


-7 


0.0 


+ 0.8 


-7 


-8 


+ 6.9 


- 10.9 


7 -8 


+ 


6.9 


+ 10.9 


' 


-6 


0.0 


0.0 


-a 


-7 


- 0.9 


- 2.9 


-6 


-8 


+ 12.7 


- 1.2 


8 -8 


+ 


3.6 


0.0 


1 


-6 


+ 6.6 


+ 5.8 


-2 


-7 


+ 0.5 


- 1.1 
























Retained Terms 


of 


the Forces. 




1 


i, 


V 


X. 


Yi 


Zi 


h 


i' 


Xi 


Hi 


z, 1 


eos 


sin 


cos 


sin 


cos 


sin 


cos 


sin 


cos 


sin 


cos 


sin 








— 


1273.1 


0.0 


+ 66.7 


0.0 


- 550.6 


0.0 


3 


-2 


+ 441.0 


- 143.0 


- 64.6 


+ 280.1 


+ 


356.7 


+ 329.5 


1 





+ 


3707.8 


- 224.0 


- 180.6 


+ 3507.2 


+1456.4 


+1647.6 


4 


-2 


+ 149.4 


^ 


0.2 


- 20.1 


+ 51.7 


+ 


62.3 


+ 85.8 


2 





+ 


271,4 


+ 29.2 


- 61,0 


+ 290.6 


+ 40.6 


+ 95.4 


5 


-2 


+ 23.8 


— 


9.4 


+ 11.4 


+ 46.9 


+ 


25.9 


+ 23.3, 


3 





+ 


55.1 


- 36.5 


+ 43.1 


+ 22.9 


+ 33.4 


+ 6,7 


6 


-2 


+ 15.9 


- 


12.6 


- 16.2 


- 13.1 








4 





+ 


11.6 


- 7.4 


+ 7.5 


+ 49.4 


+ 7.8 


+ 7.2 


7 


-2 


- 1.5 


+ 


7.7 


+ 24.8 


+ 11.7 








5 





+ 


1.2 


- 3.8 


- 13.1 


- 31.6 






8 


-2 


- 1.2 


— 


3.9 


- 15.0 


- 0.1 








6 





+ 


1.8 


0.0 


+ 27.5 


+ 27.0 


























7 





- 


1.1 


- 1.1 


- 34.1 


- 14.4 






-3 


-3 


- ■y.o 


+ 


2.2 


+ 4.8 


- 8.8 








8 





+ 


1.0 


0.0 


+ 19.0 


0.0 






-2 
-1 


-3 
-3 


+ 0.3 

- 18.7 


- 


1.2 
6.4 


- 4.2 

- 3.9 


+ 6.7 
+ 10.7 








-5 - 


-1 


+ 


17.4 


+ 4.8 


- 3.7 


+ 1.3 









-3 


+ 174.3 


+ 


60.3 


+ 50.5 


- 170.8' 


+ 


60.7 


- 32.6 


-4 - 


-1 


- 


19.3 


+ 1.9 


+ 7.6 


3.4 






1 


-3 


-1941.3 


+ 366.8 


+ 416.3 


+1909.7 


- 


252.3 


+ 387.8 


-3- 


-1 


+ 


'21.1 


+ 4.8 


+ 2.7 


+ 0.2 






2 


-3 


+5242.4 


- 845.2 


- 952.4 


-5136.7 


+ 


641.7 


- 935.1 


-2 - 


-1 


+ 


6.9 


+ 79.6 


+ 72.3 


- 30.3 


+ 33.6 


+ 6.8 


3 


-3 


+ 715.6 


- 


40.8 


- 93.8 


- 902.6 


- 


120.1 


- 238.2 


-1 - 


-1 


- 


298.8 


- 56.1 


- 5.9 


+ 290.8 


- 156.4 


+ 148.1 


4 


-3 


+ 264.1 


- 


91.3 


- 46.1 


- 51.2 


+ 


165.7 


+ 109.8 


- 


-1 


+ 


2521.5 


- 9.2 


- 274.4 


- 2319.6 


+ 946.0 


-1066.3 


5 


-3 


+ 87.3 


- 


26,9 


- 21.3 


+ 18.1 


+ 


55.0 


+ 49.7 


1 - 


-1 


- 


1310.8 


+ 148.2 


+ 146.4 


+ 239.5 


- 712.7 


- 136.9 


6 


-3 


+ 17.8 


- 


4.8 


+ 1.9 


+ 2.3 


+ 


19.4 


+ 13.1 


2 - 


-I 


+ 


1100.5 


- 208.3 


- 83.6 


+ 1111.2 


+ 742.9 


+ 793.3 


7 


-3 


+ 6.8 


- 


8.8 


- 4.0 


+ 7.0 








3 - 


-1 


+ 


170.0 


- 14.4 


- 22.2 


+ 189.0 


+ 93.1 


+ 126.7 


8 


-3 


- 4.9 


+ 


4.3 


- 1.6 


- 5.4 








4 - 


-1 


+ 


60.0 


- 18.5 


+ 4.5 


+ 46.9 


+ 30.0 


+ 21.6 






















5 - 




- 


7.9 


- 0.8 


+ 11.4 


+ 5.3 






-2 


-4 


+ 13.6 


- 


8.6 


- 0.4 


+ 1.3 


+ 


18.5 


+ 1.5 


6- 




+ 


15.4 


- 11.4 


- 4.1 


+ 7.7 






-1 


-4 


- 9.4 


+ 


16.2 


+ 2.6 


- 3.2 


- 


15.4 


+ 0.5 


7 - 




+ 


6.9 


+ 8.3 


+ 1.6 


- 6.8 









-4 


- 48.1 


- 


34.1 


- 10.2 


+ 48.4 


r- 


9.5 


+ 5.2 


8 - 




+ 


2.2 


- 6.5 


+ 5.4 


+ 2.1 






1 


-4 


+ 327.4 


+ 


6.0 


- 14.5 


- 315.9 


+ 


68.2 


- 58.1 




















2 


-4 


-1374.1 


+ 339.5 


+ 377.7 


+1337.6 


- 


155.1 


+ 274.1 


-4 - 


-2 


- 


13.7 


+ 1.2 


- 0.4 


+ 25.9 






3 


-4 


+2445.8 


- 526.9 


- 576.6 


-2365.7 


+ 290.1 


- 439.8 


-3 - 


-2 


+ 


11.1 


- 2.4 


- 7.6 


- 24.2 






4 


-4 


+ 567.4 


- 


31.7 


- 116.2 


- 665.3 


- 


48.3 


- 162.0 


-2 - 


-2 


— 


4.1 


+ 9.2 


+ 22.3 


+ 12.4 






5 


-4 


+ 204.0 


- 


55.5 


- 43.2 


- 113.2 


+ 


75.9 


+ 24.5 


-1 - 


-2 


+ 


129.5 


+ 109.7 


+ 86.1 


- 135.9 


+ 63.1 


- 15.3 


6 


-4 


+ 39.5 


- 


14.6 


- 13.4 


- 21.1 


+ 


31.9 


+ 22.7 


- 


-2 


— ' 


5339.0 


+ 294.1 


+ 393.6 


+ 3296.3 


- 428.2 


+ 589.8 


7 


-4 


+ 31.2 


- 


17.1 


- 8.3 


+ 1.9 








1 - 


-2 


+1( 


)242.4 


-1049.0 


-1302.1 


-10042.0 


-1317.9 


-1799.0 

- 271.8 


8 


-4 


- 13.2 


+ 


6.9 


- 2.7 


- 16.7 








2 - 


-2 


+ 


337.0 


+ 64.6 


+ 21.0 


- 821).] 


- 303.0 




— 












- 













Retained 


Terms of 


the Forces. 












i, i' 


Xi 


Yi 


Zi 


i, 


i' 


Xi 




Y, 


- 1 


cos 


sin 


cos 


sin 


cos 


+ 


sin 
2.5 


cos 


sin 


cos 


sin 


cos 


sin 1 


-1 -5 


- 2.3 


+ 4.6 


_ 


5.3 


+ 0.9 


+ 


33.3 


9 


-6 


- 21.0 


+ 


3.9 


_ 


3.9 


- 20.8 










-5 


+ .2.5 


- 2.0 


+ 


8.7 


- 1.4 


- 


14.4 


- 


0.2 


























1 -5 


- 46.7 


- 0.6 


- 


11.0 


+ 44.7 


— 


8.7 


4 


7.8 


1 


-7 


- 6.0 


— 


13.2 


+ 


4.5 


+ 6.9 


+ 


32.3 


- 


1.5 


2 -5 


•1- 261.0 


- 44.9 


- 


43.0 


- 252.9 


+ 


44.5 


- 


52.1 


2 


-7 


+ 21.2 


+ 


10.3 


- 


4.7 


- 12.5 


- 


2.5 


- 


1.0 


3 -5 


- 604.6 


+ 266.5 


+ 276.2 


+ 790.9 


_ 


81.9 


+ 


168.1 


3 


-7 


- 53.6 


+ 


1.2 


+ 


12.9 


+ 42.8 


- 


5.( 


+ 


8.0 


4 -5 


+1037.1 


- 288.1 


- 


306.7 


-1000.8 


+ 


122.8 


- 


191.4 


4 


-7 


+ 133.3 


_ 


42.0 


- 


51.5 


- 120.4 


+ 


13.2 


- 


27.0 


5 -5 


+ 385.4 


- 77.0 


- 


96.6 


- 407.2 


_ 


18.8 


— 


95.6 


5 


-7 


- 223.6 


+ 


106.2 


+ 


113.6 


+ 229.7 


- 


15.5 


+ 


50.5 


6 -5 


+ 119.0 


- 37.1 


- 


38.9 


- 98.4 


+ 


31.6 


- 


2.1 


6 


-7 


+ 149.6 


- 


58.5 


- 


79.5 


- 171.2 


+ 


17.1 


- 


30.6 


7 -5 


+ 40.8 


- 29.4 


- 


3.0 


- 37.0 


+ 


18.4 


+ 


5.6 


7 


-7 


+ 148.6 


— 


45.4 


- 


39.2 


- 83.3 


- 


0.5 


- 


20.7 


8 -5 


- 16.9 


+ 9.9 


- 


19.2 


- 29.0 










8 


-7 


+ 23.1 


- 


7.7 


- 


6.3 


- 45.1 










9 -5 


- 12.4 


+ 3.4 


- 


3.3 


- 12.3 










9 


-7 


- 9.7 


+ 


12.0 


- 


11.9 


- 9.7 










-2 -6 


- 11.2 


+ 6.2 


_ 


19.4 


- 19.9 










-1 


-8 


+ 5.2 


_ 


17.5 


_ 


17.5 


- 5.1 










-1 -6 


+ 1.7 


- 7.3 


+ 


24.2 


+ 11.4 


- 


30.3 


- 


2.1 





-8 


+ 2.8 


+ 


19.0 


+ 


18.9 


- 1.2 


+ 


24.0 


+ 


1.6 


-6 


+ 0.3 


+ 9.0 


- 


26.7 


+ 0.5 


+ 


25.7 


+ 


1.6 


1 


-8 


- 12.6 


— 


16.4 


- 


16.2 


+ 9.1 


- 


37.9 


+ 


1.9 


1 S 


+ 0.4 


- 6.0 


+ 


25.9 


- 16.4 


- 


8.3 


- 


2.4 


2 


-8 


+ 13.1 


+ 


12.6 


+ 


12.4 


- 12.1 


+ 


16.8 


- 


2.3 


2 -6 


- 37.7 


+ 10.0 


- 


15.1 


+ 64.1 


- 


9.8 


+ 


11.9 


3 


-8 


- 8.7 


- 


7.3 


- 


6.3 


+ 9.4 


- 


1.9 


+ 


0.8 


3 -6 


+ 175.4 


- 55.6 


- 


44.8 


- 205.8 


+ 


25.6 


- 


43.0 


4 


-8 


- 9.8 


+ 


9.3 


+ 


9.4 


+ 10.2 


- 


0.7 


+ 


3.1 


4 -6 


- 424.6 


+ 177.8 


+ 181.2 


+ 459.3 




38.5 


+ 


98.1 


5 


-8 


+ 62.0 


- 


26.9 


- 


28.9 


- 66.9 


+ 


5.6 


- 


13.7 


5 -6 


+ 411.7 


- 136.9 


- 


159.7 


- 422.5 


+ 


49.2 


- 


80.5 


6 


-8 


- 93.5 


+ 


50.5 


+ 


58.8 


+ 104.6 


- 


3.6 


+ 


21.0 


6 -6 


+ 228.2 


- 55.2 


- 


50.9 


- 192.7 


_ 


5.7 


- 


47.5 


7 


-8 


+ 42.2 


- 


4.2 


- 


16.6 


- 72.7 


+ 


5.3 


- 


9.6 


7 -6 


+ 89.2 


- 22.3 


- 


54.2 


- 93.4 


+ 


10.5 


- 


8.1 


8 


-8 


+ 24.9 


- 


38.7 


- 


19.7 


- 10.6 










8 -6 


- 22.5 


- 8.9 + 


0.8 


- 50.3 






— 




























For the computation of 
and 






•we have the above series for Xi and ^i with reversed signs, and 

dyt 



dxi 
~dt 



= —4.07365 sin M 

—0.87270 sin 2 M 
—0.21058 sinSJf 
—0.05352 sin 4 if 
—0.01402 sin 5 M 
—0.00375 sin6J!f 
—0.00100 sin 7 M 



-^ = +0.00003 + 4.02388 cos M 

+ 0.86552 cos 2 if 
+ 0.20922 cos 3 M 
+ 0.05330 cos 4 M 
+ 0.01392 cos 5 if 
+ 0.00380 cos 6 ilf 
+ 0.00112 cos 7 iW 
+ 0.00028 cos 8 M 



These multiplications furnish us now finally the material for the formation of the differential equation for 
r° 8 r, namely, of 

lSflllA.'lSl+^(r''ir)^r''R'-\-2fc''T^dt = 2. 



de 



Terms of 2 retained for integration. 1 


«, 


t' 


cos 


sin 


«, 


i' 


cos 


sin 


i, V 


cos 


sin 


«, 


V 


cos 


sin 








+ 


9109.8 


0.0 


-1 


-2 


- 214.7 


- 225.4 


4 


-4 


+8063.0 


-1850.3 


6 


-6 


+1013.5 


-350.0 


1 





- 


7631.9 


+ 561.6 





-2 


+ 3113.6 


+ 435.3 


5 


-4 


+3015.7 


- 525.3 


7 


-6 


+ 677.6 


-202.9 


2 





- 


13.2 


- 877.8 


1 


-2 


-49502.2 


+5429.7 


6 


-4 


+ 950.1 


- 251.7 


8 


-6 


+ 362.8 


-129.7 


3 





— 


31.4 


- 142.2 


2 


-2 


+51251.5 


-6036.5 


7 


-4 


+ 195.6 


- 6(^2 










4 





+ 


27.6 


- 5.0 


3 


-2 


+ 8109.5 


- 413.2 










1 


-7 


+ 28.7 


+ 53.2 


5 





- 


35.0 


- 18.2 


4 


-2 


+ 1518.4 


- 473.2 


1 


-5 


+ 77.2 


- 40.9 


2 


-7 


+ 157.4 


- 70.3 


6 





+ 


30.0 


- 2.2 


5 


-2 


+ 431.0 


- 90.6 


2 


-5 


- 638.2 


- 18.8 


3 


-7 


+ 130.5 


+ 2.7 


7 





- 


29.5 


+ 21.7 










3 


-5 


+1875.3 


- 439.1 


4 


-7 


- 307.2 


+ 62.4 


8 





+ 


14.1 


- 44.6 





-3 


- 208.1 


- 119.9 


4 


-5 


-3827.3 


+1280.4 


5 


-7 


+ 609.7 


-243.4 


9 





+ 


3.0 


+ 20.6 


1 


-3 


+ 5649.5 


+ 26.7 


5 


-5 


+2916.8 


- 851.0 


6 


-7 


- 783.2 


+388.8 












2 


-3 


-15678.7 


+3104.7 


6 


-5 


+1588.1 


- 379.9 


7 


-7 


+ 289.9 


-139.6 


-2 


-1 


+ 


10.1 


- 80.2 


3 


-3 


+20761.9 


-3605.4 


7 


-5 


+ 501.0 


- 127.7 


8 


-7 


+ 365.4 


-123.3 


-1 


-1 


+ 


578.1 


+ 686.0 


4 


-3 


+ 5454.1 


- 628.4 


8 


-5 


+ 192.7 


- 75.1 













-1 


- 


3520.7 


- 11.5 


5 


-3 


+ 1309.6 


- 321.7 










2 


-8 


+ 101.2 


+120.2 


1 


-1 


+16549.2 


-1084.2 


6 


-3 


+ 330.1 


- 126.3 





-6 


- 29.7 


- 74.4 


3 


-8 


+ 105.6 


+ 96.9 


2 


-1 


- 


2803.0 


+ 760.2 










1 


-6 


+ 92.7 


+ 123.8 


4 


-8 


- 28.5 


- 31.8 


3 


-1 


- 


261.1 


- 495.8 





-4 


+ 67.5 


+ 56.3 


2 


-€ 


+ 370.1 


+ 256.6 


5 


-8 


- 85.7 


+ 51.5 


4 


-1 


- 


99.9 


- 116.9 


1 


-4 


+ 399.3 


+ 32.9 


3 


-6 


- 440.1 


+ 30.6 


6 


-8 


+ 272.2 


-123.8 


5 


-1 


+ 


34.7 


- 45.4 


2 


-4 


+ 3281.9 


- 388.5 


4 


-6 


+1089.6 


- 344.7 


7 


-8 


- 311.7 


+153.9 












3 


-4 


- 7065.4 


+2071.6 


5 


-6 


-1794.8 


+ 723.2 


8 


-8 


+ 119.9 


+ 17.6 



For the computation of the coefficients of integratioa m& have, — 

log /x 3.008587 log p^ 9.87395n 

365.25 



log 



206266 
logju' 



7.248165 
2.475808 



« ^ -1- 0.256752 
« ,i' -\- 9.724023 

/x 1.806142 

yf 0.529691 

p and q are the coefficients in the series for Xi and yi. 



" pi 0.35322 

" Pj 9.38308 
« ps 8.58950 
« pt 7.86982 
" p, 7.19033 
« pe 6.54407 



logy, 0.34788 

" q^ 9.37951 

" 73 8.58670 

" qt 7.86747 

" qs 7.19033 

" q, 6.54407 



log 



ab 



9.288603 



log - 9.743248 



log -^--9.031851 



fi 1.806142 



^' 0.529691 



2/t 3.612284 


2/x' 


1.059382 


3^ 5.418426 


3^' 


1.589073 


4/x 7.224568 


4:tl' 


2.118764 


5^ 9.030710 


5^! 


2.648455 


6,x 10.836852 


6/ 


3.178146 


7fi 12.642996 


7^' 


3.707837 


8/1 14.449136 


8 m' 


4.237528 


9^L 16.255278 


9^' 


4.767219 


10 ,t 18.061420 






11 ^ 19.867562 







10 

Log of the " Entwichelungs-Factoren." 
i-\-4: and i — 4 



+3, +1 -H, +«, -1 

-1, -3 0,-4 +1, -5 

468480m 7.33105 7.80661m 



I -)- 3 and i — 3 
i -j- 2 and i — 2 
i-\-l and i — 1 



+2, +1 +3, +4, —1 +«. —2 • • 

-1, -2 0, -3 +1, -4 +2. -S ■ ■ 

6.02698n 7.92534 7.90573m 6.40380» 



+2, +3, -1 +4, -2 +5, -3 . , 
0, -2 +1, -3 +2, —4 +3, —5 . . 

8.54206 8.52827m 7.01565m 5.66881m 



+1, +2, -1 +3, -2 +4, -3 . . . 
0, —1 +1, —2 +2, — 3 . +3, — 4 . . . 

9.20940 9.19653m 7.65594m 6.28942m 



■• 1 +1, -1 +2, -2 +3, -3 +4, -4 . . 

\ 9.98970m 8.35223m 6.94297m 5.62793m 
The numbers above the logarithms are those which constitute ± x in i ± x. 



Specimen of the Tables of Divisors. 


For the Glass i' = O. 






-4 


-3 


—2 


-I 





+1 


+2 


+3 


+4 


+5 


+6 


+7 


+8 


+9 






9.U119„ 


9.26613„ 


9.44221k 


9.74325„ 


00 


9-74325 


9-44221 


9.26613 


9-14119 


9-04428 


8.96510 


8-89815 


8-84016 


8-78900 


-6 


9.04428„ 


8.18547 


8.31041 


8.46649 


8-78753 


8-08856„ 


8.78753„ 


8.48649» 


8.31041„ 














-4 


9.14119„ 




8.40732 


8-58340 


8-88444 


8-28238„ 


8.88444„ 


8-68340„ 


8-40732„ 


6.28238„ 












-3 


9.26613„ 






8.70834 


9-00938 


S-53226„ 


9-00938„ 


8-70834„ 


8-63226„ 


8-40732„ 


8-3104I„ 










-2 


9.44221„ 








9-18646 


8-8S442„ 


9-18566„ 


8-88442„ 


B-70834„ 


8-6eS40n 


8-48649„ 


8-40731;, 








-1 


9.74325„ 










9-48650„ 


9-48660„ 


9-18546„ 


9-0093a„ 


8-88444„ 


8-78753„ 


8-70835„ 


8.64140„ 









QD 












9.48650„ 


8-88442„ 


8-53226„ 


8.28238„ 


8-08856„ 


7-93020„ 


7-79630„ 


7-6S032„ 




+1 


9.74325 














9-18546 


9-00938 


8-88444 


8-78753 


8-70835 


8-64140 


8-58341 


8-63226 


+2 


9.44221 
















8-70834 


8-58340 


8-48649 


8-40731 


8-34036 


8-28237 


8-23121 


+3 


9.26613 


















8-40732 


8-31041 


8-23123 


8-16428 


•8-10629 


8-06513 


+4 


9.14119 




















8.18547 


8-10629 


8-03934 


7-98125 


7-93019 


+5 


9.04428 






















8-00938 


7-94243 


7-88444 


7-83328 


+6 


8.96510 
























7-86325 


7-60626 


7-75410 


+T 


8.89815 


























7-73831 


7-68715 


+8 


8.84016 




























7-62916 



When for this class i' == 0, one of the divisors in y. r — -y-. n— , becomes zero we have to put down 

(i — k)h.{i — k') fi *^ 

the negative square of that divisor which retains a real value- This table of the divisor for i' = O and for the 
coefficients of integration f- (i -\- x) is changed into the table of the divisors for /! {i -\- «) by squaring all the 
numbers and by addmg to the logarithms of the squares log (c -|- C) ;u. Excepted herefrom are the terms for 
which c or c' becomes zero. Those terms are to be multiplied by -p or — . 



11 



specimen of the Tables of the Ooefficients of Integration, 
i' = 0. 




/-i 


/-3 


/-2 


/-I 


/o 


/+1 


/+2 


/+3 


/+4 


/+B 


/■+6 


/+7 


2 


I 


= 


+0.00008 


+0.00031 


+0-00082 


-0.02532 


+0-30112* 


-0-02532 


+0-00082 


+0-00031 


+0-00008 








+0-25290 


I 


= 1 




-0.00014 


-0.00084 


-0.00806 


-0-02532 


+0-07717* 


+0-03052 


+0-00427 


+0-00073 


+0-00015 






+0-07846 


I 


= 2 






-0-00009 


-0-00085 


+0-00082 


+0-03052 


-0-09931' 


-0-00371 


-0-00073 


-0-00015 


-0-00004 




-0-07355 


t 


= 3 








-0-00014 


+O-O0O31 


+0-00427 


-0-00371 


-0-03879* 


-0-00091 


-0-00019 


-0-OOOOi 




-0-03920 


I 


= 4 










+0-00008 


+0-00073 


-0-00073 


-0-00091 


-0-02059* 


-0-00030 


-0-00007 




-0-02179 


I 


= 5 












+0-00015 


-0-00015 


-0-00019 


-0-00030 


-0-01282* 


-0-00012 




-0-01343 


I 


= 6 
















-0-00004 


-0-00007 


-0-00012 


-0-00877* 




-0-00900 


4=7 
























-0-00639* 


-0-00639 



In such a table it is only necessary to compute the values on one side of the diagonal line of asterisks, since 
the values appear oh both sides arranged in the same manner as [a 6], [a c], [6 c], with respect to [a a], [5 J] 
in the method of least squares. By means of the horizontal sums 2 the coeflBcients are checked because of 



.-1-00 



: ^ — CO . . . 



^U 



91 



2g2 



39s 



-f- 1, t') (i — 1, V) ^ (i -h 2, V) (J. — 2, V) ^ (i -K 3, i<) (» - 3, i>) ■ 



















r° 8r 


















h 


V 


cos 


sin 


i, 


ii 


cos 


sin 


i, 


i' 


cos 


sin 


«. 


V 


cos 


sin 








+ 41-67« 




0.0 





-3 


+ 9933-9 


- 754.7 


5 


-4 


- 61.9 


+11.5 


-1 


-7 


+ 1.3 


- 3.6 


1 





-125.63; 


-3697.52< 


1 


-2 


-12287-5 


+1166.2 


6 


-4 


- 15.0 


+ 3.9 





-7 


+ 7.9 


- 21.8 


2 





- 13.46< 


- 


397.69< 


2 


-2 


-21290.5 


+2442.7 


7 


-4 


- 1.8 


+ 0.5 


1 


-7 


+ 64.1 


-210.9 


3 





- 2.61* 


— 


64.08< 


3 


-2 


- 2306.4 


+ 229.2 










2 


-7 


- 31-3 


+ 22.5 


4 





0.0 


— 


]2.23< 


4 


-2 


- 371.6 


+ 50.1 


-1 


-5 


+ 2.2 


- 0.7 


3 


-7 


+148-5 


+ 87.3 


5 

! 





0.0 


— 


2.51 < 


5 


-2 


- 46.1 


+ 6.0 



1 


-5 
-5 


+ 14.2 
+127.2 


- 4.0 

- 9.3 


4 
5 


-7 
-7 


+ 51-3 
- 19-2 


+ 3.4 
+ 10.6 








+ 2936.7 




0.0 


-3 


-3 


1.0 


- 0.6 


2 


-5 


-138.4 


-29.3 


6 


-7 


+ 17-3 


- 8.0 


1 





- 989.2 


+ 


19.8 


-2 


-3 


- 44.5 


- 3.4 


3 


-5 


-433.7 


+80.6 


7 


-7 


- 3-7 


- 1.9 


2 





- 210.4 


+ 


105.3 


-1 


-3 


- 276.0 


- 23-1 


4 


-5 


+184.0 


-67.4 


8 


-7 


- 3-3 


+ 1.1 


3 





- 25.8 


+ 


11.2 





-3 


- 2694.8 


- 192-4 


5 


-5 


- 77.9 


+21.7 










4 





6.2 


+ 


1.2 


1 


-3 


- 3380.5 


+1118.1 


6 


-5 


- 25.7 


+ 5.8 





-8 


+ 1.7 


+ 2.1 












2 


-3 


+18286.1 


-3229.5 


7 


-5 


- 5.8 


+ 1.5 


1 


-8 


+ 13.0 


+ 15.7 


-3 


_][ 


- 15.5 


_ 


3.7 


3 


-3 


- 155.7 


+ 30.7 


8 


-5 


- 1.4 


0.0 


2 


-8 


+ 14.3 


+ 22-4 


-2 


—\ 


- 111.9 


_ 


15.2 


4 


-3 


+ 17.1 


- 13.5 










3 


-8 


+ 32.1 


+ 24.5 


-1 


_1 


- 969.8 


— 


293.3 


5 


-3 


+ 3.3 


- 0.4 


-1 


-6 


+ 0.2 


+ 1.2 


4 


-8 


+ 13.9 


+ 12.8 





—\ 


- 4613.1 


+ 


328.3 


6 


-3 


- 9.6 


+ 2.4 





-6 


+ 6.3 


+17.9 


5 


-8 


+ 5.6 


- 1.1 


1 


—\ 


+10401.0 


_ 


584.0 










1 


-6 


- 27.4 


+15.8 


6 


-8 


- 6.3 


+ 3.1 


2 


—1 


+ 2177.7 


— 


221.7 


-2 


-4 


+ 1.5 


- 0.4 


2 


-6 


+ 28.2 


+51.6 


7 


-8 


+ 4.5 


- 2.3 


3 


_2 


+ 291.9 


+ 


3.1 


-1 


-4 


+ 4.6 


- 2.3 


3 


-6 


+279.0 


+42.3 


8 


-8 


- 1.2 


0.0 


4 


—\ 


+ 52.3 


_ 


0.4 





-4 


+ 32.0 


- 33.7 


4 


-6 


- 55.1 


+30.5 




















1 


-4 


- 716.1 


+ 96.8 


5 


-6 


+ 59.2 


-21.5 


6 


-9 


+ 1.5 


- 0.9 


-3 


-2, 


+ 8.3 


+ 


1.5 


2 


-4 


+ 2107.7 


- 145.9 


6 


-6 


- 17.3 


+ 6.0 


7 


-9 


- 2.2 


+ 1.0 


-2 


-2 


+ 142.5 


_ 


2.2 


3 


-4 


+ 1322.8 


- 288.0 


7 


-6 


- 7.9 


+ 2.4 


8 


-9 


+ 0.4 


- 0.8 


-1 


-2 


+ 980.0 


+ 


17.4 


4 


-4 


- 264.9 


+ 66.3 


8 


-6 


- 2.8 


+ 1.0 


9 


-9 


- 0.1 


0-0 



For the formation of the diflFerential equations for fj and jji it is necessary to multiply r° 8r with 

a /£» ,3 k'' 

•^ajiand-^yi. 



12 






; + 1.04488 + 5.01118 cos M 
+ 3.00130 cos 2 M 
+ 1.38657 cosSJf 
-j- 0.56905 cos4Jf 
-j- 0.21828 cos 5 M 
-j- 0.08089 cos 6 M 
4-0.03161 cos7Jf 
+ 0.00979 cos 8 if 



Sk' 



^ y.= + 4.39501 sin i!f 
+ 2.81725 sin 2 M 
+ 1.33137 sin 3 M 
+ 0.55228 sin 4 i!f 
+ 0.21259 sin 5 M 
+ 0.07719 sin 6 if 
+ 0.02454 sin 7 M 



Having perfonned these multiplications we obtain for integration 






^^^(l±^., = x.+ ^-'^^+->- (.= ..) =.^V 



and simply 



dfi ^ ^3 Vi — "iT^ ^05 (^r or) — ^, 



<PCi I i^(l + m) ^ _ 






&=Zi- 



h 


i' 


ll 


s' 


»;i 


2 


«. 


i' 


1 


S 


Vi 


2 


COS 


sin 


cos 


sin 


cos 


sin 


cos 


sin 








- 293.0< 


0.0 


- 8731.9* 


0.0 


4 


-1 


+ 9901.6 


- 687.9 


+ 639.9 


+ 9298.1 


1 





- 157.8< 


+ 878.7< 


- 6465.1* 


+ 28.9* 


5 


-1 


+ 4485.2 


- 293.2 


+ 293.5 


+ 4324.0 


2 





- 300.4< 


- 7176.5* 


+ 5387.1* 


- 241.4* 


6 


-1 


+ 1848.4 


- 128.2 


+ 108.6 


+ 1792.8 


3 





- 204.0i( 


- 5548.U 


+ 4985.9* 


- 187.2* 


7 


-1 


+ 707.7 


- 35.2 


+ 42.0 


+ 685.0 


4 





- 103.3< 


- 2019.2« 


+ 2747.8* 


- 98.1* 














5 





- 44.5< 


- 1300.9^ 


+ 1255.3* 


- 42.8* 


-5 


-2 


+ 642.1 


+ 12.6 


+ 10.6 


- 722.2 


6 





- 17.7< 


- 525.2< 


+ 523.1* 


- 16.7* 


-4 


-2 


+ 1486.2 


+ 29.1 


+ 24.1 


- 1432.4 


7 





- 6.5t 


- 205.2< 


+ 214.3* 


5.8* 


-3 


-2 


+ 2815.4 


+ 106.1 


+ 100.8 


- 2580.8 


8 





- 2.5« 


- 86.7* 


+ 72.6* 


2.2* 


-2 


-2 


+ 2684.3 


+ 452.4 


+ 471.5 


- 1797.5 


9 





1.0t 


- 29.0* 


+ 9,4* 


0.3* 


-1 


-2 


- 7484.1 


+ 1745.8 


+ 1767.9 


+10518.1 


10 





O.lt 


— u»yf 


+ 1.6* 


0.0 





-2 


-54730.2 


+ €308.1 


+ 6527.9 


+64290.9 






Check. 




Chi 


!CK. 


1 


-2 


-33213.1 


+ 4804.2 


+ 6058.7 


+63561.3 


JaS^'o+i- 


2-<p„=+0.7 


Sb'„q^=+0.2 


= +0.2 


= -1.3 


2 


-2 


-43437.6 


+ 5071.7 


- 911.5 


- 7514.1 














3 


-2 


-67573.3 


+ 7582.9 


- 6459.1 


-56034.2 








- 1018.5 


0.0 


+ 266.3 


0.0 


4 


-2 


-43662.0 


+ 4902.5 


- 4521.2 


-40231.6 


1 





+15182.5 


- 28.1 


+ 162.6 


+15375.4 


5 


-2 


-21547.8 


+ 2409.7 


- 2290.0 


-20489.0 


2 





+ 5564.4 


+ 173.9 


- 34.7 


+ 5736.0 


6 


-2 


- 9236.7 


+ 1028.4 


- 1092.1 


- 8963.1 


3 





+ 1767.9 


+ 254.2 


- 196.5 


+ 1794.1 


7 


-2 


- 3643.3 


+ 418.6 


- 375.7 


- 3553.1 


4 





+ 493.1 


+ 187.1 


- 172.2 


+ 546.1 


8 


-2 


- 1396.3 


+ 152.9 


- 165.9 


- 1351.0 


5 





+ 117.3 


+ 92.0 


- 105.0 


+ 88.9 














6 





+ 27.6 


+ 40.7 


- 12.6 


+ • 52.6 


-4 


-3 


- 651.5 


- 85.0 


- 81.9 


+ 655.5 


7 





+ 12.2 


+ 15.1 


- 50.0 


- 14.3 


-3 


-3 


- 1374.1 


- 208.3 


- 196.8 


+ 1267.2 














-2 


-3 


- 1941.2 


- 493.8 


- 469.4 


+ 1623.6 


-5 


-1 


- 406.2 


- 85.9 


- 90.4 


+ 427.5 


-1 


-3 


+ 389.6 


- 1075.9 


- 986.1 


- 1536.3 


-4 


-1 


- 982.6 


- 212.8 


- 197.2 


+ 914.4 





-3 


+15466.8 


- 2231.2 


- 1968.7 


-19070.7 


-3 


-1 


- 1719.4 


- 439.9 


- 409.9 


+ 1568.1 


1 


-3 


+32924.0 


- 7039.1 


- 6188.3 


-44406.5 


-2 


-1 


- 1636.9 


- 655.5 


- 551.2 


+ 1006.6 


2 


-3 


+11266.3 


- 1666.8 


- 3073.1 


-16238.7 


-1 


-1 


+ 4032.3 


- 612.7 


- 215.2 


- 6026.3 


3 


-3 


+39386.4 


- 6595.6 


+ 5534.2 


+32608.6 





-1 


+24638.8 


- 2220.4 


- 1199.6 


-30750.9 


4 


-3 


+24184.2 


- 4154.3 


+ 3749.3 


+22344.9 


1 


-1 


+ 2392.2 


- 642.0 


- 633.8 


-16574.1 


5 


-3 


+11285.6 


- 1951.6 


+ 1832.9 


+10799.1 


2 


-1 


+22618.3 


- 1611.4 


+ 943.3 


+16076.1 


6 


-3 


+ 4654.2 


- 807.3 


+ 782.0 


+ 4512.8 


3 


-1 


+18183.6 


- 1301.6 


+ 1150.8 


+16159.8 


7 


-3 


+ 1770.4 


- 314.5 


+ 294.3 


+ 1739.2 



13 



«, i' 




«. 


2 






V\ 


^ 


i, 


i' 




1. 


S 






V> 


2 




cos 


sin 


cos 


sin 


cos 


sin 


cos 


sin 1 


8 -3 


+ 


643.7 


— 


106.8 


+ 


106.7 


+ 636.1 


2 


-6 


+ 


584.2 


+ 


270.1 


+ 


47.8 


_ 


556.3 


















3 


-6 


+ 


437.0 


+ 


203.4 


- 


151.2 


_ 


126.5 


-2 -4 


+ 


310.6 


- 


68.2 


- 


56.7 


- 288.9 


4 


-6 


+ 


358.0 


+ 


366.4 


_ 


36.9 


+ 


995.9 


-1 -4 


+ 


810.7 


- 


101.6 


- 


103.4 


- 799.2 


5 


-6 


+ 


709.5 


+ 


42.1 


_ 


309.6 


_ 


87.7 


-4 


+ 


2202.0 


- 


221.4 


- 


169.3 


- 2134.8 


6 


-6 


+ 


450.4 


- 


3.1 


— 


84.7 


+ 


71.9 


1 -A 


+ 


6730.5 


- 


729.0 


- 


Q15.5 


- 6538.2 


7 


-6 


+ 


162.7 


+ 


5.0 


— 


73.3 


+ 


0.4 


3 -4 


+ 


1955.1 


- 


235.7 


- 


317.0 


- 2674.6 






















3 -4 


+ 


7290.6 


- 


885.8 


- 


204.7 


+ 1960.0 


-2 


-7 


+ 


54.5 


— 


161.6 


_ 


161.9 


_ 


67.0 


4 -4 


+ 


6102.3 


- 


860.7 


+ 


698.4 


+ 4901.3 


-1 


-7 


+ 


151.6 


— 


346.6 


_ 


304.2 


_ 


128.3 


5 -4 


+ 


2681.5 


- 


386.5 


+ 


300.1 


+ 2412.3 





-7 


+ 


239.2 


- 


450.1 


_ 


367.1 


— 


210.4 


6 -4 


+ 


906.7 


- 


113.1 


+ 


92.0 


+ 861.4 


1 


-7 


+ 


259.1 


- 


101.8 


+ 


234.0 


— 


144.9 


7 -4 


+ 


293.8 


- 


37.9 


+ 


14.6 


+ 267.7 


2 


-7 


+ 


602.1 


- 


301.2 


+ 


692.7 


— 


249.8 


















3 


-7 


+ 


235.5 


- 


165.7 


+ 


292.0 


- 


25.8 


-1 -5 


+ 


23.6 


- 


23.9 


- 


30.9 


- 13.7 


4 


-7 


+ 


533.2 


+ 


74.6 


- 


117.3 


+ 


228.1 


-5 


- 


124.0 


- 


55.9 


- 


13.9 


+ 166.0 


5 


-7 


+ 


140.3 


+ 


187.4 


+ 


9.8 


+ 


518.6 


1 -5 


- 


770.1 


- 


13.7 


+ 


9.7 


+ 895.9 


6 


-7 


+ 


283.7 


+ 


4.4 


- 


151.0 


- 


31.0 


2 -5 


- 


414.6 


+ 


12.5 


+ 


81.9 


+ 801.6 


7 


-7 


+ 


228.1 


- 


28.0 


- 


54.4 


+ 


9.6 


3 -5 


- 


1078.9 


+ 


128.4 


+ 


243.3 


+ 400.4 






















4 -5 


- 


210.8 


- 


143.9 


- 


378.3 


- 1848.4 


-1 


-8 


+ 


49.6 


+ 


35.3 


+ 


32.3 


— 


47.1 


5 -5 


- 


18.1 


- 


108.7 


- 


24.7 


- 603.6 





-8 


+ 


85.2 


+ 


114.7 


+ 


104.7 


- 


75.5 


6 -5 


- 


169.1 


- 


27.5 


- 


32.8 


- 308.5 


1 


-8 


+ 


99.9 


+ 


107.1 


+ 


71.3 


_ 


74.1 


7 -5 


- 


155.7 


- 


8.3 


- 


20.1 


- 207.0 


2 


-8 


+ 


166.9 


+ 


158.9 


+ 


46.6 


- 


73.9 


8 -5 


- 


124.0 


+ 


25.8 


- 


33.9 


- 128.7 


3 


-8 


+ 


121.3 


+ 


131.4 


- 


50.9 


+ 


24.9 ' 






, 










• 


4 


-8 


+ 


123.3 


+ 


129.5 


- 


86.5 


+ 


104.0 


-1 -6 


+ 


71.7 


\+ 


112.7 


+ 


134.3 


- 55.7 


5 


-8 


+ 


154.8 


+ 


65.2 


- 


107.3 


+ 


30.4 


-6 


+ 


164.4 


+ 


183.6 


+ 


112.6 


- 154.6 


6 


-8 


- 


27.9 


+ 


89.5 


+ 


13.8 


+ 


155.1 


1 -6 


+ 


453.6 


+ 


265.6 


+ 


173.0 


- 434.8 


7 


-8 


+ 


57.3 


+ 


18.4 


- 


40.2 


- 


55.8 



The integration of the precedmg three differential equations gives finally the perturbations of the rectangu- 
lar co-ordinates. 



h 


i' 


ll 


Vi 


? 


I 


COS 


sin 


cos 


sin 


cos 


sin 








- 84.94^ 


0.0 


-1022.41* 


0.0 


+ 148.67* 


0.0 


1 





- 4.74« 


+4279.97* 


-4154.40* 


- 11.92* 


- 448.23* 


+ 493.85* 


2 





+ 25.65« 


+1241.89* 


-1226.46* 


+ 24.98* 


- 48.01* 


+ 53.12* 


3 





+ 8.30< 


+ 325.86* 


- 322.93* 


+ 8.27* 


- 7.72* 


+ 8.56* 


4 





+ 2.50( 


+ 86.21* 


- 85.92* 


+ 2.37* 


- 1.47* 


+ 1.63* 


5 





+ o.m 


+ 22.98* 


- 22.70* 


0.0 


- 0.31* 


+ 0.34* 


6 





+ 0.16« 


+ 6.19* 


- 6.02* 


0.0 • 


- 0.07* 


+ 0.08* 


7 


0. 


