IN PHYSICAL ASTRONOMY. 
369 
« = y sin y + y s ui sin (2 t — y) nearly 
[146] [147] 
s 2 = — y 2 s, 47 cos2* — ^-cos2y + y 2 Si 47 cos(2< — 2y) 
nearly 
(1) 
(62) 
(63) 
+ s s = 
, + ¥ 
+ £«•■«{ 
1 — y 2 , 
s I47 cos 2t — 
y COS 2 2/ + y 
2 s 2 147 cos (2t—2ij) 
[1] 
[62] 
[63] 
a 2 _ 
~v*~ 
> + f 
( i+ -k 
) + 2e l 
M-) 
cos x + l e 2 ^ 
| cos 2 x 
[2] 
[8] 
+ 
13 , „ ,103. 
— e 3 cos 3 x + —— e 4 
4 24 
cos 4x 
[20] 
[38] 
— = 1 + e (\ — -4 cos x + e 2 ( 1 — ) cos 2 x + -l e 3 cos 3 x + — e 4 cos 4 x 
r \ 8 / \ 3 / 8 3 
[2] [8] [20] [38] 
If the coefficients corresponding to the different arguments in the quantity y. 
be called 2 t' n and the coefficients of the different arguments in the develop¬ 
ment of the quantity 
becalled *”’ then 
2l ‘o' = { 1 + t + 2 z s *“*} {’ + y( ! + j e *)+ 2r o + r o*+ ! f + 
■} 
til + fir*! til + e Iil 
2 2 2 2 
+ + 7 
>,'= {l + |(l -|) + S{f»+r,.}+ 2 
+ e2 ( r 3 + n) r 2 -I- e* (r 6 + r 7 ) r 4 j 
'* = { 1 + i + £} { 1 + 4 eS + r -+t ( 1 " j) { 2 r °+ e ' r ‘ } + 1 r “ 
+ (r 4 + r 3 )r, + 2r 0 r 3 | 
*o*i 
* ( s i^y is intended. 
