IN PHYSICAL ASTRONOMY. 
267 
+ it eC0S (3 1 ~ X ) — ^5 eC0S ( 3 1 + *) “ T 'a* e ‘ cos * “ z ) 
[117] [118] [119] 
+ 4” e \ cos ( 3 1 + z ) — -7TT e ~ cos (3 t — 2 x) — ~ - l - e- cos (3 t + 2 a;) 
o a ( 64 ag o4 a* 
[120] [121] [122] 
225 a 3 . . 15 a 3 fo , , , , 
nr — 7 e e, cos v 3 t — x — z) + e e t cos (3 t + x + z) 
16 a; 16 a,* 
[123] [124] 
— TTi e e ‘ cos ( 3 1 ~ x + z ) ~~ —* e e ‘ cos (3 * + x — z ) 
A 0 flj A 0 
[125] [126] 
~ ^ ^ “ S (3 ' “ 2 S) ~ ® ^f' ! 008 (3 ‘ + 2 S) “ ^ ^ ^ 008 (3 ' “ 2 ^ 
[127] [128] [129] 
In the elliptic movement ; 
s = y sin (g\ — v) 
5 
X = n t + 2 esinx + - — e ~ sin 2 x 
4 
• e a , g 
s = y ( 1 — e 2 ) sin y + y e sin (ar — y) + y e sin (£ + y) + y — sin (2 x — y ) + _ ye- sin (2 x -\- y) 
[146] [149] [150] [161] [162] 
$- = ^ 3L ( 1 — 4 e 2 ) cos 2 y + y 2 e cos (x — 2 y) — y 2 e cos (x + 2 y) 
[62] [65] [66] 
+ A y 2 e 2 cos (2 x — 2 y) — A y 2 e 2 cos (2 x + 2 y) 
[77] [78] 
2 *=«y|l — sin y + 3 ^ — sin (* — y) + sin (x + y) 
[146] [149] [150] 
— sin (2x — y)+ 3a ? e - sin (2 x + y) 
[161] [162] 
— = (1 — e 2 ) sin y + ^ sin (x — y) + AL? s in (x + y) 
r a K ’ y — 2 a v 2a y 
[146] [149] [150] 
* This quantity z, which is one of the rectangular coordinates of the moon, must not be confounded 
with 2 = n t t — ot, j this latter quantity should rather be x ,, but I think it better to conform as far as 
possible to the notation of M. Damoiseau. 