0.0 


+ 1.31* 


- » 1.37* 


• - 0.0 


0.0 


0.0 








- 699.7 


0.0 


+ 75.5 


0.0 






1 





+1118.5 


- 5.6 


. - 9.4 


+ 901.6 


- 202.6 


0.0 


2 





+ 463.6 


- 31.7 


+ 28.9 


+ 433.4 


+ 129.9 


+ 143.4 


3 





+ 100.7 


- 15.4 


+ 13.1 


+ 97.4 


+ 38.2 


+ 42.2 


4 





+ 23.3 


- 5.2 


+ 4.9 


+ 21.1 


+ 5.2 


+ 6.6 


5 





+ 5.8 


- • 1.5 


+ 1.7 


+ 6.1 


+ 0.8 


+ 1.0 


6 





+ 0.8 


- 0.4 


+ 0.1 


+ 0.5 


+ 0.2 


+ 0.2 


-5 


-1 


+ 4.1 


+ 1.1 


+ 1.0 


- 4.0 


0.0 




-4 


-1 


+ 32.1 


+ 3.7 


+ 3.5 


- 32.4 


+ 0.8 


- 0.9 



14 



i, v 


i 


1 


. 


1 


cos 


sin 


cos 


sin 


cos 


sin 1 


-3 -1 


+ 122.3 


+ 11.8 


+ 11.8 


- 122.9 


+ 


4.2 


— 


4.5 


-2 -1 


+ 494.5 


+ 26.8 


+ 26.3 


- 491.7 


+ 


22.7 


- 


26.9 


-1 -1 


+ 2208.5 


- 55.3 


- 72.4 


- 2188.4 


+ 


226.2 


- 


2.36.6 


-1 


+ 7732.7 


- 671.7 


- 325.3 


- 7809.7 


+ 


428.1 


- 


312.4 


1 -1 


- 1340.7 


- 82.3 


0.9 


- 1289.8 


- 


554.6 


+ 


231.4 


2 -1 


- 3739.2 


+ 227.2 


- 192.7 


- 3658.9 


- 


202.1 


- 


114.3 


3 -1 


- 10i)2.5 


+ 72.3 


- 70.3 


- 1081.8 


- 


22.9 


- 


10.7 


4 -1 


- 300.6 


+ 19.9 


- 19.6 


- 300.2 


- 


4.2 


- 


1.6 


5 -1 


- 79.0 


+ 5.0 


5.4 


- 84.8 


- 


0.6 


- 


0.3 


6 -1 


- 21.9 


+ 1.3 


1.1 


- 20.7 










7 -1 


- 6.3 


0.0 


0.0 


- 6.1 










-5 -2 


- 6.6 


0.2 


- 0.2 


+ 7.2 










-4 -2 


- 50.0 


+ 1.9 


+ 2.0 


+ 52.5 








^ 


-3 -2 


- 192.0 


+ 7.5 


+ 7.8 


+ 192.5 


- 


1.7 


+ 


2.1 


-2 -2 


- 778.1 


+ 36.1 


+ 36.1 


+ 779.4 


- 


9.2 


+ 


12.0 


-1 -2 


- 3513.0 


+ 213.1 


+ 218.7 


+ 3500.3 


- 


72.0 


+ 


85.4 


-2 


-19149.5 


+ 2127.3 


+ 2083.7 


+19003.2 


- 


428.6 


+ ' 


600.3 


1 -2 


- 8330.7 


+ 1305.0 


+ 754.2 


+ 9254.2 


+ 


525.7 


- 


787.6 


2 -2 


+10930.4 


- 1159.0 


+ 1065.5 


+10367.5 


+ 


244.1 


- 


146.5 


3 -2 


+ 4932.9 


- 540.5 


+ 540.7 


+ 4849.2 


+ 


3.7 


- 


46.1 


4 -2 


+ 1507.9 


- 166.7 


+ 166.1 


+ 1497.3 


+ 


1.5 


- 


7.4 


5 -2 


+ 428.2 


- 47.6 


+ 47.9 


+ 432.3 


+ 


0.3 


- 


1.4 


6 -2 


+ 122.5 


- 13.7 


+ 12.7 


+ 112.6 










7 -2 


+ 30.7 


- 3.5" 


+ 3.0 


+ 29.9 










8 -2 


+ 8.0 


0.8 


+ 0.9 


+ 7.7 










-4 -3 


1.9 


+ 3.0 


+ 2.8 


+ 4.8 










-3 -3 


+ 65.9 


+ 3.6 


+ 3.5 


- 66.1 


+ 


0.6 


- 


0.7 


-2 -3 


+ 245.3 


+ 13.5 


+ 13.2 


- 263.7 


+ 


3.3 


— 


3.6 


-1 -3 


+ 1128.7 


+ 45.6 


+ 42.7 


- 1120.9 


+ 


21.1 


— 


22.1 


-3 


+ 5724.9 


+ 4.2 


- 15.3 


- 5630.2 


+ 


187.9 


— 


208.4 


1 -3 


+ 9598.9 


- 2097.8 


- 1894.6 


- 9736.8 


+ 


145.1 


- 


246.1 


2 -3 


- 5031.4 


- 17.9 


+ 509.0 


- 2272.5 


- 


842.5 


+ 


1273.3 


3 -3 


- 3779.0 


+ 539.8 


- 523.1 


- 3638.3 


- 


69.4 


+ 


141.1 


4 -3 


- 1034.5 


+ 161.6 


- 156.4 


- 1022.7 


- 


18.6 


+ 


16.8 


5 -3 


- 268.1 


+ 43.2 


- 42.6 


- 269.3 


- 


3.7 


+ 


3.0 


6 -3 


- 80.4 


+ 13.6 


9.6 


- 56.7 


- 


0.7 


+ 


0.5 


7 -3 


- 17.7 


+ 3.1 


3.0 


- 17.2 










8 -3 


- 4.0 


+ 0.7 


- 0.6 


3.9 










-4 -4 


1.1 






+ 1.1 










-3 -4 


+ 1.4 






1.3 










-2 -4 


3.2 


+ 1.4 


+ 0.9 


+ 2.7 









0.3 


-1 -4 


- 8.9 


+ 1.2 


+ 1.2 


+ 9.3 


+ 


4.3 


_ 


2.5 


-4 


+ 1.4 


- 12.1 


- 22.6 


- 4.0 


+ 


27.9 


_ 


21.9 


1 -4 


+ 1826.7 


- 182.2 


- 135.1 


- 1854.9 


+ 


59.7 


_ 


91.2 


2 -4 


+ 748.2 


- 120.8 


- 111.6 


- 32.3 


— 


131.7 


+ 


217.7 


3 -4 


- 833.4 


+ 99.3 


1.6 


- 402.4 


- 


56.4 


+ 


90.2 


4 -4 


- 294.8 


+ 40.7 


- 33.9 


- 250.5 


- 


2.5 


+ 


14.8 


5 -4 


- 72.0 


+ 10.1 


- 8.1 


- 65.4 


_ 


2.4 


+ 


0.9 


6 -4 


- 14.5 


+ 1.8 


1.8 


- 16.4 


_ 


0.5 






7 -4 


3.4 


+ 0.3 




2.9 










-2 -5 


1.6 






+ 1.7 











15 



i, »■' 


Si 


Vi 


1 


COS 


sin 


cos 


sin 


cos 


sin 


-1 -5 


- 10.1 


+ 


1.9 


+ 


2.1 


+ 10.4 


2.1 


+ 0.2 


-5 


- 47.7 


+ 


7.9 


+ 


4.1 


+ 46.9 


+ 1.8 


+ 1.3 


1 -5 


- 222.1 


— 


13.4 


- 15.2 


+ 218.3 


- 11.5 


+ 10.6 


2 -5 


- 148.9 


+ 


21.4 


+ 52.2 


+ 188.6 


+ 13.8 


9.1 


3 -5 


+ 204.2 


- 


30.9 


- 40.0 


+ 7.4 


+ 20.9 


- 39.4 


4 -5 


+ 20.8 


+ 


7.2 


+ 20.2 


+ 113.3 


- 5.5 


+ 8.6 


5 -5 


+ 2.5 


+ 


2.9 


+ 


1.1 


+ 20.6 


+ 0.6 


+ 2.5 


6 -5 


+ 3.1 


- 


0.5 


+ 


0.5 


+ 6.1 


- 0.5 




7 -5 


• + 1.7 










+ 2.4 






8 -5 


+ 0.9 










+ 0.9 






-2 -6 


+ 0.7 


+ 


0.3 


+ 


0.2 


0.7 






-1 -6 


+ 1.3 


- 


2.8 


- 


4.2 


1.9 


+ 1.2 




-6 


+ 14.0 


— 


2.3 


+ 


2.1 


- 14.4 


4.0 


0.3 


1 -6 


+ 191.1 


+ 


141.0 


+ 126.8 


- 187.8 


1.4 


2.7 


2 -6 


+ 166.8 


+ 


64.2 


- 


52.6 


- 66.6 


+ 2.7 


2.5 


3 -6 


- 153.2 


_ 


78.5 


+ 


95.3 


- 77.5 


- 14.6 


+ 22.4 


4 -6 


- 37.1 


— 


32.5 


+ 


11.8 


- 87.9 


. + 1.6 


5.5 


5 -6 


- 25.6 


— 


3.1 


+ 


11.6 


1.8 


1.7 


+ 2.6 


6 -6 


9.0 


- 


0.3 


+ 


1.9 


2.2 




+ 0.9 


7 -6 


2.2 






+ 


0.9 








-3 -7 


0.6 


+ 


0.5 


_ 


0.2 


+ 0.4 






-2 -7 


2.0 


+ 


4.3 


+ 


4.3 


+ 2.1 






-1 -7 


9.4 


+ 


16.8 


+ 


15.9 


+ 9.2 


1.9 




-7 


- 41.5 


+ 


57.1 


+ 


54.6 


+ 41.9 


- 5.3 


0.5 


1 -7 


- 237.0 


+ 


146.4 


+ 103.9 


+ 234.6 


- 83.3 


5.1 


2 -7 


+ 162.0 


_ 


86.7 


+ no.3 


- 238.0 


+ 29.9 


4.7 


3 -7 


+ 290.3 


_ 


153.9 


+ 137.5 


+ 272.2 


8.9 


+ 17.8 


4 -7 


- 20.6 


_ 


30.8 


+ 


37.4 


0.0 


- 2.5 


+ 4.9 


5 7 


2.3 


_ 


11.4 


+ 


4.1 


- 17.7 


+ 0.3 


1.6 


•6 -7 


5.4 


- 


1.0 


+ 


4.1 


+ 0.5 


- 0.4 


+ 0.7 


7 -7 


2.4 


- 


0.3 


+ 


1.3 


0.3 






-1 -8 


1.6 / 





1.4 


_ 


1.4 


+ 1.7 






-8 


5.8 


_ 


8.3 


- 


6.4 


+ 6.1 


0.5 




1 -8 


- 16.8 


_ 


21.4 


— 


22.0 


+ 18.8 


+ 15.5 


1.0 


2 -8 


+ 46.1 


+ 


43.3 


+ 


39.6 


- 43.5 


+ 1.4 


- 0.7 


3 -8 


+ 44.0 


+ 


50.4 


— 


46.7 


+ 39.6 


4.0 


+ 0.9 


4 8 


- 12.4 


_ 


11.7 


+ 


9.6 


- 14.1 


0.4 


- 0.4 


5 -8 

6 -8 


7.7 
+ 0.6 


- 


3.0 
2.2 


+ 


5.4 
0.1 


- 2.0 
4.0 


0.3 


+ 0.7 
0.5 


7 -8 


0.9 


+ 


0.3 


+ 


0.6 


+ 0.8 








Normal Places referred to 


the Mean Equinox 1 


3540. 




Berlin M. 1 


r. 


a 


3 


Berlin M. T. 


a 


d 


1852, July 

1852, October 

1853, January 

1854, January 


1.0 

1.0 

1.0 

28.0 


1 11 

271 35 16.53 
274 56 46.92 
322 28 46.75 
128 3 16.18 


( II 

- 8 35 16.00 
-18 24 28.78 
-16 2 17.53 
+12 2 48.34 


1855, April 26.0 

1856, October 22.0 

1858, March 20.0 

1859, July 8.0 


223° 23 31.65 

39 13 48.02 

182 4 41.86 

278 7 52.10 


- 58 16.38 

- 5 12 59.07 
+ 7 34 3.35- 

- 9 19 9.96 



16 



The perturbations computed with the above coefficients for the times of the normals are : ■ 



+11421 

+ 4084 
+ 1750 
+39074 
+ 2042 
+ 1754 
+ 5642 
+ 8584 



-15176 

-19862 
-33592 

- 4084 

- 2185 
-14556 
-2660 
-10494 



6i 
-2756 
-2823 
-2105 
+3665 
+ 532 
- 380 
+2672 
-4500 



I 
+14787 
+ 9001 
+10510 
+38902 
+ 2592 
+ 5556 
+ 6360 
+10653 



-10133 
-16524 
-30074 
+ 6322 

- 1580 
-12885 

- 1575 

- 6160 



- 6858 

- 8192 
-11002 
+ 1899 

- 98 

- 4268 
+ 1788 

- 7252 



For Si, 9)1, Si) the plane of the orbit of Melpomene is the fundamental plane, but S, ij, J are referred to the 
equator. The transformation is effected by means of the formulas on pages 391 and 392. 

We derive from n' = 16° 16' 53".3, g?' = 19° 16' 43".7, and i' = 15° 28' 17".2 for 1854.0 : — 



cos (a;, a;) = -1- 0.959273 
cos (yi a;) = — 0.268411 
cos (z, x)—-\- 0.088074 



cos {x^y) =-1-0.282146 
cos (j^iy)=-i- 0.925742' 
cos {zi y)= — 0.251799 



cos (x, ») = — 0.013949 
cos (2^1 z)—-\- 0.266394 
cos [zy z)=-\- 0.963765 



The computation of the normal places from the osculating elements for 1854.0 with the perturbations |, ri, J, 
gives the following equations of condition for the determination of the corrections of the elements : — 



+1.72507 


-3.46371 




+1.76341 


-0.01327 


+0.11791 


- 9.60585 


+ 157.29 


+1.05428 


-2.12179 




+0.96271 


-0.00356 


+0.03244 


- 5.53250 


+ 26.24 


+0.98888 


-1.13494 




+0.69111 


-0.02955 


+0.01693 


- 3.91254 


- 184.68 


+1.54040 


+3.09070 




+1.69341 


-0.05026 


-0.05610 


+ 0.38965 


- 508.67 


+1.05335 


-1.21848 




+1.51267 


-0.04736 


+0.35622 


+ 5.19856 


+ 75.05 


+3.21295 


+1.63979 




+2.06075 


-0.07675 


+0.47456 


+33.30130 


-1902.90 


+1.01318 


+0.73413 




+1.50797 


-0.08393 


+0.19514 


+15.62610 


- 219.44 


+1.85143 


-3.64800 




+1.80356 


-0.01777 


+0.07135 


+37.14650 


- 606.95 




dM 


Sq> S n 


S9, S 


i 100 3 11 


-0.08528 


+0.22198 




-0.13034 


+0.17877 


+1.44227 


+ 0.73639 


- 87.12 


-0.12241 


+0.18470 




-0.09555 


+0.17529 


+0.48963 


+ 0.52905 


- 26.89 


+0.12166 


-0.18671 




+0.08963 


+0.12534 


-0.11444 


- 0.53821 


- 35.08 


-0.11837 


-0.24087 




-0.14720 


-0.27302 


-0.64995 


- 0.13495 


+ 82.14 


-0.25846 


+0.20020 




-0.38766 


-0.08737 


+1.41267 


- 1.07558 


- 23.25 


+0.92431 


-0.01619 




+0.57207 


+0.16001 


-1.80113 


+ 9.04078 


- 511.75 


-0.27122 


-0.25501 




-0.39779 


-0.21930 


+0.73969 


- 4.07944 


+ 93.35 


-0.04169 


+0.15224 




-0.08194 


+0.20950 


+1.35572 


- 0.58380 


- 67.39 


From which, by 


the method of least squares, is obtained : — 








3ilf=-l-12'16".46 


8 


y = _|_ 1' 33" 


.89 


3 71 = — 9' 


0".57 


5g2=4- 






8 


; = 4- 0' 12" 


.08 


dn =-1-0". 


15125 




and thus finally 1 


the pure elliptica; 


elements : — 
















1854, Jan. 0, Washington Mean Time. 








M: 


= 


80° 8 53.31 












n - 


^:^ 


15 5 30.95 


) 


o 

n' = 16 


7 48!6 






Q, 


= 


150 3 49.70 


M. Eq. Ep 


S'=19 


16 5.9 






i ■- 


= 


10 9 16.85 




i' =15 


27 48.0 






<P '■ 


= 


12 34 20.18 












. i" 


r= 


1020".11977 












log a: 


=: 


0.3609032 











= 



17 

With these elements, and the above perturbations, I have constructed tables which represent the normals as 
follows : — 



« cos d 


JS 


^i a cos 3 


Jd 


+1:8 


-1.5 


-L2 


+1.2 


—3.6 


—4.3 


+3.8 


—0.3 


—2.0 


—1.3 


+5.5 


—4.9 


—1.3 


—2.3 


—0.6 


+1.4 



This result is certainly satisfactory, since the perturbations by Saturn have been neglected. 

For curiosity's sake I have computed an approximation of the secular variations of the elements from the 
terms multiplied by t. They are : — 



Jn =-\- 32.01 " 

J£l= — 35.01 

Ji =- 0.33 /in one year. 

Jq, =-\- 0.68 



11. ON THE CONSTRUCTION OF THE TABLES OF MELPOMENE. 



"DEFOEE entering into the details of the construction of the tables, I would take the liberty of making some 
general remarks on the treatment of asteroids at the present time. 

Afler two oppositions it is possible to determine the elements of an asteroid near enough the truth for 
computing the perturbations, and I think those by Jupiter are sufficient for our present purposes. Three 
oppositions, then, admit the more accurate determination of the elements, and after about eight oppositions 
they can be finally corrected for the computation of the general perturbations of the first order by Jupiter. 
Preliminary tables constructed upon them will give, for the next fifty years, the ephemeris near enough to find 
the planet, and for forming normal places. After that, a computer can do something definite ; then he may 
compute the perturbations of the second order by tising those known of the first order, or he may find it 
necessary to recompute the first order with the elements upon which the preliminary tables are based. And 
only then it will be necessary to calculate the perturbations by Saturn also. Our duty in our time with re- 
spect to the asteroids is, to avoid all superfluous work on them, and to get out as soon as possible such prehm- 
inary tables. Those asteroids which are of special interest, as, for instance, Leucothea and Euphrosyne for the 
determination of the mass of Jupiter, must of course be . treated in a different manner. For those it will be 
best to carry on the special perturbations by Saturn, Jupiter, Mars, Earth, and Venus for a number of years. 

A number of small terms and equations have been omitted, since six decimal places were found to be suffi- 
cient in the tables. If we denote the Arguments in the following manner. 



I = - 


— 


M' 


11 = 


M- 


■ M' 


111 = 


M— 


■SM' 


IV = 


M— 


■2M> 


v = 


■iM— 


■3M' 


VI = 


SM— 


■2M' 


VII = 


2M— 


■ M' 


VIII = - 


- M— 


■2M' 


IX = - 


- M— 


■ M' 


x = 


M— 


■AM' 


XT — 


M 




XII = 


3M— 


■ M' 


XIII — 


3M- 


■AM' 


XIV = - 


-2M— 


■ M' 


XV = 


AM— 


■ M' 



XVI = - 


- M- 


-3M' 


XXXI = 


5M- 


-AM 


xvn = 


AM- 


-3M' 


XXXII = 


3M— 


-8M' 


XVIII = 


5M- 


-2M' 


XXXIII = - 


-AM- 


■ M' 


XIX — 


3M- 


-1 M' 


XXXIV = 


1 M- 


■2M' 


XX = 


5M— 


■3M' 


XXXV = 


5M— 


■ 6 if' 


XXI = - 


-2M- 


■3M' 


XXXVI = 


6M- 


- M' 


XXII = 


M- 


-7M' 


xxxvn = 


AM- 


■5 if' 


xxm — 


M- 


-5 if' 


XXXVIII = 


AM- 


-7 if' 


XXIV = 


ZM- 


-5M' 


XXXIX = 


M- 


-8 if 


XXV = - 


-SM- 


■2M' 


XL = 


7M— 


-3 if' 


XXVI = 


M- 


-6M' 


XLI = - 


- M- 


-5 if' 


XXVII = 


2M- 


-7M' 


XLII = - 


- M — 


-7if 


iCXVIII = 


2M— 


■5M' 


XLIII = - 


- M- 


-4 if' 


XXIX = - 


-3M- 


- M' 


XLIV = 


5M~ 


-8 if' 


XXX — 


5M- 


- M' 


XLV = 


5M- 


-7 if' 



the perturbations are : — 



19 





& 


'ii 


1 


cos 


siu 


cos 


sin 


cos 


sin 1 


OM 


- 84.94« 




-1022.41* 




+ 


148.67* 






M 


- 4.74< 


+4279.97* 


-4154.40* 


- ■ 11.92* 


- 


448.23* 


+ 


493.85* 


2M 


+ 25.65« 


+1241.89* 


-1226.46* 


+ 24.98* 


- 


48.01* 


+ 


53.12* 


3M 


+ 8.30* 


+ 325.86* 


- 322.92* 


+ 8.27* 


- 


7.72* 


+ 


8.56* 


iM 


+ 2.50* 


+ 86.21* 


- 85.92* 


+ 2.37* 


- 


1.47* 


+ 


1.63* 


5M 


+ 0.68« 


+ 22.98* 


- 22.70* 




- 


0.31* 


+ 


0.34* 


6M 


+ 0.16< 


+ 6.19* 


- 6.02* 




- 


0.07* 


+ 


0.08* 


7M 




+ 1.31* 


- 1.37* 












I 


+ 7732.7 


- 671.7 


- 325.3 


- 7809.7 


+ 


428.1 


_ 


312.4 


21 


-19149.5 


+ 2127.3 


+ 2083.7 


+19003.2 


- 


428.6 


+ 


600.3 


31 


+ 5724.9 


+ 4.2 


- 15.3 


- 5630.2 


+ 


187.9 


- 


208.4 


41 


+ 1.4 


- 12.1 


- 22.6 


4.0 


+ 


27.9 


- 


21.9 


51 


- 47.7 


+ 7.9 


+ 4.1 


+ 46.9 


+ 


1.8 


+ 


1.3 


61 


+ 14-0 


2.3 


+ 2.1 


- 14.4 


- 


4.0 


- 


0.3 


71 


- 41.5 


+ 57.1 


+ 54.6 


+ 41.9 


- 


5.3 


- 


0.5 


81 


5.8 


8.3 


8A 


+ 6.1 


- 


0.5 






n 


- 1340.7 


- 82.3 


0.9 


- 1289.8 


_ 


554.6 


■ + 


231.6 


211 


+10930.4 


- 1159.0 


+ 1065.5 


+10367.5 


+ 


244.1 


- 


146.5 


sn 


- 3779.0 


+ 539.8 


- 523.1 


- 3638.3 


- 


69.4 


+ 


141.1 


4n 


- 294.8 


+ 40.7 


- 33.9 


- 250.5 


- 


2.5 


+ 


14.8 


5n 


+ 2.5 


+ 2.9 


+ 1.1 


+ 20.6 


+ 


0.6 


+ 


2.5 


611 


9.0 


0.3 


+ 1.9 


2.2 






+ 


0.9 


7n 


2.4 


0.3 


+ 1.3 


0.3 










in 


+ 9598.9 


- 2097.8 


- 1894.6 


- 9736.8 


+ 


145.1 


_ 


261.1 


am 


+ 166.8 


+ 64.2 


- 62.6 


- 66.6 


+ 


2.7 


- 


2.5 


IV 


- 8330.7 


+ 1305.0 


+ 754.2 


+ 9254.2 


+ 


525.7 


-, 


787.6 


2 IV 


+ 748.2 


- 120.8 


- 111.6 


- 32.3 


- 


131.7 


+ 


217.7 


3 IV 


- 153.2 


- 78.5 


+ 95.3 


- 77.5 


- 


14.6 


+ 


22.4 


4 IV 


- 12.4 


- 11.7 


+ 9.6 


- 14.1 


- 


0.4 


- 


0.4 


V 


- 5031.4 


- 17.9 


+ 509.0 


- 2272.5 


_ 


842.5 


+ 


1273.3 


2V 


- 37.1 


- 32.5 


+ 11.8 


- 87.9 


+ 


1.6 


— 


5.5 


VI 


+ 4932.9 


- 540.5 


+ 540.7 


+ 4849.2 


+ 


3.7 


- 


46.1 


2VI 


- 14.5 


+ 1.8 


1.8 


- 16.4 










Vil 


- 3739.2 


+ 227.2 


- 192.7 


- 3658.9 


- 


202.1 


- 


114.3 


2 VII 


+ 1507.9 


- 166.7 


+ 166.1 


+ 1497.3 


+ 


1.5 


- 


7.4 


3 VII 


- 80.4 


+ 13.6 


9.6 


- 56.7 


— 


0.7 


+ 


0.5 


vm 


- 3513.0 


+ 213.1 


+ 218.7 


+ 3500.3 


- 


72.0 


+ 


85.4 


2vin 


3.2 


+ 1.4 


+ 0.9 


+ 2.7 










IX 


+ 2208.5 


- 55.3 


- 72.4 


- 2188.4 


+ 


226.2 


- 


236.6 


2 IX 


- 778.1 


+ 36.1 


+ 36.1 


+ 779.4 


- 


9.2 


+ 


12.0 


3 IX 


+ 65.9 


+ 3.6 


+ 3.5 


- 66.1 


+ 


0.6 


- 


0.7 


4 IX 


1.1 






+ 1.1 










X 


+ 1826.7 


- 182.2 


- 135.1 


- 1854.9 


+ 


59.7 


- 


91.2 


2X 


+ 46.1 


+ 43.? 


+ 39.6 


- 43.5 


+ 


1.4 




0.7 



20 





51 


Vi 


Si 




COS 


sin 


cos 


sin 


cos 


sin 


OXI 


- 699.7 






+ 


75.5 




- 


202.6 






XI 


+ 1118.5 


_ 


5.6 


_ 


9.4 


+ 901.6 


+ 


129.9 


+ 


143.4 


2X1 


+ 463.6 


_ 


31.7 


+ 


28.9 


+ 433.4 


+ 


38.2 


+ 


42.2 


3X1 


+ 100.7 


_ 


15.4 


+ 


13.1 


+ 97.4 


+ 


5.2 


+ 


6.6 


4X1 


+ 23.3 


- 


5.2 


+ 


4.9 


+ 21.1 


+ 


0.8 


+ 


1.0 


5X1 


+ 5.8 


- 


1.5 


+ 


1.7 


+ 6.1 










xn 


- 1092.5 


+ 


72.3 


_ 


70.3 


- 1081.8 


- 


22.9 


- 


10.7 


2XTT 


+ 122.5 


- 


13.7 


+ 


12.7 


+ 112.6 










xnr 


- 833.4 


+ 


99.3 


_ 


1.6 


- 402.4 


- 


56.4 


+ 


90.2 


2 XIII 




- 


2.2 






- 4.0 










XIV 


+ 494.5 


+ 


26.8 


+ 


26.3 


- 491.7 


+ 


22.7 


- 


26.9 


2 XIV 


- 50.0 


+ 


1.9 


+ 


2.0 


+ 52.5 










XV 


- 300.6 


+ 


19.9 


_ 


19.6 


- 300.2 


- 


4.2 


- 


1.6 


2 XV 


+ 8.0 


- 


0.8 


+ 


0.9 


+ 7.7 










XVI 


+ 1128.7 


+ 


45.6 


+ 


42.7 


- 1120.9 


+ 


21.1 


- 


22.1 


XVII 


- 1034.5 


+ 


161.6 


- 


156.4 


- 1022.7 


- 


18.6 


+ 


16.8 


xvm 


•1- 428.2 


- 


47.6 


+ 


47.9 


+ 432.3 






- 


1.4 


XIX 


+ 290.3 


- 


153.9 


+ 


137.5 


+ 272.2 


- 


8.9 


+ 


17.8 


XX 


- 268.1 


+ 


43.2 


- 


42.6 


- 269.3 


- 


3.7 


+ 


3.0 


XXI 


+ 245.3 


+ 


13.5 


+ 


13.2 


- 263.7 


+ 


3.3 


- 


3.6 


XXII 


- 237.0 


+ 


146.4 


+ 


103.9 


+ 234.6 


- 


83.3 


- 


5.1 


XXIII 


- 222.1 


- 


13.4 


- 


15.2 


+ 218.3 


- 


11.5 


+ 


10.6 


XXIV 


+ 204.2 


- 


30.9 


- 


40.0 


+ 7.4 


+ 


20.9 


- 


39.4 


XXV 


- 192.0 


+ 


7.5 


+ 


7.8 


+ 192.5 


- 


1.7 


+ 


2.1 


XXVI 


+ 191.1 


+ 


141.0 


+ 


126.8 


- 187.8 


- 


1.4 


- 


2.7 


XXVII 


+ 162.0 


- 


86.7 


+ 


110.3 


- 238.0 


+ 


29.9 


- 


4.7 


XXVIII 


- 148.9 


+ 


21.4 


+ 


52.2 


+ 188.6 


+ 


13.8 


- 


9.1 


XXIX 


+ 122.3 


+ 


11.8 


+ 


11.8 


- 122.9 


+ 


4.2 


- 


4.5 


XXX 


- 79.0 


+ 


5.0 


- 


5.4 


- 84.8 










XXXI 


- 72.0 


+ 


10.1 


- 


8.1 


- 66.4 


- 


2.4 


+ 


0.9 


XXXII 


+ 44.0 


+ 


50.4 


- 


46.7 


+ 39.6 


- 


4.0 


+ 


0.9 


XXXIII 


+ 32.1 


+ 


3.7 


+ 


3.5 


- 32.4 


+ 


0.8 


- 


0.9 


XXXIV 


+ 30.7 


- 


3.5 


+ 


3.0 


+ 29.9 










XXXV 


- 25.6 


- 


3.1 


+ 


11.6 


1.8 


- 


1.7 


+ 


2.6 


XXXVI 


- 21.9 


+ 


1.3 


- 


1.1 


- 20.7 










XXXVII 


+ 20.8 


+ 


7.2 


+ 


20.2 


+ 113.3 


- 


5.5 


+ 


8.6 


XXXVIII 


- 20.6 


- 


30.8 


- + 


37.4 


0.0 


- 


2.5 


+ 


4.9 


XXXIX 


- 16.8 


- 


21.4 


- 


22.0 


+ 18.8 


+ 


15.5 


- 


1.0 


XL 


- 17.7 


+ 


3.1 


- 


3.0 


- 17.2 










XLI 


- 10.1 


+ 


1.9 


+ 


2.1 


+ 10.4 


- 


2.1 


+ 


0.2 


XLII 


9.4 


+ 


16.8 


+ 


15.9 


+ 9.2 


- 


1.9 


, 


0.0 


XLin 


- 8.9 


+ 


1.2 


+ 


1.2 


+ 9.3 


+ 


4.3 


- 


2.5 


XLIV 


7.7 


- 


3.0 


+ 


5.4 


2.0 










XLV 


2.3 


- 


11.4 


+ 


4.1 


- 17.7 




0.0 


- 


1.6 



Tables for the equation of the centre and the radius vector have been superseded by solving Keplek's 
problem in the manner I have shown in Vol. III. No. 53 of the Astronomical Journal, viz. : — If we sup- 
pose one of the radii vectores to turn uniformly about one of the foci, describing therefore the mean anomaly, 



21 

the other radius vector will then, in not very eccentric ellipses, describe nearly the true anomaly. This 
auxiliaxy anomaly, denoting with v', we have, simply, 

1 g 

cot J- »' = -— j— cot i M. 



The logarithm of the constant factor — j— is for Melpomene = 9.8078595, and log p = 0.3398226 for the 
computation of the radius vector by means of r = . " . 

The correction c, to be added to v' in order to get the true anomaly v, is given in Table II., with M as the 
argument. For the construction of this table I had c developed in the following series : — 



c = — 526.495 sin M 
+ 2282.957 sin 2 Jf 
-j- 819.532 sin 3 M 
-\- 245.033 sm 4 ilf 



c = -\- 68.825 sin 5 M 
+ 18.848 sin 6 M 
4- 5.096 sin 7 JIf 
-j- 1.395 sin 8 ilf 



: + 0.373 sin 9 M 
-\- 0.103 sin 10 M 
-j- 0.053 sin 11 M 



Example for compvting a Place from the Tahles. 
1861, Feb. 5^ 5" 58" 15' Washington M. T. = Feb. 5" 12" Berlin M. T. 
We write down on a scrap of paper the constants to be used. From Table V. the logarithms 



of 



log c 
9.337800 


9.807860 


logp 

0.339823 


cos (xi x) 
9.982068 


cos (y\ x) 
9.427362» 


cos (zi x) 

8.943100 


cos (xi y) 
9.449004 


cos (y\ y) 
9.966656 


cos (21 y) 
9.400622W 


cos (xi z) 
8.144356m 


cos (yi z) 
9.424948 


cos (zi z) 
9.984015 



and fi?om Table VI., 

A' 
105° 34' 42".6 



16" 53' 23".8. 



CI 
357° 0' 0".6 



log sin a 
9.998323 



log SIQ h 

9.985806 



log sin c 
9.425543 



Mz= mean anomaly, and t = time since 1854.0 are taken from Table I. 



M 



1861, 84 42 59.56 +7.00068 

Feb. 8 47 3.72 0.08488 

5 days 1 25 0.60 0.01369 

0.00057 



5 hours 


3 32.53 


58 minutes 


41.09 


15 seconds 


0.17 



94 59 17.67 +7.09982 



cotiM 


47 29 38.8 


9.962142 


i=^cot^ilf==cot^«' 


59 30 30.4 


9.770002 


v' 


119 1 0.8 




From Table 11. c - 


26 10.1 




V 


118 34 50.7 




cos V 




9.679789« 


e cos V 


—0.104133 


9.017589m 


1 + cos « 
r 


0.895867 


9.952243 
0.387580 



22 



Formation of the Arguments from Tahh III.* 





I. 


n. 


III. 


IV. 


V. 


VI. 


VII. 


VIII. 


IX. 


1861, 


237.828 


322.545 


78.202 


200.37 


162.92 


9.81 


47.26 


30.94 


153.11 


Feb. 


357.425 


6.209 


1.058 


3.63 


9.85 


21.20 


14.99 


346.07 


348.64 


5 days 


359.584 


1.001 


0.171 


0.59 


1.59 


3.42 


2.42 


357.75 


358.17 


6 hours 


359.979 


0.050 


0.008 


0.03 


0.08 


0.17 


0.12 


359.89 


359.91 



234.816 



329.805 



79.439 



204.62 



174.44 



34.60 



64.79 



14.65 



139.83 







XI. 


XII. 


xm. 


XIV. 


XV. 


XVI. 


xvn. 


xvin. 


1861, 


316.03 


84.72 


131.98 


125.46 


68.40 


216.7 


268.8 


332.4 


179.2 


Feb. 


358.48 


8.78 


23.78 


16.05 


339.85 


32.6 


343.5 


27.4 


38.8 


5 days 


359.76 


1.42 


3.84 


2.59 


356.75 


5.3 


357.3 


4.4 


6.3 


6 hours 


359.99 


0.07 


0.19 
159.79 


0.13 
144.23 


3.59.84 
44.84 


0.3 
254.9 


359.9 


0.2 


0.3 




314.26 


94.99 


249.5 


4.4 


224.6 





XIX. 


XX. 


XXI. 


xxn. 


XXlll. 


XXIV. 


XXV. 


XXVI. 


XXVII 


1861, 


118.9 


57.1 


184.1 


309.5 


193.9 


3.3 


221.5 


71.7 


34.2 


Feb. 


8.3 


36.2 


334.7 


350.8 


355.9 


13.5 


328.5 


353.3 


359.5 


5 days 


1.3 


5.8 


355.9 


358.5 


359.3 


2.2 


354.9 


358.9 


359.9 


6 hours 


0.1 


0.3 


359.8 


359.9 


0.0 


0.1 


359.8 


0.0 


0.0 




128.6 


99.4 


154.5 


298.7 


189.1 


19.1 


184.7 


63.9 


33.6 





XXVIII. 


XXIX. 


XXX. 


XXXI. 


XXXIl. 


xxxin. 


XXXIV. 


XXXV. 


XXX^ 


1861, 


278.6 


343.7 


301.4 


294.9 


356.8 


259.0 


348.7 


50.6 


26.1 


Feb. 


4.7 


331.1 


41.3 


33.6 


5.7 


322.3 


56.3 


28.5 


50.1 


5 days 


0.8 


355.3 


6.7 


5.4 


0.9 


353.9 


9.1 


4.6 


8.1 


6 hours 


0.0 


359.8 


0.3 


0.3 


0.1 


359.7 


0.5 


0.2 


0.4 




284.1 


309.9 


349.7 


334.2 


3.5 


214.9 


54.6 


83.9 


84.7 





XXXVII. 


xxxvrn. 


XXXIX. 


XL. 


XLI. 


XLH. 


xLin. 


XLIV. 


XLV 


1861, 


88.0 


203.7 


187 


226 


24 


140 


147 


166 


288 


Feb. 


22.3 


17.1 


348 


54 


338 


333 


341 


23 


26 


5 days 


3.6 


2.8 


358 


9 


357 


356 


357 


4 


4 


6 hours 


0.2 


0.1 
223.7 



173 




289 



359 



109 



125 



193 







114.1 


318 



With these Arguments the perturbations are computed from Table IV. 



* These Arguments being expressed in degrees and decimals, 360.0, 720.0, or 1080 0, must be subtracted when one of the sums 
I greater than one of those numbers. 



23 





h 


m 


fl 










+ 


_ 


+ 


- 


+ 


- 








Terms with t 


2608.5 




264.9 




502.0 




cos (a;i x) ii + 4820.0 






I 


1008.2 




2527.7 




95.0 




cos \yi x) III - 265.9 






II 


491.3 






397.8 




50.1 


cos (2:1 x) Ci + 49.0 






III 




43.5 




988.5 




21.9 


S + 4603.1 






IV 


753.4 






460.7 




8.8 








V 


497.6 






68.8 


96.4 




co3(xij/)|i + 1412.5 






VI 


375.1 




316.2 






2.3 


cos (j» y) VI + 920.2 






vu 




240.2 




232.2 




19.6 


cos (21 2;) ti - 140.4 






VIII 




334.7 


109.8 






4.8 


., + 2192.3 






IX 




185.2 




217.4 




33.9 








X 


136.1 




127.3 




10.8 




cos (n z) ii - 70.0 






XI 




119.6 


79.7 






12.0 


cos (^1 z) 1)1 + 264.3 






XII 


115.2 






37.1 


1.8 




cos (si z) Ci + 537.9 






XTTT 
XIV 


73.6 
37.1 






23.1 

27.5 


9.9 














0.3 


i + 732.2 


Reduction to the appar- 




XV 


5.1 




29.8 




0.3 




1 ti 


ent equinox. 




XVI 




43.8 


104.2 




1.4 




sin (A' + w) 224 9 33.3 9.843018„ 


/+20.03 




xvn 




101.9 




23.5 




1.7 


r sin a 0.385903 




xvni 

XIX 




27.2 
30.1 


12.7 


33.8 


0.1 
1.9 




X 0.228921,, 


9 , 0.9765 
G338 24 




sin (B' + v) 135 28 14.5 9.845888 




XX 


8.7 






25.8 


0.3 




r sin i 0.373386 


sin (G+ a') 111 9 9.9697 




XXI 
X Xll 




21.7 
24.2 




12.3 
15.6 




0.5 
3.6 


y 0.219274 


tan 3' 9.3529 




+ 1.99 0.2991 




sin (C + u) 115 34 51.3 9.955195 




XXIII 


22.1 






2.0 


1.0 




r sin c 9.813123 


J a! +22.22 




XXIV 
XXV 


18.3 
19.1 






3.5 
2.5 


0.7 
0.1 




z 9.768318 


cos(G + a) 9.5573„ 








XXVI 


21.2 






11.3 




0.3 


y +1.656815 


/1 3'- 3.42 0.5338„ 




xxvn 


8.7 






3.9 


2.2 




7, + 2192 






xxvin 




5.7 




17.0 


1.2 




Y -0.614699 






XXIX 


7.0 




10.2 




0.6 




^cosJ'sina' +1.044308 0.018828 






XXX 




7.9 


0.9 








X -1.694031 






XXXI 




6.9 


2.0 






0.3 


1 + 4603 






XXXII 


4.6 






4.4 




0.4 


X +0.723955 






XXXIII 




2.8 


1.6 








^cos^'cosa' -0.965473 9.984740„ 






XXXTV 


1.5 




2.6 














XXXV 


0.6 


0.1 






sin a' ^ , ,, 9.865861 


1 II 




XXXVI 




0.1 




2.1 






tan a' 132 45 13.3 0.034088„ 


a = 132 45 35.5 




XXXVII 
XXXVIII 


3.6 


0.2 


9.5 


2.7 


1.0 


0.1 








z +0.586568 




XXXTX 


1.5 




2.4 






1.5 


? + 732 






XL 




0.9 


1.5 








Z -0.266747 






XLI 




1.0 


0.2 






0.2 


J sin di +0.320553 9.505900 






XLII 


1.9 




0.3 








// cos 31 0.152967 






XLin 


0.6 




0.7 






0.4 


cos 3' ^ ,r„ 9.989240 






XLIV 


0.8 






0.5 






tan ii +12 42 5.8 9.352933 


3 = +12 42 3.4 




XLV 


0.6 




1.5 




0.1 




J 0.163727 








6221.4 


1198.2 


3607.7 


2614.1 


720.8 


162.7 




h, Vn ?i 


+ 5023.2 




+ 993.6 




+ 558.1 




0' and 3' are referred to the mean 






L 


3.700980 




2.997212 




2.746712 




equinox 1861.0. 






My compu 


tations fo 


r 1861, 1 


mth the o 


sculatii 


ig elemen 


ts for 1854.0 and the special perturbations 


by Jupiter and Saturn, give 




for the same 


time: — 








a = 

J3 


= 132° 4^ 33.3 

= + 12 42 2.0 

2.2 

1.4 







24 

By this close agreement between the two different computations, the correctness of the tables is satisfactorily 
proved. 

For the computation of an exact opposition ephemeris, it will be necessary only to compute the perturbations 
from 16 to 16 days from the tables, and then to interpolate them twice in the middle, in order to get them 
from 4 to 4 days, with which interval such ephemerides are commonly calculated. For an approximate 
ephemeris for the whole year, the terms multipUed with the time and the first four equations will be suffi- 
cient, and also a direct computation of the perturbations only from 40 to 40 days, with afterwards two 
interpolations in the middle, if the ephemeris is to be computed from 10 to 10 days. 



25 







TABLE I. 








FOE THE MEAN ANOMALY." 






The times are referred to the meridian of Washington. 




Years. 


M 


t 


Years. 


