IN PHYSICAL ASTRONOMY. 
369 
=^+^-K*4) s }{‘^} 
5 = y sin y + y $ l47 sin (2 1 — y) nearly 
[146] [147] 
s 2 = ^-' + — y- s, 4 7 cos 2 1 — 1~- cos 2y + y- s 147 cos (2t — 2y) 
nearly 
(0 
(62) 
(63) 
+ s 2 = 
, + ¥ 
*“l47 | 
1 — y 2 . 
s, 47 cos 2 t — 
COS 2 y + y 2 
s 2 147 cos (2 * - 2 y) j 
[1] 
[62] 
[63] 
II 
%\°L 
( 1 + 
3_ e „' 
) + 2e l 
cos x -j- 4. e 2 ^ 1 
| cos 2 x 
[2] 
[8] 
+ 
13 , o , 103 . 
— e 3 cos 3 x + — — e 4 
4 94 
cos 4x 
[20] 
[38] 
u. | , 
— = l + e 
r 
(l-|)cos* +e *(l -|) 
[2] [8] 
9 4 
cos 2 x + — e 3 cos 3 x 4 e 4 cos 4 x 
8 3 
[ 20 ] 
[38] 
• • CL* 
If the coefficients corresponding to the different arguments in the quantity^, 
be called 2 and the coefficients of the different arguments in the develop- 
ment of the quantity 
-” 0 {/jx-‘““2T*{/i^ < “ t } ! } be called Ja "’ then 
2r o' = { 1 +T +^* 8 >47*} I 1 +y( 1 + f 2r 0 + v + !1 2 + !!|l + !^l ?!|£ + 
, e / 2 r 6 2 , e, 2 r 7 2 \ 
+ + 
Ti ' = {* + Z r + ^ s9 ‘ 47 } | r * “ y 2 s > 47 + ~ it ) { ,-3 + r4 } + |{ r9+ri °} + 2r ° r < 
+ e 2 (r 3 + r 4 ) r 2 + e, 2 (r 6 + r 7 ) r 5 | 
r * = { 1 + ¥ + T } { 1 + 4 e! + r « + T (‘ - |) { 2r » + e ' r > } + 5 r * 
+ (r 4 + r 3 )r, + 2r 0 r 2 j 
* (s H7 ) 2 is intended. 
