IN PHYSICAL ASTRONOMY. 
377 
+ | 60 - i- (m + g) C, B lb6 (2-2 m + g) C b B lis J e, y sin (2 1 + 2 + y) 
[160] 
In order to verify these expressions, suppose 
4- = vl 2 ecos (ex'— w) s = y J3 u6 sin (g\' — v) n t = A' + C, sin (2 A' — 2 m a') 
r 
Then by Lagrange’s theorem, neglecting A 3 , A 2 c, &c. 
— = e cos x -f c e Ac, C l sin 2 < sin x nearly 
= A„e cos x + c ^ e cos (2 t — x) — c e cos (2 < + x) 
[2] “ [3] " [4] 
which terms are found in the expression which I have given above. 
Again, by Lagrange’s theorem, 
S = 7 B 146 sin y — gyC l R 146 sin 2 tcosy 
= yB u6 smy — 8 Cl ^ l46 y sin (2 t — y) — 8 sin (2 t + y) 
[146] ~ [147] [148] 
which terms are found in the expression which I have given above. 
The numerical values of the quantities a, b, c, according to M. Damoiseau, 
are 
4> 
= ? 
[30] 
A x 
= -00709538 
[1] 
Ao 
= 
*[3I] 
= -2024622 
[32] 
A . 4 
= -•00369361 
[16] 
A b 
= - -0056375 
[33] 
a 6 
= -0289158 
[34] 
Arj 
= - -0030859 
[2] 
A 8 
= •003183? 
[35] 
Ay 
= -347942 
[36] 
A 10 
= -001970 
[19] 
A n 
= - -19737 
[41] 
A 12 
= -516174 
[42] 
A\3 
= •0026238 
[18] 
An 
= - -286046 
[39] 
A\$ 
= - -060625 
[40] 
A\6 
= — -014546 
[17] 
A\ 7 
= _ -006930 
[43] 
Am 
= •08125 
[30] 
c, 
= - -009216 
[1] 
Co 
= - 2-0044055 
[31] 
C 3 
= - -4138664 
[32] 
C 4 
= •012939 
[16] 
C-o 
= - -194385 
[33] 
C 6 
= - -394172 
[34] 
C 7 
= •0038267 
[2] 
Cs 
= •745169 
[35] 
C a 
= - -286413 
[36] 
B 10 
= - 012575 
[19] 
C n 
= •365516 
[41] 
C l2 
= — 1-08891 
[42] 
B 13 
= --008551 
[18] 
C, 4 
= - -607534 
[39] 
Cn 
= -11587 
[40] 
B 16 
= -055936 
[17] 
C l7 
= -12755 
[43] 
C\s 
= --11432 
* These are the indices of the arguments in M. Damoiseau’s work. 