M 


t 


1852 B 


1 II 

233 17 25.88 


- 1.99863 


1877 


300 42 39.50 


+23.00068 


1853 


336 43 9.59 


- 0.99932 . 


1878 


44 8 23.22 


24.00000 


1854 


80 8 53.31 


0.00000 


1879 


147 34 6.93 


24.99932 


1855 


183 34 37.03 


+ 0.99932 


1880 B 


251 16 50.77 


26.00137 


1856 B 


287 17 20.86 


2.00137 


1881 


354 42 34.48 


27.00068 


1857 


30 43 4.58 


3.00068 


1882 


98 8 18.20 


28.00000 


1858 


134 8 48.29 


4.00000 


1883 


201 34 1.92 


28.99932 


1859 


237 34 32.01 


4.99932 


1884 B 


305 16 45.75 


30.00137 


1860 B 


341 17 15.85 


6.00137 


1885 


48 42 29.47 


31.00068 


1861 


84 42 59.56 


7.00068 


1886 


152 8 13.18 


32.00000 


1862 


188 8 43.38 


8.00000 


1887 


255 33 56.90 


32.99932 


1863 


291 34 26.99 


8.99932 


1888 B 


359 16 40.74 


34.00137 


1864 B 


35 17 10.83 


10.00137 


1889 


102 42 24.45 


35.00068 


1865 


138 42 54.55 


11.00068 


1890 


206 8 8.17 


36.00000 


1866 


242 8 38.26 


12.00000 


1891 


309 33 51.88 


36.99932 


1867 


345 34 21.98 


12.99932 


1802 B 


53 16 35.72 


38.00137 


1868 B 


89 17 5.81 


14.00137 


1893 


156 42 19.44 


39.00068 


1869 


192 42 49.53 


15.00068 


1894 


260 8 3.15 


40.00000 


1870 


296 8 33.25 


16.00000 


1895 


3 33 46.87 


40.99932 


1871 


39 34 16.96 


16.99932 


1896 B 


107 16 30.70 


42.00137 


1872 B 


143 17 0.80 


18.00137 


1897 


210 42 14.42 


43.00068 


1873 


246 42 44.51 


19.00068 


1898 


314 7 58.14 


44.00000 


1874 


350 8 28.23 


20.00000 


1899 


57 33 41.85 


44.99932 


1875 


93 34 11.95 


20.99932 


1900 B 


161 16 25.69 


+46.00137 


1876 B 


197 16 55.78 


+22.00137 








Months. 


M 


t 


Days. 


M 


t 


January 


1 II 

0.00 


+0.00000 


1 


O 1 n 

17 0.12 


+0.00274 


February 


8 47 3.72 


0.08488 


2 


34' 0.24 


0.00548 


March 


16 43 7.08 


0.16154 


3 


51 0.36 


0.00821 


April 


25 30 10.78 


0.24642 


4 


1 8 0.48 


0.01095 


May 


34 14.38 


0.32856 


5 


1 25 0.60 


0.01369 


June 


42 47 18.10 


0.41344 


6 


1 42 0.72 


0.01643 


July 


51 17 21.68 


0.49558 


7 


1 59 0.84 


0.01917 


August 


60 4 25.40 


0.58046 


8 


2 16 0.96 


0.02190 


S6ptember 


68 51 29.12 


0.66534 


S 9 


2 33 1.08 


0.02464 


October 


77 21 32.72 


0.74748 ' 


10 


2 50 1.20 


• 0.02738 


November 


86 8 36.44 


0.83236 


20 


5 40 2.40 


0.05476 


December 


94 38 40.04 


+0.91450 


30 


8 30 3.60 


+0.08214 





In Bissextile Years on 


3 day must be subtracted from the date in the first two mont 


hs. 



26 







TABLE I. — Concluded. 






• 


FOR THE MEAN ANOMALY. 






The times are referred to the meridian of Washington. 




Houi-s. 


M 


t 


Hours. 


M 


t 


1 


1 II 
42.51 


+0.00011 


13 


1 II 
9 12.57 


+0.00149 


2 


1 25.01 


0.00023 


14 


9 55.07 


0.00160 


3 


2 7.52 


0.00034 


15 


10 37.58 


0.00172 


4 


2 50.02 


0.00046 


16 


ir 20.08 


0.00183 


5 


3 32.53 


0.00057 


17 


12 2.59 


0.00195 


6 


4 15.03 


0.00069 


18 


12 45.09 


0.00206 


7 


4 57.54 


0.00080 


19 


13 27.60 


0.00218 


8 


5 40.04 


0.00092 


"20 


14 10.10 


0.00229 


9 


6 22.55 


0.00103 


21 


14 52.61 


0.00241 


10 


7 5.05 


0.00114 


22 


15 35.11 


0.00252 


11 


7 47.56 


0.00126 


23 


16 17.62 


0.00264 


13 


8 30.06 


+0.00137 


24 


17 0.12 


+0.00275 




M 




1 


For Minutes. 


For Seconds. 


For Minutes. 


For Seconds. 


1 


0.71 


If 
0.01 


31 


2l!96 


0.36 


2 


1.42 


0.02 


32 


22.67 


0.37 


3 


2.13 


0.03 


33 


23.38 


' 0.39 


4 


2.83 


0.05 


34 


24.09 


0.40 


5 


3.54 


0.06 


^5 


24.80 


0.41 


6 


4.25 


0.07 


36 


25.50 


0.42 


7 


4.96 


0.08 


37 


26.21 


0.44 


8 


5.67 


0.09 


38 


26.92 


0.45 


9 


6.38 


0.11 


39 


27.63 


0.46 


10 


7.08 


0.12 


40 


28.34 


0.47 


11 


7.79 


0.13 


41 


29.05 


0.48 


12 


8.50 


0.14 


42 


29.76 


0.50 


13 


9.21 


0.15 


43 


30.47 


0.51 


14 


9.91 


0.16 


44 


31.17 


0.52 


15 


10.62 


0.17 


45 


31.88 


0.53 


16 


11.33 


0.19 


46 


32.59 


0.54 


17 


12.04 


0.20 


47 


33.29 


0.55 


18 


12.75 


0.21 


48 


34.00 


0.57 


19 


13.46 


0.22 


49 


34.71 


0.58 


20 


14.17 


0.23 


50 


35.42 


0.59 


21 


14.88 


0.25 


51 


36.12 


0.60 


22 


15.58 


0.26 


52 


36.83 


0.61 


23 


16.29 


0.27 


53 


37.54 


0.62 


24 


17.00 


0.28 


54 


38.25 


0.64 


25 


17.71 


0.29 


55 


38.96 


0.65 


26 


18.42 


0.31 


56 


39.67 


0.66 


27 


19.13 


0.32 


57 


40.38 


0.67 


28 


19.84 


0.33 


58 


41.09 


0.68 


29 


20.54 


0.34 


59 


41.80 


0.70 


30 


21.25 


0.35 


60 


42.51 


0.71 





27 











TABLE 11 














FOR THE CORRECTION 


C TO BE ADDED TO THE AUXILIARY ANOMALY v'. 






Argument = ilif. For Af > 180° the Argument 


is 360°- 


- M, and the sign of c to be reversed. 






Arg. 


c 


Diff. 


Arg. 


c 


Diif. 


Arg. 


c 


Diff. 


Arg. 


c 


Diff 




o 


1 M 


u 





1 II 


It 


o 


1 II 


11 





1 11 


II 




0.0 


0.00 




22.5 


+40 58.26 




45-0 


+39 29.45 




67.5 


+ 8 45.17 






.5 


+ 1 8.81 


+68.81 


23.0 


41 26.80 


+28.64 


.5 


39 0.24 


-29-21 


68.0 


7 59.33 


-45-84 




1.0 


2 17.58 


68.77 


.5 


41 53.88 


27-08 


46.0 


38 30.16 


30.08 


.5 


7 13.57 


46-76 




.5 


3 26.26 


68.68 


24.0 


42 19.51 


25-63 


.5 


37 59.23 


30-93 


69.0 


6 27.90 


46-67 




2.0 


4 34.79 


68.63 


.5 


42 43.66 


24-16 


• 47.0 


37 27.48 


31-76 


.5 


5 42.35 


46-55 




.5 


5 43.14 


68.36 


25.0 


43 6.35 


22-69 


.5 


36 54.93 


32-55 


70.0 


4 56-93 


45-42 




3.0 


6 51.27 


68.13 


.5 


43 27.56 


21-21 


48.0 


36 21.61 


33-32 


.5 


4 11-65 


45-28 




.5 


7 59.10 


67.83 


26.0 


43 47.30 


19-74 


.5 


35 47.54 


34-07 


71.0 


3 26-53 


46-13 




4.0 


9 6.61 


67.61 


.5 


44 5.57 


18-37 


49.0 


35 12.75 


84-79 


.5 


2 41-58 


44-95 




.5 


10 13.75 


67.14 
66.72 


27.0 


44 22.37 


16-80 
16-33 


.5 


34 37.25 


36-60 
36-18 


72.0 


1 56-82 


44-76 
44.57 




5.0 


+11 20.47 




.5 


+44 37.69 




50.0 


+34 1.07 




.5 


+ 1 12-25 






.5 


12 26.74 


+66.27 


28.0 


44 51.56 


+13-87 


.5 


33 24.25 


-36-82 


73.0 


+ 27.90 


-44.36 




6.0 


13 32.50 


66.76 


.5 


45 3.96 


12-40 


51.0 


32 46.80 


37-46 


.5 


- 16.23 


44-13 




.5 


14 37.71 


66.31 


29.0 


45 14.90 


10-94 


.5 


32 8.74 


38-06 


•74-0 


1 0.13 


43.90 




7.0 


15 42.33 


64-62 


' .5 


45 24.40 


9-50 


52.0 


31 30.10 


38-64 


.5 


1 43.78 


43-66 




.5 


16 46.31 


63.98 


30.0 


45 32.46 


8-06 


.5 


30 50.90 


39-20 


75.0 


2 27.17 


43-39 




8.0 


17 49.61 


63.30 


.5 


45 39.07 


6-61 


• 53.0 


30 11.17 


39-73 


.5 


3 10.29 


43-12 




.5 


18 52.21) 


62-59 


31.0 


45 44.27 


6-30 


.5 


29 30.93 


40-24 


76.0 


3 53.12 


43-83 




9.0 


19 54.04 


61-84 


.5 


45 48.04 


3-77 


54.0 


28 50.19 


40-74 


.5 


4 35.67 


43-55 




.5 


2a 55.08 


61-04 
60-20 


32.0 


45 50.40 


3-36 
+ 0-98 


.5 


28 8.99 


41-20 
41-63 


77.0 


5 17.91 


43-24 
41-98 




10.0 


+21 55.28 




.5 


+45 51.38 




55.0 


+27 27.36 




.5 


- 5 59.84 






.5 


22 54.61 


+59-33 


33.0 


45 50.97 


- 0-41 


.5 


26 45.30 


-42-06 


78.0 


6 41.45 


-41-61 




11.0 


23 53.03 


68-42 


.5 


45 49.19 


1-78 


56.0 


26 2.84 


42-46 


.5 


7 22.73 


41-38 




.5 


24 50.51 


57-48 


34.0 


45 46.05 


3-14 


.5 


25 20.01 


42-83 


79.0 


8 3.66 


40-93 




12.0 


25 47.02 


56-61 


.5 


45 41.57 


4-48 


57.0 


24 36.82 


43-19 


.5 


8 44-24 


40-68 




.5 


26 42.51 


65-49 


35.0 


45 35.76 


6-81 


.5 


23 53.31 


43-51 


80.0 


9 24-46 


-40 -S3 




13.0 
.5 


27 36.96 

28 30.33 


64-45 
53-37 


.5 
36.0 


45 28.65 
45 20.23 


7-11 

8-42 


58.0 
.5 


23 9.48 
22 25.37 


43-63 
44-11 


.5 

81.0 


10 4-31 
10 43-79 


39-85 
39-48 




14.0 


29 22.60 


52-27 


.5 


45 10.53 


9-70 


59.0 


21 40.99 


44-38 


.5 


11 22.88 


39-09 




.5 


30 13.73 


61-13 
49-97 


37.0 


44 59.58 


10-95 
12-19 


.5 


20 56-37 


44-62 
44-85 


82.0 


12 1.57 


33-69 
38-30 




15.0 


+31 3.70 




.5 


+44 47.39 




60.0 


+20 11.52 




.5 


-12 39.87 






.5 


31 52.48 


+48-78 


38.0 


44 33.97 


-13-42 


.5 


19 26.47 


-45-05 


83.0 


13 17.76 


—37-89 
37-47 
37-06 
30-63 
36-19 
35-75 
36-31 
34-86 




16.0 


32 40.04 


47-56 


.5 


44 19.35 


14.62 


61.0 


18 41.24 


45-23 


.5 


13 55.23 




.5 

17.0 


33 26.36 

34 11.42 


46-32 
45-06 


39.0 
.5 


44 3.55 
43 46.58 


15.80 
16.97 


.5 
62.0 


17 55.84 
17 10.30 


45-40 
46-54 


84.0 
.5 


14 32.29 

15 8.92 




.5 

18.0 


34 55.19 

35 37.66 


43-77 

42-47 


40.0 
.5 


43 28.48 
43 9.25 


18-10 
19-23 


.5 
63.0 


16 24.63 
15 38.86 


46-67 
46-77 


85.0 
.5 


15 45.11 

16 20.86 




.5 


36 18.80 


41-14 


41.0 


42 48.93 


20-32 


.5 


14 53.01 


46-85 
46-93 
45.97 


86.0 


16 56.17 




19.0 


36 58.60 


39-80 


.5 


42 27.52 


21-41 


64.0 


14 7.08 


.5 


17 31.03 


34-40 




.5 


37 37.03 


38-43 


42.0 


42 5.07 


22-45 


.5 


13 21.11 


87.0 


18 5.43 










37-05 






23-49 






46-01 






33-94 




20.0 


+38 14.08 




.5 


+41 41.58 




65.0 


+12 35.10 


-46.03 


.5 


-18 39.37 


—33-48 




.5 


38 49.75 


+35-67 


43.0 


41 17.08 


-24-60 


.5 


11 49.07 


88.0 


19 12.85 


33-00 




21.0 


39 24.01 


34-26 


.5 


40 51.60 


25-48 


€6.0 


11 3.05 


46.02 


.5 


19 45.85 


83-53 




.5 


39 56.85 


32-84 


44.0 


40 25.15 


26-45 


.5 


10 17.05 


46-00 

46-97 

-46.91 


89.0 


20 18.38 


33-04 




22.0 
.5 


40 23.27 
+40 58.26 


81-42 
+29.99 


.5 

45.0 


39 57.76 
+39 29.45 


27-39 
-38-31 


67.0 
.5 


9 31.08 
+ 8 45.17 


.5 
90.0 


20 50.42 
-21 21.98 


-31-66 





28 



TABLE II.— Concluded. 
FOR THE CORRECTION c TO BE ADDED TO THE AUXILIARY ANOMALY v'. 

Argument = M. For Jlf > 180° the Argument is 360° — M, and the sign of c to be reversed. 



Arg. 



90.0 

.5 
91.0 

.5 
92.0 

.5 
93.0 

.5 
94.0 

.5 

95.0 

.5 
96.0 

.5 
97.0 

.5 
98.0 

.5 
99.0 

.5 

100.0 
.5 

101.0 
.5 

102.0 

;5 

103.0 
.5 

104.0 
.5 

105.0 
.5 

106.0 
.5 

lor.o 

.5 
108.0 

.5 
109.0 

.5 

110.0 
.5 

111.0 
.5 

112.0 
.5 



-21 21.98 

21 53.05 
28 23.63 

22 53.72 

23 23.31 

23 52.40 

24 20.98 

24 49.05 

25 16.62 

25 43.67 

-26 10.21 

26 36.24 

27 1.75 

27 26.74 

27 51.20 

28 15.14 

28 38.56 

29 1.45 
29 23.82 

29 45.66 

-30 6.98 

30 27.77 

30 48.03 

31 7.76 
31 26.97 

31 45.64 

32 3.79 
32 21.41 
32 38.50 

32 55.06 

-33 11.10 

33 26.61 
33 41.59 

33 56.05 

34 9.99 
34 23.40 
34. 36.30 

34 48.68 

35 0.54 
35 11.88 

-35 22.71 
35 33.02 
35 42.82 

35 52.10 

36 0.88 
-36 9.15 



Diff. 



-31.07 
30-58 
30.09 
29-69 
39-09 
2B.58 
28,07 
27-57 
27-05 

26-54 

-26-03 
25-51 
24-99 
24-46 
23.94 
23-43 
22-69 
22-37 
21-84 

21-32 

-20-79 
20-26 
19-73 
19-21 
18-67 
18-15 
17-62 
17-09 
16-56 

16-04 

-15-61 
14-98 
14-46 
13-94 
13-41 
12-90 
12-38 
11-86 
11-34 

10-83 

-10-31 
9-80 
9-28 
8-78 

- 8-27 



Arg. 



112-5 

113-0 

.5 

114.0 
.5 

115.0. 
.5 

116.0 
.5 

117.0 

.5 

118.0 

.5 

119.0 

.5 

120.0 

.5 

121.0 

' .5 

122.0 

.5 
123.0 

.5 
124.0 

.5 
125.0 

.5 
126.0 

.5 
127.0 

.5 
128.0 

.5 
129.0 

.5 
130.0 

.5 
131.0 

.5 
132.0 

.5 
133-0 

-5 
134.0 

.5 
135.0 



-36 9.15 
36 16.91 
36 24.18 
36 30.94 
36 37.20 
36 42.97 
36 48.25 
36 53.03 

36 57.33 

37 1.14 

-37 4.46 
37 7.31 
37 9.67 
37 11.55 
37 12-97 
37 13-91 
37 14.38 
37 14-39 
37 13.93 
37 13.01 

-37 11.64 
37 9.81 
37 7.53 
37 4.81 
37 1.64 
36 58.04 
36 54.00 
36 49.53 
36 44.63 
36 39.31 

-36 33.57 
36 27.41 
36 20.83 
36 13.84 
36 6.44 
35 58.63 
35 50.41 
35 41.80 
35 32.79 
35 23.39 

-35 13.60 

35 3.43 

34 52.87 

34 41.94 

34 30.64 

-34 18.97 



Diff. 



- 7-76 
7-27 
6-76 
6 26 
6-77 
6.28 
4-78 
4-30 
3-81 

3-32 

- 2-85 
2-36 
1-88 
1-42 
0-94 
0-47 

- 0-01 
+ 0-46 

0-92 

1-37 

+ 1-S3 
2.28 
2-72 
3-17 
3-60 
4-04 
4-47 
4-90 
6-32 

6-74 

+ 6-16 
6-58 
6-99 
7-40 
7-81 
8-22 
8-61 
9.01 
9-40 

9-79 

+10-17 
10-66 
10-93 
11-30 

+11-67 



Arg. 



135.0 

.5 
136.0 

.5 
137.0 

.5 
138.0 

.5 
139.0 

.5 

140.0 

.5 
141-0 

-5 
142.0 

.5 
143.0 

.5 
144.0 

.5 

145.0 

-5 
146-0 

.5 
147.0 

.5 
148-0 

.5 
149.0 

.5 

150.0 

.5 
151.0 

.5 
152.0 

.5 
153.0 

.5 
164.0 

.5 

155.0 
.5 

156.0 
.5 

157.0 
.5 



-34 18.97 
34 6.94 
33 54.55 
33 41.80 
33 28.70 
33 15.25 
33 1.46 
32 47.32 
32 32.85 
32 18.04 

-32 2.90 
31 47.44 
31 31.65 
31 15.55 
30 59.13 
30 42.41 
30 25.37 
30 8.04 
29 50.41 
29 32.48 

-29 14.26 
28 55.75 
28 36-96 
28 17-89 
27 58-54 
27 36.93 
27 19-05 
26 58.91 
26 38-51 
26 17-86 

-25 56.96 
25 35.81 
25 14.41 
24 52.78 
24 30.92 
24 8.83 
23 46-51 
23 23-98 
23 1.23 
22 38.27 

-22 15.10 
21 51.72 
21 28.14 
21 4.36 
20 40.38 

-20 16.21 



Diff. 



+12-03 
12-39 
12-75 
13-10 
13-46 
13-79 
14.14 
14-47 
14-81 

16-14 

+J5-46 
15-79 
16-10 
16-42 
16-72 
17-04 
17-33 
17-63 
17-93 

18-22 

+16-51 
18-79 
19-07 
19-35 
19-61 
19-88 
20-14 
20-40 
20-66 

20-90 

+21.16 
21.40 
21.63 
21.86 
32-09 
22-32 
22-63 
22-76 
32-96 

23.17 

+33-38 
33-68 
33-78 
33-98 

+34-17 



Arg- 



157.5 
158.0 

.5 
159.0 

.5 
160.0 

.5 
161.0 

.5 
162.0 

.5 
163.0 

.5 
164.0 

.5 
165.0 

.5 
166.0 

.5 
167.0 

■ .5 

168.0 

.5 
169.0 

.5 
170.0 

.5 
171.0 

.5 
172.0 

.5 
173.0 

.5 
174.0 

.5 
175.0 

.5 
176.0 

.5 
177.0 

.5 

178.0 
.5 

179.0 
.5 

180.0 



-20 16.21 

19 51.85 
19 27.32 
19 2.61 
18 37.73 
18 12-68 
17 47.47 
17 22-10 
16 56.58 
16 30.90 

-16 5.08 
15 39.11 
15 13.00 
14 46.76 
14 20.38 
13 53.88 
13 27.25 
13 0.5] 
12 33.65 
12 6-68 

-11 39-61 

11 12.43 

10 45.15 

10 17-78 

9 50.32 

9 22.77 

8 55.14 

8 27.43 

7 59.64 

7 31.79 

- 7 3.87 
6 35.89 
6 7.65 
5 39.76 
5 11.62 
4 43-44 
4 15-21 
3 46.94 
3 18.65 
2 50.32 

- 2 21.97 
1 53.60 
1 25.21 
56.81 

- 28.41 
0.00 



Diff 



+24.36 
24.53 
24-71 
34-68 
35.05 
35.21 
36.37 
36.62 
26.68 

25-82 

+26-97 
26-11 
26-24 
26.38 
26.60 
36-63 
36-74 
36-86 
26-97 

37-07 

+37-18 
37-28 
37-37 
37-46 
27-55 
27-63 
27-71 
37.79 
37.86 

27.92 

+27-98 
38-04 
38-09 
28-14 
28-18 
28-23 
28.27 
38.39 
36.33 

3S.35 

+38.37 
38.39 
38.40 
38.40 

+28.41 



29 











TABLE III. 
















FOE 


THE ARGUMENTS. 










A. 


For the different Years. 


The times are referred to the meridian of Washington. 




Tears. 


I. 


11. 


III. 


IV. 


V. 


VI. 


VII. 


VIII. 


IX. 




O 


o 


o 


O 


o 








O 


o 


1852 B 


150.924 


24.214 


326.061 


175.14 


199.35 


281.72 


257.50 


68.56 


277.63 


1853 


120..598 


97.317 


338.513 


217.92 


315.23 


171.35 


74.04 


264.48 


143.88 


1854 


90.273 


170.420 


350.966 


260.69 


71.11 


60.99 


250..57 


100.40 


10.12 


1855 


59.947 


243.524 


3.418 


303.47 


187.00 


310.63 


67.10 


296.32 


236.37 


1856 S 


29.539 


316.828 


15.905 


346.37 


303.19 


200.94 


244.12 


131.79 


102.25 


1857 


359.213 


29.931 


28.357 


29.14 


59.07 


90.58 


60.65 


327.71 


328.50 


1858 


328.868 


103.035 


40.810 


71.92 


174.96 


340.22 


237.18 


163.63 


194.74 


1859 


298.562 


176.138 


53.263 


114.70 


290.84 


229.85 


53.71 


359.55 


60.99 


1860 B 


268.154 


249.442 


65.749 


157.59 


47.04 


120.17 


230.73 


195.02 


266.67 


1861 


237.828 


322.545 


78.202 


200.37 


162.92 


9.81 


47.26 


30.94 


153.11 


1862 


207.503 


35.648 


90.654 


243.15 


278.60 


259.44 


223.79 


226.86 


19.36 


1863 


177.178 


108.752 


103.108 


285.93 


34.68 


149.08 


40.33 


62.78 


245.60 


1864 B 


146.769 


182.056 


115.594 


328.62 


150.88 


39.40 


217.34 


256.25 


111.46 


1865 


116.444 


255.159 


128.047 


11.60 


266.76 


269.03 . 


33.67 


94.17 


337.73 


1866 


86.119 


328.263 


140.500 


54.38 


22.64 


178.67 


210.41 


290.09 


203.97 


1867 


55.793 


41.366 


152.953 


97.16 


138.53 


68.30 


26.94 


126.01 


70.22 


1868 B 


25.385 


114.670 


165.440 


140.05 


254.72 


318.62 


203.95 


321.48 


296.10 


1869 


355.060 


197.774 


177.893 


162.83 


10.62 


208.26 


20.49 


157.41 


162.35 


1870 


324.734 


260.877 


190.346 


225.61 


126.49 


97.90 


197.02 


353.33 


28.59 


1871 


294.409 


333.981 


202.799 


268.39 


242.37 


347.53 


13.55 


189.25 


254.84 


1872 B 


264.001 


47.284 


215.236 


311.29 


358.57 


237.85 


190.57 


24.72 


120.72 


1873 


233.676 


120.388 


227.740 


354.06 


114.45 


127.49 


7.10 


220.64 


346.96 


1874 


203.350 


193.492 


240.192 


36.84 


230.33 


17.12 


183.63 


56.56 


213.21 


1875 


173.025 


266.595 


252.646 


79.62 


346.22 


266.76 


0.17 


252.48 


79.46 


1876 B 


142.617 


339.899 


265.134 


122.52 


102.42 


157.08 


177.18 


87.95 


305.34 


1877 


112.292 


53.003 


277.586 


165.29 


218.30 


46.72 


353.71 


283.67 


171.58 


1878 


81.967 


126.107 


290.040 


208.07 


334.18 


296.35 


170.25 


119.80 


37.84 


1879 


51.642 


199.210 


302.494 


250.85 


90.06 


185.99 


346.78 


315.71 


264.07 


1880 B 


21.234 


272.514 


314.981 


293.74 


206.26 


76.30 


163.80 


151.19 


129.95 


1881 


350.908 


345.618 


327.434 


336.53 


322.14 


325.95 


340.33 


347.11 


356.20 


1882 


320.583 


58.721 


■ 339.887 


19.30 


78.02 


215.58 


156.86 


163.03 


222.44 


1883 


290.258 


131.825 


352.340 


62.08 


193.91 


105.22 


333.39 


18.95 


88.69 


1884 B 


259.849 


205.129 


4.827 


104.98 


310.11 


355.54 


150.41 


214.42 


314.57 


1885 


229.524 


278.232 


17.280 


147.76 


65.99 


245.17 


326.94 


50.34 


160.82 


1886 


199.198 


351.335 


29.732 


190.53 


181.67 


134.81 


143.47 


246.26 


47.06 


1887 


168.873 


64.439 


42.185 


233.31 


297.75 


24.44 


320.00 


82.16 


273.31 


1888 B 


138.465 


137.743 


54.672 


276.21 


53.95 


274.76 


137.02 


277.65 


139.19 


1889 


108.139 


210.846 


67.125 


318.98 


169.83 


164.40 


313.55 


113.58 


5.43 


1890 


77.814 


283.950 


79.578 


1.76 


285.71 


54.03 


130.09 


309.49 


231.68 


1891 


47.489 


357.053 


92.031 


44.54 


41.59 


303.67 


306.62 


145.41 


97.92 


1892 B 


17.080 


70.357 


104.517 


87.44 


157.79 


193.99 


123.63 


340.86 


323.60 


1893 


346.755 


143.460 


116.970 


130.23 


273.68 


83.63 


300.17 


176.61 


190.05- 


1894 


316.430 


216.564 


129.423 


172.99 


29.56 


333.26 


116.70 


12.73 


56.30 


1895 


286.104 


289.667 


141.876 


215.77 


145.44 


222.90 


293.23 


206.65 


282.54 


1896 B 


255.696 


2.971 


154.363 


258.67 


261.64 


113.22 


110.25 


44.12 


148.42 


1897 


225.371 


76.075 


166.816 


301.49 


17.52 


2.85 


286.78 


240.04 


14.67 


1898 


195.045 


149.178 


179.268 


344.22 


133.30 


252.49 


103.31 


75.96 


240.91 


1899 


164.720 


222.282 


191.721 


27.00 


249.28 


142.12 


279.84 


271.66 


107.16 


1900 B 


.134.311 


295.585 


204.208 


69.90 


5.48 


32.44 


96.86 


107.35 


333.04 



30 



TABLE III.— Continued. 

FOR THE ARGUMENTS. 

A. For the different Years. The times are referred to the meridian of Washington. 



Years. 



X. 



1852 B 

1853 

1854 

1855 

1856 B 

1857 

1858 

1859 

1860 B 

1861 

1862 

1863 

1864 B 

1865 

1866 

1867 

1868 B 

1869 

1870 

1871 

1872 B 

1873 

1874 

1875 

1876 b 

1877 

1878 

1879 

1880 B 

1881 

1882 

1883 

1884 B 

1885 

1886 

1887 

1888 B 

1889 

1890 

1891 

1892 B 

1893 

1894 

1895 

1896 B 

1897 

1898 

1899 

1900 B 



116.98 

99.11 

81.24 

63.37 

45.44 

27.57 

9.70 

351.82 

333.90 

316.03 

298.16 

280.29 

262.36 

244.49 

226.62 

208.75 

190.82 

172.95 

155.08 

137.21 

119.29 

101.42 

83.54 

65.67 

47.75 

29.88 

12.01 

354.13 

336.21 

318.34 

300.47 

282.60 

264.68 

246.80 

228.93 

211.06 

193.14 

175.26 

157.39 

139.52 

121.60 

103.73 

85.85 

67.98 

50.06 

32.19 

14.31 

356.44 

338.52 



XI. 



233.29 
336.72 

80.15 
183.58 
287.29 

30.72 
134.15 
237.58 
341.29 

84.72 
188.15 
291.57 

35.29 
138.72 
242.14 
345.57 

89.29 
192.71 
296.14 

39.57 
143.28 
246.71 
350.14 

93.57 
197.28 
300.71 

44.14 
147.57 
251.23 
354.71 

98.14 
201.57 
305.28 

48.71 
1.52.14 
255.57 
359.28 
102.71 
206.14 
309.56 

53.28 
156.71 
260.13 

3.56 
107.28 
210.70 
314.13 
57.56 
161.27 



XII. 



130.80 
50.76 
330.72 
250.68 
171.41 
91.37 
11.33 
291.29 
212.02 
131.98 
51.94 
331.90 
252.63 
172.59 
92.55 
12.51 
293.24 
213.20 
133.16 
53.12 
333.85 
253.81 
173.77 
93.74 
14.46 
294.42 
214.39 
134.35 
55.08 
335.04 
255.00 
174.96 
95.69 
15.65 
295.61 
215.57 
136.30 
56.96 
336.22 
256.18 
176.91 
96.87 
16.83 
296.79 
217.52 
137.48 
57.44 
337.40 
258.13 



XIII. 



223.57 

52.55 
241.53 

70.52 
260.02 

89.01 
277.99 
106.98 
296.48 
125.46 
314.45 
143.43 
332.93 
161.92 
350.91 
179.89 
9.39 
198.38 

27.37 
216.35 

45.85 
234.84 

63.83 
252.81 

82.32 
271.30 
100.29 
289.27 
118.78 
307.76 
136.75 
325.73 
155.23 
344.22 
173.20 

2.19 

191.69 

20.68 

209.66 

38.65 

228.15 

57.14 

246.12 

75.11 

264.61 

93.59 

282.58 

111.56 

301.07 



XIV. 



44.34 
167.16 
289.98 
52.79 
174.96 
297.78 
60.59 
183.41 
305.58 
68.40 
191.21 
314.03 
76.20 
199.01 
321.83 
84.65 
206.81 
329.63 
92.45 
215.27 
337.43 
100.25 
223.07 
345.89 
108.05 
230.87 
353.69 
116.50 
238.67 
1.49 
124.31 
247.12 
^ 9.29 
132.11 
254.92 
17.74 
139.91 
262.73 
25.54 
148.36 
270.53 
33.34 
156.16 
278.98 
41.15 
163.96 
286.78 
49.60 
171.76 



XV. 



4.1 
27.5 
50.9 
74.3 
98.7 
122.1 
145.5 
168.9 
193.3 
216.7 
240.1 
263.5 
287.9 
311.3 
334.7 
358.1 
22.5 
45.9 
69.3 
92.7 
117.1 
140.5 
163.9 
187.3 
211.7 
235.1 
2.58.5 
281.9 
306.3 
329.7 
353.1 
16.5 
41.0 
64.4 
87.7 
111.1 
135.6 
159.0 
182.4 
205.7 
230.2 
253.6 
277.0 
300.4 
324.8 
348.2 
11.6 
35.0 
59.4 



XVI. 



219.5 
25.1 
190.7 
356.3 
.161.3 
326.9 
132.5 
298.1 
103.2 
268.8 
74.4 
240.0 
45.0 
210.6 
16.2 
181.8 
346.9 
152.5 
318.1 
123.7 
288.7 
94.3 
259.9 
65.5 
230.6 
36.2 
201.8 
7.4 
172.4 
338.0 
143.6 
309.2 
114.3 
279.9 
85.5 
251.1 
56.1 
221.7 
27.3 
192.9 
358.0 
163.6 
329.2 
134.7 
299.8 
105.4 
271.0 
76.6 
241.7 



XVII. 



XVIII. 



305.9 
268.7 
231.4 
194.1 
157.8 
120.5 
83.3 
46.0 
9.6 
332.4 
295.1 
257.8 
221.5 
184.2 
146.9 
109.7 
73.3 
36.0 
a58.8 
321.5 
285.1 
247.9 
210.6 
173.4 
137.0 
99.7 
62.5 
25.2 
348.8 
311.6 
274.3 
237.0 
200.7 
163.4 
126.1 
88.9 
52.5 
15.2 
338.0 
300.7 
264.3 
227.1 
189.8 
152.6 
116.2 
78.9 
41.7 
4.4 
328.0 



28.3 
124.8 
221.3 
317.8 
55.5 
152.0 
248.5 
345.0 
82.7 
179.2 
275.7 
12.2 
110.0 
206.5 
303.0 
39.5 
137.2 
233.7 
330.2 
66.7 
164.4 
260.9 
357.4 
93.9 
191.6 
288.1 
24.6 
121.1 
218.9 
315.4 
51.9 
148.4 
246.1 
342.6 
79.1 
175.6 
273.3 
9.8 
106.3 
202.8 
300.5 
37.0 
133.5 
230.0 
327.8 
64.3 
160.8 
257.2 
355.0 



31 









TABLE lll.—Coiitmued. 














FOR THE AEGUMENTS. 










A. 


For the different Years. 


The times are referred to the meridian of Washington. 




Years. 


XIX. 


XX. 


XXI. 


XXII. 


XXIII. 


XXIV. 


XXV. 


XXVI. 


XXVII. 


1852 S 


316°.3 


179^2 


346°2 


209'!6 


267^9 




14.5 


322!o 




58.8 


83°.0 


1853 


54.3 


245.4 


46.4 


100.9 


219.7 


173.1 


311.0 


340.3 


77.6 


1854 


152.4 


311.6 


110.5 


352.1 


171.5 


331.8 


300.0 


261.8 


72.2 


1855 


250.4 


17.7 


172.7 


243.2 


123.3 


130.5 


289.2 


183.3 


66.8 


1856 B 


346.6 


85.1 


234.0 


134.1 


75.0 


289.6 


277.2 


104.5 


61.3 


1857 


66.6 


151.2 


296.2 


25.2 


26.8 


■88.2 


266.3 


26.0 


55.9 


1658 


184.7 


217.4 


356.4 


276.4 


336.6 


246.9 


255.3 


307.5 


50.5 


1859 


282.7 


283.6 


60.5 


167.5 


290.4 


45.5 


244.4 


228.9 


45.1 


1860 B 


20.9 


350.9 


121.9 


56.4 


242.1 


204.6 


232.4 


150.2 


39.7 


1861 


118.9 


57.1 


184.1 


309.5 


193.9 


3.3 


221.5 


71.7 


34.2 


1862 


217.0 


123.2 


246.2 


200.7 


145.7 


162.0 


210.6 


353.2 


28.8 


1863 


315.0 


169.4 


306.4 


91.6 


97.5 


320.6 


199.6 


274.6 


23.4 


1864 B 


53.2 


256.7 


369.7 


342.7 


49.1 


119.7 


187.7 


195.9 


18.0 


1865 


151.3 


322.9 


71.9 


233.8 


0.9 


276.4 


176.7 


117.4 


12.5 


1866 


249.3 


29.1 


134.1 


125.0 


312.7 


77.0 


165.8 


38.9 


7.1 


1867 


347.3 


95.2 


196.2 


16.1 


264.5 


235.7 


154.9 


320.3 


1.7 


1868 B 


85.5 


162.6 


257.6 


267.0 


216.2 


34.8 


142.9 


241.6 


356.3 


1669 


183.6 


228.7 


319.7 


158.1 


168.0 


193.4 


132.0 


163.1 


350.8 


1670 


281.6 


294.9 


21.9 


49.3 


119.8 


352.1 


121.0 


84.5 


345.4 


1871 


19.6 


1.1 


84.1 


300.4 


71.6 


150.8 


110.1 


6.0 


340.0 


1872 B 


117.9 


68.4 


145.4 


191.3 


23.3 


309.9 


98.2 


287.3 


334.6 


1873 


215.9 


134.6 


207.6 


82.4' 


335.1 


108.5 


67.2 


208.8 


329.2 


1874 


313.9 


200.8 


269.8 


333.6 


286.9 


267.2 


76.3 


130.2 


323.7 


1875 


51.9 


266.9 


331.9 


224.7 


238.7 


65.8 


65.3 


51.7 


318.3 


1876 B 


150.2 


334.3 


33.3 


115.6 


190.4 


224.9 


53.4 


333.0 


312.9 


1877 


248.2 


40.4 


95.5 


6.8 


142.2 


23.6 


42.5 


254.5 


307.5 


1878 


346.2 


106.6 


157.6 


2.57.9 


94.0 


182.3 


31.5 


175.9 


302.0 


1879 


84.2 


172.8 


219.8 


149.0 


45.8 


340.9 


20.6 


97.4 


296.6 


1680 B 


182.5 


240.1 


281.1 


39.9 


357.5 


140.0 


6.6 


18.7 


291.2 


1881 


280.5 


306.3 


343.3 


291.1 


309.3 


296.7 


357.7 


300.2 


285.6 


1882 


16.5 


12.4 


45.5 


182.2 


261.1 


97.3 


346.8 


221.6 


280.4 


1883 


116.5 


76.6 


107.6 


73.4 


212.9 


256.0 


335.8 


143.1 


274.9 


1864 B 


214.8 


145.9 


169.0 


324.2 


•164.5 


55.1 


323.9 


64.4 


269.5 


1885 


312.6 


212.1 


231.2 


215.4 


116.3 


213.7 


312.9 


345.9 


264.1 


1886 


50.8 


278.3 


293.3 


106.5 


68.1 


12.4 


302.0 


267.3 


256.7 


1887 


148.8 


344.4 


355.5 


357.7 


19.9 


171.1 


291.0 


168.6 


253.2 


1688 B 


247.1 


51.8 


56.8 


248.5 


331.6 


330.2 


279.1 


110.1 


247.8 


1889 


345.1 


118.0 


119.0 


139.7 


283.4 


128.8 


268.2 


31.5 


242.4 


1890 


83.1 


184.1 


181.2 


30.6 


235.2 


287.5 


257.2 


313.0 


237.0 


1891 


181.1 ■ 


250.3 


243.3 


282.0 


187.0 


86.1 


246.3 


234.5 


231.5 


1892 B 


279.4 


. 317.6 


304.7 


172.8 


138.7 


245.3 


234.3 


155.8 


226.1 


1893 


17.4 


23.6 


6.9 


64.0 


90.5 


43.9 


2S3.4 


77.2 


220.7 


1894 


115.4 


90.0 


69.0 


315.1 


42.3 


202.6 


212.5 


358.7 


215.3 


1895 


213.4 


156.1 


131.2 


206.3 


354.1 


1.2 


201.5 


280.2 


209.9 


1896 B 


311.7 


223.5 


192.5 


97.1 


305.8 


160.3 


189.6 


201.4 


204.4 


1897 


49.7 


289.6 


254.7 


346.3 


257.6 


319.0 


178.6 


122.9 


199.0 


1698 


147.7 


355.8 


316.9 


239.4 


209.4 


117.6 


167.7 


44.4 


193.6 


1899 


245.7 


62.0 


19.0 


130.6 


161.2 


276.3 


156.8 


325.9 


188.2 


1900 B 


344.0 


129.3 


60.4 


21.5 


112.6 


75.4 


144.8 


247.1 


182.7 



32 



TABLE III. — Continued. 

FOR THE AEGUMENTS. 

A. For the different Years. The times are referred to the meiidian of Washington. 



Years. 



1852 B 

1853 

1854 

1855 

1856 B 

1857 

1858 

1859 

1860 B 

1861 

1862 

1863 

1864 B 

1865 

1866 

1867 

1868 B 

1869 

1870 

1871 

1872 B 

1873 

1874 

1875 

1876 B 

1877 

1878 

1879 

1880 B 

1881 

1882 

1883 

1884 B 

1885 

1886 

1887 

1888 B 

1889 

1890 

1891 

1892 B 

1893 

1894 

1895 

1896 B 

1897 

1898 

1899 

1900 B 



XXVIII. 



141.2 
196.4 
251.7 
306.9 
2.3 

57.5 
112.7 
168.0 
223.4 
278.6 
333.8 

29.0 
'84.4 
139.6 
194.9 
250.1 
305.5 
0.7 

56.0 
111.2 
166.6 
221.8 
277.0 
332.3 

27.6 

62.9 
138.1 
193.3 
248.7 
304.0 
359.2 

54.4 
109.8 
165.0 
220.3 
275.5 
330.9 

26.1 

81.3 
136.6 
192.0 
247.2 
302.4 
357.6 

53.0 
108.3 
163.5 
218.7 
274.1 



XXIX. 



171.1 

190.4 

209.7 

229.2 

247.7 

267.1 

286.4 

305.8 

324.3 

343.7 

3.1 

22.5 

40.9 

60.3 

79.7 

99.1 

117.5 

136.9 

156.3 

175.7 

194.1 

213.5 

232.9 

252.3 

270.8 

290.2 

309.5 

328.9 

347.4 

6.8 

26.2 

45.5 

64.0 

83.4 

102.8 

122.2 

140.6 

160.0 

179.4 

198.8 

217.3 

236.6 

256.0 

275.4 

293.9 

313.3 

332.6 

352.0 

10.5 



XXX. 



