IN PHYSICAL ASTRONOMY. 
247 
=z nt 
+ cos 2 t 
+ eAoCOSx 
+ e Aj cos (2 t — x) 
+ e a 4 cos (2 1 + x) 
+ e, A 3 cosz &c. &c, 
The quantities X correspond to the quantities b in M. Damoiseau’s notation. 
= y s u 6 sin y 
. + y *i47 sin (2 t — y) 
+ ys us sin (2 t + y) 
+ eys 14y sin ( x — 'J ) &c - &c - 
y = tan t 
! (A — A,) J 
f r'r ( cos (A 
= m 'i 
{r 2 _ 2 rr, cos (A' — A ( ) + r 
•r }4 
: m 
1 r 2 3 {2 r'r, c os (A' — A,) — r 2 } 15 {2 r r t cos (A x — A,) — r 2 } 3 \ 
1 ~~ V t + 27 } T r? 48 »7 J 
3 r 2 r 2 
f 1 r 2 3 r 2 r.~ . 3 r-rr, , . 5 . v .1 
= { - 77 + 27 / - “2 ~ vf cos ( + 2 cos (A - - t tt- cos - A <> 3 } 
= ™, [- 1 - ^ {l + 3cos (2 A' -2 A,) -2 s 2 } 
- 2^1 1 3 (1 — 4 s 2 ) cos (A' — A,) + 5 cos (3 A' — 3 A,) J 
’’ C < X '- X -> = Tr ‘ { cosS Tsta < X - V + si "*4sin ( x + X, - 2.) } 
1 _V-^V. 0 S i-i- e A -£lV- os (<-*) 
2 IV 2 64/ V 2 64 / sin 2 V 2 / sin ^ ' 
+ K i - 4 c! ) 0 - f )“» <*+.)+ 4 -<i -*»(.- c t 
+ rSc+»»)+ii‘‘S< ,+4 *) + T( 1 + 1) (* 
=* a a t cos 2 
,9 cos , . . s 
4 ee, • (f — x + z) 
1 4 ' sin v ' 
~T ee { ] -f cS )“„ s (' + * + a ) 
9 o cos 0 , v e 3 e, cos , , 0 . 3 „ cos,, „ , * 
— Y6 e e ' sin (^ + 2x + .~) -y sin (^ + o a: + z) — — e 2 e ; sin (<-2z + z) 
WDCCCXXXI. 
* See Phil. Trans. 1830, p. 343. 
2 K 
