IN PHYSICAL ASTRONOMY. 377 
+ {-Biso - + g) C i B lb6 (2-2 m + g) C 5 H 14S J e,ysin (2 t + z + y ) 
[ 160 ] 
In order to verify these expressions, suppose 
= A 3 e cos (c X' — tz) s = y B u6 sin (g\' — v) n t = A' + C] sin (2 A' — 2 m A') 
T 
Then by Lagrange’s theorem, neglecting A 3 , A* c, &c. 
— = A i e cos x + c e A 2 C x sin 2 t sin x nearly 
= Ao e cos x + C — 1 e cos (2 i — x) — 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 — y s i46 sin y — g y C x B 146 sin 2 t cos y 
= yB u6 siny — g — 1 ^ B - s y sin (2t — y) — gC| ^ 146y sin (2 t + e/) 
[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 
A 0 
— } 
[30] 
A x 
= -00709538 
[1] 
A„ 
= ) 
*[31] A, 
= -2024622 
[32] 
A, 
= - -00369361 
[16] 
A b 
= - -0056375 
[33] A e 
= -0289158 
[34] 
A 1 
= - -0030859 
[2] 
As 
= -003183 ? 
[35] A y 
= -347942 
[36] 
A io 
= -001970 
[19] 
An 
= - -19737 
[41] A l2 
= •516174 
[42] 
A 13 
= -0026238 
[18] 
An 
= - -286046 
[39] A ls 
= - -060625 
[40] 
A 16 
= - -014546 
[17] 
A \7 
= - -006930 
[43] A 1h 
= -08125 
[30] C 4 
= - -009216 
[1] 
c 2 
= - 2-0044055 
[31] 
c 3 
= - -4138664 
[32] C 4 
= •012939 
[16] 
c 6 
= - -194385 
[33] 
C 6 
= - -394172 
[34] C 7 
= -0038267 
[2] 
C s 
= •745169 
[35] 
= - -286413 
[36] C l0 
= - -012575 
[19] 
C n 
= •365516 
[41] 
c , 2 
= - 1-08891 
[42] C, 3 
= - -008551 
[18] 
C 14 
= - -607534 
[39] 
= -11587 
[40] C l6 
= -055936 
[17] 
C 1V 
= -12755 
[43] 
<7,8 
= - -11432 
* These are the indices of the arguments in M. Damoiseau’s work. 