237.4 

4.2 

131.0 

257.8 

26.0 
152.8 
279.6 

46.4 
174.6 
301.4 

68.2 
195.0 
323.2 

90.0 
216.8 
343.7 
111.8 
238.6 
5.4 
132.3 
260.4 

27.2 
154.1 
280.9 

49.0 
175.8 
302.7 

69.5 
197.6 
324.5 

91.3 
218.1 
346.2 
113.1 
239.9 
366.7 
134.9 
261.7 

28.5 
155.3 
283.5 

50.3 
177.1 
303.9 

72.1 
198.9 
325.7 

92.5 
220.7 



XXXI. 



330.1 

6.0 

41.8 

77.7 

114.6 

150.4 

186.3 

222.1 

259.1 

294.9 

330.7 

6.6 

43.5 

79.4 

115.2 

151.0 

188.0 

223.8 

259.7 

295.5 

332.4 

8.3 

44.1 

80.0 ■ 

116.9 

152.7 

188.6 

224.4 

261.3 

297.2 

333.0 

8.9 

45.8 

81.6 

117.5 

153.3 

190.2 

226.1 

261.9 

297.8 

334.7 

10.6 

46.4 

82.2 

119.2 

155.0 

190.8 

226.7 

263.6 



XXXII. 



107.3 

174.9 

242.6 

310.3 

18.2 

85.9 

153.5 

221.2 

289.1 

356.8 

64.5 

132.1 

200.0 

267.7 

335.4 

43.1 

110.9 

178.6 

246.3 

314.0 

21.9 

89.5 

157.2 

224.9 

292.8 

0.5 

68.2 

135.8 

203.7 

271.4 

339.1 

46.8 

114.6 

182.3 

250.0 

317.7 

25.6 

93.2 

160.9 

228.6 

296.5 

4.2 

71.8 

139.5 

207.4 

275.1 

342.8 

50.4 

118.3 



XXXIII. 



297.8 
213.7 
129.7 

45.6 
320.4 
236.3 
152.3 

68.3 
343.0 
259.0 
174.9 

90.9 

5.6 

281.6 

197.5 

113.5 

28.2 
304.2 
220.2 
136.1 

50.9 
326.8 
242.8 
158.7 

73.5 
349.4 
265.4 
181.4 

96.1 

12.1 
288.0 
204.0 
118.7 

34.7 
310.7 
226.6 
141.4 

57.3 
333.3 
249.2 
164.0 

79.9 
355.9 
271.9 
186.6 
102.6 

18.5 
294.5 
209.2 



XXXIV. 



134.9 

78.2 

21.6 

324.9 

270.1 

213.5 

156.8 

100.2 

45.3 

348.7 

292.0 

235.4 

180.5 

123.9 

67.2 

10.6 

315.8 

259.1 

202.5 

145.8 

' 91.0 

34.3 

337.7 

281.0 

226.2 

169.6 

112.9 

56.3 

1.4 

304.8 

248.1 

191.5 

136.7 

80.0 

23.4 

326.7 

271.9 

215.2 

158.6 

101.9 

47.1 

350.4 

293.8 

237.1 

182.3 

125.6 

69.0 

12.4 

317.5 



XXXV. 



XXXVI. 



272.0 

247.2 

22?.4 

197.6 

173.7 

148.9 

124.1 

99.3 

75.4 

50.6 

25.7 

0.9 

337.0 

312.2 

287.4 

262.6 

238.7 

213.9 

189.1 

164.3 

140.4 

115.6 

90.8 

66.0 

42.1 

17.3 

352.5 

327.7 

303.8 

279.0 

254.2 

229.4 

205.5 

180.7 

155.9 

131.1 

107.2 

82.4 

57.6 

32.8 

8.9 

344.1 

319.2 

294.4 

270.6 

245.7 

220.9 

196.1 

172.2 



110.7 
340.9 
211.2 

81.4 
313.3 
183.5 

53.8 
284.0 
155.9 

26.1 
256.4 
126.6 
358.5 
228.7 

99.0 
329.2 
201.1 

71.3 
301.6 
171.8 

43.7 
274.0 
144.2 

14.4 
246.3 
116.6 
346.8 
217.1 

88.9 
319.2 
189.4 

59.7 
291.5 
161.8 

32.0 
262.3 
134.1 
4.6 
234.6 
104.9 

336.7 

207.0 

77.2 

307.5 

179.3 
49.6 

279.8 

150.1 
22.0 



33 



TABLE HI.— Continued. 

FOR THE AEGUMENTS. 

A. For the different Years. The times are referred to the meridian of Washington. 



Tears. 



XXXVII. 



1852 B 

1853 

1854 

1855 

1856 B 

1857 

1858 

1859 

1860 B 

1861 

1862 

1863 

1864 B 

1865 

1866 

1867 

1868 B 

1869 

1870 

1871 

1872 B 

1873 

1874 

1875 

1876 B 

1877 

1878 

1879 

1880 B 

1881 

1882 

1883 

1884 B 

1885 

1886 

1887 

1888 B 

1889 

1890 

1891 

1892 B 

1893 

1894 

1895 

1896 B 

1897 

1898 

1899 

1900 B 



247.8 
149.9 
52.0 
314.0 
216.8 
118.9 

21.0 
283.1 
185.9 

88.0 
350.1 
252.2 
155.0 

57.1 
319.2 
221.3 
124.1 

26.2 
288.2 
190.3 

93.1 
355.2 
257.3 
159.4 

62.2 
324.3 
226.4 
128.5 

31.3 
293.4 
195.5 

97.6 

0.4 

262.5 

164.5 

66.6 
329.4 
231.5 
133.6 

35.7 
298.5 
200.6 
102.7 
4.8 
267.6 
169.7 

71.8 
333.8 
236.7 



xxxvin. 



189.6 

31.1 
232.5 

73.9 
275.9 
117.4 
318.8 
160.2 

2.2 
203.7 

45.1 
246.5 

88.5 
290.0 
131.4 
332.8 
174.8 

16.3 
217.7 

59.2 
261.1 
102.6 
304.0 
145.5 
347.4 
188.9 

30.3 
231.8 

73.8 
275.2 
116.6 
318.1 
160.1 
1.5 
202.9 

44.4 
306.4 

87.8 
289.2 
130.7 
332.7 
174.1 

15.5 
217.0 

59.0 
,260.4 

101.8 

303.3 
145.3 



XXXIX. 



1 
221 

82 
303 
164 

24 
245 
106 
327 
187 

48 
269 
129 
350 
211 

72 
292 
153 

14 
235 

95 
3] 6 
177 

38 
258 
119 
340 
201 

61 

282 

143 

4 

224 

85 
306 
166 

27 
248 
109 
329 
190 

51 
272 
132 
353 
214 

74 
295 

156 



XL. 



286 
199 
112 
25 
300 
213 
126 

39 
313 
226 
140 

53 
327 
240 
153 

67 
341 
254 
167 

80 
355 
268 
181 

94 

9 

282 

195 

108 

23 
296 
209 
122 

37 
310 
223 
136 

50 
323 
236 
149 

64 
337 
250 
163 

78 
351 
264 
177 

92 



XLI. 



161 
266 

11 
116 
220 
325 

70 
175 
279 

24 
a29 
234 
339 

84 
188 
293 

38 
143 
248 
352 

97 
202 
307 

52 
156 
261 
6 
111 
215 
320 

65 
170 
274 

19 
124 
229 
333 

78 
183 
288 

32 
137 
242 
347 

91 
196 
301 

46 

150 



XLII. 



103 

147 

192 

236 

279 

324 

8 

52 

96 

140 

184 

229 

272 

316 

1 

45 

88 

133 

177 

221 

265 

309 

353 

38 

81 

125 

170 

214 

257 

302 

346 

30 

74 

118 

162 

207 

250 

294 

339 

23 

66 

111 

155 

199 

243 

287 

331 

15 

59 



XLIII. 



10 
146 
281 
56 
191 
326 
101 
237 
371 
147 
282 

57 
192 
327 
102 
238 

12 
148 
283 

58 
193 
328 
103 
239 

13 
148 
284 

59 
194 
329 
104 
239 

14 
149 
285 

60 
195 
330 
105 
240 

15 
150 
286 

61 
195 
331 
106 
241 

16 



XLIV. 



214 
128 
43 
317 
233 
147 
62 
336 
252 
166 

81 
355 
271 
185 
100 

14 
290 
204 
119 

33 
308 
223 
138 

52 
327 
262 
156 

71 
346 
261' 
175 

90 

5 

280 

194 

109 

23 
299 
213 
128 

43 
318 
232 
147 

62 
336 
251 
166 

81 



XLV. 

O 

63 
8 
313 
258 
203 
148 
93 
38 
344 
288 
233 
178 
124 
69 
14 
318 
264 
209 
154 
99 
44 
349 
294 
239 
185 
130 
74 
19 
325 
270 
215 
160 
105 
50 
355 
300 
246 
191 
135 
80 
26 
331 
276 
221 
166 
111 
56 
1 
307 



34 









TABLE III.— Continued. 
















FOR 


THE ARGUMENTS. 










B. Variations of the Argument 


s for the different Months 


. The times 


are referred to the meridian of Washington. 




Months. 


I. 


II. 


III. 


IV. 


V. 


VI. 


VII. 


VIII. 


IX. 




January 


0?000 


0°000 


o!ooo 


o!oo 


0°00 


0°.00 


0°.00 


0°.00 


0°.00 




February 


357.425 


6.209 


1.058 


3.63 


9.85 


21.20 


14.99 


346.07 


348.64 




March 


355.09S 


11.817 


2.014 


6.91 


18.74 


40.35 


28.53 


333.48 


338.38 




April 


352.523 


18.026 


3.072 


10.54 


28.59 


61.55 


43.52 


319.55 


327.02 




May 


350.031 


24.035 


4.096 


14.06 


38.12 


82.07 


58.03 


306.07 


316.03 




June 


347.456 


30.244 


5.154 


17.69 


47.97 


103.27 


73.02 


292.14 


304.67 




July 


344.964 


36.253 


6.178 


21.21 


57.50 


123.79 


87.53 


278.66 


293.68 




August 


342.389 


42.462 


7.236 


24.84 


67.35 


144.99 


102.52 


264.73 


282.32 




September 


339.814 


48.671 


8.294 


28.47 


77.19 


166.19 


117.51 


250.80 


270.96 




October 


337.322 


54.680 


9.318 


31.99 


86.72 


186.71 


132.02 


237.32 


259.97 




November 


334.747 


60.889 


10.376 


35.62 


96.57 


207.91 


147.01 


223.39 


248.61 




December 


332.255 


66.898 


11.400 


39.14 


106.10 


228.43 


161.52 


209.91 


237.62 




Months. 


X. 


XI. 


XII. 


XIII. 


XIV. 


XV. 


XVI. 


XVII. 


xvm. 




January 


o°.oo 


0°.00 


o°.oo 


0.00 


0°.00 




0.0 


o 
0.0 


o 
0.0 


o 

0.0 




February 


358.48 


8.78 


23.78 


16.05 


339.85 


32.6 


343.5 


27.4 


38.8 




March 


357.11 


16.72 


45.26 


30.55 


321.65 


62.0 


328.6 


52.2 


73.8 




April 


355.59 


25.50 


69.04 


46.60 


301.50 


94.6 


312.1 


79.6 


112.6 




May 


354.12 


34.00 


92.05 


62.13 


282.00 


126.1 


296.1 


106.1 


150.1 




June 


352.60 


42.78 


115.83 


78.18 


261.85 


158.7 


279.6 


133.5 


188.9 




July 


351.13 


51.28 


138.84 


93.71 


242.35 


190.2 


263.6 


160.0 


226.4 




August 


349.61 


60.06 


162.62 


109.76 


222.20 


222.8 


247.1 


187.4 


265.2 




September 


348.09 


68.84 


186.39 


125.81 


202.05 


255.3 


230.6 


214.8 


303.9 




October 


346.62 


77.34 


209.40 


141.34 


182.55 


286.8 


214.6 


241.3 


341.4 




November 


345.10 


86.12 


233.18 


157.39 


162.40 


319.4 


198.1 


268.7 


20.2 




December 


343.63 


94.62 


256.19 


172.92 


142.90 


350.9 


182.1 


295.3 


57.7 




Months. 


XIX. 


XX. 


XXI. 


XXII. 


XXIII. 


XXTV. 


XXV. 


XXVI. 


xxvn. 




January 


o 

0.0 


o 

0.0 


o 

0.0 




0.0 




0.0 


o 

0.0 


o 
0.0 


o 
0.0 


o 
0.0 




February 


8.3 


36.2 


334.7 


350.8 


355.9 


13.5 


328.5 


353.3 


359.5 




March 


15.8 


68.9 


311.9 


342.4 


352.2 


25.6 


300.1 


347.3 


359.1 




April 


24.1 


105.1 


286.6 


333.2 


348.1 


39.1 


268.6 


340.6 


358.6 




May 


32.2 


140.1 


262.1 


324.2 


344.1 


52.2 


238.1 


334.2 


358.2 




June 


40.5 


176.3 


236.8 


315.0 


340.0 


65.6 


206.6 


327.5 


357.7 




July 


48.6 


211.3 


212.3 


306.1 


336.0 


78.7 


176.1 


321.0 


357.3 




August 


56.9 


247.5 


187.0 


296.8 


331.9 


92.1 


144.6 


314.3 


356.8 




September 


65.2 


283.7 


161.7 


287.6 


327.8 


105.6 


113.1 


307.6 


356.3 




October 


73.3 


318.7 


137.2 


278.6 


323.8 


118.6 


82.6 


301.2 


355.9 




November 


81.6 


354.9 


111.9 


269.4 


319.7 


132.1 


51.1 


294.5 


355.4 




December 


89.7 


29.9 


87.4 


260.5 


315.7 


145.2 


20.6 


288.0 


355.0 






In 


Bissextile 1 


fears subtrac 


t one day f 


pom the date 


in the first 


two months 









35 





TABLE IlI.—CoAued. 








FOR THE ARGUMENTS. 






B. Variations of the Arguments for the different Months. The times are referred to the meridian of Washington. 


Months. 


XXVIII. 


XXIX. 


XXX. 


XXXI. 


XXXII. 


XXXIII. 


XXXIV. 


XXXV. 


XXXVI. 




o 


o 











o 


o 





o 


January 


0.0 


0.0 


0.0 


0.0 


0.0 


0.0 


0.0 


0.0 


0.0 


February 


4.7 


331.1 


41.3 


33.6 


5.7 


322.3 


56.3 


28.5 


50.1 


March 


8.9 


304.9 


78.7 


64.0 


10.9 


288.3 


107.2 


54.2 


95.4 


April 


13.5 


276.0 


120.0 


97.6 


16.6 


250.6 


163.5 


82.6 


145.5 


May 


18.0 


248.0 


160.0 


130.2 


22.2 


214.1 


218.0 


110.2 


194.0 


June 


22.7 


219.1 


201.3 


163.8 


27.9 


176.4 


274.4 


138.6 


244.1 


July 


37.2 


191.1 


241.3 


196.4 


33.5 


139.9 


328.9 


166.2 


292.6 


August 


31.8 


162.2 


282.6 


230.0 


39.2 


102.2 


25.2 


194.6 


342.7 


September 


36.5 


133.3 


323.9 


263.6 


44.9 


64.5 


81.6 


223.1 


32.8 


October 


41.0 


105.3 


3.9 


296.2 


50.5 


28.0 


136.1 


250.6 


81.3 


November 


45.6 


76.4 


45.2 


329.8 


56.2 


350.3 


192.4 


279.1 


131.4 


December 


50.1 


48.4 


85.2 


2.4 


61.8 


313.8 


246.9 


306.6 


179.9 


Months. 


XXXVII. 


XXXVIII. 


XXXTX. 


XL. 


XLI. 


XLII. 


XLIII. 


XLIV. 


XLV. 











o 


o 


o 


o 


o 


o 


January 


0.0 


0.0 























February 


22.3 


17.1 


348 


54 


338 


333 


341 


23 


26 


March 


42.4 


32.5 


338 


102 


319 


309 


324 


44 


50 


April 


64.6 


49.6 


326 


156 


297 


282 


305 


67 


76 


May 
June 


86.2 


66.2 


314 


208 


276 


256 


286 


90 


101 


108.4 


83.3 


303 


262 


254 


229 


267 


113 


127 


July 
August 


130.0 


99.9 


291 


314 


233 


203 


248 


136 


152 


152.2 


117.0 


279 


7 


212 


177 


229 


159 


178 


September 


174.5 


134.1 


268 


61 


190 


150 


210 


182 


204 


October 


196.0 


150.6 


256 


113 


169 


124 


192 


205 


229 


November 
December 


218.3 
239.8 


167.7 
184.3 


244 
233 


167 
219 


147 
126 


97 
71 


173 
154 


228 
250 


255 
280 


In Bissextile Tears subtract one day from the date in the first two months. 

^ -' . . " ■- '■•" ■ 



36 









TABLE 111.— ConHmed. 
















FOR THE ARGUMENTS. 










C. Variations of the Arguments for the different Days. The times are referred to the meridian of Washington. 




Days. 


I. 


II. 


III. 


IV. 


V. 


VI. 


vn. 


vni. 


IX. 




1 


359!917 


0^200 


o!o34 


o 
0.12 


o 

0.32 


0°.68 




0.48 


359°.55 


359°.63 




2 


359.834 


0.401 


0.068 


0.23 


0.64 


1.37 


0.97 


359.10 


359.27 




3 


359.751 


0.601 


0.102 


0.35 


0.95 


2.05 


1.45 


358.65 


358.90 




4 


359.667 


0.801 


0.137 


0.47 


1.27 


2.74 


1.93 


358.20 


358.53 




5 


359.584 


1.001 


0.171 


0.59 


1.59 


3.42 


2.42 


357.75 


358.17 




6 


359.501 


1.202 


0.205 


0.70 


1.90 


4.10 


2.90 


357.30 


357.80 




7 


359.418 


1.402 


0.239 


0.82 


2.22 


4.79 


3.39 


356.85 


357.43 




8 


359.335 


1.602 


0.273 


0.94 


2.54 


5.47 


3.87 


356.40 


357.07 




9 


359.252 


1.803 ■ 


0.307 


1.06 


2.86 


6.16 


4.35 


355.95 


356.70 




10 


359.169 


2.003 


0.341 


1.17 


3.18 


6.84 


4.84 


355.51 


356.34 




20 


358.338 


4.006 


0.683 


2.34 


6.35 


13.68 


9.67 


351.01 


352.67 




30 


357.508 


6.009 


1.024 


3.52 


9.53 


20.52 


14.51 


346.52 


349.01 




Days. 


X. 


XI. 


XII. 


xni. 


XIV. 


XV. 


XVI. 


XVII. 


XVIII. 




1 


359°.95 




0.28 


o 
0.77 


0°52 


359°.35 


o 

1.1 


359°5 


o 

0.9 




1.3 




2 


359.90 


0.57 


1.53 


1.04 


358.70 


2.1 


358.9 


1.8 


2.5 




3 


359.85 


0.85 


2.30 


1.55 


358.05 


3.2 


358.4 


2.7 


3.8 




4 


359.80 


■1.13 


3.07 


2.07 


357.40 


4.2 


357.9 


3.5 


5.0 




5 


359.76 


1.42 


3.84 


2.59 


356.75 


5.3 


357.3 


4.4 


6.3 




6 


359.71 


1.70 


•4.60 


3.11 


356.10 


6.3 


356.8 


5.3 


7.5 




7 ■ 


359.66 


1.98 


5.37 


3.62 


355.45 


7.4 


356.3 


6.2 


8.8 




8 


359.61 


2.27 


6.14 


4.14 


354.80 


8.4 


355.7 


7.1 


10.0 




9 


359.56 


2.55 


6.90 


4.66 


354.15 


9.5 


355.2 


8.0 


11.3 




10 


359.51 


2.83 


7.67 


5.18 


353.50 


10.5 


354.7 


8.8 


12.5 




20 


359.02 


5.67 


15.34 


10.36 


347.00 


21.0 


349.4 


17.7 


25.0 




30 


358.53 


8.50 


23.01 


15.53 


340.50 


31.5 


344.0 


26.5 


37.5 




Days. 


XIX. 


XX. 


XXI. 


XXII. 


XXIII. 


XXIV. 


XXV. 


XXVI. 


xxvn. 




1 


o 
0.3 


o 

1.2 


359'!2 


359^7 


359°.9 


o 

0.4 


359°.0 


359°.8 


o 

0.0 




2 


0.5 


2.3 


358.4 


359.4 


359.7 


0.9 


358.0 


359.6 


0.0 




3 


0.8 


3.5 


357.6 


359.1 


359.6 


1.3 


356.9 


359.4 


0.0 




4 


1.1 


4.7 


356.7 


358.8 


359.5 


1.7 


355.9 


359.1 


359.9 




5 


1.3 


5.8 


355.9 


358.5 


3.59.3 


2.2 


354.9 


358.9 


359.9 




6 


1.6 


7.0 


355.1 


358.2 


359.2 


2.6 


353.9 


358.7 


359.9 




7 


1.9 


8.2 


354.3 


357.9 


359.1 


3.0 


352.9 


358.5 


359.9 




8 


2.2 


9.3 


353.5 


357.6 


358.9 


3.5 


351.9 


358.3 


359.9 




9 


2.4 


10.5 


352.7 


357.3 


358.8 


3.9 


350.9 


358.1 


359.9 




10 


2.7 


11.7 


351.8 


357.0 


358.7 


4.4 


349.8 


357.9 


359.9 




20 


5.4 


23.4 


343.7 


354.0 


357.4 


8.7 


339.7 


355.7 


359.7 




30 


8.1 


35.0 


335.5 


351.1 


356.0 


13.0 


329.5 


353.6 


359.6 





37 



TABLE III. Continued. 
FOR THE ARGUMENTS. 

C. Variations of the Arguments for the different Days. The times are referred to the meridian of Washington. 


Days. 


xxvin. 


XXIX. 


XXX. 


XXXI. 


XXXII. 


XXXIII. 


XXXIV. 


XXXV. 


XXXVI. 


1 
2 
3 

4 
5 
6 

7 

8 

9 

10 

20 

30 


o 

0.2 
0.3 
0.5 
0.6 
0.8 
0.9 
1.1 
1.2 
1.4 
1.5 
3.0 
4.5 


359°1 
358.1 
357.2 
356.3 
355.3 
354.4 
353.5 
352.5 
351.6 
350.7 
341.3 
332.0 


o 

1.3 
2.7 
4.0 
5.3 

6.7 
8.0 
9.3 
10.7 
12.0 
13.3 
26.7 
40.0 


o 

1.1 

2.2 
3.3 
4.3 

5.4 

6.5 

7.6 

8.7 

9.8 

10.9 

21.7 

32.6 




0.2 
0.4 
0.6 
0.7 
0.9 
1.1 
1.3 
1.5 
1.7 
1.9 
3.7 
5.6 


358°8 
357.6 
356.3 
355.1 
353.9 
352.7 
351.5 
350.3 
349.0 
347.8 
335.7 
323.5 


o 
1.8 

3.6 

5.5 

7.3 

9.1 

10.9 

12.7 

14.5 

16.4 

18.2 

36.3 

54.5 


o 

0.9 

1.8 
2.8 
3.7 
4.6 
5.5 
6.4 
7.3 
8.3 
9.2 
18.4 
27.5 




1.6 

3.2 

4.9 

6.5 

8.1 

9.7 

11.3 

12.9 

14.6 

16.2 

32.3 

48.5 




Days. 


XXXVII. 


XXXVIII. 


XXXIX. 


XL. 


XLI. 


XLII. 


XLIII. 


XLIV. 


XLV. 


1 
2 
3 

4 

5 

6 

7 

8 

9 

10 

20 

30 


o 

0.7 
1.4 
2.2 
2.9 
3.6 
4.3 
5.0 
5.7 
6.5 
7.2 
14.4 
21.5 


O 

0.6 
1.1 
1.7 
2.2 
2.8 
3.3 
3.9 
4.4 
5.0 
5.5 
11.0 
16.6 


o 


359 

359 

359 

358 

358 

357 

357 

357 

356 

352 

349 


O 

2 

3 

5 

7 

9 

10 

12 

14 

16 

17 

35 

52 


O 

359 
359 
358 
357 
357 
356 
355 
354 
354 
353 
346 
339 


o 

359 
358 
3.57 
357 
356 
355 
354 
353 
352 
351 
343 
334 




359 
359 
358 
358 
357 
356 
356 
355 
354 
354 
348 
342 




1 

2 
2 
3 

4 
5 
5 

^ 

7 

8 
15 
23 




1 
2 
3 
3 

4 
5 
6 
7 
8 
8 
17 
25 





38 









TABLE lll.—Cordinued. 














FOR THE ARGUMENTS. 








D. Variations of the Arguments for the different Hours. 


The times are referred to the meridian of Washington. 1 


Hours. 


I. 


II. 


III. 


IV. 


V. 


VI. 


VII. 


VIII. 


IX. 


1 


359!997 


0°008 


0^001 


o!oo 


o 

0.01 


0°.03 


0°.02 


359°.98 


359°99 


2 


359.993 


0.017 


0.003 


0.01 


0.03 


0.06 


0.04 


359.96 


359.97 


3 


359.990 


0.025 


0.004 


0.02 


0.04 


0.09 


0.06 


359.94 


359.95 


4 


359.986 


0.033 


0.006 


0.02 


0.05 


0.11 


0.08 


359.92 


359.94 


5 


359.983 


0.042 


0.007 


0.03 


0.07 


0.14 


0.10 


359.90 


359.92 


6 


359.979 


0.050 


0.008 


0.03 


0.08 


0.17 


0.12 


359.89 


359.91 


7 


359.976 


0.058 


0.010 


0.03 


0.09 


0.20 


0.14 


359.87 


359.89 


8 


359.972 


0.066 


0.011 


0.04 


0.11 


0.23 


0.16 


359.85 


359.88 


9 


359.969 


0.075 


0.013 


0.04 


0.12 


0.26 


0.18 


359.83 


359.86 


10 


359.965 


0.083 


0.014 


0.05 


0.13 


0.29 


0.20 


359.81 


359.85 


20 


359.930 


0.166 


0.028 


0.10 


0.26 


0.57 


0.40 


359.62 


359.70 


Hours. 


X. 


XI. 


Xll. 


XIII. 


XIV. 


XV. 


XVI. 


XVII. 


XVIII. 




o 


O 


o 


o 


o 


O 


o 


o 


o * 


1 


0.00 


0.01 


0.03 


0.02 


359.97 


0.0 


0.0 


0.0 


0.1 


2 


0.00 


0.02 


0.06 


0.04 


359.95 


0.1 


0.0 


0.1 


0.1 


3 


359.99 


0.04 


0.10 


0.07 


359.92 


0.1 


359.9 


0.1 


0.2 


4 


359.99 


0.05 


0.13 


0.09 


359.89 


0.2 


359.9 


0.2 


0.2 


5 


359.99 


0.06 


0.16 


0.11 


359.87 


0.2 


359.9 


0.2 


0.3 


6 


359.99 


0.07 


0.19 


0.13 


359.84 


0.3 


359.9 


0.2 


0.3 


7 


359.99 


0.08 


0.22 


0.15 


359.81 


0.3 


359.9 


0.3 


0.4 


8 


359.98 


0.10 


0.26 


0.17 


359.78 


0.4 


359.8 


0.3 


0.4 


9 


359.98 


0.11 


0.29 


0.20 


359.76 


0.4 


359.8 


0.3 


0.5 


10 


359.98 


0.12 


0.32 


0.22 


359.73 


0.4 


359.8 


0.4 


0.5 


20 


359.96 


0.24 


0.64 


0.24 


359.46 


0.9 


359.6 


0.7 


1.0 


Hours. 


XIX. 


XX. 


XXI. 


XXII. 


XXIII. 


XXIV. 


XXV. 


XXVI. 


xxvn. 











o 





o 


o 


o 





1 


0.0 


0.0 


0.0 


0.0 


0.0 


0.0 


0.0 


0.0 


0.0 


2 


0.0 


0.1 


359.9 


0.0 


0.0 


0.0 


359.9 


0.0 


0.0 


3 


0.0 


0.2 


359.9 


0.0 


0.0 


0.1 


359.9 


0.0 


0.0 


4 


0.0 


0.2 


359.9 


0.0 


0.0 


0.1 


359.8 


0.0 


0.0 


5 


0.1 


0.2 


359.8 


359.9 


0.0 


0.1 


359.8 


0.0 


0.0 


6 


0.1 


0.3 


359.8 


359.9 


0.0 


0.1 


359.8 


0.0 


0.0 


7 


0.1 


0.3 


359.8 


359.9 


0.0 


0.1 


359.7 


0.0 


0.0 


8 


0.1 


0.4» 


359.7 


359.9 


0.0 


0.1 


359.7 


0.0 


0.0 


9 


0.1 


0.4 


359.7 


359.9 


0.0 


0.2 


359.6 


0.0 


0.0 


10 


0.1 


0.5 


359.7 


359.9 


0.0 


0.2 


359.6 


0.0 


0.0 


20 


0.2 


1.0 


359.3 


359.8 


0.0 


0.4 


359.2 


0.0 


0.0 



39 









TABLE 111.— Concluded. 










. 


FOR THE ARGUMENTS. 






D. Variations of the Arguments for the different Hours. The times are referred to the meridian of Washington. 1 


Hours. 


XXVTTT. 


XXIX. 


XXX. 


XXXI. 


XXXII. 


xxxm. 


XXXIV. 


XXXV. 


XXXVI. 







o 


o 





o 





o 






1 


0.0 


0.0 


0.1 


0.0 


0.0 


359.9 


0.1 


0.0 


0.1 


3 


0.0 


359.9 


0.1 


0.1 


0.0 


359.9 


0.2 


0.1 


0.1 


3 


0.0 


359.9 


0.2 


0.1 


0.0 


359.8 


0.2 


0.1 


0.2 


• 4 


0.0 


359.8 


0.2 


0.2 


0.0 


359.8 


0.3 


0.2 


0.3 


5 


0.0 


359.8 


0.3 


0.2 


0.0 


359.7 


0.4 


0.3 


0.3 


. 6 


0.0 


359.8 


0.3 


0.3 


0.1 


359.7 


0.5 


0.2 


0.4 


7 


0.0 


359.7 


0.4 


0.3 


0.1 


359.6 


0.5 


0.3 


0.5 


8 


0.0 


359.7 


0.5 


0.4 


0.1 


359.6 


0.6 


0.3 


0.5 


9 


0.0 


359.7 


0.5 


0.4 


0.1 


359.5 


0.7 


0.3 


0.6 


10 


0.0 


359.6 


0.6 


0.5 


0.1 


359.5 


0.8 


0.4 


0.7 


20 


0.0 


359.2 


1.1 


0.9 


0.2 


359.0 


1.5 


0.8 


1.3 


Hours. 


XXXVII. 


xxxviii. 


TXXTX. 


XL. 


XLI. 


XLII. 


XLIII. 


XLIV. 


XLV. 




o 


o 








o 


b 





o 





1 


0.0 


0.0 























2 


0.1 


0.1 























3 


0.1 


0.1 























4 


0.1 


0.1 























5 


0.2 


0.1 























6 


0.2 


0.1 























7 


0.2 


0.2 























8 


0.2 


0.2 





1 

















9 


0.3 


0.2 


^ 


1 

















10 


0.3 


0.2 





1 

















, 20 


0.6 


0.5 





1 


359 


359 





1 


1 



40 



TABLE IV. 
PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 

Terras multiplied with t. Argument = M. 



Arg. 




1 
2 
3 
4 
5 
6 
7 
8 
9 

10 
11 
12 
13 
14 
15 
16 
17 
18 
19 

20 
21 
22 
23 
24 
25 
26 
27 
28 
29 

30 
31 
32 
33 
34 
35 
36 
37 
38 
39 

40 
41 
42 
43 
44 
45 



- 5.24 

+ 9.15 

23.51 

37.83 

52.09 

66.27 

80.37 

94.35 

108.20 

121.91 

+135.47 
148.84 
162.03 
175.01 
187.77 
200.31 
212.60 
224.65 
236.45 
247.98 

+259.22 
270.19 
280.86 
291.23 
301.29 
311.04 
320.46 
329.56 
338.32 
346.74 

354.83 
+363.62 
370.07 
377.21 
384.01 
390.48 
396.63 
402.45 
407.95 
413.13 

+418.00 
422.57 
426.82 
430.78 
434.45 

+437.82 



Diff. 



+14.39 
14.36 
14.33 
14.26 
14-18 
14.10 
13-98 
13.35 
13.71 

13-56 

+13-37 
13-19 
12.98 
12.76 
12-54 
12-29 
12-05 
11-80 
11-53 

11-24 

+10-97 
10-67 
10-37 
10-06 
9-76 
9-42 
9-10 
8-76 
8-42 

8-09 

+ 7-79 
7-45 
7-14 
6-80 
6-47 
6-15 
5-82 
6.50 
6.18 

4.87 

+ 4.67 
4-25 
3-96 
3-67 

+ 3-37 



'!l 



-684.22 

683.87 
683.09 
681.88 
680.23 
678.17 
675.69 
672.80 
669.51 
665.82 

-661.73 
657-27 
652.42 
647.19 
641.62 
635.69 
629.42 
622.84 
615.94 
608.74 

-601.26 
593.51 
585.50 
577.25 
568.77 
560.07 
551-17 
542-08 
532-81 
523-39 

-513.81 
504.09 
494.25 
484.30 
474.25 
464.12 
453.91 
443.65 
433.35 
423.01 

-412.65 
402.27 
391.88 
381.49 
371.11 

-360.75 



Diff. 



+ 0-35 
0-78 
1-21 
1-65 
2-06 
2-48 
2-89 
3-29 
3-69 



+ 4-46 
4-85 
5-23 
6-67 
6-93 
6-27 
6-68 
6-90 
7-20 

7-48 

+ 7-75 
8-01 
8-25 
8-48 
8-70 
8-90 
9-09 
9-27 
9-42 

9-68 

+ 9-72 
9-84 
9-95 
10-05 
10-13 
10-21 
10-26 
10-30 
10-34 

10-36 

+10-38 
10-39 
10-39 
10-38 

+10-36 



?1 



-35.71 
34.59 
33.45 
32.29 
31.11 
29.91 
28.69 
27-45 
26-19 
24-92 

-23.63 
22.33 
21.01 
19.68 
18.34 
16.99 
15.63 
14.25 
12.87 
11.48 

-10.09 
8.69 
7.28 
5.87 
4.45 
3.03 
1.61 
- 0.19 
+ 1.23 
2.65 

+ 4.07 

5.48 

6-90 

8.31 

9.71 

11.11 

12.51 

13.89 

15.27 

16.65 

+18.01 
19.37 
20.72 
22.05 
23.38 

+24.69 



Diff. 



+1-12 
1-14 
1-16 
1-18 
1-20 
1-22 
1-24 
1-26 
1-27 

1-29 

+1-30 
1-32 
1-33 
1-34 
1-35 
1-36 
1-38 
1-33 
1-39 

1-39 

+1-40 
1-41 
1-41 
1-42 
1-42 
1-42 
1-42 
1-42 
1-42 

1-42 

+1-41 
1-42 
1-41 
1-40 
1-40 
1-40 
1-38 
1-38 
1-38 



+1-36 
1-35 
1-33 
1-33 

+1-31 



Arg. 



45 

46 
47 
48 
49 
50 
51 
52 
53 
54 

55 
56 
57 
58 
59 
60 
61 
62 
63 
64 

65 
66 
67 
68 
69 
70 
71 
72 
73 
74 

75 
76 
77 
78 
79 
80 
81 
82 
83 
84 

85 
86 

87 



90 



li 



+437.82 
440.91 
443.73 
446.27 
448.56 
450.58 
452.36 
453.88 
455.17 
456.22 

+457.04 
457.64 
458.02 
458.19 
458.16 
457.94 
457.53 
456.94 
456.17 
455.23 

+454.12 
452.85 
451.42 
449.84 
448.12 
446.26 
444.26 
442.13 
439.88 
437.51 

+435.02 
432.42 
429.72 
426.92 
424.02 
421.02 
417.93 
414.76 
411.50 
408.17 

+404.76 
401.29 
397.75 
394.14 
390.47 

+386.75 



Diff. 



+3-09 
2-82 
2-54 
2-29 
2-02 
1-78 
1-52 
1.29 
1.06 

0-82 

+0-60 
0-38 
+0-17 
-0-03 
0-22 
0-41 
0-59 
0-77 
0-94 

1-11 

-1-27 
1-43 
1-58 
1-72 
1-86 
2-00 
2-13 
2-25 
2-37 



-2-60 
2-70 
2-80 
2-90 
3-00 
3-09 
3-17 



3-41 

-3-47 
3.54 
3-61 
3-67 

-3.72 



% 



-360.75 

350.43 
340.15 
329-91 
319.74 
309-63 
299-58 
289.61 
279.72 
269.90 

-260.17 
250.53 
240.98 
231.53 
222-18 
212.93 
203.79 
194.75 
185.82 
177.01 

-168.31 
159.72 
151.25 
142.89 
134.65 
126.53 
118.54 
110.66 
102.91 
95.28 

- 87.77 
80.39 
73.12 
65.98 
58.96 
52.07 
45.29 
38.64 
32.10 
25.68 

- 19.38 
13.20 

7.13 

- 1.18 
+ 4.66 
+ 10.39 



Diff. 



+10.32 
10-28 
10-24 
10-17 
10-11 
10-05 
9.97 



9-73 

+ 9-64 
9-55 
9-45 
9-36 
9-26 
9-14 
9-04 
8-93 
8-81 

8.70 

+ 8-69 
8-47 
8-36 
8-24 
8-12 
7-99 
7-88 
7-76 
7-63 

7-61 

+ 7-38 
7-27 
7-14 
7-02 
6-89 
6-78 
6-05 
6-64 
6.42 

6.30 

+ 6.18 
6.07 
5.96 
5.84 

+ 6.73 



+24.69 
26.00 
27.29 

:i8.57 

29.84 
31.10 
32.34 
33-57 
34.79 
35.99 

+37.17 
38.34 
39.50 
40.64 
41.77 
42.88 
43.97 
45.05 
46.11 
47.15 

+48.18 
49.19 
50.18 
51.16 
52.12 
53.06 
53.98 
54.89 
55.78 
56.65 

+57.50 
58.33 
59.15 
59.94 
60.72 
61.48 
62.23 
62.95 
63.66 
64.35 

+65.02 
65.67 
66.30 
66.92 
67.51 

+68.09 



Diff. 



+1.31 
1.29 
1-28 
1-27 
1-26 
1.24 
1-23 
1-22 
1-20 

1-18 

+1-17 
1-16 
1-14 
1-13 
1-11 
1-09 
1-08 
1-06 
1-04 

1-03 

+1-01 
0-99 
0.98 
0-96 
0-94 
0-92 
0-91 
0-89 
0*-87 

0-85 

+0-83 
0-82 
0-79 
0-73 
0-76 
0-75 
0-72 
0-71 
0-69 

0-67 

+0-65 
0-63 
0-62 
0-59 

+0-58 



41 











1 

TABLE lY.— Continued 












PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 










Terms multiplied with t. Argument = M. 










Arg. 


h 


Diff. 


Vl 


Difif. 


?1 


Diff. 


Arg. 


h 


Diff. 


Vl 


Diff. 


Si 


Diff. 




90 


+386.75 




+ 10.39 




+68.09 





135 


+192.61 




+173.00 




+76.34 




91 


382.97 


-3.78 


16.00 


+6.61 


68.65 


+0.66 


136 


188.14 


-4.47 


174.96 


+1.96 


76.16 


-0.18 


92 


379.14 


3-83 


21.51 


5.51 


69.20 


0.56 


137 


183.66 


4.48 


. 176.86 


1-00 


75.96 


0.20 


93 


375.26 


3.68 


26.90 


6.39 


69.72 


0.53 


138 


179.19 


4.47 


178.70 


1.84 


75.75 


0-21 


94 


371.33 


3-93 


32.19 


5.29 


70.23 


0.50 


139 


174.72 


4.47 


180.49 


1.79 


75.53 


0.22 


95 


367.37 


3-96 


37.37 


6.18 


70.71 


0.48 


140 


170.25 


4.47 


182.23 


1.74 


75.29 


0-24 


96 


363.36 


4.01 


42.45 


6.08 


71.18 


0.47 


141 


165.78 


4.47 


183.92 


1.69' 


75.03 


0-26 


97 


359.31 


4.05 


47.43 


4-98 


71.63 


0.46 


142 


161.32 


4.46 


185.56 


1/64 


74.77 


0.26 


98 


355.23 


4-08 


52.30 


4.87 


72.07 


0.44 


143 


156.87 


4-45 


187.14 


1.58 


74.49 


0.28 


99 


351.11 


4.12 
4.15 


57.07 


4.77 
4.67 


72.49 


0.42 
0-40 


144 


152.41 


4.48 
4.48 


188.68 


1.54' 
1.49 


74.20 


0.29 
0.31 


100 


+346.96 




+ 61.74 




+72.89 




145 


+147.96 




+190.17 




+73.89 




101 


342.78 


-4-18 


66.32 


+4.68 


73.27 


+0-38 


146 


143.52 


-4.44 


191.61 


+1.44 


73.57 


-0.32 


102 


338.58 


4.20 


70.79 


4.47 


73.63 


0-36 


147 


139.07 


4.45 


193.00 


1.39 


73.24 


0*33 


103 


334.35 


4.23 


75.18 


4.39 


73.98 


0.36 


148 


134.64 


4.43 


194.34 


1.34 


72.89 


0'35 


104 


330.09 


4-26 


79.46 


4.28 


74.31 


0.33 


149 


130.20 


4.44 


195.64 


1.30 


72.53 


0.36 


105 


325.81 


4-28 


83.66 


4.20 


74.62 


0.31 


150 


125.77 


4.43 


196.90 


1.26 


72.16 


0-37 


106 


321.51 


4.30 


87.76 


4.10 


74.92 


0-30 


151 


121.34 


4.43 


198.11 


1.21 


71.77 


0.39 


107 


317.19 


4-32 


91.78 


4.02 


75.19 


0-27 


152 


116.92 


4.42 


199.28 


1.17 


71.38 


0.39 


108 


312.85 


4.34 


95.70 


3.92 


75.45 


0-26 


153 


112.50 


4.42 


200.40 


1.12 


70.97 


0-41 


109 


308.50 


4.35 
4-37 


99.54 


3.84 
3.76 


75.70 


0.25 
0.22 


154 


108.08 


4-42 
4.41 


201.48 


l.OS 
1.04 


70.54 


0.43 
0-43 


110 


+304.13 




+103.30 




+75.92 




155 


+103.67 




+202.52 




+70.11 




111 


299.75 


-4.38 


106.97 


+3.67 


76.13 


+0.21 


156 


99.26 


-4-41 


203.52 


+1-00 


69.66 


-0.45 


112 


295.35 


4-40 


110.55 


3.58 


76.32 


0.19 


157 


94.85 


4-41 


204.48 


0-96 


69.20 


0.46 


113 


290.94 


4.41 


114.06 


3.51 


76.51) 


0.18 


158 


90.45 


4.40 


205.40 


0.92 


68.73 


0.47 


114 


286.52 


4.42 


117.48 


3.42 


76.66 


0.16 


159 


86.05 


4.40 


206.28 


0.88 


68.25 


0.48 


115 


282.09 


4.43 


120.83 


3.35 


76.80 


0.14 


160 


81.65 


4.40 


207.12 


0.84 


67.75 


0.60 


116 


277.66 


4.43 


124.10 


3.27 


76.93 


0.13 


.161 


77.25 


4.40 


207.92 


0.60 


67.24 


* 0.51 


117 


273.21 


4.45 


127.29 


3.19 


77.04 


o-n 


162 


72.86 


4.39 


208.68 


0-76 


66.72 


0.62 


118 


269.76 


4.4s 


130.41 


3.12 


77.13 


0-09 


163 


68.47 


4.39 


209.40 


0.72 


66.19 


0.53 


119 


264.30 


4-46 
4.46 


133.45 


3.04 
2.97 


77.21 


0.08 
0.06 


164 


64.08 


4.39 
4.39 


210.09 


0.69 
0.66 


65.65 


0.64 
0.66 


120 
121 


+259.84 
255.37 


-4.47 


+136.42 
139.32 


+2.90 


+77.27 
77.32 


+0.05 


165 
166 


+ 59.69 
55.30 


-4.39 


+210.74 
211.35 


+0-61 
0.67 


.+65.10 
64.'54 


-0.56 
0-68 
0.59 
0.59 
0.61 
0-62 
0-63 
0.63 


122 


250.89 


4.4s 


142.14 


2.82 


77.35 


0.03 


167 


50.92 


4.38 


211.92 


63.96 


123 
124 
125 
126 
127 


246.42 
241.94 
237.46 
232.97 
228.49 


4-47 
4.48 
4.48 
4-49 
4-48 


144.90 
147.60 
150.22 

152.78 
155.27 


2.76 
2.70 
2.62 
3.56 
2.49 


77.36 
77.36 
77.34 
77.31 
77.26 


+0.01 
0-00 

-0.02 
0-03 
0-05 


168 
169 
170 
171 
172 


46.53 
42.15 
37.77 
33.38 
29.00 


4.39 
4.38 
4.38 
4.39 
4-38 
4-38 
4.39 


2)2.46 
212.96 
213.42 
213.85 
214.24 


0.54 

o.so 

0.46 
0.43 
0-39 
C.35 
0.32 


63.37 
62.78 
62.17 
61.55 
60.92 


128 


224.00 


4.49 


. 157.70 


2.43 


77.20 


0-06 


173 


24.62 


214.59 


60.29 


0.65 


129 


219.51 


4.49 


160.07 


2.37 


77.12 


0-08 


174 


20.23 


214.91 


59.64 








4.48 




2.30 




0.09 






4-38 




0.29 




0.66 


130 


+215.03 




+162.37 




+77.03 




175 


+ 15.85 


-4.39 
4.38 
4.39 
4.39 

-4.39 


+215.20 


+0.24 


+58.98 


-0-67 


131 


210.54 


-4.49 


164.62 


+2.26 


76.92 


-0.11 


176 


11.46 


215.44 


0-21 
0,17 


58.31 


0.68 


132 


206.06 


4.48 


166.80 


2.18 


76.80 


0.12 


177 


7.08 


215.65 


57.63 


0-68 


133 


201.58 


4.48 


168.92 


2.12 


76.66 


0.14 


178 


+ 2 69 


215.82 


0'14 


56.95 


0-70 


134 
135 


197.09 
+192.61 


4.49 

-4-48 


170.99 
+173.00 


2.07 
+2.01 


76.51 
+76.34 


0.15 

-0-17 


179 
180 


- 1.70 

- 6.09 


215.96 
+216.06 


+0.10 


56.25 
+55.54 


-0.71 































42 











TABLE IV. 


Continued. 












PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH 


DECIMAL. 












Terms multiplied with t. Argument = 


M. 












Arg. 


h 


DiflF. 


Vl 


Diff. 


& 


Diff. 


Arg. 


k 


Diff. 


ilx 


Diff. 


& 


Diff 






180 


6.09 




+216.06 




+55.54 






225 


-208.16 




+178.25 




+35.94 






181 


10.48 


-4.39 


216.12 


+0.06 


54.82 


-0.72 


226 


212.78 


-4.63 


176.30 


-1.95 


14.94 


-1-00 




182 


14.88 


4.40 


216.15 


+0.03 


54.10 


0.72 


. 227 


217.40 


4.63 


174.29 


2.01 


13.94 


1.00 




183 


19.27 


4.39 


216.13 


-0.02 


53.36 


0.74 


228 


222.02 


4.63 


172.23 


2.06 


12.93 


1. 01 




134 


23.67 


4.40 


216.09 


0-04 


52.62 


0.74 


229 


226.64 


4.63 


170.11 


2.12 


11.92 


1.01 




185 


28.07 


4.40 


216.00 


0-09 


51.86 


0.76 


230 


231.27 


4.63 


167.92 


2-19 


10.91 


1.01 




186 


32.48 


4.41 


215.88 


0.13 


51.10 


0.76 


231 


235.90 


4.63 


165.68 


2-24 


9.90 


1-01 




187 


36.88 


4.40 


215.72 


0-16 


50.33 


0.77 


232 


240.53 


4.63 


163.37 


2.31 


8.68 


1-02 




188 


41.29 


4-41 


215.52 


0.20 


49.55 


0.78 


233 


245.16 


4.63 


160.99 


2.38 


7.86 


1.02 




189 


45.71 


4.42 
4.43 


215.29 


0.23 
0.27 


48.77 


0.78 
0-80 


234 


249.79 


4.63 
4-63 


158.55 


2.46 
2.51 


6.84 


1-02 
1-02 




190 


- 50.13 




+215.02 




+47.97 




235 


-254.42 




+156.04 




+ 5.82 






191 


54.55 


-4.4s 


214.71 


-0-31 


47.17 


-0-80 


236 


259.05 


-4.63 


153.46 


-2.68 


4.80 


-104 




192 


58.97 


4-42 


214.37 


0.34 


46.36 


0-81 


237 


263.67 


4.62 


150.80 


266 


3.78 


102 




193 


63.40 


4.43 


213.99 


0-38 


45.54 


0.83 


238 


268.30 


4.63 


148.08 


2.72 


2.76 


1.02 




194 


67.84 


4.44 


213.57 


0-42 


44.71 


0-83 


239 


272.92 


4.62 


145.28 


2.60 


1.73 


1-03 




195 


72.28 


4.44 


213.11 


0.16 


43.87 


84 


240 


277.54 


4.62 


142.40 


3-88 


+ 0.71 


1-02 




196 


76.72 


4.44 


212.61 


0-50 


43.03 


0.84 


241 


282.16 


4.62 


139.44 


2-96 


- 0.31 


1-02 




197 


81.17 


4-45 


212.07 


0.54 


42.18 


0.85 


242 


286.77 


4-61 


136.40 


3 04 


1.34 


1.03 




198 


85.63 


4.46 


211.49 


0-68 


41.32 


0.66 


243 


291.37 


4.6O 


133.28 


3.13 


2.36 


1.03 




199 


90.09 


4.46 
4.46 


210.87 


0-62 
0-67 


40.46 


0.86 
0.87 


244 


295.96 


4.59 
4.59 


130.08 


3-20 
3.28 


3.39 


1-03 
1.03 




200 


- 94.55 




+210.20 




+39.59 




245 


-300.55 




+126.80 




- 4.41 






201 


99.02 


—4.47 


209.50 


-0.70 


38.71 


-0.88 


246 


305.13 


-4.68 


123.44 


-3.36 


5.43 


-1 02 




202 


103.50 


4.4s 


208.75 


0-75 


37.82 


0.89 


247 


309.70 


4.67 


119.99 


3.46 


6.45 


1.02 




203 


107.98 


4.48 


207.95 


0.80 


36.93 


0.89 


248 


314.25 


4.56 


116.45 


3.54 


7.47 


1.02 




204 


112.47 


4-49 


207.10 


0.86 


36.03 


0.90 


249 


318.79 


4.54 


112.83 


3 62 


8.49 


1.02 




205 


116.97 


4.50 


206.21 


0.S9 


35.13 


0.90 


250 


323.32 


4-53 


109.12 


3.71 


9.51 


1 03 




206 


121.47 


4.S0 


205.28 


0.93 


34.22 


0.91 


251 


327.83 


4-61 


105.32 


3 80 


10.52 


r.oi 




207 


125.98 


4.51 


204.30 


0-98 


33.30 


0-92 


252 


332.33 


4.50 


101.43 


3.89 


11.53 


l-Ol 




208 


130.49 


4.51 


203.28 


1.02 


32.38 


0.92 


253 


336.81 


4-48 


97.45 


3.98 


12.54 


101 




209 


135.01 


4.53 
4.63 


202.20 


1-08 
1.12 


31.45 


0.93 
0-93 


254 


341.27 


4.46 
4.44 


93.38 


4.07 
4.I6 


13.55 


1 01 
I'OO 




210 


, -139.54 




+201.08 




+30.52 




255 


-345.71 




+ 89.22 




-14.55 






211 


144.07 


—4.53 


199.91 


—1-n 


29.58 


-0-94 


256 


350.12 


-4.41 


84.96 


-4.26 


15.55 


-1.00 




212 


148.61 


4.54 


198.70 


1.21 


28.63 


0.95 


257 


354.51 


4.39 


80.60 


4-36 


16.54 


0.99 




213 


153.16 


4.55 


197.43 


1.27 


27.68 


0-96 


258 


358.88 


4.37 


76.14 


4.46 


17.54 


1.00 




214 


157.71 


4.55 


196.12 


1-31 


26.73 


0.95 


259 


363.21 


4.33 


71.58 


4.66 


18.52 


0.98 




215 


162.27 


4.56 
4.fi6 
4.58 


194.75 


1.37 


25.77 


0.96 


260 


367.51 


4.30 


66.92 


4-66 


19.51 


0.99 




216 


166.83 


193.34 


1.41 


24.81 


0-96 


261 


371.79 


4-28 


62.16 


4.76 


20.49 


0.98 




217 


171.41 


191.87 


1.47 


23.84 


0-97 


262 


376.03 


4.24 


57.29 


4-87 


21.46 


0-97 




218 


175.98 


4.67 
.4-58 


190.35 


1.52 


22.87 


0.97 


263 


380.23 


4.20 


52.32 


4.97 


22.43 


0.97 




219 


180.56 


188.79 


1.56 


21.89 


0.98 


264 


384.39 


4-16 


47.24 


6.08 


23.39 


0.06 








4-59 




1.03 




0.9S 






4.12 




6.19 




0.96 




220 
221 


-185.15 
189.74 


-4.69 
4-60 
4.6O 
4.6I 

-4.6I 


+187.16 
185.49 


-1-67 


+20.91 
19.92 


-0.99 


265 
266 


-388.51 
392.59 


-4.O8 


+ 42.05 
36.75 


-6.30 


-24.35 
25.30 


-0.95 




222 


194.34 


183.76 


1.73 


18.93 


0.99 


267 


396.62 


4.03 


31.34 


6.41 


26.24 


0.94 




223 


198.94 


181.98 


1.78 


17.94 


0.99 


268 


400.60 


3-98 


25.82 


6.62 


27.18 


0-94 




224 

225 


203.55 
-208.16 


180.14 

+178.25 


1.84 
-1-89 


16.94 
+15.94 


1.00 
-LOO 


269 
270 


404.53 
-408.40 


3-93 

-3.87 


20.18 
+ 14.43 


6.64 
-6.75 


28.11 
-29.03 


0.93 
-0.93 





43 











TABLE I Y .—Continued. 










PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. | 










Terms multiplied with t. Argument = M. 










Arg. 


?i 


Diff. 


Vl 


Diff. 


ri 


Diff. 


Arg. 


«i 


Diff 


Vl 


Diff. 


?1 


Diff 


270° 


-408.40 




+ 14.43 




-29.03 






315 


-457-24 




-365-32 




-56.92 




271 


412.21 


-3-81 


8.56 


- 6.87 


29.95 


-0.92 


316 


453-65 


+ 8.59 


375-78 


-10.46 


57.09 


-0-17 


272 


415.97 


3.76 


+ 2.57 


6.99 


30.86 


0.91 


317 


449.75 


3.90 


386-26 


10-48 


57.23 


0-14 


273 


419.65 


3-68 


- 3.54 


6-11 


31.76 


0.90 


318 


445.57 


4.18 


396-75 


10-49 


57.35 


0-12 


274 


423.27 


3-63 


9.77 


6.23 


32.65 


0-69 


319 


441.07 


4.60 


407.22 


10-47 


57.44 


09 


275 


426.82 


3.56 


16.11 


6-34 


33-53 


0.8S 


320 


436.26 


4.81 


417.67 


10-46 


57.50 


0-06 


276 


430.29 


3-47 


22.58 


6.47 


34-40 


0.87 


321 


431.15 


6-11 


428.09 


10-42 


57.54 


0-04 


277 


433.68 


3.39 


29.18 


6-60 


35-26 


0-86 


322 


425.71 


6-44 


438.48 


10-39 


57-55 


-0-01 
+0-02 


278 


436.99 


3.31 


35.89 


6.71 


36.12 


0-86 


323 


419.95 


6-76 


448.82 


10.34 


57.53 


279 


440.21 


3.32 
3-13 


42.73 


6-84 
6.96 


36.96 


0-84 
0-83 


324 


413.87 


6-08 
6-41 


459.11 


10.29 
10-23 


57.48 


0-06 
0-08 


280 


-443.34 




- 49.69 




-37.79 




325 


-407.46 




-469.34 




-57^0 




281 


446.38 


-3.04 


56.78 


- 7.09 


38.61 


-0-82 


326 


400.72 


+ 6-74 


479.48 


-10-14 


57.29 


+0-11 


282 


449.32 


2.94 


63.99 


7.21 


39.41 


0-eo 


327 


393.66 


7.06 


489.53 


10-05 


57.15 


0-14 


283 


452.15 


2.83 


71.33 


7-34 


40.21 


0-80 


328 


386.26 


7-40 


499.48 


9-95 


56.98 


0-17 


284 


454.87 


2.72 


78.80 


7.47 


40.99 


0-78 


329 


378.53 


7-73 


509.30 


9-82 


56.78 


0-20 


285 


457.49 


2.*62 


86.39 


7.59 


41.76 


0-77 


330 


370.48 


8.05 


519.00 


9-70 


56.55 


0-23 


286 


459.98 


2.49 


94.10 


7.71 


42.52 


0-76 


331 


362.10 


8-38 


528.54 


9-64 


56.29 


0-26 


287 


462.36 


2.38 


101.94 


7.84 


43.26 


0-74 


332 


353.39 


8-71 


537.91 


9-37 


56.00 


0-29 


288 


464.60 


2.24 


109.90 


7-96 


43.99 


0-73 


333 


344.36 


9-03 


547.12 


9-21 


55.68 


0-32 


289 


466.72 


2-12 
1.98 


117.99 


8-09 
8.21 


44.71 


0-72 
0-70 


334 


335.01 


9-35 
9-07 


556.14 


9-02 
8-81 


55.33 


0-36 
0-38 


290 


-468.70 




-126.20 




-45.41 




335 


-325.34 




-564.95 




-54.95 




291 


470.54 


-1.84 


134.53 


- 8.33 


46.10 


-0-69 


336 


315.35 


+ 9-99 


573.56 


- 8-61 


54.54 


+0-41 


292 


472.23 


1.69 


142.98 


8-45 


46.77 


0-67 


337 


305.03 


10-32 


581.93 


8 37 


54.10 


0-44 


293 


473.76 


1.S3 


151.55 


8.57 


47.42 


0-65 


338 


294.42 


10-61 


590.06 


8-13 


53.62 


0-48 


294 


475.14 


1.38 


160.24 


8-69 


48.06 


0.64 


339 


283.51 


10-91 


597.95 


7.89 


53.12 


0-60 


295 


476.36 


1-22 


169.05 


8.81 


48.68 


0-62 


340 


272.30 


11.21 


605.56 


7-61 


52.58 


0-54 


296 


477.40 


1.04 


177.97 


8-92 


49.29 


0-61 


341 


260.82 


11-48. 


612.89 


7-33 


52.01 


0-57 


297 


478.27 


0.87 


187.01 


9.04 


49.87 


0-68 


342 


249.07 


11-76 


619.93 


7-04 


51.42 


0-59 
0-63 


298 


478.96 


0-69 


196.16 


9-16 


50.44 


0-57 


343 


237.06 


12-01 


626-66 


6-73 


50.79 


299 


479.46 


0.50 
0-32 


205.42 


9-26 
9.36 


50.99 


0-55 
0-53 


344 


224.81 


12-25 
12-60 


633.06 


6.40 
6.08 


50.13 


0-66 
0-69 


300 


-479.78 




-214.78 




-51.52 




345 


-212.31 




-639.14 




-49.44 


+0-72 
0.75 
0-78 
0-80 
0-84 
0-36 


301 


479.90 


-0.12 


224.25 


- 9-47 


52.03 


-0-61 


346 


199.59 


+12-72 


644.88 


— 5.74 


48.72 


302 


479.81 


+0.09 


233.82 


9-57 


52.52 


0-49 


347 


186.65 


12-94 


650.26 


6.38 


47.97 


303 


479.52 


0-29 


243.48 


9.66 


52.99 


0-47 


348 


173.50 


13-15 


655.28 


6.02 
4-63 
4.25 
3-86 
3-46 
3-05 
2-66 


47-19 


304 
305 


479.00 
478.27 


0.52 
0-73 


253.24 
263.09 


9.76 
9.88 


53.44 
53.87 


0-45 
0-43 


349 
350 


160.15 
146.64 


13-35 
13-61 


659.91 
664-16 


46-39 
45.-55 


306 


477.30 


0-97 


273.02 


9-93 


54.28 


0-41 


351 


132.95 


13-69 


668-02 


44.69 


0-90 


307 


476.10 


1.20 


283.02 


10.00 


54.67 


0-39 


352 


119.11 


13-84 


671.48 


43.79 


0-92 


308 


474.65 


1.45 


293.10 


10-08 


55.03 


0-36 


353 


105.16 


13-95 


674.53 


42.87 


0-94 


309 


472.96 


1.69 
1.95 


303.26 


10.16 
10-22 


55.37 


0-34 
0-32 


354 


91.08 


14-08 
14-17 


677.18 


2-24 


41.93 


0-98 


310 
311 
312 
313 
314 


-471.01 
468.79 
466.32 
463.57 
460.55 


+2.22 
2.47 
2-75 
9.02 


-313.48 
323.75 
334.08 
344.46 

354.88 


-10-27 
10-33 
10.38 
10.42 


-55.69 
55.99 
56.26 
56.50 
56.72 


-0-30 
0-27 
0-24 
0-22 


355 
356 
357 
358 
359 


- 76.91 
62.67 
48.36 
34.01 
19.63 


+14-24 
14-31 
14-35 
14-38 

+13-39 


-679.42 
681.24 
682.63 
683.60 
684.12 


- 1-82 
1-39 
0-97 
0-52 

— 0-10 


-40.95 
39.95 
38.93 
37.88 
36-81 


+1-00 
1-02 
1-06 
1-07 

+1-10 


315 


-457.24 


+3.31 


-365.32 


-10.44 


-56.92 


—0-20 


360 


- 5.24 


-684.22 




-35-71 





44 



TABLE IV. — Continued. 






PERTURBATIONS OF THE CO-ORDINATES IN UNITS 


OF THE SIXTH DECIMAL. 


ARGUMENT I. 






Arg. 


Ji 


Diff. 


n\ 


Diff. 


Si 


Diff. 


Arg. 


h 


Diff. 


Vl 


Diff. 


& 


Diff. 


O 


1 


-577 
570 


+ 7 


+177 

201 


+24 


+21 
21 







45 
46 


+ 303 
339 


+36 


+928 
933 


+ 6 
3 


+37 
38 


+1 



2 


562 


8 


225 


24 


21 





47 


375 


36 


936 


n 


38 


1 


3 


554 


8 


248 


2S 


22 


+1 


48 


412 


37 

38 


938 


+ 2 


39 


1 


4 ■ 


545 


9 


271 


23 


22 





49 


450 


940 


— \ 


40 


1 


5 


536 


9 


294 


23 


22 





50 


488 


38 


939 


1 

g 


41 





6 


526 


10 


316 


22 


22 





51 


527 


39 


938 


41 


J 


7 


515 


11 


338 


22 


23 


1 


52 


567 


40 


935 


6 
6 


42 


1 


8 


504 


11 


360 


22 


23 





53 


607 


40 


930 


43 


■ 1 


9 


493 


11 


381 


21 


23 





54 


» 648 


41 


925 


44 








12 




21 











41 




8 




1 


10 


-481 




+402 




+23 




55 


+ 689 




+917 




+45 


+1 



1 
1 
1 
1 



1 




11 


468 


+ 13 


423 


+21 


24 


+1 


56 


1U 


+42 


908 


— 9 


46 


12 


455 


IS 


444 


31 


24 





57 


773 


42 


898 


10 


46 


13 


441 


14 


464 


20 


24 





58 


815 


42 


885 


13 


47 


14 


427 


14 


484 


20 


24 





59 


857 


42 


871 


» 14 


48 


15 


413 


14 


503 


19 


24 





60 


900 


43 


856 


15 


49 


16 


398 


16 


522 


19 


25 


1 


61 


942 


42 


838 


18 


50 


17 


383 


15 


542 


20 


25 





62 


985 


43 


819 


19 


50 


18 


367 


16 


560 


18 


25 





63 


1027 


42 


798 


21 


51 


19 


350 


17 


579 


19 


25 





64 


1069 


42 


775 


23 


51 






17 




18 




1 






43 




26 




1 


20 
21 


-333 
316 


+17 


+597 
615 


+18 


+26 
26 


+0 


65 
66 


+1111 
1153 


+43 


+750 
723 


-27 


+52 
52 


+0 


22 


298 


18 


633 


18 


26 





67 


1194 


41 


695 


28 


53 


1 


23 
24 


279 
260 


19 
19 


650 
667 


17 
17 


26 

27 




1 


68 
69 


1234 
1274 


40 
40 


665 
632 


30 
33 


53 
54 




+1 


25 


241 


19 


684 


17 


27 





70 


1314 


40 


598 


34 


54 





26 


220 


21 


701 


17 


27 





71 


1352 


38 


563 


35 


54 





27 


200 


20 


717 


16 


28 


1 


72 


1390 


38 


525 


38 


54 





28 


178 


32 


733 


16 


28 





73 


1427 


37 


485 


40 


54 





29 


156 


22 
S3 


749 


16 
15 


28 




1 


74 


1463 


36 
35 


444 


41 
43 


54 




-1 


30 


-133 




+764 




+29 




75 


+1498 




+401 




+53 




31 


109 


+24 


779 


+15 


29 


+0 


76 


1532 


+34 


356 


-46 


53 


-0 


32 


85 


24 


793 


14 


29 





77 


1564 


33 


310 


46 


53 





33 


60 


25 


807 


14 


30 


1 


78 


1595 


31 


262 


48 


52 




34 


34 


26 


821 


14 


30 





79 


1625 


30 


212 


50 


51 




35 


- 8 


26 


834 


13 


31 


1 


80 


1653 


38 


161 


51 


51 




36 


+ 20 


28 


847 


13 


31 





81 


1680 


37 


108 


63 


50 




37 


48 


28 


859 


12 


32 


1 


82 


1705 


25 


+ 54 


64 


49 




38 


77 


29 


870 


11 


32 





83 


1729 


24 


- 2 


66 


47 




39 


107 


30 
30 


881 


11 
10 


33 


1 




84 


1751 


22 
20 


59 


57 
69 


46 




40 


+137 




+891 




+33 




85 


+1771 




-118 




+45 




41 


169 


+32 


900 


+ 9 


34 


+1 . 


86 


1789 


+18 


178 


-60 


43 


-2 


42 


201 


32 


908 


8 


35 


1 


87 


1805 


16 


239 


61 


41 


2 


43 


234 


33 


916 


B 


35 





88 


1819 


14 


301 


62 


40 


1 


44 


268 


34 


923 


7 


36 


1 


89 


1831 


12 


365 


«4 


38 


2 


45 


+303 


+35 


+928 


+ M +37 


+1 


90 


+1841 


-tilO 


-429 


-64 


+36 


-2 



45 











TABLE IV. Contmied. 














PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 












ARGUMENT I. 














Atg. 


Si 


Diff. 


•ni 


Diff. 


& 


Diff. 


Arg. 


h 


Diff. 


Vl 


Diff. 


?1 


Diff. 




o 
90 


+1841 




- 429 




+ 36 





135 


- 408 




-2839 




-116 






91 


1848 


+ 7 


495 


-66 


34 


-2 


136 


506 


-98 


2840 


- 1 


119 


-3 




92 


1854 


6 
+ S 


561 


66 


31 


3 


137 


605 


99 


2837 


+ 3 


122 


3 




93 


1857 


628 


67 


29 


2 


138 


704 


99 


2831 


6 


125 


3 




94 


1857 





696 


68 


27 


2 


139 


803 


99 


2820 


11 


127 


2 




95 


1856 


- 1 


765 


69 


24 


3 


140 


902 


9D 


2806 


14 


130 


3 




96 


1851 


a 


834 


69 


21 


3 


141 


1001 


99 


2788 


18 


132 


2 




97 


1844 


7 


904 


70 


18 


3 


142 


1100 


99 


2767 


21 


134 


2 




98 


. 1835 


9 


975 


71 


15 


3 


143 


1198 


98 


2741 


26 


136 


2 




,99 


1823 


12 
IS 


1045 


70 
71 


12 


3 
3 


144 


1295 


97 
90 


2712 


29 
33 


138 


2 
2 




100 


+1808 




-1116 




+ 9 




145 


-1391 




-2679 




-140 






101 


1791 


-17 


1187 


-71 


6 


-3 


146 


1487 


-96 


2642 


+ 37 


341 


-1 




102 


1771 


20 


1259 


72 


+ 3 


3 


147 


1581 


94 


2602 


40 


143 


2 




103 


1748 


23 


1330 


71 





3 


148 


1674 


93 


2558 


44 


144 






104 


1722 


26 


1401 


71 


- 4 


4 


149 


1766 


92 


2510 


48 


145 






105 


1693 


29 


1471 


70 


7 


3 


150 


1856 


90 


2459 


51 


146 






106 


1661 


32 


1542 


71 


11 


4 


151 


1944 


88 


2405 


64 


147 






107 


1626 


33 


1612 


70 


14 


3 


152 


2030 


86 


2347 


68 


148 






108 


1589 


37 


1681 


69 


18 


4 


153 


2114 


84 


2286 


61 


148 







109 


1548 


11 
44 


1749 


68 
G8 


22 


4 
3 


154 


2196 


62 
80 


2221 


65 
67 


149 


—1 





110 


+1504 




-1817 




- 25 




155 


-2276 




-2154 




-149 






111 


1458 


-46 


1883 


-66 


29 


-4 


156 


2354 


-78 


2083 


+ 71 


149 







112 


1409 


49 


1949 


66 


33 


4 


157 


2429 


75 


2009 


74 


149 



+1 




113 


1356 


53 


2013 


64 


37 


4 


158 


2501 


73 ' 


1933 


76 


148 




114 


1301 


35 


2975 


62 


41 


4 


159 


2571 


70 


1854 


79 


148 







115 


1243 


68 


2136 


61 


45 


4 


160 


2637 


66 


1772 


82 


147 






116 


1182 


61 


2196 


60 


48 


3 


161 


2701 


64 


1688 


84 


146 






117 


1118 


64 


2253 


57 


52 


4 


162 


2762 


61 


1601 


87 


145 




118 


1052 


66 


2309 


56 


56 


4 


163 


2819 


57 


1512 


89 


144 






119 


983 


C9 

72 


2363 


54 
51 


60 


4 

4 


164 


2874 


55 
61 


1420 


92 
93 


143 


2 




120 


+ 911 




-^14 




-64 




165 


-2925 




-1327 


+ 95 
97 
99 
101 
102 
1C3 
104 
106 
107 


-141 


+1 




121 


837 


-74 


3463 


-49 


68 


-4 


166 


2973 


—48 


1232 


140 


2 
2 




122 


760 


77 


2509 


46 


72 


4 


167 


3017 


44 


1135 


138 




123 


681 


79 


2553 


44 


75 


3 


168 


3058 


41 


1036 


136 


a 




124 


600 


81 


2595 


42 


79 


4 


169 


3095 


37 


935 


134 


2 




125 
126 


516 
431 


SI 
83 


2633 

2668 


38 
33 


83 
86 


4 
3 


170 
171 


3128 
3158 


33 
30 


833 

730 


132 
129 


3 

2 




127 


344 


87 


2701 


33 


90 


4 


172 


3184 


26 


626 


127 


3 




128 


255 


89 


, 2730 


29 


94 


4 


173 


3206 


22 


521 


124 


3 




129 


164 


91 


2756 


26 


97 


3 


174 


3224 


18 


414 


121 










93 




22 




3 






15 




107 




3 




130 


+ 71 




-2778 




-100 




175 


-3239 


-10 

6 

- 8 

+ 2 
+ S 


- 307 


+107 


-118 


+S 




131 


- 22 


-93 


2797 


-19 


104 


—4 


176 


3249 


200 


108 
109 


115 


3 




132 


117 


95 


2813 


16 


107 


3 


177 


3255 


- 92 


112 


3 




133 


213 


9S 


2825 


12 


110 


3 


178 


3258 


+ 17 


108 


109 


4 




134 


310 


97 


2834 


9 


113 


3 


179 


3256 


125 


+109 


105 


+3 




135 


-408 


-98- 


-2839 


— 5 


-116 


—3 


180 


-3251 


+ 234 




-102 





































46 











TABLE lY .—Continued. 


PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 










ARGUMENT- I. | 


Arg. 


& 


Diff. 


Vl 


Diff 


?1 


Diff 


Arg. 


li 


Diff. 


Vl 


Diff. 


& 


Diff. 


180° 
181 
182 


-3251 
3241 

3228 


+ 10 
13 


+ 234 
342 
450 


+108 
108 


-102 
98 
94 


+4 
4 


o 

225 
226 
227 


+ 122 
220 
316 


+98 
96 


+2878 
2857 
2832 


-21 

25 


+78 
80 
82 


+2 
2 
2 
2 
2 
2 
2 


183 


3210 


18 


558 


108 


91 


3 


228 


411 


96 


2804 


28 


84 


184 

185 ^ 


3188 
3163 


22 
25 


664 
771 


106 
107 


87 
83 


4 
4 


229 
230 


505 
596 


94 
91 


2773 
2738 


31 

35 


86 

88 


186 


3133 


80 


876 


103 


79 


4 


231 


,686 


90 


2700 


38 


90 


187 


3099 


34 


980 


104 


75 


4 


232 


774 


88 


2659 


41 


92 


188 


3062 


37 


1083 


103 


70 


6 


233 


859 


83 


2615 


44 


93 


1 


189 


3020 


42 
45 


1184 


101 
100 


66 


4 
4 


234 


942 


83 
81 


2568 


47 
60 


94 


1 

• 
1 


190 
191 


-2975 
2926 


+ 49 


+1284' 
1382 


+ 98 


- 62 

57 


+5 


235 
236 


+1023 
1101 


+78 


+2518 
2466 


-62 


+95 
96 


+1 


192 


2874 


62 


1476 


96 


53 


4 


237 


1177 


76 


2411 


65 


97 


1 


193 


2817 


57 


1572 


94 


49 


4 


238 


1250 


73 


2354 


57 


98 


1 


194 


2758 


69 


1664 


92 


44 


6 


239 


1320 


70 


2294 


60 


98 





195 


2695 


63 


1754 


90 


40 


4 


240 


1388 


68 


2233 


61 


98 





196 


2628 


67 


1841 


87 


35 


5 


241 


1453 


63 


2169 


64 


98 • 




+1 
-1 


197 
198 


2558 
2485 


70 
73 


1926 

2008 


85 
82 


31 

26 


4 
6 


242 
243 


1514 
1573 


61 
39 


2103 
2036 


66 
67 


99 

98 


199 


2410 


75 
79 


2087 


79 
76 


22 


4 
5 


244 


1629 


36 
33 


1967 


69 
71 


98 






200 
201 


-2331 
2249 


+ 82 


+2163 
2236 


+ 73 


- 17 
13 


+4 


245 
246 


+1682 
1732 


+30 


+1896 
1824 


-72 


+98 
97 


-1 


202 


2165 


84 


2306 


70 


8 


3 


247 


1778 


46 


1751 


73 


97 





203 


2079 


86 


2372 


66 


- 4 


4 


248 


1822 


44 


1676 


78 


96 


1 


204 


1990 


89 


2435 


63 


+ 1 


5 


249 


1862 


40 


1601 


75 


95 


1 


205 


1899 


91 


2495 


60 


5 


4 


250 


1899 


37 


1524 


77 


94 


1 


206 


1806 


93 


2551 


56 


10 


6 


251 


1933 


34 


1447 


77 


93 


1 


207 


1711 


95 


2603 


62 


14 


4 


252 


1963 


30 


1369 


78 


92 


1 


208 


1614 


97 


2651 


48 


18 


4 


253 


1990 


27 


1291 


78 


90 


2 


209 


1516 


98 
99 


2696 


43 
41 


23 


5 

4 


254 


2015 


25 
20 


1212 


79 
78 


89 


1 
2 


210 
211 
212 
213 


-1417 
1316 
1214 
1112 


+101 
102 
102 


+2737 
2774 
2807 
2836 


+ 37 
33 

29 


+ 27 
31 
35 
39 


+4 
4 
4 


255 
256 
257 

258 


+2035 
2053 
2067 
2079 


+18 
14 
12 


+1134 

1055 

976 

897 


-79 
79 
79 


+87 
86 
84 
82 


-1 

2 
2 


214 


1008 


104 


2861 


25 


43 


4 


259 


2087 


8 


818 


79 


80 


9 


215 


905 


103 


2882 


21 


46 


3 


260 


2093 


6 


740 


78 


78 


2 


216 
217 


801 
697 


104 
104 


2900 
2913 


18 
13 


50 
54 


4 
4 


261 
262 


2095 
2094 


+ 2 
- 1 


663 
586 


77 
77 


76 

74 


2 
2 


218 


593 


104 


2922 


9 


57 


3 


263 


2090 


4 


509 


77 


72 


2 


219 


489 


104 
104 


2927 


6 
+ 2 


60 


3 
3 


264 


2083 


7 
9 


434 


75 
74 


70 


2 
2 


220 
221 


- 365 

282 


+103 


+2929 
2926 


- 3 


+ 63 
67 


+4 


265 
266 


+2074 
2061 


-13 


+ 360 
286 


-74 


+68 
66 


-2 


222 


180 


102 


2920 


6 


70 


3 


267 


2046 


IS 


214 


72 


63 


3 


223 


- 76 


102 


2910 


10 


72 


2 


268 


2029 


17 


143 


71 


61 


2 


224 

225 


+ 22 
+ 122 


100 

+100 


2896 

+2878 


14 

- 18 


75 

+ 78 


3 

+3 


269 
270 


2008 
+1985 


21 
-23 


74 
+ 6 


69 
-68 


59 
+56 • 


2 
-3 



47 





TABLE IV. Continued. 










PERTURBATIONS OP THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 


• 


ARGUMENT I. 










Arg. 


& 


DifF. 


Vl 


Diff. 


?1 


Diff. 


Arg. 


fi 


Diff. 


V\ 


Diff. 


tx 


Diff. 


o 
270 


+1985 




+ 6 




"+56 






315 


- 20 




-962 




-10 




271 


1960 


-25 


- 61 


-67 


54 


-2 


316 


55 


-35 


944 


+18 


9 


+1 


272 


1933 


27 


126 


66 


51 


3 


317 


89 


34 


925 


19 


9 




273 


1903 


30 


189 


63 


49 


2 


318 


122 


33 


905 


20 


8 




274 


1871 


32 


250 


61 


46 


3 


319 


154 


32 


884 


21 


8 




275 


1837 


34 


309 


69 


44 


2 


320 


185 


31 


863 


21 


7 




276 


1802 


35 


367 


58 


42 


2 


321 


215 


30 


841 


22 


6 




277 


1764 


38 


422 


66 


39 


3 


322 


243 


28 


818 


23 


6 




278 


1725 


39 


475 


53 


37 


2 


323 


270 


27 


795 


23 


5 




279 


1684 


41 
43 


527 


52 
49 


34 


3 
2 


324 


296 


26 
25 


771 


24 
24 


4 




280 


+1641 




- 576 




+32 




325 


-321 




-747 




- 3 




231 


1597 


-44 


623 


-47 


30 


-2 


326 


345 


-24 


722 


+25 


2 


+1 


282 


1552 


45 


668 


45 


27 


3 


327 


368 


23 


697 


26 


1 




283 


1505 


47 


710 


42 


25 


2 


328 


390 


22 


671 


26 


- 1 




234 


1458 


47 


750 


40 


23 


3 


329 


410 


20 


645 


26 







235 


1409 


49 


788 


38 


21 


2 


330 


430 


20 


619 


26 


+ 1 




236 


1360 


49 


824 


36 


18 


3 


331 


448 


18 


593 


26 


2 




287 


1310 


50 


857 


33 


16 


2 


332 


465 


17 


566 


27 


3 




288 


1259 


61 


888 


31 


14 


2 


333 


481 


16 


539 


27 


4 




289 


1208 


61 
52 


916 


28 
26 


12 


2 
2 


334 


497 


16 
14 


512 


27 
27 


5 




290 


+1156 




- 942 




+10 




335 


-511 




-485 




+ 6 




291 


1104 


-62 


966 


-24 


8 


-2 


336 


524 


-13 


458 


+27 


7 


+1 


292 


1052 


bi 


988 


22 


7 


1 


337 


536 


12 


431 


. 27 


8 




293 


999 


53 


1008 


20 


5 


2 


338 


548 


12 


403 


28 


8 




294 


947 


52 


1025 


17 


3 


2 


339 


558 


10 


376 


27 


9 




295 


895 


52 


1040 


15 


+ 2 


1 


340 


567 


9 


348 


28 


10 




296 


843 


62 


1053 


13 





2 


341 


576 


9 


321 


27 


11 




297 


791 


62 


1064 


11 


- 1 


1 


342 


583 


7 


293 


28 


12 




298 


740 


61 


1072 


8 


2 


1 


343 


590 


7 


266 


27 


12 




299 


689 


SI 
61 


1079 


7 
5 


4 


2 
1 


344 


595 


6 
6 


239 


27 
28 


13 




300 
301 


+ 638 

588 


-SO 


-1084 
1087 


- 3 


- 5 
6 


-1 


345 
346 


-600 
604 


- 4 


-211 

184 


+27 


+14 
14 


+0 


302 


539 


49 


1088 


- 1 


7 


1 


347 


607 


3 


157 


27 


15 




303 


490 


49 


1087 


+ 1 


7 





348 


609 


2 


130 


27 


16 




304 


443 


47 


1085 


2 


8 


1 


349 


611 


- 2 


103 


27 


16 




305 


396 


47 


1081 


4 


9 


1 


350 


611 





77 


26 


17 




306 


350 


46 


1075 


6 


9 





351 


611 





50 


27 
26 
26 
26 


17 




307 


304 


46 


1068 


7 


10 


-I 


352 


610 


+ 1 


- 24 


18 


308 


260 


44 


1059 


9 


10 





353 


609 


1 


+ 2 


18 


309 


217 


43 


1049 


10 


10 





354 


606 


3 


28 


19 






42 




12 











3 




25 






310 
311 


+ 175 
134 


-41 


-1037 
1024 


+13 


-10 
10 





355 
356 


-603 
599 


+ 4 


+ 53 

79 


+26 
26 
25 
24 

+24 


+19 
19 


+0 


312 


94 


40 


1010 


14 


10 





357 


595 


4 


104 


20 




313 


55 


39 


995 


15 


10 





358 


590 


6 


129 


20 




314 

315 


+ 17 
- 20 


38 
-37 


979 
- 962 


16 

+17 


10 
-10 






359 
360 


584 
-577 




+ 7 


153 

+177 


20 
+21 


+1 



48 



TABLE lY .—Gmdinued. 
PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 

ARGUMENT H. 



Arg. 




1 
2 
3 

4 
5 
6 

7 
8 
9 

10 
11 
12 
13 
14 
15 
16 
17 
18 
19 

20 
21 
22 
23 
24 
25 
26 
27 
28 
29 

30 
31 
32 
33 
34 
35 
36 
37 
38 
39 

40 
41 
42 
43 
44 
45 



li 



+551 
550 
548 
547 
546 
544 
542 
540 
538 
536 

+534 
531 
528 
525 
521 
517 
513 
508 
503 
498 

+492 
485 
478 
470 
462 
453 
444 
434 
423 
411 

+399 
386 
372 
358 
342 
396 
309 
291 
273 
253 

+233 
211 

189 

166 

142 

+118 



Diff. 



- 7 

. 7 

8 

8 

9 

9 

10 

11 

12 



-13 

U 
14 
16 
16 
17 
18 
13 
20 

20 

-22 
22 
23 
24 

-24 



ni 



+ 51 

65 

78 

91 

105 

118 

134 

146 

160 

174 

+188 
202 
217 
231 
246 
261 
276 
292 
307 
323 

+339 
355 
371 
387 
404 
420 
437 
453 
470 
487 

+503 
520 
536 
553 
569 
585 
601 
€17 
632 
647 

+661 
676 
689 
703 
715 

+727 



Diff. 



+14 
13 
13 
14 
13 
14 
14 
14 
14 

14 

+14 
15 
14 
15 
15 
15 
IS 
15 
16 

16 

+16 
16 
16 
17 
16 
17 
16 
17 
17 

16 

+17 
16 
17 
16 
16 
16 
16 
15 
19 

14 

+15 
13 

14 

12 

+12 , 



Kx 



-38 
37 
37 
36 
35 
34 
34 
33 
32 
• 31 

-31 

30 
29 
28 
28 
27 
27 
26 
25 
25 

-24 
24 
24 
23 
23 
22 
22 
22 
22 
22 

-21 
21 
21 
21 
21 
21 
21 
21 
21 
21 

-22 

22 

22 

22 

22 
-23 



Diff. 



+1 



1 
1 
1 



1 

1 
1 



+1 
1 
1 



1 



1 
1 



1 

+0 


1 

D 
1 





+1 













Arg. 



45 
46 
47. 
48 
49 
50 
51 
52 
53 
54 



65 
66 
67 
68 
69 
70 
71 
72 
73 
74 

75 
76 

77 
78 
79 
80 
81 
82 
83 
84 

85 
86 

87 



90 



h 



+ 118 

92 

66 

39 

+ 12 

^ 17 

46 

76 

106 

137 



55 


- 169 


56 


201 


57 


233 


58 


266 


59 


299 


60 


333 


61 


367 


62 


401 


63 


435 


64 


470 



- 504 
538 
573 
607 
641 
674 
708 
740 
773 
805 

-836 

866 

896 

925 

9S3 

980 

1006 

1031 

1055 

1077 

-1098 
1118 
1137 
1154 
1170 

-1184 



Diff. 



-26 
26 
27 
27 
29 
29 
30 
30 
31 



-32 
32 
33 
33 
34 
34 
34 
34 
35 

34 

-34 
35 
34 
34 
33 
34 
32 
33 
32 

31 

-30 
30 
29 
28 
27 
26 
25 
24 
22 

21 

-20 

19 

17 

16 
-14 



■ni 



+727 

739 
750 
760 
769 

777 
785 
791 
797 
802 

+805 
808 
810 
810 
809 
807 
804 
799 
793 
786 

+778 
768 
756 
744 
730 
714 
697. 
679" 
660 
638 

+616 
592 
567 
540 
512 
483 
453 
421 
388 
354 

+319 

282 

245 

206 

167 
+127 



Diff. 



+12 
11 
10 



G 

5 

3 

+ 3 
+ 2 

- 1 
2 
3 
9 
6 
7 



-10 
12 
.12 
14 
16 
17 
IS 
19 
20 



-24 
25 
27 
28 
29 
30 
32 
33 
34 

35 

-37 

37 



-23 
23 
23 
24 
24 
24 
24 
25 
25 
25 

-26 
26 
26 

27 
27 
27 
27 
27 
28 
28 



28 
28 
28 
28 
28 
28 
28 
27 
27 

-27 
26 
26 
26 
25 
24 
24 
23 
22 
22 

-21 

20 
19 
18 
17 
-15 



Diff. 



-0 



1 





1 






-0 


1 






-1 













+1 




+1 




1 

1 



1 
1 



1 

+1 

1 
1 
1 

+2 



49 











TABLE 1\.— Continued 














PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 












ARGUMENT 11. 














Arg. 


h 


Diff. 


Vl 


DifF. 


Si 


Diff. 


Arg. 


li 


Diff. 


Vi 


Diff. 


?1 


Diff. 






90 


-1184 




+ 127 




-15 




o 
135 


+ 5 




-1420 




+ 76 






91 


1196 


-12 


86 


-41 


14 


+1 


136 


61 


+56 


1424 


- 4 


77 


+1 




92 


1207 


11 


44 


42 


13 


1 


137 


117 


56 


1425 


- 1 

+ 1 


79 


2 




93 


1216 


9 


+ 1 


43 


11 


♦ 2 


138 


174 


57 


1424 


81 


2 




94 


1223 


7 


- 42 


43 


10 


1 


139 


230 


56 


1421 


3 


83 


2 




95 


1228 


5 


85 


43 


,9 


1 


140 


286 


66 


1416 


6 


85 


2 




96 


1232 


4 


130 


46 


7 


2 


141 


342 


66 


1408 


8 


86 


1 




97 


1234 


- 3 


174 


44 


5 


2 


342 


398 


66 


1399 


9 


88 


2 




98 


1234 





219 


45 


4 


1 


143 


453 


55 


1387 


12 


89 


1 




99 


1232 


+ 2 
4 


265 


46 

46 


- 2 


2 
2 


_ 144 


509 


56 

64 


1374 


13 
16 


91 


2 

1 




100 


-1228 




- 310 









145 


+ 563 




-1358 




+ 92 






101 


1222 


+ 6 


356 


-46 


+ 1 


+1 


146 


617 


+54 


1340 


+18 


93 


+1 




102 


1214 


8 


401 


45 


3 


2 


147 


670 


63 


1320 


20 


94 


1 




103 


1204 


10 


447 


46 


5 


2 


148 


723 


63 


1298 


22 


96 


2 




104 


1193 


11 


492 


45 


7 


2 


149 


774 


61 


1274 


24 


97 


1 




105 


1179 


14 


538 


46 


9 


2 


150 


825 


61 


1248 


26 


98 


1 




106 


1163 


16 


583 


45 


11 


2 


151 


875 


60 


1221 


27 


99 


1 




107 


1146 


17 


627 


44 


13 


2 


152 


923 


48 


1191 


30 


99 







108 


1126 


20 


671 


44 


15 


2 


153 


971 


48 


1159 


32 


100 


1 




109 


1104 


22 
23 


715 


44 
43 


17 


2 
3 


154 


1017 


46 
44 


1126 


33 
35 


101 


1 






110 
111 


-1081 
1056 


+25 


- 758 
800 


-42 


+20 
22 


+2 


155 
156 


+1061 
1105 


+44 


-1091 
1054 


+37 


+101 
102 


+1 




112 


1028 


28 


842 


42 


24 


2 


157 


1147 


42 


1016 


38 


102 







113 


999 


29 


882 


40 


26 


2 


158 


1187 


40 


976 


40 


102 







114 


968 


31 


922 


40 


29 


3 


159 


1225 


38 


934 


42 


102 




+1 




115 


936 


32 


961 


39 


31 


3 


160 


1262 


37 


891 


43 


103 




116 


901 


35 


999 


38 


33 


2 


161 


1297 


36 


847 


44 


103 







117 


865 


36 


1035 


36 


35 


2 


162 


1330 


33 


801 


46 


102 


—1 




118 


827 


38 


1070 


35 


38 


3 


163 


1362 


32 


755 


46 


102 







119 


788 


39 
41 


1104 


34 
33 


40 


2 
2 


164 


1391 


29 
28 


707 


48 
60 


102 








120 
121 
122 


- 747 
705 
661 


+42 
44 


-1137 
1168 
1197 


-31 
29 


+42 
45 
47 


+3 
2 


165 
166 
167 


+1419 
1445 
1468 


+26 
23 


- 657 
607 
556 


+50 
61 
62 
62 
54 
64 
64 


+102 
101 
101 


-1 



1 

2 




123 


616 


45 


1225 


28 


49 


2 


168 


1489 


31 
30 
17 
15 
13 
10 
9 


504 


100 




124 


569 


47 


1252 


27 


52 


3 


169 


1509 


452 


99 







125 
126 


522 
473 


47 
49 


1277 
1300 


25 
23 


54 
56 


2 
2 


170 
171 


1526 
1541 


398 
344 


99 
98 


1 

1 




127 


423 


50 


1321 


21 


59 


3 


172 


1554 


290 


55 


97 


1 




128 


372 


61 


1340 


19 


• 61 


2 


173 


.1564 


235 


66 


96 


1 




129 


320 


52 


1357 


17 


63 


2 


174 


1573 




179 




95 






130 


- 267 


63 


-1373 


16 


+65 


2 

+2 


175 


+1579 


6 
+ 3 


- 124 


65 
+66 


+ 93 


2 
-1 




131 


214 


+53 


1386 


-13 


67 


176 


1582 


+ 2 


68 


56 


92 


1 




132 


160 


64 


1398 


12 


69 


3 


177 


1584 


— 1 


- 12 


56 


91 


1 




133 


105 


65 


1408 


10 


72 


3 


178 


1583 


3 


+ 44 


6C 


90 


2 




134 


- 50 


65 


1415 


7 


74 


3 

+2 


179 


1580 


- 6 


100 


+86 


88 


-1 




135 


+ 5 


+66 


-1420 


+ 5 


+76 


180 


+1575 


+ 156 




+ 87 







50 



TABLE IN.— Continued. 






PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 




AKGUMENT II. 






Arg. 


h 


Diff. 


■ni 


Diff. 


?I 


Diff. 


Arg. 


h 


Diff. 


% 


Diff 


tx 


Diff. 




O 

180 
181 


+1575 
1567 


— s 


+ 156 
211 


+66 


+87 
'85 


-2 




225 

226 


- 291 
342 


-51 


+1353 
1337 


-16 


- 6 
8 


-2 




182 


1557 


10 


266 


55 


83 


2 


227 


393 


61 


1318 


19 


10 


2 




183 


1545 


12 


321 


55 


82 


1 


228 


443 


60 


1298 


20. 


11 






184 


1531 


14 


375 


64 


80 


2 


229 


492 


49 


1276 


22 


12 






1S5 


1514 


17 


428 


63 


78 


2 


230 


539 


47 


1252 


24 


14 






186 


1496 


18 


481 


63_ 


76 


2 


231 


586 


47 


1226 


,26 


15 






187 


1475 


21 


533 


52 


74 


2 


232 


631 


45 


1199 


27 


17 






188 


1452 


23 


584 


61 


72 


2 


233 


675 


44 


1170 


29 


18 






189 


1427 


25 

27 


635 


51 

49 


70 


2 
2 


234 


717 


42 
41 


1140 


30 
32 


19 






190 
191 


+1400 
1372 


-28 


+ 684 
732 


+48 


+68 
66 


-2 


235 
236 


- 758 
798 


-40 


+1108 
1075 


-S3 


-20 
21 


-1 




192 


1341 


31 


779 


47 


64 


2 


237 


836 


38 


1040 


35 


22 






193 
194 


1308 
1274 


33 
34 


825 
870 


46 
46 


62 
60 


2 
2 


238 
239 


872 
907 


36 
35 


1004 
967 


36 
37 


23 
24 






195 


1238 


36 


913 


43 


57 


3 


240 


940 


33 


929 


38 


25 






196 


1200 


38 


955 


42 


55 


2 


241 


971 


31 


890 


39 


26 






197 


1160 


40 


995 


40 


53 


2 


242 


1001 


30 


850 


40 


27 






198 


1119 


41 


1033 


33 


51 


2 


243 


1028 


27 


809 


41 


27 






199 


1076 


43 

44 


1071 


38 
35 


48 


3 

2 


244 


1054 


26 
24 


767 


42 
43 


28 






200 
201 


+1032 

987 


-45 


+1106 
1140 


+34 


+46 
44 


-2 


245 
246 


-1078 
1100 


-22 


+ 724 
681 


-43 


-29 
29 


-0 




202 


941 


46 


1172 


32 


41 


3 


247 


1120 


20 


637 


44 


30 






203 


893 


48 


1202 


30 


39 


2 


248 


1138 


18 


593 


44 


30 






204 


844 


49 


1230 


28 


37 


2 


249 


1154 


16 


548 


45 


31 






205 


794 


50 


1256 


26 


34 


3 


250 


1168 


14 


503 


46 


31 






206 


743 


61 


1281 


26 


32 


2 


251 


1181 


13 


458 


45 


32 






207 


691 


52 


1303 


22 


30 


2 


252 


1191 


10 


412 


46 


32 






208 


639 


62 


1324 


21 


28 


2 


253 


1199 


8 


367 


46 


32 






209 


585 


64 
64 


1342 


IS 
16 


25 


3 

2 


254 


1205 


6 
5 


321 


46 
46 


33 







210 
211 
212 


+ 531 

477 
422 


-64 
66 


+1358 
1373 
1385 


+15 
12 


+23 
21 
19 


-2 
3 


255 
256 
257 


-1210 
1212 
1213 


- 2 

- 1 

+ 2 


+ 276 
230 
185 


-46 
46 


-33 
33 
33 


-0 





213 


367 


55 


1395 


10 


17 


2 


258 


1211 


141 


44 


33 







214 


311 


56 


1403 


8 


15 


2 


259 


1208 


3 


96 


45 


34 


1 




215 


256 


55 


1409 


6 


12 


3 


260 


1203 


6 


52 


44 


34 







216 


200 


66 


1413 


4 


10 


2 


261 


1196 


7 


+ 9 


43 


34 







217 


144 


56 


■ 1414 


+ 1 


8 


2 


262 


1187 


9 


- 34 


43 


34 







218 
219 


69 
+ 33 


56 
66 

66 


1414 
1412 




- 2 

6 


4 


2 

3 

1 


263 
264 


1177 
1165 


10 

12 

14 


76 
118 


42 
42 

40 


34 
34 










220 
221 


- 22 

77 


-65 


+1407 
1400 


- 7 


+ 3 

+ 1 


-2 


265 
266 


-1151 
1136 


+15 


- 158 
198 


-40 


-34 
34 


-0 




222 


131 


54 


1391 


9 


- 1 


2 


267 


1119 


17 


237 


39 


34 







223 
I 224 

1 225 


185 

238 

- 291 


54 

53 

-53 


1381 

1368 

+1353 


10 

13 

-15 


3 

5 

- 6 


2 

2 

-1 


268 

, 269 

270 


noi 

1081 
-1060 


18 

20 

+21 


274 
311 

- 347 


37 

37 

-36 


34 

34 

-34 






-0 





51 



TABLE I Y.— Continued. 
PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 

ARGUMENT H. 



Arg. 



270 
271 
272 
273 
274 
275 
276 
277 
278 
279 

280 
281 
282 
283 
284 
2S5 
286 
287 
238 
289 



-1060 
1037 
1013 

988 
962 
935 

907 
878 
848 
818 

- 786 
754 
722 
689 
655 
621 
587 
552 
517 
483 



290 


- 448 


291 


413 


292 


378 


293 


344 


294 


309 


295 


275 


296 


241 


297 


208 


298 


175 


299 


143 


300 


- Ill 


301 


79 


302 


48 


303 


- 18 


304 


+ 12 


305 


41 


306 


69 


307 


96 


308 


123 


309 


148 


310 


+ 173 


311 


197 


312 


221 


313 


243 


314 


265 


315 


+ 285 



Diff. 



+S!3 
24 
35 
26 
27 
3S 
29 
SO 
30 

32 

+32 
83 
33 
84 
34 
34 
35 
3S 
34 

SS 

+35 
35 
34 
35 
34 
34 
33 
33 
32 

32 

+32 
. 31 
30 
30 
29 
28 
27 
27 
35 

25 

+24 
24 
22 
22 

+20 



Vl 



-347 
382 
415 
447 
478 
508 
536 
564 
590 
614 

-€37 
658 
678 
697 
714 
730 
744 
757 
769 
779 

-788 
795 
801 
806 
810 
812 
813 
813 
811 
809 

-805 
800 
795 
788 
780 
772 
762 
752 
741 
729 

-717 
704 
690 
676 
662 

-647 



DifiF. 



32 
31 

30 
23 
28 
20 
24 

23 

-21 
20 
19 
17 
16 
14 
13 
12 
10 



- 7 
6 
5 
4 
2 

- 1 


+ 2 
2 



+ 5 
5 
7 
8 
8 
10 
10 
11 
12 

12 

+13 
14 
14 
14 

+15 



?1 



-34 
34 
34 
34 
34 
34 
34 
34 
34 
34 

-34 
34 
34 
34 
34 
35 
35 
35 
35 
35 

-36 
36 
36 
36 
37 
37 
37 
38 
38 
38 

-39 
39 
40 
40 
40 
41 
41 
42 
42 
43 

-43 

44 
44 
45 
45 
-46 



Diff. 



-1 



1 



-1 



Arg. 



.315 
316 
317 
318 
319 
320 
321 
322 
323 
324 

325 
326 
327 
328 
329 
330 
331 
332 
333 
334 

335 
336 
337 
338 
339 
340 
341 
342 
343 
344 

345 
346 
347 
348 
349 
350 
351 
352 
353 
354 

355 
356 
357 
358 
359 
360 



Si 



+385 
305 
324 
342 
359 
375 
391 
405 
419 
432 

+444 
455 
466 
476 
485 
493 
501 
508 
514 
520 

+525 
530 
534 
538 
541 
544 
547 
549 
551 
552 

+553 
554 
555 
556 
556 
556 
556 
556 
556 
555 

+555 
554 
553 
553 
552 

+551 



Diff. 



+20 
19 
18 
17 
16 
16 
14 
14 
13 

12 

+11 
11 
10 



Vl 



+ 5 
4 
4 
3 
3 
3 
2 
2 
1 

1 

+ 1 
1 

+ 1 






- 1 



-647 
631 
615 
599 
583 
566 
549 
532 
575 
498 

-481 
463 
446 
429 
412 
394 
377 
360 
343 
327 

-310 
294 
277 
261 
245 
230 
214 
199 
184 
169 

-154 

140 

125 

111 

97 

83 

69 

56 

42 

29 

- 15 

- 2 
+ 11 

25 

38 

+ 51 



Diff. 



+16 
16 
16 
16 

17 

n 

17 
17 
17 

n 

+18 
17 
17 
17 
18 
17 
17 

n 

16 

17 

+16 
17 
16 
16 
15 
16 
15 
15 
15 

15 

+14 
15 
14 
14 
14 
14 
13 
14 
13 

14 

+13 
13 
14 
13 

+13 



fl 



-46 
46 
46 
47 
47 
48 
48 
48 
49 
49 

-49 
49 
50 
50 
50 
50 
50 
50 
50 
50 

-50 
50 
50 
50 
50 
49 
49 
49 
49 
48 

-48 
47 
47 
46 
46 
45 
45 
44 
43 
43 

^2 
41 
40 
40 
39 



Diff. 



-0 
-1 








+1 





1 



+1 



1 



I 



1 
1 



1 

+1 
1 



1 

+1 



52 



TABLE lY .—Continued. 








PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 




ARGUMENT HI. 








Arg. 


h 


Diff. 


n\ 


Diff. 


?i 


Diff. 


Arg. 


k 


Diff. 


ni 


Diff. 


?1 


Diff. 




o 



+977 




-196 




+15 




O 

45 


+537 


-15 
16 


-829 


-9 


- 7 






1 


973 


- 4 


213 


-17 






46 


522 


838 


9 




-2 




2 


969. 


4 


230 


17 




-2 


47 


506 


847 


9 








3 


965* 


4 


247 


17 


13 




48 


491 • 


16 
16 
16 


856 


9 


9 






4 


960 


9 


264 


17 






49 


475 


865 


8 




1 




5 


955 


6 


281 


17 




1 


50 


460 


873 


g 








6 


950 


S 


298 


17 


12 




51 


444 


16 


881 


g 


10 






7 
8 


945 
939 


9 
6 


314 
331 


16 
17 




1 


52 
53 


428 
412 


16 
16 


889 
896 


7 
7 




2 




9 


933 


G 


347 


16 


11 




54 


395 


17 


903 


12 










6 




17 










16 




7 








10 
11 


+927 ■ 
920 


- 7 


-364 
380 


-16 




2 


55 
56 


+379 
363 


-16 


-910 
917 


-7 




1 




12 


913 


7 


396 


16 


9 




57 


346 


17 


923 


Q 


13 






13 


906 


7 


412 


16 






58 


329 


17 


929 


g 




1 




14 


898 


S 


428 


16 




1 


59 


312 


17 


935 


g 




» 




15 


890 


8 


444 


16 


8 




60 


296 


16 


941 


9 


14. 






16 


882 


8 


459 


16 






61 


279 


17 


946 




2 




17 


874 


8 


475 


16 




2 


62 


261 


18 


951 


4 
6 








18 


865 


9 


490 


16 


6 




63 


244 


17 


955 


16 






19 


856 


9 


505 


16 






64 


227 


17 


960 












9 




16 




1 






17 




4 




1 




20 


+847 




-520 








65 


+210 




-964 


— 3 








21 


838 


- 9 


535 


—19 


5 




66 


192 


—18 


967 


4 
3 
3 

2 

2 

2 

, 2 


17 






22 


828 


10 


550 


15 






67 


175 


17 


971 




1 




23 


818 


10 


564 


14 




2 


68 


158 


17 


974 






24 


808 


10 


578 


14 


3 




69 


140 


18 


977 


18 






25 


797 


11 


592 


14 






70 


123 


17 


979 




1 




26 


786 


11 


606 


14 




1 . 


71 


105 


18 


981 






27 


775 


11 


620 


14 


+ 2 




72 


87 


18 


983 


19 






28 


764 


11 


633 


13 






73 


70 


17 


985 




1 




29 


752 


13 


647 


14 




2 


74 


52 


18 


986 


1 










12 




13 










17 




1 








30 


+740 




-660 









75 


+ 35 




-987 


-1 

-J 





+1 

1 


20 






31 
32 


728 
716 


-Vi 
12 


673 
685 


-13 
12 




1 


76 

77 


+ 17 
- 1 


—18 
IS 


988 
989 




1 




33 


703 


13 


698 


13 


- 1 




78 


18 


17 


989 


21 






34 
35 


691 

678 


13 
13 


710 
722 


12 

12 




2 


79 
80 


36 
53 


18 
17 


989 

988 




1 




36 


665 


13 


734 


12 


3 




81 


71 


18 


987 


22 






37 


651 


14 


745 


11 






82 


88 


17 ■ 


986 


1 








38 


638 


13 


756 


n 




1 


83 


106 


18 


985 


1 




1 




39 


624 


14 
14 


768 


12 

n 


4 




84 


123 


17 
18 


983 


2 
2 


23 






40 
41 


+610 
595 


-15 


-779 
789 


-10 




2 


85 
86 


-141 

158 


-17 


-981 
979 


+2 




1 




42 


581 


14 


800 


11 


6 




87 


175 


17 


977 


2 


24 






43 
44 
45 


567 

552 

+537 


14 

18 

-16 


810 

820 

-829 


10 

10 

- 9 


- 7 


-1 


88 
89 
90 


192 

209 

-226 


17 

17 

-17 


974 

971 

-967 


3 
3 

+4 


-25 


-1 





53 





TABLE IV. Continued. 






PERTURBATIONS OF THE CO-ORDINATES IN UNITS OP THE SIXTH DECIMAL. 






ARGUMENT III. 






Aig. 


h 


Diff. 


Vl 


Diff. 


?1 


Diff. 


Arg. 


h 


Diff. 


Vl 


Diff. 


?1 


Diff. 




o 
90 


-226 




-967 




-25 






135 


-834 




-548 




-27 






91 


243 


-17 


964 


+ 3 






136 


842 


-8 


534 


+14 








92 


260 


17 


960 


4 




-1 


137 


850 


8 


519 


13 




+0 




93 


277 


17 


956 


4 


26 




138 


858 


8 


505 


14 


27 






94 


294 


17 


951 


5 






139 


866 


8 


490 


15 








95 


310 


16 


946 


5 







140 


874 


8 


475 


15 




1 




96 


327 


17 


941 


5 


26 




141 


881 


7 


460 


13 


26 






97 


343 


16 


936 


5 






142 


888 


7 


445 


13 








98 


359 


16 


930 


6 




1 


143 


894 


6 


430 


13 









99 


375 


16 
IB 


924 


6 
6 


27 




144 


901 


7 
6 


415 


15 
16 


26 






100 


-391 




-918 








145 


-907 




-399 










101 


407 


-16 


911 


+ 7 







146 


913 


-6 


384 


+15 




1 




102 


423 


16 


905 


6 


27 




147 


918 


5 


368 


16 


25 






103 


433 


15 


898 


7 






148 


924 


6 


352 


16 








104 


454 


16 


890 


8 




-I 


149 


929 


3 


336 


16 









105 


469 


15 


883 


7 


28 




150 


933 


4 


320 


16 


25 






106 


484 


13 


875 


8 






151 


938 


3 


304 


16 








107 


499 


13 


767 


8 







152 


942 


4 


288 


16 




1 




108 


513 


14 


859 


8 


28 




153 


946 


4 


272 


16 


24 






109 


528 


13 
14 


850 


9 
9 







154 


950 


4 
3 


255 


17 
16 




1 




110 


-543 




-841 








155 


-953 




-239 










111 


557 


-13 


832 


+ 9 


28 




156 


956 


-3 


222 


+ 17 


23 






112 


571 


14 


823 


9 






157 


959 


3 


206 


16 








113 


584 


13 


813 


10 







158 


961 


2 


189 


17 




1 




114 


598 


14 


803 


10 


28 




159 


963 


2 


172 


17 


22 






115 


611 


13 


793 


10 






160 


965 


2 


155 


17 








116 


625 


14 


783 


10 







161 


967 


2 


139 


16 




1 




117 


638 


13 


772 


11 


28 




162 


968 


1 


122 


17 


21 






118 


651 


13 


762 


10 






163 


969 


1 


105 


17 








119 


663 


12 
13 


751 


11 
11 







164 


970 


—1 



88 


17 
17 




I 




120 
121 


-676 

688 


-12 


-740 

728 


+12 


28 




165 
166 


-970 
970 





- 71 
54 


+17 


20 






122 


700 


12 


717 


11 







167 


970 





37 


17 
17 
17 
17 
17 
17 
17 
17 




1 




123 
124 


711 
723 


11 
12 


705 
693 


12 
12 


28 




168 
169 


970 
969 




+1 


20 
- 3 


19 


1 




125 


734 


11 


681 


12 







170 


968 


1 


+ 14 






126 


745 


11 


668 


13 


28 




171 


967 


1 
2 

1 
2 


31 


18 






127 


756 


11 


*55 


13 






172 


965 


48 




1 




128 


767 


11 


643 


12 







173 


964 


65 








129 


777 


10 


630 


13 


28 




174 


962 


82 


17 










10 




14 










3 




17 








130 


-787 




-616 








175 


-959 


+2 


+ 99 


+17 




2 




131 


797 


-10 


603 


+13 







176 


957 


3 

4 
3 


116 


17 








132 


806 


9 


590 


13 


28 




177 


954 


133 


17 


15 






133 


816 


10 


576 


14 




+1 


178 


950 


150 


16 




+1 




134 


825 


9 


56'^ 


14 




179 


947 


+4 


166 


+17 








135 


-834 


.- 9 


-548 


+ 14 


-27 




180 


-943 




+183 




-14 







54 









TABLE lY.—Cofdmued 








PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 








ARGUMENT HI. 








Arg. 


fi 


Diff. 


Vi 


Diff. 


fl 


Diff. 


Arg. 


h 


Diff. 


Vl 


Diff. 


?1 


Diff. 


o 

180 


-943 




+183 




-14 




O 

225 ■ 


-524 




+816 


+10 
9 


+ 7 




181 
182 


939 
935 


+ 4 
1 


200 
217 


+17 
17 




+1 


226 
227 


510 
496 


+ 14 
14 


826 
835 




+1 


183 


930 


5 


233 


16 


13 




228 


482 


14 


844 


9 


8 




184 


925 


5 


250 


17 






229 


467 


15 


853 


9 






185 


920 


6 


266 


16 




1 


230 


453 


14 


862 


9 




2 


186 


915 


6 


283 


17 


12 




231 


438 


15 


871 


9 


10 




187 


909 


6 


299 


16 






232 


423 


15 


879 


8 






188 


903 


6 


315 


16 




2 


233 


409 


14 


887 


8 




1 


189 


897 


6 


331 


16 


10 




234 


394 


15 


895 


8 


11 




190 
191 


-891 
884 


6 

+ 7 


+347 
363 


16 
+16 




1 


235 
236 


-378 
363 


16 

+15 


+902 
909 


7 
+ T 




1 


192 


877 


7 


379 


16 


9 




237 


348 


IS 


916 


7 


12 




193 


870 


7 


395 


16 






238 


332 


16 


923 


7 






194 


863 


7 


411 


16 




1 


239 


317 


15 


929 


6 




2 


195 


855 


8 


426 


15 


8 




240 


301 


16 


935 


6 


14 




196 


847 


8 


442 


16 






241 


285 


16 


941 


6 






197 


839 


8 


457 


15 




2 


243 


269 


16 


947 


6 




I 


' 198 


831 


8 


473 


15 


6 




243 


253 


16 


952 


S 


15 




199 


822 


9 


487 


16 






244 


237 


16 


957 


6 






200 
201 


-813 

804 


9 
+ 9 


+502 
517 


15 
+16 


5 


1 


245 
246 


-221 

205 


16 
+16 


+961 
966 


4 
+ 5 


16 


1 


202 
203 


795 

785 


9 
10 


531 
546 


14 
15 




2 


247 

248 


189 
173 


16 
16 


970 
974 


4 
4 




1 


204 


776 


9 


560 


14 


3 




249 


156 


17 


977 


3 


17 




205 
206 


766 
755 


10 
11 


574 

588 


14 
14 




1 


250 
251 


140 
123 


16 
17 


980 
983 


3 
3 




2 


207 


745 


10 


602 


14 


- 2 




252 


107 


16 


986 


3 


19 




208 
209 


734 
724 


11 
10 


615 
629 


13 
14 




2 


253 

254 


90 

74 


17 
16 


988 
990 


2 
2 




1 


210 
211 
212 


-713 

701 
690 


11 

+12 
11 


+642 
655 
668 


13 

+13 
13 





1 


255 
256 
257 


-57 
40 
24 


17 

+17 
16 


+992 
993 
994 


2 

+ 1 
1 


20 


1 


213 
214 
215 


678 
666 
654 


12 
12 
12 


681 
693 
705 


13 
12 
12 


+ 1 


2 


258 
259 
260 


- 7 

+ 10 

26 


17 
17 
16 


995 
995 
995 


1 




21 


1 


216 
217 
218 


642 
630 
617 


12 
12 
13 


717 
729 
741 


12 
12 
12 


3 


1 


261 
262 
263 


43 
60 

77 


17 
17 
17 


995 
995 
994 





- 1 


22 


1 


219 


604 


13 


752 


11 


4 




264 


93 


16 


993 


1 


23 




220 
221 


-591 

578 


13 

+ 13 


+763 

774 


11 

+11 




1 


265 
266 


+110 
127 


17 

+17 


+991 
990 


2 
- 1 




1 


222 
223 
224 


565 
551 

538 


13 
14 
13 

+14 


785 
796 
806 


11 
U 
10 


5 


+2 


267 
268 
269 


143 
160 
177 


16 
17 
17 


988 
985 
983 


2 
3 

2 


24 


+0 


225 


-524 


+816 


+10 


+ 7 




270 


+193 


+16 


+980 


~ 3 


+24 





55 



TABLE IV. Continued. 








PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 




ARGUMENT HI. 








Aig. 


h 


Diff. 


IJl 


Diff. 


;i 


Diff. 


Arg. 


fi 


Diff 


% 


Diff 


& 


Diff. 




o 
270 


+193 




+980 




+24 




o 
315 


+821 




+561 




+28 






271 


210 


+17 


977 


- 3 






316 


830 


+ 9 


547 


-14 








272 


226 


16 


973 


4 




+1 


317 


840 


10 


533 


14 




-0 




273 


242 


16 


969 


4 


25 




318 


849 


9 


518 


IS 


28 






274 


259 


17 


965 


4 






319 


858 


9 


502 


16 








275 


275 


16 


961 


4 




1 


320 


867 


9 


486 


16 




1 




276 


291 


16 


956 


6 


26 




321 


875 


8 


471 


15 


27 






277 


307 


16 


951 


5 






322 


883 


8 


455 


16 








278 


324 


17 


946 


S 







323 


891 


8 


439 


16 









279 


340 


16 
15 


940 


6 
6 


26 




324 


899 


8 
7 


423 


16 
16 


27 






280 


+355 




+934 








325 


+906 




+407 










281 


371 


+16 


928 


- 6 




1 


326 


913 


+ 7 


391 


-16 




1 




282 


387 


16 


921 


7 


27 ■ 




327 


920 


7 


375 


16 


26 






283 


403 


16 


915 


6 






328 


927 


7 


359 


16 








284 


418 


IS 


908 


7 







229 


933 


6 


342 


17 




1 




283 


433 


15 


900 


8 


27 




330 


939 


6 


325 


17 


25 






286 


449 


16 


893 


7 






331 


945 


6 


309 


16 








287 


464 


16 


885 


8 




1 


332 


950 


6 


292 


17 




1 




288 


479 


15 


876 


9 


28 




333 


955 


5 


275 


17 I 


24 






289 


494 


IS 
15 


868 


B 
9 







334 


960 


5 
4 


258 


17 
17 









290 


+509 




+859 








335 


+964 




+241 










291 


523 


+14 


850 


- 9 


28 




336 


969 


+ 6 


224 


—17 


24 






292 


538 


5 


841 


9 






337 


973 


4 


206 


18 








293 


552 


14 


831 


10 







338 


976 


3 


■ 189 


17 




1 




294 


566 


14 


822 


9 


28 




339 


979 


3 


172 


17 


23 






295 


580 


14 


812 


10 






340 


982 


3 


154 


18 








296 


594 


14 


801 


11 




+1 


341 


985 


3 


137 


17 




1 




297 


608 


14 


791 


10 


29 




342 


987 


2 


120 


17 


22 






298 


621 


13 


780 


11 






343 


989 


2 


102 


18 








299 


635 


14 
13 


769 


11 

12 







344 


991 


2 
2 


84 


18 
17 




1 




300 
301 


+648 
661 


+13 


+757 
746 


-11 


■ 29 




345 
346 


+993 
994 


+ 1 
+ 1 


+ 67 
49 


-18 
17 
18 
IB 
17 
18 

n 

18 


21 


1 




302 


673 


12 


734 


12 




" 


347 


995 


32 








303 


686 


13 


722 


12 


29 




348 


995 





+ 14 


20 






304 


698 


12 


710 


12 






349 


995 





- 4 




\ 




305 


711 


13 


697 


13 







350 


995 





21 








306 


723 


32 


685 


12 


29 




351 


995 




- 1 

1 
1 


39 


19 






307 


734 


11 


672 


13 






352 


994 


56 




2 




308 


746 


12 


659 


13 




— i 


353 


993 


74 


17 








309 


757 


11 


. 645 


14 


28 




354 


992 


91 




17 










11 




13 










2 




18 








310 


+768 




+632 








355 


+990 


- 2 
3 
2 


-109 


—17 




1 




311 


779 


+11 


618 


—14 







356 


988 


126 


18 








312 


790 


11 


604 


14 


28 




357 


985 


144 


17 


16 






313 


801 


11 


590 


14 






358 


983 


3 


161 


17 




-1 




314 
315 


811 
+821 


10 
+10 


576 
+561 


14 
-15 


+28 





359 
360 


980 

+977 


- 3 


178 
-196 


-18 


+15 







66 







TABLE lY .—Cmtinued. 




PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 






ARGUMENT IV. 


1 


Arg. 


^1 


Diff. 


Vl 


Diff. 


?1 


Diff. 


Arg. 


h 


Diff. 


■ni 


Diff. 


& 


Diff. 






1 

2 


-775 
773 

772 


+ 2 

1 


+ 75 

90 

106 


+16 
16 


+38 


-2 


o 
45 

46 

47 


-502 
492 

482 


+10 
10 


+691 
702 
713 


+11 
11 


+ 6 


-i 


3 

4 


770 
768 


2 
2 


131 
137 


15 
16 


36 




48 
49 


471 
460 


11 
11 


723 
734 


10 

11 


+ 2 




5 


765 


3 


152 


13 




1 


50 


450 


10 


744 


10 




i 


6 


763 


2 


167 


15 


35 




51 


439 


11 


754 


10 
9 


- 2 




7 


760 


3 


182 


15 






52 


427 


12 


763 






8 


757 


3 


197 


15 




1 


53 


416 


11 


773 


10 




4 


9 


754 


3 

4 


213 


16 

15 


34 




54 


405 


11 
12 


782 


9 
9 


6 




10 


-750 




+228 








55 


-393 




+791 








11 


747 


+ 3 


243 


+15 




9 


56 


382 


+11 


800 


+ 9 




4 


12 


743 


4 


257 


14 


39 




57 


370 


12 


809 


9 


10 




13 


739 


4 


272 


15 






58 


358 


12 


817 


8 






14 


735 


4 


287 


15 




2 


59 


346 


12 


825 


8 




s 


15 


730 


5 


302 


15 


30 




60 


334 


12 


833 


8 


15 




16 


725 





316 


14 






61 


322 


12 


841 


S 






17 


720 


D 


331 


15 




1 


62 


310 


13 


848 


7 




5 


18 


715 


5 


345 


14 


29 




63 


298 


13 


856 


8 


20 




19 


710 


5 
6 


359 


14 
15 




2 


64 


285 


13 
12 


863 


7 
6 




5 


20 
21 


-704 
699 


+ 6 


+374 

388 


+14 


27 




65 
66 


-273 
260 


+13 


+869 
876 


+ 7 


25 




22 


693 


6 


402 


14 






67 


248 


13 


882 


6 






23 


687 


6 


416 


14 




2 


68 


235 


13 


888 


6 




5 


24 


680 


7 


430 


14 


25 




69 


222 


13 


894 


6 


30 




25 


674 


6 


443 


13 






70 


909 


13 


899 


5 






26 


667 


7 


457 


14 




2 


71 


196 


13 


904 


5 




5 


27 


660 


7 


470 


13 


23 




72 


183 


13 


909 


5 


35 




28 


653 


7 


484 


14 






73 


170 


13 


914 


5 






29 


645 


8 

7, 


. 497 


13 

13 




2 


74 


157 


13 
13 


918 


4 
4 




6 


30 
31 


-638 
630 


•+ 8 


" +510 
523 


+13 


21 




75 
76 


-144 
130 


+14 


+922 
926 


+ 4 


41 




32 


692 


S 


536 


13 




3 


77 


117 


13 


929 


3 




5 


33 


614 


8 


549 


is 


18 




78 


103 


14 


932 


3 


46 




34 


605 


1 9 


562 


13 






79 


90 


13 


935 


3 






35 


597 


■ 8 


574 


13 




3 


80 


76 


14 


937 


2 


• 


6 


,36 


' 588 


9 


587 


13 


15 




81 


63 


13 


940 


3 


52 




37 


579 


9 


599 


12 






89 


49 


14 


942 


2 






38 


570 


9 


611 


12 




3 


83 


35 


14 


943 


1 




5 


39 ; 


■ 561 


9 
9 


623 


12 
12 


12 




84 


21 


14 
13 


944 


1 
1 


57 




40 


-552 




+635 








85 


- 8 




+945 








41 


542 


+10 


646 


+11 




3 


86 


+ 6 


+14 


946 


+ 1 




6 


42 ■ 


532 


10 


658 


.12 


9 




87 


20 


14 


946 





63 




43 


523 


9 


669 


11 






88 


34 


14 


946 









44 


513 


10 


680 


11 




-3 


89 


48 


14 


946 







-6 


45 


-502 


+11 


+691 


+ 11 


+ 6 




90 


+ 62 


+14 


+945 


- 1 


-68 





57 



TABLE IV. Continued. 






PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. | 


ARGUMENT IV. 






Arg. 


& 


Dlflf. 


ni 


DifF. 


?1 


DifF. 


Arg. 



135 


li 


Diff. 


ni 


Diff. 


?i 


Diff. 


o 
90 


+ 62 




+945 




- 68 




+678 




+605 




-114 




91 


77 


+15 


944 


- 1 






136 


690 


+12 


591 


-14 






92 


91 


14 


943 


1 




-6 


137 


701 


11 


578 


13 







93 


105 


14 


941 


2 


73 




138 


712 


11 


564 


14 


114 




94 


^119 


14 


939 


2 






139 


723 


11 


550 


14 






95 


133 


14 


937 


2 




S 


140 


734 


11 


536 


14 




+1 


96 


147 


14 


935 


2 


78 




141 


745 


11 


522 


14 


113 




97 


162 


13 


932 


3 






142 


755 


10 


507 


15 






98 


176 


14 


929 


3 




6 


143 


765 


10 


493 


14 




1 


99 


190 


14 
14 


925 


4 
4 


83 




144 


775 


10 
9 


478 


15 
IS 


112 




100 


+204 




+921 








145 


+784 




+463 








101 


219 


+15 


917 


- 4 




4 


146 


794 


+10 


448 


-15 




2 


102 


233 


14 


912 


6 


87 




147 


803 


9 


433 


15 


110 




103 


247 


14 


908 


4 






148 


812 


9 


418 


15 






104 


262 


IS 


903 


5 




e 


149 


820 


8 


403 


15 




2 


105 


276 


14 


897 


6 


92 




150 


828 


8 


388 


15 


108 




106 


290 


14 


891 


6 






151 


836 


8 


372 


16 






107 


305 


18 


885 


6 




4 


152 


844 


8 


357 


15 




3 


108 


319 


14 


879 


6 


96 




153 


851 


7 


341 


16 


105 




109 


333 


14 
14 


873 


7 
7 




3 


154 


858 


7 
7 


325 


16 
16 




3 


110 


+347 




+865 








155 


+865 




+309 








111 


362 


+15 


858 


- 7 


99 




156 


872 


+ 7 


293 


—16 


102 




112 


376 


14 


851 


7 






157 


878 


6 


277 


16 






113 


390 


14 


843 


8 




4 


158 


884 


6 


261 


16 
16 
16 




3 


114 


404 


14 


835 


8 


103 




159 


889 


6 


245 


99 




115 


418 


14 


826 


9 






160 


894 


5 


229 






116 


432 


14 


817 


9 




3 


161 


899 


5 


213 . 


16 
16 
16 
17 




4 


117 


446 


14 


808 


9 


106 




162 


904 


5 


197 


95 




118 


459 


13 


799 


9 






163 


908 


4 


181 






119 


473 


14 


790 


9 




2 


164 


912 


4 


164. 




4 






14 




10 










3 




16 




, 


120 
121 
122 
123 


+487 
500 
514 
527 


+13 
14 
13 


+780 
770 
760 
749 


-10 
10 
11 


108 
110 


2 


165 
166 
167 
168 


+915 
918 
921 
923 


+ 3 
3 
2 
3 
2 
1 

4- 1 


+148 

132 

115 

99 


-16 
17 
16 
16 


91 

86 


5 


124 
125 


541 

554 


14 
13 


738 

727 


11 
11 




2 


169 
170 


925 
927 


83 
67 


16 
17 




5 


126 


567 


13 


716 


11 


112 




171 


928 


50 


16 


81 




127 


580 


13 


704 


12 






172 


929 






34 


16 




5 


128 


593 


13 


693 


11 




1 


173 


929 


18 


17 






129 


605 


12 


681 


12 


113 




174 


929 


+ 1 




76 








13 




12 















16 






130 


+618 




+669 








175 


+929 


— 1 


- 15 


—16 




6 


131 


630 


+12 


656 


-13 




-1 


176 


928 


1 

1 


31 


16 






132 


643 


13 


644 


12 


114 




177 


927 


47 


16 


70 




133 


655 


13 


631 


13 






178 


926 


2 


63 


16 




+6 


134 


667 


12 


618 


13 







179 


924 


— 2 


79 


—16 






135 


+678 


+11 


+605 


-13 


-114 




180 


+922 




- 95 




- 64 





58 



TABLE IV. — Continued. 
PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 

ARGUMENT IV. 



Arg. 



180 
181 
182 
183 
184 
185 
186 
187 
188 
189 

190 
191 
192 
193 
194 
195 
196 
197 
198 
199 

200 
201 
202 
203 
204 
205 
206 
207 
208 
209 

210 
211 
212 
213 
214 
215 
216 
217 
218 
219 

220 
221 
222 
223 
224 
225 



Ji 



+922 
919 
916 
913 
909 
905 
901 
896 
691 
885 

+879 
873 
866 
859 
852 
844 
836 
828 
819 
810 

+801 
791 
781 
771 
760 
749 
738 
727 
715 
703 

+691 
678 
665 
652 
639 
626 
612 
598 
584 
570 

+555 
541 
526 
511 

496 

+481 



Di£F. 



- 6 

1 
7 
7 
8 
8 
8 
9 



-10 
10 
10 
11 
II 
11 
11 
13 
12 



-13 
13 
13 
13 
13 
14 
14 
14 
14 



-14 
15 
15 
IS 

-15 



fl 



- 95 
111 

127 
143 

158 
174 
190 
205 
221 
236 

-351 
266 
281 
296 
311 
326 
340 
355 
369 
383 

-397 
411 
425 
438 
452 
466 
479 
492 
505 
518 

-530 , 
543 
555 
567 
579 
591 
603 
614 
626 
637 

-648 

658 

669 

679 

690 
-700 



Diff. 



-16 
16 
16 
15 
16 
16 
15 
16* 
15 



-15 
15 
15 
15 
15 
14 
15 
14 
14 



-14 
14 
13 
14 
14 
13 
13 
13 
13 



-13 
12 
12 
12 
12 
12 
11 
12 
11 



-10 
11 
10 
11 

-10 



?1 



-64 



58 



52 



45 



38 



31 



24 



17 



10 



+ 4 



11 



18 



25 



31 



+38 



Diff. 



+6 



Arg. 



+7 



225 
226 
227 
228 
229 
230 
231 
232 
233 
234 

235 
236 
237 
238 
239 
240 
241 
242 
243 
244 

245 

246 
247 
248 
249 
250 
251 
252 
253 
254 

255 
256 
257 
258 
259 
260 
261 
262 
263 
264 

265 
266 
267 
268 
269 
270 



+481 
465 
450 
434 
419 
403 
387 
371 
355 
339 

+323 
307 
291 
274 
258 
242 
226 
210 
193 
177 

+161 
145 
129 
113 

97 
81 
65 
49 
34 
18 

+ 3 
- 13 

28 

43 

58 

73 

88 

102 

117 

131 

-145 
160 
174 

187 

201 

-214 



Diff. 



-16 
16 
16 
15 
16 
16 
16 
16 
16 

16 

-16 
16 
17 
16 
16 
16 
16 
17 
IB 

16 

-16 
16 
16 
16 
16 
16 
16 
15 
16 



-16 
IS 
16 
16 
16 
16 
14 
IS 
14 



-15 
14 
13 
14 

-13 



ni 



-700 
710 
719 
729 
738 
747 
756 
764 
773 
781 

-789 
797 
805 
812 
819 
826 
833 
839 
846 
852 

-857 
863 
868 
873 
878 
883 
887 
891 
895 
899 

-902 
905 
908 
911 
913 
915 
917 
919 
920 
921 

-922 
922 
922 
922 
922 

-921 



Diff. 



-ID 
9 




- 6 
5 
5 
6 
6 
4 
4 
4 



- 3 
3 
3 
2 
2 
3 
3 
1 
1 

- 1 






+ 1 



& 



+38 

44 

/ 

50 

56 

61 

66 

■ 71 

75 

79 
82 

85 
88 
90 
92 

93 

+94 



Diff. 



+6 



+1 



59 





TABLE IV. Conimued 










PERTURBATIONS OP THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL; 




. 


ARGUMENT IV. 










Arg. 


fi 


Diff. 


Vi 


Diff. 


?1 


Diff. 


Arg. 


h 


Diff. 


Vi 


Diff. 


?1 


Diff 




o 
270 


-214 




-921 




+94 




o 
315 


-652 




-600 




+71 






271 


228 


-14 


920 


+ 1 






316 


658 


-6 


587 


+13 








272 


241 


13 


919 


1 




+1 


317 


664 


6 


574 


13 




-3 




273 


254 


13 


917 


2 


95 




318 


670 


6 


561 


13 


68 






274 


V 267 
279 


13 


915 


2 






319 


676 


6 


548 


13 








275 


12 


913 


3 







320 


681 


6 


• 535 


13 




3 




276 


292 


13 


911 


2 


95 




321 


687 


6 


521 


14 


65 






277 


304 


12 


908 


3 






322 


692 


5 


507 


14 








278 


316 


12 


905 


3 




-1 


323 


697 


d 


493 


14 




3 




279 


328 


13 
12 


902 


3 

4 


94 




324 


702 


5 
6 


. 479 


14 
14 


62 






280 


-340 




-898 








325 


-707 




-465 










281 


352 


-12 


894 


+ 4 







326 


712 


-5 


450 


+15 




2 




282 


363 


11 


890 


4 


94 




327 


716 


4 


436 


14 


60 






283 


375 


13 


886 


4 






328 


721 


5 


421 


15 








284 


386 


11 


881 


5 




• 1 


329 


725 


4 


406 


15 




3 




285 


397 


11 


876 


S 


93 




330 


729 


4 


392 


14 


57 






286 


408 


11 


871 


5 






331 


733 


4 


377 


15 








237 


418 


10 


865 


6 




1 


332 


737 


4 


362 


15 




2 




288 


429 


11 


859 


6 


92 




333 


741 


4 


347 


15 


55 






289 


439 


10 
10 


853 


6 
6 




3 


334 


744 


3 

4 


332 


15 
16 




3 




290 


-449 




-847 








335 


-748 




-316 


+15 
15 
16 
15 
16 
16 
15 
16 








291 


459 


-10 


840 


+ 7 


90 




336 


751 


—3 


301 


52 






292 
293 


469 
479- 


10 
10 


833 

825 


7 
8 




2 


337 
338 


754 
757 


3 
3 


286 
270 




3 




294 


488 


9 


818 


7 


88 




339 


760 


3 

2 
3 


255 


50 






295 
296 


497 
507 


9 
10 


810 
802 


8 
8 




3 


340 
341 


762 
765 


239 
223 




2 




297 


516 


9 


793 


9 


86 




342 


767 


2 
2 
2 
(J 


208 


48 






298 
299 


524 
533 


8 
9 


785 
776 


6 
9 




2 


343 

344 


769 
771 


192 

177 


16 
16 




2 




300 


-542 


9 


-767 


9 


64 




345 


-773 




-161 


+10 
16 
15 


46 






301 
302 


550 
553 


- 8 
8 


757 
747 


+10 
10 




3 


346 
347 


774 
775 




145 
129 




2 




303 


566 


8 


737 


10 


81 




348 


776 




114 


16 


44 






304 


574 


8 


727 


10 




2 


349 


777 




98 


16 




1 




305 


582 


8- 


717 


10 




350 


778 




82 


16 








306 


590 


8 


706 


11 


79 




351 


779 


— 


66 


15 


43 






307 


597 




695 


11 




3 


352 


779 


Q 


51 


16 




2 




308 


604 




684 


11 




353 


779 






35 


16 








309 


612 




673 


11 


76 




354 


779 


19 


16 


41 






310 


-619 




-661 


13 
+12 




3 


355 


-779 





- 3 


+15 




3 




311 


626 




649 






356 


779 


+1 


+ 12 


16 








312 


632 




637 


13 


73 




357 


778 


1 


28 


10 


39 






313 


639 




625 


12 




—2 


358 


777 


1 


44 


15 




-1 




314 
315 


645 
-652 


-7 


613 

-600 


12 
+13 


+71 




359 
360 


776 

-775 


+1 


59 
+ 75 


+16 


+38 







60 



TABLE lY .— Continued. 
PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 

ARGUMENT V. 



Arg. 





3 

6 

9 

12 

15 

18 

21 

24 

27 

30 
33 
36 

39 
42 
45 
48 
51 
54 
57 

60 
63 
66 
69 
72 
75 
78 
81 
84 
87 

90 

93 

96 

99 

102 

105 

108 

111 

114 

117 

120 
123 
126 
129 
132 
135 



^1 



-507 
507 
505 
502 
497 
491 
484 
475 
465 
454 

-441 
427 
412 
396 
379 
360 
340 
320 
299 
277 

-254 

230 

206 

181 

156 

130 

104 

78 

51 

- 25 

+ 2 

29 

55 

81 

107 

133 

159 

184 

208 

232 

+255 
277 
298 
319 
339 

+358 



DifF. 





+ 2 

3 

5 



10 
11 
13 

+14 
16 
16 
17 
19 
20 
20 
21 
22 

23 

+24 
24 
25 
25 
26 
26 
26 
27 
26 

27 

+27 
26 
26 
26 
26 
26 
25 
24 
24 
23 

+22 
21 
21 
20 

+19 



Vl 



+ 52 
39 
26 

+ 13 


- 13 
• 26 

39 
52 
64 

- 77 
89 

100 
112 
123 
133 
143 
153 
163 
171 

-179 
187 
194 
201 
207 
212 
216 
220 
224 
226 

-228 
230 
231 
231 
230 
229 
228 
226 
223 
219 

-215 
211 
206 
200 
194 

-188 



DifF. 



-13 
13 
13' 
13 
13 
13 
13 
13 
12 



-12 
11 
12 
11 
10 
10 
10 
10 



2 
2 

- 2 

- 1 


+ 1 
1 
1 
2 
3 
4 

4 

+ 4 
5 



+ 6 



fl 



- 84 
77 
70 
63 
56 
49 
41 
33 
25 
18 

- 10 

- 2 
+ 6 

14 
22 
30 
38 
45 
53 
60 

+ 68 

75 

82 

88 

95 

101 

107 

112 

118 

123 

+127 
131 
135 
139 
142 
145 
147 
149 
151 
152 

+153 
153 
153 
152 
151 

+150 



Diff. 



+7 
7 
7 
7 
7 
S 



+8 



7 
8 

7 

8 

+7 
7 



Arg. 



+4 



3 

2 
2 
2 
1 

+1 




-1 
1 

-1 



135 
138 
141 
144 
147 
150 
153 
156 
159 
162 

165 

168 

171 

174 

177 ■ 

180 

183 

186 

189 

192 

195 
198 
201 
204 
207 
210 
213 
216 
219 
222 

225 
228 
231 
234 
237 
240 
243 
246 
249 
252 

255 
258 
261 
264 
267 
270 



li 



+358 
376 
392 
408 
422 
436 
448 
459 
469 
477 

+484 
490 
494 
497 
499 
499 
498 
496 
493 
488 

+482 
474 
465 
455 
444 
432 
418 
404 
388 
371 

+354 
335 
316 
295 
274 
252 
230 
207 
183 
158 

+133 

108 

83 

57 

31 

+ 5 



Diff. 



+ 18 
16 
16 
14 
14 
12 
11 
10 



+ 6 
4 



ni 



10 

11 

12 
14 
14 
16 
17 



-19 
19 
21 
21 
22 
22 
23 
24 
25 



-25 
26 
26 
26 

-26 



-188 

181 
174 
166 
158 
150 
141 
132 
122 
113 

-103 
92 
82 
71 
61 
50 
39 
28 
16 

- 5 

+ 6 

18 
29 
40 
51 
63 
74 
84 
95 
106 

+116 
126 
136 
145 
154 
163 
172 
180 
187 
194 

+201 
207 
213 
218 
222 

+226 



Diff. 



+ 7 
7 
8 



10 

+11 

10 

11 

10 
11 
11 
11 
12 
11 

11 

+12 
11 
11 
11 
12 
11 
10 
11 
11 

10 

+10 
10 
9 
9 



7 

7 

7 

+ 6 
6 
5 

4 

+ 4 



& 



+150 
148 
146 
144 
141 
137 
133 
129 
125 
120 

+115 
109 
103 
97 
91 
84 
78 
71 
63 
56 

+ 48 
41 
33 
25 
17 
9 

+ 1 

- 7 
15 
23 

- 31 
39 
47 
54 
61 
69 
76 
83 
89 
G6 

-102 
107 
113 
118 
123 

-127 



Diff. 



61 



TABLE lY .—Continued. 
PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 

ARGUMENT V. 



Arg. 

o 
270 

273 
276 
279 
2S2 

285 
288 
291 
294 
297 

300 
303 
306 
309 
312 
315 



& 


Diff. 


Vl 


DifF. 


?1 


Diff. 


Arg. 


5i 


Diff. 


ni 


Diff. 


Si 


+ 5 




+226 




-127 




o . 

315 


-351 




+205 




-149 


- 21 


-36 


229 


+3 


132 


-6 


318 


370 


-19 


199 


- 6 


147 


47 




232 




135 


3 


321 


387 


17 


191 


8 


145 


72 


35 


234 


^ 


139 


4 


324 


404 


17 


183 


8 


142 


98 




235 




142 




327 


420 


16 


175 


8 


139 


124 




236 


+1 


145 


3 


330 


434 


14 


166 


9 


136 


149 


35 


236 





147 


3 


333 


447 


13 


156 


10 


132 


174 


35 


235 


-1 


149 


3 


336 


459 


13 


146 


10 


128 


198 




234 




150 


1 


339 


470 


11 


136 


10 


124 


222 


34 
33 


232 


3 
3 


151 


1 
-1 


342 


479 


9 

8 


125 


11 
13 


119 


-245 




+229 




-152 




345 


-487 




+113 




-114 


268 


-S3 


226 


-3 


152 





348 


494 


- 7 


102 


-11 


109 


290 




222 


4 


152 





351 


499 


6 


90 


13 


103 


311 




217 




151 




354 


503 


4 


77 




97 


332 


31 


211 


6 


150 


1 


357 


506 


3 


65 


13 


91 


-351 


-19 


+205 


-6 


-149 


+1 


360 


-507 


- 1 


+ 52 


-13 


- 84 



Diff. 

+3 
3 



4 
4 
4 
5 

6 

+5 



ARGUMENT VI. 



Arg. 





3 

6 

9 

12 

15 

18 

21 

24 

27 

30 
33 
36 
39 
42 
45 
48 
51 
54 
57 

60 
63 
66 
69 



li 



+492 
488 
483 
477 
470 
461 
451 
440 
428 
414 

+400. 
384 
367 
349 
330 
311 
290 
269 
247 
224 

+201 
177 
152 

+127 



Diff. 



- 4 

5 

6 

7 

9 

10 

11 

13 

14 

14 

-16 
17 
18 
19 
19 
31 
31 
33 
33 



-24 

33 

-25 



Vl 



+ 54 

79 
104 
129 
153 
177 
200 
223 
245 
267 

+288 
308 
327 
346 
363 
379 
395 
409 
423 
435 

+446 
455 
464 

+471 



Diff. 



+25 
35 
35 
34 
24 
23 
33 
33 
21 

21 

+20 
19 
19 
17 
16 
16 
14 
14 
12 

11 

+ 9 
9 

+ 7 






-1 
1 

2 

2 

2 
3 
3 
3 

4 
-4 



Arg. 



69 
72 

75 
78 
81 
84 
87 
90 
93 
96 

99 
102 
105 
108 
111 
114 
117 
120 
123 
126 

129 
132 
135 
138 



+127 

102 

77 

51 

+ 25 

- 1 

27 

53 

78 

104 

-129 
154 
179 
203 
226 
249 
271 
293 
314 
333 

-352 
370 
387 

-403 



Diff. 



-35 
35 
36 
36 



-25 
35 
24 
23 
33 
22 
22 
21 
19 

19 

-18 

17 

-16 



% 



+471 

477 
482 
485 
487 
488 
487 
485 
482 
477 

+471 
464 
455 
446 
435 
422 
409 
394 
379 
362 

-344 
326 
306 

-286 



Diff. 



+ 6 
5 
3 
2 

+ 1 

- 1 
2 
3 

' 6 

6 

- 7 
9 
9 

11 
13 
13 
15 
15 
17 



-18 

20 

-20 



62 



TABLE lY .—Continued. 






PERTURBATIONS OP THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 




ARGUMENT VI. 






Arg. 


h 


Diff, 


ni 


Diff. 


Kx 


Arg. 


h 


Diff. 


ni 


Diff. 


^1 




o 
138 


-403 




+286 




-3 




249 


-125 




-473 








141 


418 


-15 


265 


-21 




252 


100 


+25 


479 


- 6 


+4 




,145 


431 


13 


243 


22 


3 


255 


74 


36 


483 


4 






147 


444 


13 


220 


23 




258 


48 


26 


486 


3 


4 




150 


455 


11 


197 


23 


3 


261 


- 22 


26 


488 


- 2 






153 


465 


10 


173 


24 




264 


+ 4 


26 


488 



+ 1 


5 




156 


474 


9 


149 


24 


2 


267 


30 


26 


487 






159 


481 


7 


124 


25 




270 


56 


26 


485 


2 


5 




162 


487 


6 


99 


25 


2 


273 


81 


25 


481 


4 






165 


492 


6 
3 


74 


25 
26 




276 


107 


36 
25 


476 


5 
6 


5 




168 


-495 




+ 48 




1 


279 


+132 




-470 








171 


497 


- 2 


+ 23 


-25 




282 


157 


+25 


462 


+ 8 


5 




174 


498 


- 1 


- 3 


26 


-1 


285 


181 


24 


453 


9 






177 


497 


+ 1 


29 


26 




288 


205 


24 


443 


10 


5 




180 


495 


3 


54 


25 





291 


228 


23 


432 


11 






183 


491 


4 


80 


26 




294 


251 


33 


420 


12 


4 




186 


486 


5 


105 


35 





297 


273 


22 


406 


14 






189 


480 


6 


130 


25 




300 


294 


31 


391 


15 


4 




192 


472 


8 


155 


25 


■ +1 


303 


314 


20 


376 


15 






195 


464 


8 
10 


179 


34 
33 




306 


334 


30 
19 


359 


17 
18 


4 




198 


-454 




-202 




1 


309 


+353 




-341 








201 


442 


+12 


225 


-23 




312 


370 


+17 


323 


+18 


4 




204 


430 


12 


248 


23 


2 


315 


387 


17 


303 


20 






207 


416 


14 


270 


33 




318 


402 


15 


283 


20 


3 




210 


401 


15 


291 


31 


2 


321 


417 


15 


262 


21 






213 


385 


16 


311 


30 




324 


430 


13 


240 


23 


3 




216 


368 


17 


330 


19 


2 


327 


442 


12 


217 


23 






219 


349 


19 


349 


19 




330 


453 


11 


194 


33 


3 




222 


330 


19 


366 


17 


3 


333 


463 


10 


171 


33 






225 


,310 


20 
20 


383 


17 
15 




336 


472 


9 

7 


147 


24 
35 


2 




228 


-290 




-398 




3 


339 


+479 




-132 








231 


268 


+22 


412 


-14 




342 


485 


+ 6 


98 


+34 


2 




234 


246 


22 


426 


14 


4 


345 


489 


4 


73 


25 






237 


223 


23 


438 


13 




348 


492 


3 


47 


36 


1 




240 


199 


24 


448 


10 


4 


351 


494 


2 


- 22 


25 






243 


175 


24 


458 


10 




354 


495 


+ 1 


+ 3 


25 


+1 




246 


150 


2S 


466 


8 


+4 


357 


494 


- 1 


29 


26 






249 


-125 


+25 


-473 


- 7 




360 


+492 


- 2 


+ 54 


+26 












63 



TABLE lY.— Continued, 
PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL, 

ARGUMENT VII. 



Arg. 





3 

6 

9 
12 
15 
18 
21 
24 
27 

30 
33 
36 
39 
42 
45 
48 
51 
54 
57 

60 
63 
66 
69 
72 
75 
78 
81 
84 
87 

90 

93 

96 

99 

102 

105 

108 

111 

114 

117, 

120 
123 
126 
129 
132 
135 



-231 
232 
233 
234 
236 
238 
240 
243 
245 
248 

-250 
253 
255 
256 
258 
258 
258 
258 
256 
253 

-249 
244 
237 
229 
220 
209 
196 
182 
166 
149 

-129 

109 

86 

62 

37 

- 10 

+ 18 

47 

76 

107 

+138 
169 
200 
231 
262 

+292 



Difif. 



- 1 
1 
I 

3 
2 
3 
3 
3 
3 

3 

- 3 
3 
1 

- 2 




+ 2 



+ S 
7 
8 
9 
II 
13 
14 
16 
17 

20 

+20 
33 
34 
36 
27 
28 
29 
39 
31 

31 

+31 
31 
31 
31 

+30 



»!l 



- 4 

8 

13 
18 
23 
29 
35 
42 
50 
58 

- 67 
77 
88 
99 

112 
126 
140 
155 
171 
187 

-204 
222 
239 
257 
275 
293 
311 
328 
345 
362 

-377 
391 
404 
416 
426 
434 
441 
445 
448 
448 

-446 
442 
435 
426 
414 

-400 



DifF. 



- 4 
6 
5 
6 



7 
8 
8, 

9 

-10 
11 
11 
13 
14 
14 
15 
16 
16 

17 

-18 
17 
18 
18 
18 
IB 
17 
17 
17 

15 

-14 
13 
12 

10 

8 
7 
4 
- 3 


+ 2 

+ 4 
7 
9 
13 

+14 



-20 
21 
22 
23 

24 

24 
24 
23 
23 
22 

21 
19 

18 

14 

12 

9 

7 

4 

- 2 

+ 1 

3 

+ 6 



Arg. 



135 
138 
141 
144 
147 
150 
153 
156 
159 
162 

165 
168 
171 
174 
177 
180 
183 
186 
189 
192 

195 
198 
201 
204 
207 
210 
213 
216 
219 
222 

225 
228 
231 
234 
237 
240 
243 
246 
249 
252 

255 
258 
261 
264 
267 
270 



h 



+292 
322 
350 
377 
403 
426 
448 
468 
485 

500 

+513 
522 
529 
533 
534 
533 
528 
521 
511 
498 

+482 
464 
444 
422 
398 ' 
372 
345 
316 
286 
256 

+225 

194 

162 

131 

100 

69 

40 

+ 11 

- 17 
44 

- 69 
93 

115 

136 

155 

-172 



Diff. 



Vi 



+30 
28 
27 
26 
23 
23 
20 
17 
U 

13 

+ 9 
7 
4 
+ 1 
- 1 
5 
7 

10 
13 

16 

-18 
20 
22 
24 
26 
27 
39 
30 



-31 
S3 
31 
31 
31 
29 
39 
28 
37 



-34 
33 
31 
19 

-17 



-400 

383 
364 
342 
319 
293 
266 
236 
205 
173 

-140 

1C6 

70 

- 35 

+ 1 

37 

72 

107 

142 

175 

+207 
238 
' 267 
294 
320 
343 
364 
383 
400 
414 

+425 
434 
441 
445 
447 
447 
444 
440 
433 
424 

+414 
402 
389 
375 
360 

+344 



Diff. 



+17 
19 
33 
23 
26 
27 
30 
31 
32 

33 

+34 
36 
35 
36 
36 
33 
35 
35 
33 



+31 
29 
27 
36 
23 
21 
19 
17 
14 

11 

+ 9 
7 
4 

+ 2 


- 3 
4 
7 
9 

10 

-12 
13 
14 
15 

-16 



?1 



+ 8 
10 
13 
15 
16 

]8 
19 
20 
21 
22 

22 
23 
23 
22 
22 

21 
20 
19 
18 
17 

15 

13 

+11 



64 





TABLE IV. — Cmtimed. 








I 


PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 




ARGUMENT Vll. 










Arg. 


li 


DifF. 


ll 


Diff. 


fl 


Arg. 


f. 


Diff. 


ni 


Diff 


& 


o 

270 


-172 




+344 




+11 


o 
315 


-259 




+100 






273 


188 


-16 


327 


-17 




318 


257 


+2 


88 


-12 


,- 7 


276 


202 


14 


309 


18 


9 


321 


255 


2 


78 


10 




279 


214 


13 


292 


17 




324 


252 


3 


68 


10 


9 


282 


225 


11 


274 


18 


7 


327 


249 


3 


59 


9 




285 


234 


9 


256 


18 




330 


247 


2 


51 


8 


11 


288 


242 


8 


238 


18 


5 


333 


244 


3 


43 


8 




291 


248 


6 


220 


18 




336 


241 


3 


36 


7 


13 


294 


253 


a 


203 


17 


+ 3 


339 


239 


2 


30 


6 




297 


257 


4 
3 


186 


* 17 
16 




342 


237 


2 
2 


24 


6 
S 


15 


300 


-260 




+170 







345 


-235 




+ 19 






303 


261 


- 1 


155 


-15 




348 


233 


+2 


14 


- 6 


17 


306 


262 


- 1 


140 


IS 


- 2 


351 


232 


1 


9 


5 




309 


262 



+ 1 


126 


14 




354 


231 


+1 


5 


4 


19 


312 


261 


112 


14 


- 4 


357 


231 





+ 1 


4 




315 


-259 


+ 2 


+100 


-12 




360 


-231 





- 4 


- 5 


-20 


ARGUMENT Vm. 


Arg. 


-352 


Diff. 


Vi 


Diff. 


& 


Arg. 


ii 


Diff. 


ni 


Diff. 


?i 







■ 


+ 22 




-7 


69 


-106 




+335 






3 


350 


+ 2 


40 


+18 




72 


88 


+18 


340 


+ 5 


+ 6 


6 


347 


3 


58 


18 


6 


75 


70 


18 


344 


4 




9 


344 


3 


76 


18 




78 


52 


18 


347 


3 


7 


12 


339 


6 


94 


18 


5 


81 


34 


18 


349 


2 




15 


334 


5 


112 


18 




84 


- 15 


19 


350 


1 


8 


18 


328 


6 


129 


17 


4 


87 


+ 3 


18 


351 


+ 1 




21 


320 


8 


146 


n 




90 


22 


19 


350 


- 1 


9 


24 


312 


8 


163 


17 


3 


93 


40 


18 


348 


2 




27:, 


303 


9 
9 


179 


16 
15 




96 


58 


18 
13 


346 


2 
4 


9 


30 


-294 




+194 




2 


99 


+ 76 




+342 






33 


283 


+11 


209 


+15 




102 


94 


+18 


338 


- 4 


10 


36 


272 


11 


224 


15 


-1 


105 


112 


18 


332 


6 




39 


260 


12 


238 


14 




108 


129 


17 


326 


6 


10 


42 


247 


13 


251 


13 





111 


146 


17 


319 


7 




45 


233 


14 


263 


12 




114 


162 


16 


311 


8 


11 


48 


219 


14 


275 


12 


+2 


117 


178 


16 


302 


9 




51 


204 


15 


286 


11 




120 


194 


16 


292 


10 


11 


54 


189 


15 


296 


10 


3 


123 


209 


15 


281 


11 




57 


173 


16 
16 


306 


10 
8 




126 


224 


15 

14 


270 


11 
12 


11 


60 


-157 




+314 




4 


129 


+238 




+258 






63 


140 


+17 


322 


+ 8 




132 


251 


. +13 


245 


-13 


11 


66 


123 


17 


329 


7 


+5 


135 


263 


12 


232 


13 




69 


-106 


+17 


+335 


+ 6 




138 


+275 


+12 


+218 


-14 


+11 



65 



TABLE lY .—Cmdmued. 


PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 


ARGUMENT VIII. 


Atg. 


h 


Diff. 


ni 


Diif. 


?1 


Arg. 


li 


Diff. 


1l 


Diff. 


?! 


o 
138 


+275 




+218 




+11 


249° 


+106 




-335 




- 6 


141 


286 


+11 


203 


-15 




252 


89 


-17 


340 


- 6 




144 


297 


11 


188 


IS 


11 


255 


71 




344 




7 


147 


306 




172 


16 




258 


53 




347 






150 


315 




156 


16 


11 


261 


34 


19 


349 


2 


8 


153 


322 




139 


17 




264 


+ 16 




350 






156 
159 


329 
335 




122 

105 


17 
17 ■ 


10 


267 
270 


- 3 
21 


18 


351 

350 


+ 1 
1 
3 


9 


162 


340 




87 




9 


273 


39 




349 


9 


165 


344 




69 


18 




276 


58 




346 












IS 








18 




4 




168 
171 
174 


+348 
350 
351 


+ 2 


+ 51 

33 

+ 15 


-18 
18 


9 

8 


279 
282 
285 


- 76 

94 

111 


-18 
17 


-342 
338 
333 


+ 4 
6 


10 
10 


177 


352 


+ 1 


- 3 


IB 




288 


129 


17 
16 
16 
16 
15 
IS 


326 


7 
8 
9 
10 
10 
11 




180 


351 


~ 1 


22 




7 


291 


146 


319 




183 


349 




40 


18 




294 


162 


311 




186 
189 
192 
195 


347 
343 
339 
334 




58 

76 

94 

112 


18 
18 
18 


6 
5 


297 
300 
303 
306 


178 
194 
209 
224 


302 
292 
282 
271 












17 








14 




12 




198 
201 


+327 
320 


- 7 


-129 
146 


-17 


4 


309 
312 


-238 
251 


-13 
13 
12 
11 
10 


-259 
• 246 


+13 




204 


312 


8 


162 




3 


315 


264 


232 


14 




207 


303 


9 


178 






318 


276 


218 


15 




210 


294 


9 


194 




2 


321 


287 


203 






213 


283 


11 


209 






324 


297 


188 




• 


216 


272 


11 


223 




+ 1 


327 


306 




173 






219 


260 


12 


237 


14 




330 


315 




156 


IB 




222 


247 


13 


250 







333 


323 


7 


140 


17 


10 


225 


233 


14 


263 






336 


330 


123 










14 




12 








6 




18 




228 


+219 




-275 




- 2 


339 


-336 


— 5 


-105 


+18 


9 


231 


205 


-14 


286 






342 


341 




87 


17 




234 


189 


16 


296 




3 


345 


345 


3 


70 


19 


9 

1 


237 


173 


16 


305 






348 


348 




51 


IS 




240 


157 


16 


314 




4 


351 


, 351 




33 


IS 


8 


243 


141 


16 


322 






354 


352 




- 15 


19 




246 


124 


17 


329 




- 5 


357 


352 





+ 4 


+18 


+ 7 


249 +106 


-18 


-335 


4 




360 


-352 




+ 22 




i 



66 



TABLE lY .—Contimed. 
PERTURBATIONS OF THE CO-ORDINATES IN WITS OF THE SIXTH DECIMAL. 

ARGUMENT IX. 



Arg. 

o 

5 
10 
15 
20 
25 
30 
35 
40 
45 

50 
55 
60 
65 
■70 
75 
80 
85 
90 
95 

JOO 
105 
110 
115 
120 
125 
130 
135 
140 
145 

150 
155 
160 
165 
170 
175 
180 



+150 
150 
150 
151 
152 
153 
153 
153 
153 
152 

+149 

146 

141 

134 

126 

116 

104 

89 

72 

53 

+ 31 

+ 7 

- 18 

45 

73 

101 

130 

159 

186 

212 

-236 
257 
274 
288 
298 
304 

^305 



Diff. 






+ 1 
1 

+ 1 





- 1 

3 

- 3 

6 
7 
8 
10 
13 
IS 
17 
19 



-24 
35 
27 
38 
28 
29 
29 
27 



-21 
17 
14 
10 
6 

- 1 



- 3 

11 

18 
26 
34 
43 
53 
63 
75 
87 

-100 
114 
128 
143 
158 
173 
188 
202 
216 
228 

-238 
246 
252 
255 
255 
251 
243 
232 
217 
198 

-176 

150 

121 

90 

58 

- 24 

+ 11 



Diff. 



7 
8 
8 
9 
10 
10 
12 
12 



-14 
14 
15 
IS 
15 
15 
14 
14 
12 



- 3 


+ 4 

8 
11 
15 
19 

22 

+26 
29 
31 
32 
34 

+35 



?1 

+22 

20 

18 

16 

13 

11 

8 

6 

+ 3 



- 2 

5 
8 
10 
13 
16 
18 
20 
23 
25 

-27 
28 
30 
31 
32 
33 
34 
34 
34 
34 

-33 
32 
31 
29 
28 
26 

-24 



Arg. 

o 
180 
185 
190 
195 
200 
205 
210 
215 
220 
225 

230 
235 
240 
245 
250 
255 
260 
265 
270 
275 

280 
285 
290 
295 
300 
305 
310 
315 
320 
325 

330 
335 
340 
345 
350 
355 
360 



-305 
302 
294 
282 
267 
247 
225 
200 
172 
144 

-115 
86 
57 
29 
- 3 
+ 22 
45 
65 
83 
99 

+113 
124 
132 
139 
144 
148 
150 
152 
152 
152 ' 

+152 

151 

150 
' 150 

150 

149 
+150 



Diff. 



+ 3 
8 
12 
IS 
20 
33 
3S 
38 
28 

29 

+29 
29 
28 
36 
35 
33 
20 
18 
16 

14 

+11 
8 
7 
6 
4 
3 

+ 2 





- 1 
1 




- 1 

+ 1 



ll 
+ 11 

45 
78 
110 
140 
167 
192 
212 
230 
243 

+252 
257 
259 
257 
252 
244 
234 
222 
209 
194 

+178 

163 

147 

131 

116 

102 

89 

76 

64 

54 

+ 44 
35 
27 
19 
11 
+ 4 
- 3 



Diff. 



+34 
33 
S3 
30 
27 
25 
20 
IS 
13 

9 

+ 6 

+ 3 

- 2 

S 

8 

10 

13 

13 

IS 



-16 
16 
16 
15 
14 
13 
13 
13 
10 



-24 

21 

19 

16 

13 

10 

7 

4 

- 1 

+ 2 

+ 5 
8 
11 
13 
16 
18 
21 
23 
25 
26 

+28 

ha 

30 
31 
31 
32 
32 
32 
31 
31 

+30 
29 
28 
27 
25 
24 

+22 



67 



TABLE lY. — Conimued. 








BEEi?ORBATI0NS OF THE CO-ORDINATES IN UNITS OF THE 


SIXTH 


DECIMAL. 




ARGUMENT X. 








Arg. 


h 


Diff. 


»!l 


Diff. 


fl 


Arg. 


Ji 


Diff. 


% 


Diff. 


Si 




o 



+187 




- 10 




+ 6 




180 


-178 




+ 17 




- 6 




5 


186 


- 1 


26 


-16 


5 


185 


175 


+ 8 


33 


+16 


5 




10 


183 




43 


17 


4 


' 190 


171 


4 


48 


15 


4 




15 


178 


5 


60 


17 


3 


' 195 


166 


5 


62 


14 


3 




20 


172 


6 


76 


16 


3 


' 200 


159 


7 


76 


14 


2 




23 


164 


8 


91 


15 


2 


' 205 


152 


7 


90 


14 


2 




30 


155 


9 


106 


15 


+ 1 


210 


143 




103 


13 


- 1 




35 


145 


10 


120 


14 





■ 215 


134 




115 









40 


133 


13 


133 


13 


- 1 


i 220 


123 


11 


126 


11 


+ 1 




45 


121 


12 
14 


145 


12 
11 


2 


225 


112 


12 


136 


10 


2 




50 


+107 




-156 




- 3 


230 


-100 




+146 




+ 3 




55 


92 


-15 


165 


- 9 


4 


235 


87 


+13 


154 


+ 8 


4 




60 


77 


15 


173 


B 


5 


240 


74 




162 




5 




65 


61 


16 


180 


7 


6 


245 


60 


14 


168 




6 




70 


45 


16 


185 


5 


7 


250 


46 


14 


173 


5 


6 




75 


28 


17 


188 


3 


7 


i 255 


32 


14 


177 




7 




80 


+ 11 


17 


190 


3 


8 


! 260 


17 




180 




8 




85 


- 6 


17 


191 


- 1 


9 


265 


- 2 


15 


181 


1 


8 




90 


23 


17 


189 


+ 2 


9 


270 


+ 14 


16 


182 


+ 1 


9 




95 


39 


16 
16 


187 


2 
4 


10 


275 


29 


15 

15 


180 


3 
3 


9 




100 


- 55 




-183 




-10 


280 


+ 44 




+178 




+10 




105 


71 


-16 


177 


+ 6 


10 


285 


59 


+15 


174 


- 4 


10 




110 


86 


IS 


170 


7 


11 


290 


73 




169 




11 




115 


100 


14 


162 


8 


11 


295 


87 




163 




11 




120 


113 


13 


152 


10 


11 


300 


101 




156 . 




11 




125 
130 


■ 125 
136 


13 
11 


141 
130 


11 
11 


11 
11 


305 
310 


114 
126 


12 


147 
137 


10 


11 
11 




135 
140 
145 


146 
155 
163 


10 
9 
8 

6 


117 

104 
90 


13 
13 
14 

15 


11 
10 
10 


315 
320 
325 


138 

148 
158 


10 
10 

8 


126 
114 
101 


12 
13 

14 


11 

11 
10 




150 
155 


-169 
174 


- 6 


- 75 
60 


+15 


-10 
9 


330 
335 


+166 
173 


+ 7 
6 
4 
3 

4. I 


+ 87 
72 


-16 
15 

IS 
17 
17 


+10 
9 




160 
165 


177 
179 


3 
2 


45 
29 


15 
16 


9 

8 


- 340 
345 


179 
183 


57 
41 


9 

8 




170 


180 


- 1 


- 14 




7 


350 


186 


24 


8 




175 


180 





+ 2 




7 


! 355 


187 




+ 7 




7 




180 


-178 


+ 2 


+ 17 


+15 


- 6 


360 


• +187 




- 10 




+ 6 




: \ 





68 





TABLE lY.— Continued. 




PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 






AEGUMENT XI. 




Arg. 


h 


Diff. 


1J1- 


DifF. 


fi 1 Arg. 


h 


Diff. 


Vl 


' Diff. 


fi 









+101 




+ 11 




- 3 



180 


-144 




+ 10 




-30 




5 


98 


- 3 


30 


+19 


- 1 


185 


144 





8 


— 2 


31 




10 


92 


6 


48 


18 


+ 1 


190 


144 





6 


2 


31 




15 


83 


9 


65 


n 


2 


195 


145 


- 1 


+ 3 


3 


32 




20 


72 


11 


79 


14 


3 


200 


145 








3 


32 




25 


58 


14 


92 


13 


4 


205 


145 





- 3 


3 


33 




30 


43 


la 


102 


10 


4 


210 


146 


- 1 


6 


3 


34 




35 


27 


16 


110 


8 


4 


215 


146 





10 


4 


34 




40 


+ 11 


16 


116 


6 


. 4 


220 


146 





14 


4 


35 




45 


- 5 


16 
16 


119 


3 

+ 1 


3 


225 


146 




+ 1 


18 


4 
6 


36 




50 


- 21 




+120 




+ 2 


230 


-145 




- 23 




-36 




55 


36 


-15 


119 


- 1 


+ 1 


235 


144 


+ 1 


28 


— 6 


37 




60 


51 


IS 


117 


2 





240 


142 


2 


34 


6 


37 




65 


64 


13 


114 


3 


- 2 


245 


140 


2 


41 


7 


37 




70 


76 


12 


110 


4 


3 


250 


137 


3 


47 


6 


38 




75 


87 


11 


105 


5 


5 


255 


133 


4 


54 


7 


38 




80 


97 


10 


99 


6 


7 


260 


128 


s 


61 


7 


38 




85 


106 


9 


93 


6 


9 


265 


122 


6 


69 


8 


38 




90 


113 


7 


86 


7 


10 


270 


115 


7 


76 


7 


38 




95 


120 


7 
9 


80 


6 

7 


12 


275 


106 


9 
9 


83 


7 
7 


37 




100^ 


-125 




+ 73 




-14 


280 


- 97 




- 90 




-37 , 




105' 


130 


- 5 


67 


- 6 


15 


285 


86 


+11 


96 


- 6 


36 




110 


133 


3 


61 


6 


17 


290 


74 


12 


101 


5 


35 




115 


136 


3 


55 


6 


18 


295 


60 


14 


106 


6 


34 




120 


139 


3 


49 


6 


19 


300 


46 


14 


109 


3 


32 




125 


140 


1 


44 


6 


21 


305 


30 


16 


111 


- 2 


30 




130 


141 


1 


40 


4 


22 


310 


- 13 


17 


111 





28 




135 


142 


1 


36 


4 


23 


315 


+ 4 


17 


108 


+ 3 


26 




140 


143 


1 


32 


4 


24 


320 


21 


17 


103 


5 


24 




145 


143 






29 


3 
3 


25 


325 


38 


17 
16 


96 


7 
9 


21 




150 


-143 




+ 96 




-26 


330 


+ 54 




- 87 




-19 




155 


143 


- 


23 


- 3 


26 


335 


■ 68 


+14 


75 


+12 


16 




160 


143 





20 


3 


27 


340 


80 


12 


60 


15 


13 




165 


143 





18 


2 


28 


345 


90 


10 


44 


16 


10 




170 


143 





15 


3 


29 


350 


97 


7 


26 


18 


8 




175 


144 


- 1 


13 


2 


29 


355 


101 


+ 4 


- 7 


5 




180 


-144 





+ 10 


- 3 


-30 


360 


+101 





+ 11 


+.8 _3 









69 





« 


TABLE lY.— Continued. 










PEETURBATIONS OF THE 


CO-ORDINATES IN UNITS OF THE 


SIXTH 


DECIMAL. 








ARGUMENT XII. 










Arg. 


Si 


Diflf. 


% 


Diff. 


Si 


Arg. 


li 


Di«F. 


iji 


Diff. 


fl 









- 97 




- 6 




-2 




180 


+122 




+ 8 




+2 




5 


96 


+ 1 


13 


- 7 




185 


120 


— 3 


20 


+12 






10 


95 


1 


21 


6 


2 


190 


117 


3 


31 


11 


2 




15 


94 


1 


28 


7 




195 


114 


3 


42 


11 






20 


92 


3 


35 


7 


3 


200 


109 


9 


52 


10 


3 




25 


89 


3 


43 


8 




205 


103 


6 


62 


10 






30 


86 


3 


50 


7 


3 


210 


96 


7 


71 


9 


3 




35 


82 


4 


57 


7 




215 


88 


8 


79 


8 






40 


78 


4 


64 


7 


2 


220 


80 


8 


86 


7 


2 




45 


74 


4 
6 


70 


6 

7 




225 


71 


9 . 
10 


93 


7» 
S 






50 


- 68 . 




- 77 




2 


230 


+ 61 




+ 98 




2 




55 


62 


+ 6 


83 


- 6 




235 


51 


-10 


103 


+ 5 






60 • 


56 


6 


88 


5 


2 


240 


41 


10 


106 


3 


2 




65 


49 


7 


93 


S 




245 


31 


10 


109 


3 






70 


41 


8 


98 


5 


2 


250 


20 


11 


110 


1 


2 




75 


33 


8 


102 


4 




255 


+ 10 


10 


111 


+ 1 






80 


24 


9 


105 


3 


1 


260 





10 


110 


- 1 


1 




85 


15 


9 


108 


3 




265 


- 10 


10 


109 


1 






90 


- 5 


10 


109 


1 


1 


270 


19 


9 


107 


3 


1 




95 


+ 5 


10 
10 


110 


- 1 





275 


29 


10 
8 


104 


3 

4 






100 


+ 15 




-110 




-1 


280 


- 37 




+100 




+1 




105 


25 


+10 


109 


+ 1 




285 


45 


- 8 


96 


- 4 






110 


36 


11 


107 


3 





290 


53 


8 


91 


5 







115 


46 


10 


105 


3 




295 


60 


7 


86 


6 






120 


56 


10 


101 


4 





300 


66 


6 


80 


6 







125 


66 


10 


96 


5 




305 


72 


6 


74 


6 






130 


75 


9 


90 


6 


+1 


310 


77 


5 


67 


7 


-1 




135 


84 


9 


83 


7 




315 


81 


4 


60 


7 






140 


92 


8 


75 


8 


1 


320 


85 


4 


53 


7 


1 




145 


99 


7 
7 


66 


9 
9 




325 


88 


3 
3 


46 


7 
7 






150 
155 
160 
165 


+106 
111 
115 
119 


+ S 

4 

4 


- 57 
47 
37 
26 


+10 
10 
11 


1 
2 


330 
335 
340 
345 


- 91 
93 
■95 
96 


- 2 
3 
1 

— 1 


+ 39 
32 
24 
17 


- 7 
8 
7 
8 


1 
2 




170 


121 


2 


15 


11 


2 


350 


' 97 


1 




9 


2 




175 

180 


122 
+122 


+ 1 



- 3 

+ 8- 


12 
+11 


+2 


355 
360 


97 
- 97 


+ 2 
- 6 


7 
- 8 


-2 





70 





TABLE lY.— Conimued. 






PERTURBATIONS OF THE CO-ORDINATES IN UNITS OP THE SIXTH DECIMAL. 




ARGUMENT XIII. 






Arg. 


«i 


Diflf. 


111 


Biff. 


Si 


Arg. 


h 


DifF. 


Vi 


Diff. 


& 


O 




-83 









- 6 


o 
180 


+83 




+ 




+ 6 


5 


82 


+1 


- 4 


—4 




185 


82 


-1 


3 


+3 




10 


80 


2 


7 


3 


4 


190 


80 


2 


7 


4 


4 


15 


78 


2 


11 


4 




195 


78 


2 


10 


S 




20 


75 


3 


14 


3 


- 2 


200 


75 


3 


14 


4 


+ 2 


25 


72 


3 


17 


3 




205 


71 


4 


17 


3 




30 


68 


4 


21 


4 





210 


67 


4 


20 


3 





35 


63 


S 


24 


3 




215 


62 


6 


23 


3 




40 


58 


6 


26 


2 


+ 1" 


220 


57 


S . 


26 


3 


- 1 


45 


■ 52 


6 
6 


29 


3 

2 




225 


52 


5 
6 


28 


2 
3 




50 


-46 




-31 




3 


230 


+46 




+31 




3 


55 


40 


+6 


33 


-2 




235 


39 


-7 


33 


+2 




60 


33 


7 


35 


2 


5 


240 


33 


6 


35 


2 


5 


65 


26 


7 


37 


2 




245 


26 


7 


36 


1 




70 


19 


7 


38 


1 


7 


250 


19 


7 


38 


2 


7 


75 


12 


7 


39 


1 




255 


12 


7 


39 


1 




80 


- 5 


7 


40 


-1 


8 


260 


+ 5 


7 


40 


+1 


8 


85 


+ 3 


8 


40 







265 


- 3 


8 


40 







90 


10 


7 


40 





9 


270 


10 


7 


40 





9 


95 


17 


7 
7 


40 




+1 




275 


17 


7 
7 


40 








100 


+24 




-39 




10 


280 


-24 




+40 




10 


105 


31 


+7 


39 


+0 




285 


31 


-7 


39 


-1 




110 


38 


7 


33 


1 


10 


290 


38 


7 


38 


1 


10 


115 


44 


6 


36 


2 




295 


44 


6 


37 


1 




120 


50 


6 


34 


2 


11 


300 


50 


6 


35 


2 


11 


125 


56 


6 


32 


2 




305 


56 


6 


33 


2 . 




130 


61 


6 


30 


2 


11 


310 


61 


S 


31 


2 


11 


135 


66 


6 


28 


2 




315 


66 


S 


29 


2 




140 


70 


4 


25 


3 


10 


320 


70 


4 


26 


3 


10 


145 


74 


4 
3 


23 


2 
3 




325 


74 


4 
3 


23 


3 
3 




150 


+77 




-20 




9 


330 


-77 




+20 




9 


155 


80 


+3 


17 


+3 




335 


80 


-3 


17 


-3 




160 


82 


3 


13 


4 


8 


340 


82 


2 


14 


3 


8 


165 


83 


I 


10 


3 




345 


83 


1 


10 


4 




170 


84 


+1 


7 


3 


7 


350 


84 


-1 


7 


3 


7 


175 


84 





- 3 


4 




355 


84 





+ 3 


4 




180 


+83 


-1 





+3 


+ 6 


360 


-83 


+1 





-3 


-6 






- 





71 



TABLE lY .—Continued. 












PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE 


SIXTH 


DECTMAT,. 




ARGUMENT XIV. 












Arg. 


?i 


DiflF. 


■ni 


Diff. 


?1 


Arg. 


h 


Diff. 


ni 


Diff. 


& 




o 



+44 




+ 3 




+2 




ISO 


-54 




-2' 




-2 




5 


45 


+1 


- 1 


-4 




185 


54 





+ 3 


+6 






10 


45 





4 


3 


2 


190 


54 





8 


6 


2 




15 


44 


-1 


7 


3 




195 


53 


+1 


13 


5 






20 


44 





11 


4 


1 


200 


51 


2 


18 


6 


1 




25 


43 


1 


14 


3 




2(35 


49 


2 


23 


6 






30 


42 


1 


18 


4 


+1 


210 


47 


2 


27 


4 


-1 




35 


41 


1 


21 


3 




215 


44 


3 


31 


4 






40 


39 


2 


24 


3 





220 


40 


4 


35 


4 







45 


37 


2 
2 


28 


4 
3 




225 


37 


3 

4 


38 


3 
3 






50 
55 


+35 
32 


-3 


-31 
34 


-3 


-1 


230 
235 


-33 

29 


+4 


+41 
44 


+3 


+1 




60 


30 


2 


37 


3 


1 


240 


24 


5 


46 


2 


1 




65 


27 


3 


40 


3 




245 


20 


4 


47 


1 






70 


23 


4 


42 


2 


2 


250 


15 


S 


48 


1 


2 




75 


20 


3 


44 


2 




255 


11 


4 


49 


1 

+1 






80 


16 


4 


46 


2 


2 


260 


6 


5 


50 


2 




85 


12 


4 


48 


2 




265 


- 2 


4 


49 


~1 






90 


8 


4 


49 


1 


3 


270 


+ 2 


4 


49 





3 




95 


+ 3 


S 

4 


50 


1 
-1 




275 


7 


5 

4 


48 


1 

1 






100 
105 


- 1 

6 


-5 


-51 
51 





3 


280 
285 


+11 
14 


+3 


+47 
45 


-2 


3 




110 


11 


6 


51 





3 


290 


18 


4 


44 


1 


3 




115 


15 


4 


^50 


+1 




295 


22 


4 
3 
3 
2 

Q 


42 


2 
3 
2 
3 

Q 






120 


20 


5 


49 


1 


3 


300 


25 


39 


3 




125 


25 


S 


47 


2 




305 


28 


37 






130 


29 


4 


45 


2 


4 


310 


30 


34 


4 




135 


33 


4 


42 


3 




315 


33 


2 


31 


Q 






140 


37 


4 


39 


3 


3 


320 


35 


A 


28 


3 


3 




145 


41 


4 


35 


4 




325 


37 


* 


25 










3 




4 








2 




3 






150 
155 


-44 

47 


-3 


-31 

27 


" +4 


3 


330 
335 


+39 
40 


+1 
n 


+22 
19 


-3 
3 


3 




160 


50 


3 


23 


4 


3 


340 


42 


] 


16 


3 


3 




165 


52 


2 


18 


5 




345 


43 





13 


3 






170 


53 


1 


13 


6 


3 


350 


43 


+1 


10 


4 


3 




175 


54 


-1 


8 


5 




355 


44 





6 


—3 






180 


-54 





- 2 


+0 


-2 


360 


+44 




+ 3 




+2 





72 



TABLE lY. —Cmiinued. 
PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 

AEGTJMENT XV. 



Arg. 

o 


5 

10 

15 

20 

25 

30 

35 

40 

45 

50 
55 
60 
65 

70 
75 
80 
85 
90 
95 

100 
105 
110 
115 
120 
125 
130 
135 
140 
145 

150 
155 
160 
165 
170 
175 
180 



-29 
29 
29 
28 
27 
26 
25 
23 
22 
20 

-18 

16 

14 

11 

9 

7 

4 

- 1 

+ 1 

4 

+ 6 
9 
12 
14 
16 
19 
21 
23 
25 
26 

+28 
29 
30 
30 
31 
31 

+31 



Diff. 






+1 
1 
1 
1 
a 
1 

2 

3 

+2 
2 



2 

+3 
3 
2 
2 
3 
2 
2 
2 
1 



+1 
1 


+1 





- 2 

4 
7 
9 

12 
14 
16 
18 
20 
22 

-24 
25 
26 
27 
28 
29 
30 
30 
30 
30 

-30 
29 
28 
27 
26 
24 
23 
21 
19 
16 

-14 

11 

9 

6 

3 

- 1 
+ 2 



Diff. 



+1 
1 
1 
1 

2 
1 
2 
2 
3 

2 

+3 
2 



+3 














































Arg. 

o 
180 
185 
190 
195 
200 
205 
210 
215 
220 
225 

230 
235 
240 
245 
250 
255 
260 
265 
270 
275 

280 
285 
290 
295 
300 
305 
310 
315 
320 
325 

330 
335 
340 
345 
350 
355 
360 



Diff. 



+31 
31 
30 
29 

28 
27 
25 
24 
22 
20 

+18 

15 

13 

10 

8 

5 

+ 2 



- 3 
5 

- 8 
10 
13 
15 
17 
19 
21 
23 
24 
25 

-27 
28 
28 
29 
29 
29 

-29 



+ 2 
5 
7 
10 
13 
15 
17 
20 
22 
23 

+25 
26 
28 
29 
29 
30 
30 
30 
30 
30 

+29 
28 
27 
26 
24 
23 
21 
19 
17 
15 

+13 

10 

8 _ 

6 

3 

+ 1 

-2 



Diff. 

+3 
3 
3 
3 
2 
2 
3 
2 
1 



+1 
2 
1 


+1 







Si 












































73 



TABLE lY .—Cmtinued. 






PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE STTTB 


. DECTMAT, 


ARGUMENT XVI. 


ARGUMENT XVII. 


Arg. 


s\ 


DifF. 


ll 


Diff. 


?1 


Arg. 


li 


DifF. 


■ni 


Diff. 


.■;,Sl 


O 




+113 




+ 4 




+2 


O 




-103 




- 16 




-2 


5 


113 





- 6 


-10 




5 


102 


+1 


24 


-8 




10 


112 


- 1 


15 


9 


2 


10 


99 


3 


33 


9 


2 


15 


110 




25 


10 




15 


96 


3 


42 


9 




20 


108 




34 


9 


1 


20 


92 


4 


50 


8 


1 


25 


104 




43 


9 




25 


87 


5 


57 


7 




30 


100 




52 




+1 


30 


82 




64 


7 


-1 


35 


95 




61 


9 




35 


76 


6 


71 


7 




40 


89 




69 







40 


69 


7 


78 


7 





45 


83 


7 


76 


7 
7 




45 


62 


7 
8 


83 


S 
6 




50 


+ 76 




- 83 







50 


- 54 




- 88 







55 


68 


- 8 


89 


- 6 




55 


46 


+8 


93 


-5 




60 


60 




95 




-1 


60 


38 




96 




+1 


65 


52 




100 






65 


29 




99 


3 




70 


43 




104 




1 


70 


20 




101 




1 


75 


34 


9 


107 


3 




75 


11 


9 


103 


-2 




80 


24 




110 




2 


80 


- 2 




103 




1 


■85 


14 


10 


111 


1 




85 


+ 7 




103 







90 


+ 5 


9 


112 


- 1 


2 


90 


16 


9 


102 


+1 


2 


95 


- 5 


10 
10 


112 




+ 1 




95 


25 


9 


101 


1 
3 




100 


- 15 




-111 




3 


100 


+ 34 




- 98 




2 


105 


25 


-10 


109 


+ 2 




105 


42 


+8 


95 


+3 




110 


34 


9 


107 




3 


110 


50 




91 




2 


115 


43 


9 


103 


4 




115 


58 




86 






120 


52 


9 


99 


4 


3 


120 


66 




81 




2 


125 


61 


9 


94 


6 




125 


73 




75 






130 


69 


8 


88 


6 


3 


130 


79 




68 




2 


135 


77 


8 


82 


6 




135 


85 




61 


7 




140 


84 


7 


75 




3 


140 


90 




54 




3 


145 


90 


6 
5 


68 


7 
8 




145 


94 


4 


46 


8 




150 
155 


- 95 
100 


- 6 


-60 
51 


+ 9 


3 


150 
155 


+ 98 
101 


+3 


- 38 
29 


+9 
9 


2 


160 


105 


S 


42 




3 


160 


103 




20 


2 


165 
170 


108 
110 


3 
2 


33 
24 


9 


2 


165 
170 


104 
105 


+1 

-1 

,-1 


11 
- 2 


9 


2 


175 

180 


112 
-113 


2 
- 1 


14 
- 4 


10 • 
+10 


-2 


175 

180 


104 
+103 


+ 7 
+ 16 


+9 


.+2 i 


180° are to be subtracted from the Arguments > 180°, and £i, iji, and fi to be taken with the rev( 


irsed sign 







10 



74 





TABLE lY , -^Continued. 




PERTURBATIONS OP THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 




ARGUMENT XVIII. 


ARGUMENT XIX. 




Arg. 


h 


Diff. 


n\ 


Diff. 


?i 


Arg. 


h 


Diff. 


fli 


Diff. 


?i 




o 


10 


+43 
41 


-3 


+ 5 
12 


+7 






o 


10 


+29 
26 


-8 


+14 

18 


+4 


-1 
-1 




20 


39 


3 


19 


7 





20 


22 


4 


22 


4 







30 


35 


4 


26 


7 





30 


17 


6 


26 


4 







40 


30 




31 


6 





40 


12 


s 


28 









50 


24 


6 


36 


6 


■0 


50 


7 


6 


30 


+2 


+1 




60 


17 


7 


40 


4 





60 


+ 1 


6 


30 





1 




70 
80 


10 
+ 3 


7 
7 


42 
43 


2 
+1 







70 
80 


- 5 
10 


6 
5 


30 
29 



-1 


1 

2 




90 


- 5 


8 
7 


43 




-1 





90 


15 


a 

5 ! 


27 


3 
3 


2 




100 
110 


-12 
19 


-7 


+42 
39 


-3 






100 
110 


-20 
24 


-4 : 


+24 
21 


-3 


+2 
2 




120 


26 


7 


35 


4 





120 


28 


4 


17 


4 


2 




130 


31 




30 







130 


30 


2 


12 


a 


2 




140 


36 




24 


6 





140 


32 


2 


7 


6 ' 


2 




150 


39 




17 


7 





150 


33 


-1 


. + 2 


8 


1 




160 
170 

180 


42 

43 

-43 


-1 



10 
+ 3 
- 5 


7 

7 

-8 







160 
170 
180 


33 
31 

-29 




+2 
+2 ■ 


- 4 

9 

-14 


6 ; 

e 1 

-' i 


1 

1 

+1 




ARGUMENT XX. 


ARGUMENT XXI. 


ARGUMENT XXII. 




Arg. 


h 


Vi 


?i 


Arg. 


ll 


ni 


?i 


Arg. 


h 


^1 


£i 




o 



-27 


- 4 





o 



+25 


+ 1 





o 



-24 


+10 


-8 




10 


26 


9 





10 


24 


- 3 





10 


21 


14 


8 




20 


24 


13 





20 


24 


8 





20 


17 


18 


8 




30 


21 


17 





30 


22 


12 





30 


13 


21 


7 




40 


18 


21 





40 


20 


16 





40 


9 


23 


7 




50 


14 


23 





50 


17 


19 





50 


- 4 


25 


6 




60 


10 


25 





60 


13 


22 





60 


+ 1 


26 


, 5 




70 


- 5 


27 





70 


10 


24 





70 


6 


26 


3 




80 





27 





80 


6 


26 





80 


10 


25 


2 




90 


+ 4 


27 





90 


+ 1 


26 





90 


15 


23 


-1 




100 


+ 9 


-26 





100 


- 3 


-26 





100 


+19 


+21 


+1 




110 


13 


24 





110 


7 


25 





110 


22 


19 


2 




120 


17 


21 





120 


11 


24 





120 


25 


15 


4 




130 


21 


18 





130 


15 


21 





130 


26 


11 


5 




140 


23 


14 





140 


18 


18 





140 


28 


7 


6 




150 


25 


10 





150 


21 


14 





150 


28 


+ 3 


7 




160 


27 


- 5 





160 


23 


10 


0- 


160 


27 


- 2 


8 




170 


27 








170 


24 


6 





170 


26 


6 


8 




180 


+27 


+ 4 





180 


-25 


- 1 





180 


+24 


-10 


+8 ' 




1 


80° are to be subtracted from the Arguments > 180°, and |i, i^, and ti to be taken with the reversed sign. i 





75 



TABLE IV. — CmHnued. 
PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL, 




ARGUMENT XXin. 


ARGUMENT XXIV. 


ARGUMENT XXV. 




Arg. 


k 


% 


ix 


Arg. 


k 


■ni 


?i 


Arg. 


Ji 


rii 


k 




o 


10 

20 

30 

40 

50 

60 

70 

80 

90 

100 
110 
120 
130 
140 
150 
160 
170 
180 


-22 

22 

21 

20 

18 

15 

12 

9 

5 

- 1 

+ 3 

6 

10 

13 

16 

• 18 

20 

22 

+22 


- 2 
+ 2 
6 
10 
13 
16 
18 
20 
21 
22 

+22 

21 

20 

18 

15 

12 

9 

5 

+ 2 


-1 

1 

-1 






+1 

1 
1 

+1 
1 

2 

2 
2 
2 

1 

1 

+1 


o 


10 

20 

30 

40 

50 

60 

70 

80 

90 

100 
110 
120 
130 
140 
150 
160 
170 
180 


+20 

20 

18 

16 

14 

11 

8 

+ 4 



- 3 

- 7 
10 
13 
16 
18 
19 
20 
21 

--20 


-4 
4 
4 
3 
3 
2 
1 

-1 


+1 

+1 
2 
3 
3 
4 
4 
4 
4 

+4 


+2 

1 

+1 

;' 
-1 

2 

2 
3 
4 

4 

-4 
4 
4 
4 
4 
4 
3 
3 

-2 





10 
20 
30 
40 
50 
60 
70 
80 
90 

100 
110 
120 
130 
140 
150 
160 
170 
160 


-19 

19 

18 

16 

14 

12 

9 

6 

- 3 

+ 1 

+ 4 
7 
10 
13 
15 
17 
18 
19 

+19 


+ 1 

4 

7 
10 
13 
15 
17 
18 
19 
19 

+19 

18 

16 
14 

12 i 
9 ! 
6 
+ 3 
- 1 





















' 












ARGUMENT TOTVI. 


ARGUMENT XXVII. 


ARGUMENT XXVIII. 




Arg. 


h 


Vi 


fi 


Arg. 


li 


■ni 


& 


Arg. 


& 


■n\ 


ii 




o 

10 
20 
30 
40 
50 
60 
70 
80 
90 

100 
110 
120 
130 
140 
150 
160 
170 
180 


+19 
21 
23 
24 
24 
23 
22 
20 
17 
14 

+11 

7 

+ 3 

- 1 

6 

10 

13 

16 

-19 


+13 

9 

6 

+ 2 

- 2 

6 

10 

13 

16 

19 

-21 
22 
23 
23 
22 
20 
18 
16 

-13 
























o 



10 

20 

30 

40 . 
50 
60 
70 
80 
90 

100 
110 
120 
130 
140 
150 
160 
170 
180 


+16 
14 
12 
10 

7 

4 
+ 1 < 
- 3 

6 

9 

-11 

14 
16 
17 

18 
18 
18 
17 
-16 


+11 

7 

+ 2 

- 2 

7 

11 

15 

19 

22 

24 

-25 
26 
26 
25 
24 
21 
19 
15 

-11 


+3 
3 
3 
2 
2 
2 
1 

+1 



-1 
1 
2 
2 
3 
3 
3 
3 

-3 


o 


10 
20 
30 
40 
50 
60 
70 
80 
90 

100 • 

110 

120 

130 

140 

150 

160 

170 

180 


-15 

14 

13 

12 

10 

8 

6 

- 3 



+ 2 

+ 5 

7 

9 

11 

13 

14 

15 

15 

+15 


+ 5 i 
8 
11 
14 
16 
18 
19 
20 
19 
19 

+18 

16 

14 

11 

8 

5 

+ 2 

- 2 

- 5 


# +1 

1 

1 

+1 






-1 

1 

-1 
1 

1 

2 

a 

2 
2 
2 

-1 




180° are to be subtracted from the Aiguments > 180°, and 5i, n, and ti to be taken with the reversed sign. 





76 





TABLE lY.— Continued. 






PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 




ARGUMENT XXIX. 


ARGUMENT XXX. 


ARGUMENT XXXI. 




Arg. 


li 


Vi 


k 


Ai^.- 


fi 


m 


& 


Arg. 


& 


Vl 


ri 




o 



+12 


+ 1 





o 



-8 


-1 





o 



-7 


-1 







10 


12 


- 1 





10 


8 


2 





10 


7 


2 







20 


12 


3 





20 


7 


3 





20 


6 


3 







30 


11 


5 





30 


7 


5 





30 


6 


4 







40 


10 


7 





40 


6 


6 





40 


5 


5 







i 50 


9 


9 





50 


5 


7 





50 


4 


6 







1 60 


7 


10 





60 


4 


8 





60 


3 


6 







! 70 


5 


11 





70 


3 


8 





70 


-2 


7 







! 80 


3 


12 





80 


-1 


8 





80 





7 







1 90 


' + 1 


12 





90 


+1 


8 





90 


+1 


7 







100 


- 1 


-12 


-1 


100 


+2 


-8 





100 


+2 


-6 







; no 


3 


12 




no 


3 


8 





110 


3 


6 







i 120 


5 


11 




180 


4 


7 





120 


4 


5 







130 


7 


10 




130 


5 


6 





130 


5 


5 







140 


9 


9 




140 


6 


5 





140 


6 


4 







150 


10 


7 




150 


7 


4 





150 


7 


3 







160 


11 


5 


-1 


160 


8 


2 





160 


7 


-2 







170 


12 


3 





170 


8 


* -1 





170 


7 










180 


-12 


- 1 





180 


+8 


+1 





180 


+7 


+1 







ARGUMENT XXXU. 


ARGUMENT XXXIH. 


ARGUMENT XXXIV. 




Arg. 


h 


■ni 


?1 


Arg. 


s^ 


Vl 


?! 


A.^. 


h 


Vl 


& 




o 



+4 


-5 





o 



+3 








o 



+3 










10 


5 


4 





10 


3 








10 


3 


+1 







20 


6 


3 





20 


3 


-1 





20 


3 


1 







30 


6 


2 





30 


3 


1 





30 


2 


2 







40 


7 


-1 





40 


3 


2 





40 


2 


2 







50 


7 








50 


2 


2 





50 


2 


2 







60 


7 


+1 





60 


2 


3 





60 


1 


3 







70 


6 


2 





70 


1 


3 





70 


+1 


3 







f ^° 


6 


3 





80 


+1 


3 





80 





3 







^- 90 


5 


4 





90 





3 





90 





3 







100 


+4 


+5 





100 





-3 





100 


-1 


+3 







no 


3 


5 





110 


-1 


3 





no 


1 


3 







120 


2 


6 





120 


1 


3 





120 


2 


2 







130 


+1 


6 





130 


2 


3 





130 


2 


2 







140 





6 





140 


2 


2 





140 


3 


2 







150 


-1 


6 





150 


3 


2 





150 


3 


1 







160 


2 


6 





160 


3 


1 





160 


3 


+1 







170 


3 


5 





170 


3 


-1 





170 


3 










180 


-4 


+5 





180 


-3 








180 


-3 










180° are to be subtrac 


ted from the Arguments > 180°, and h, m, and fi to be taken with the reversed sign. 







77 



TABLE lY .—Continued. 
PEETUKBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 



ARGUMENT XXXV. 



Arg. 




10 
20 
30 
40 
50 
60 
70 
80 
90 

100 
110 
120 
130 
140 
150 
160 
170 
180 



-3 
3 
3 
2 
2 
2 
2 
1 

-1 



+1 
1 
1 
2 
2 
2 
2 
+3 



11 



























ARGUMENT XXXVI. 



ARGUMENT XXXVIII. 



Arg. 



20 

40 

60 

80 

100 

120 

140 

160 

180 



-2 
3 

4 
4 
3 
3 

-2 


+1 
+2 



ni 



+4 
4 
3 
2 

+1 

-1 
2 
3 
4 

-4 









+1 
1 

+1 





Arg. 




10 
20 
30 
40 
50 
60 
70 
80 
90 

100 
1]0 
120 
130 
140 
150 
160 
170 
180 



-2 
2 
2 
2 
2 
1 
1 

-1 



+1 
1 
1 
2 
2 
2 
2 
2 

+2 



% 


























ARGUMENT XXXVII. 



Arg. 




10 
20 
30 
40 
50 
60 
70 
80 
90 

100 
110 
120 
130 
140 
150 
160 
170 
180 



+2 
2 
2 
2 
2 
2 
2 
1 
1 

+1 



-1 
1 
1 

2 
2 



Vi 



+ 2 

4 

6 

7 

9 

10 

11 

11 

12 

11 

+11 
10 
9 
7 
6 
4 

+ 2 


- 2 



ARGUMENT XXXIX. 



Arg. 




20 
40 
60 
80 
100 
120 
140 
160 
180 



-2 
2 
3 
3 
2 
2 

-1 


+1 

+2 



Vi 



-2 

-1 


+1 
1 
2 
3 
3 
3 

+2 



+2 
1 
1 

+1 



-1 
1 
1 

-2 



ARGUMENT XL. 



Arg. 





20 

40 

60 

80 

100 

120 

140 

160 

ISO 



ll 


Vi 


-2 





2 


-1 


1 


1 


-1 


2 





2 


+1 


2 


1 


1 


2 


-1 


2 





+2 






-1 







+ 



180° are to be subtracted from the Arguments > 180°, and h, m, and tj to be taken with the reversed sign. 



78 



1 TABLE lY .—Cmcluded. 


PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 


ARGUMENT XLI. 


ARGUMENT XLII. 


ARGUMENT XLUI. 


Arg. 


h 


l)! 


?1 


Arg. 


h 


iJi 


?i 


Arg. 


& 


% 


& 




























, 


-1 











-1 


+2 








-1 








20 


1 


+1 





20 





2 





30 


1 








40 


-1 







40 





2 





40 


-1 


+1 





60 










60 


+1 


2 





60 










80 










80 


1 


1 





80 










100 










100 


2 


+1 





100 










120 


+1 


1 





120 


2 








120 


+1 







140 


1 


+1 





140 


2 


-1 





140 


1 


+1 





160 


1 








160 


1 


1 





160 


1 








180 


+1 








180 


+1 


-2 





180 


+1 








ARGUMENT XLIV. 


ARGUMENT XTiV. 


Arg. 


k 


JJl 


?i 


Arg. 


h 


% 


?1 


o 



-1 


+1 





o 












20 


1 








20 


-1 








40 


1 








40 




-1 





60 


-1 








60 




1 





80 











80 




2 





100 











100 




2 





120 











120 




2 





140 





-1 





140 


-1 


1 





160 


+1 


1 





160 





-1 





180 


+1 


-1 





1.80 











180° are to be subtracted from the Arguments > 180°, and ?i, vi, and tj to be taken with the reversed sign. 





79 



• 








TABLE V 












LOGARITHMS FOR REFERRING THE PERTURBATIONS TO THE EQUATOR. 










Mean Equinox of the beginning 


of the Year. 










Years. 


cos (xi x) 


cos (?/i x) 


cos {zi x) 


cos {xi y) 


cos (i/i y) 


COS (zj_y) 


cos (zi z) 


COS (yi z) 


COS (z\, z) 




1852 B 


9.982316 


9.423945W 


8.944771 


9.446013 


9.066907 


9.400926ra 


8.169765m 


9.425327 


9.983960 




1853 


9.982289 


9.424326re 


8.944586 


9.446346 


9.966880 


9.400892re 


8.167022m 


9.425285 


9.963984 




1854 


9.982261 


9.424707W 


8.944400 


9.446679 


9.966852 


9.400856W 


8.164265m 


9.425243 


9.983988 




1855 


9.982234 


9.425088M 


8.944215 


9.447012 


9.966624 


9.400824W 


8.161488m 


9.425201 


9.983992 




1856 B 


9.982206 


9.425468W 


8.944029 


9.447345 


9.966706 


9.400791« 


8.158674M 


9.425159 


9.983996 




1857 


9.982179 


9.425S48M 


6.943844 


9.447677 


9.966768 


9.400757ra 


8.155832m 


9.425117 


9.984000 




1858 


9.982151 


9.426227n 


6.943658 


9.448009 


9.966740 


9.400723n 


8.152991m 


9.425075 


9.984004 




1859 


9.962123 


9.426606ra 


8.943472 


9.448341 


9.966712 


9.400689ra 


8.150142M 


9.425033 


9.984006 




1860 B 


9.982095 


9.426984n 


8.943286 


9.448673 


9.966684 


9.400656ra 


8.147263m 


9.424990 


9.964011 




1861 


9.962068 


9.427362M 


8.943100 


9.449004 


9.966656 


9.40062aw 


8.144356m 


9.424948 


9.984015 




1862 


9.982040 


9.427740ra 


8.942914 


9.449335 


9.966628 


9.400586ra 


8.141418M 


9.424905 


9.984019 




1863 


9.982012 


9.4281 17w 


8.942728 


9.449666 


9.966600 


9.400554ra 


8.138472m 


9.424863 


9.984023 




1864 B 


9.981984 


9.428494W 


6.942541 


9.449996 


9.966572 


9.400521m 


6.135514m 


9.424820 


9.984027 




1865 


9.981956 


9.423871« 


8.942355 


9.450326 


9.966544 


9.4004S7M 


8.132548m 


9.424778 


9.984031 




1866 


9.981928 


9.429247W 


6.942166 


9.450656 


9.966516 


9.400454m 


8.129549m 


9.424735 


9.984035 




1867 


9.981900 


• 9.429623W 


6.941981 


9.450986 


9.966488 


9.400420M 


8.126521m 


9.424693 


9.984039 




1668 B 


9.961872 


9.429999W 


8.941794 


9.451315 


9.966459 


9.400387M 


8.123466W 


9.424650 


9.984042 




1869 


9.981844 


9.430374n 


8.941607 


9.451644 


9.966431 


9.400353m 


.8.120409m 


9.424608 ■ 


9.984046 




1870 


9.981816 


9.430749ra 


8.941420 


9.451972 


9.966403 


9.400320M 


8.117338m 


9.424565 


9.964050 




1871 


9.981788 


9.431124ra 


6.941233 


9.452301 


9.966375 


9.400286m 


8.114244M 


9.424522 


9.984054 




1872 B 


9.981760 


9.431498m 


6.941045 


9.452629 


9.966346 


9.400253m 


8.111114m 


9.424479 


9.984058 




1873 


9.981732 


9.431872ra 


8.940856 


9.452957 


9.966318 


9.400219m 


8.107956m 


9.424437 


9.984C62 




1874 


9.981704 


9.432245ra 


8.940670 


9.453284 


9.966290 


9.400186m 


8.104794m 


9.424394 


9.984C66 




1875 


9.981676 


9.432618re* 


8.940483 


9.453612 


9.966262 


9.400152m 


6.101610m 


9.424351 


9.964070 




1876 B 


9.981647 


9.432991W 


8.940295 


9.453939 


9.966233 


9.400119W 


6.098387m 


9.424306 


9.984073 




1877 


9.981619 


9.433364m 


8.940107 


9.454266 


9.966205 


9.400085m 


8.095134m 


9.424265 


9.984077 




1878 


9.981591 


9.433736re 


8.939919 


9.454592 


9.966177 


9.400052m 


8.091678m 


9.424222 


9.984081 




1879- 


9.981563 


9.434108*1 


8.939731 


9.454918 


9.966149 


9.400019M 


8.088597m 


9.424179 


9.984085 




1880 B 


9.981534 


9.434479W 


8.939543 


9'.455244 


9.966120 


9.399986W 


8.085275m 


9.424136 


9.984088 




1881 


9.981506 


9.434850W 


8.939355 


9.455570 


9.966092 


9.399952JI 


6.081923m 


9.424093 


9.984092 




1882 


9.961478 


9.435221JI 


8.939167 


9.455895 


9.966063 


9.399919M 


8.078529m 


9.424050 


9.E840E6 




1883 


9.981450 


9.435591M 


8.938979 


9.456220 


9.966035 


9.399686M 


8.075119m 


9.424007 


9.96410O 




1884 B 


9.961421 


9.435961W 


6.936790 


9.456545 


9.966006 


9.399853M 


8.071711M 


9.423964 


9.984103 




1885 


9.981393 


9.436331W 


8.938602 


9.456869 


9.965978 


9.399819M 


8.C66265M 


9.423S21 


9.984107 




1886 


9.981364 


9.436700W 


6.938413 


9.457193 


9.965949 


9.399786" 


8.064795m 


9.423876 


9.984111 




1887 


9.981336 


9.437069M 


8.938224 


9.457517 


9.965921 


9.399753W 


6.061 302m 


9.423835 


9.984115 




1888 B 


9.981307 


9.437438M 


8.936035 


9.457841 


9.965892 


9.399720M 


8.057762m 


9.423791 


9.984119 




1889 


9.961279 


9.437807W 


8.937846 


9.458164 


9.965864 


9.399687M 


6.054192m 


9.423748 


9.984123 




1890 


9.981250 


9.4381 75« 


8.937657 


9.458487 


9.965835 


9.399654M 


8.050612m 


9.423704 


9.984127 




1891 


9.981222 


9.438543W 


8.937468 


9.458810 


9.965806 


9.399621W 


8.046982m 


9.423661 


9.984131 




1892 B 


9.981193 


9.438910W 


8.937278 


9.459133 


9.965777 


9.399588« 


8.043323m 


9.423617 


9.984 J 34 




1893 


9.981165 


9.439277n 


6.937089 


9.459455 


9.965749 


9.399555M 


6.039652m 


9.423573 


9.964136 ' 




1894 


9.981136 


9.439644W 


8.936809 


9.459777 


9.965720 


9.399522M 


8.035950m 


9.423529 


9.964142 




1895 


9.981106 


9.44001 Iw 


6.936709 


9.469099 


9.965691 


9.399489M 


8.032216m 


9.423485 


9.984146 




1896 B 


9.981079 


9.440377W 


8.936519 


9.460420 


9.965662 


9.399456W 


8.028449m 


9.423442 


9.984149 




1897 


9.981051 


9.440743M 


8.936329 


9.460741 


9.965634 


9.399423M 


8.024650m 


9.423396 


9.984153 




1898 


9.981022 


9.441106W 


8.936139 


9.461061 


9.965605 


9.399390n. 


8.020617m 


9.423355 


9.984157 




1899 


9.980993 


9.441474W 


8.935949 


9.461382 


9.965576 


9.399357m 


8.016950m 


9.423311 


9.984161 




1900 B 


9.980964 


9.441839W 


8.935758 


9.461702 


9.965547 


9.399325m 


8.013048m 


9.423268 


9.984164 





80 



TABLE VI. 

CONSTANTS FOR THE EQUATOR. 

Equator and mean Equinox at the beginning of the Year. 



Years. 



A' 



1852 B 


105 27 14.0 


1853 


105 28 3.8 


1854 


105 28 53.6 


1855 


105 29 43.5 


1856 B 


105 30 33.4 


1857 


105 31 23.2 


1858 


105 32 13.0 


1859 


105 33 2.9 


1860 B 


105 33 52.8 


1861 


105 34 42.6 


1862 


105 35 32.4 


1863 


105 36 22.2 


1864 B 


105 37 12.2 


1865 


105 38 2.0 


1866 


105 38 51.8 


1867 


105 39 41.6 


1868 B 


105 40 31.6 


1869 


105 41 21.4 


1870 


105 42 11.2 


1871 


105 43 1.0 


1872 B 


105 43 50.9 


1873 


105 44 40.7 


1874 


105 45 30.5 


1875 


105 46 20.3 


1876 B 


105 47 10.3 


1877 


105 48 0.1 


1878 


105 48 49.9 


1879 


105 49 39.7 


1880 B 


105 50 29.7 


1881 


105 51 19.5 


1882 


105 52 9.3 


1883 


105 52 59.1 


1884 B 


105 53 49.0 


1885 


105 54 38.8 


1886 


105 55 28.6 


1887 


105 56 18.4 


1888 B 


105 57 8.4 


1889 


105 57 58.2 


1890 


105 58 48.0 


1891 


105 59 37.8 


1892 B 


106 27.7 


1893 


106 1 17.5 


1894 


106 2 7.3 


1895 


106 2 57.2 


1896 S 


106 3 47.1 


1897 


106 4 36.9 


1898 


106 5 ^6.7 


1899 


106 6 16.5 


1900 B 


106 7 6.5 



B' 



16 46 17.2 
16 47 4.6 
16 47 52.0 
16 48 39.2 
16 49 26.8 
16 50 14.2 
16 51 1.6 
16 51 49.0 
16 52 36.5 
16 53 23.8 
16 54 11.2 
16 54 58.6 
16 55 46.1 
16 56 33.5 
16 57 20.9 
16 58 8.2 
16 58 55.8 

16 59 43.1 

17 30.5 



C 



17 
17 
17 
17 
17 
17 
17 
17 
17 
17 
17 
17 



17.9 
5.4 
52.8 
40.2 
27.6 
15.1 
2.5 
49.8 
37.2 

8 24.7 

9 12.1 
9 59.5 

17 10 46.9 
17 n 34.4 
17 12 21.8 
17 13 9.1 
17 13 56.5 
17 14 44.0 
17 15 31.4 
17 16 18.8 
17 17 6.2 
17 17 53.7 
17 18 41.1 
17 19 28.5 
17 20 15.9 
17 21 3.4 
17 21 50.8 
17 22 38.1 
17 23 25.5 
17 24 13.0 



356 49 
356 50 
356 51 
356 52 
356 54 
356 55 
356 56 
356 57 

356 58 

357 
357 1 
357 
357 
357 
357 
357 

357 8 
357 9 
357 10 
357 11 
357 13 
357 14 
357 15 
357 16 
357 17 
357 19 
357 20 
357 21 
357 22 
357 23 
357 24 
357 26 
357 27 
357 28 
357 29 
357 30 
357 32 
357 33 
357 34 
357 35 
357 36 
357 38 
357 39 
357 40 
357 41 
357 42 
357 44 
357 45 
357 46 



20.7 
31.7 
42.7 
53.8 

5.0 
16.1 
27.1 
38.2 
49.5 

0.6 
11.7 
22.9 
34.2 
45.4 
56.5 

7.7 
19.1 
30.3 
41.5 
52.7 

4.1 
15.4 
26.6 
37.9 
49.3 

0.6 
11.9 
23.2 
34.7 
46.0 
57.3 

8.7 
20.2 
31.6 
42.9 
54.3 
5.9 
17.3 
28.7 
40.2 
51.8 
3.2 
14.7 
26.2 
37.8 
49.4 
0.9 
12.4 
24.1 



log sin a. 



9.998310 

9.998311 

9.998313 

9.998314 

9.998316 

9.998317 

9.998319 

9.998320 

9.998321 

9.998323 

9.998324 

9.998326 

9.998327 

9.998329 

9.998330 

9.998331 

9.998333 

9.998334 

9.998336 

9.998337 

9.998339 

9.996340 

9.998342 

9.998343 

9.998344 

9.998346 

9.998347 

9.998349 

9.998350 

9.998352 

9.998353 

9.998354 

9.998356 

9.998357 

9.998359 

9.998360 

9.998361 

9.998363 

9.998364 

9.998366 

9.998367 

9.998369 

9.998370 

9.998371 

9.998373 

9.998374 

9.998376 

9.998377 

9.998379 



log fiin b. 



9.985785 

9.985787 

9.985790 

9.985792 

9.985794 

9.985797 

9.985799 

9.985801 

9.985804 

9.985806 

9.985808 

9.985811 

9.985813 

9.985815 

9.985818 

9.985820 

9.985822 

9.985825 

9.985827 

9.985629 

9.985831 

9.985834 

9.985836 

9.985838 

9.985840 

9.985643 

9.985845 

9.985847 

9.985849 

9.985852 

9.985854 

9.985856 

9.985858 

9.985660 

9.985863 

9.985865 

9.985867 

9.985869 

9.985871 

9.985874 

9.985876 

9.985678 

9.985880 

9.985882 

9.985864 

9.985686 

9.985868 

9.985890 

9.985893 



9.425995 

9.425945 

9.425895 

9.425844 

9.425794 

9.425744 

9.425694 

9.425644 

9.425593 

9.425543 

9.425493 

9.425443 

9.425392 

9.425342 

9.425292 

9.425242 

9.425192 

9.425142 

9.425092 

9.425042 

9.424991 

9.424941 

:9.424891 

9.424641 

9.424791 

9.424741 

9.424691 

9.424641 

9.424591 

9.424541 

9.424491 

9.424441 

9.424391 

9.424341 

9.424291 

9,424241 

9.424191 

9.424141 

9.424091 

9.424041 

9.423991 

9.423941 

9.423891 

9.423841 

9.423792 

9.423742 

9.423692 

9.423642 

9.423592 



