IN THE MOTIONS OF THE EARTH AND VENUS. 
95 
(4) (4) 
36. For the calculation of the terms C 3 , C 5 , &c., we shall adopt the general 
T T 
notation 
__ f a! „ , a J 
J a' a. I — - 2 cos X+^r| 
1 (0) (1) (2) 
= ~o c s + C s cos % 4 - C s cos 2 x + &c. 
which, it will be seen, includes those of (17), ( 21 ), and (25); and proceeding 
as in (35) we shall find this general equation 
..(*+1) k 
C 
- k ( 1 < \ n ( ) Jc ~ 1 + 
& + 1 — sy a ' a ) * & + l — 
(*) k — l + s JJt- 0 
s * 
And since 
~ 2cos % + -z} 
(^-+ a - 2 cos X 
/- fa' ^ a J s + 1 
Jala- (t- 2cos X + ^} 
we find on substituting the expansions and comparing the coefficients of cos k 
r <*> _ / 1 4_ c {k) r ( * _1) c {k+l) 
* s — + a ) c s+i — L 5+i — s+i 
(4+1) 
Removing C J + j by means of the relation just found (putting s + 1 for s ) 
c s - - + a ) c *+i + 
In nearly the same manner, 
c * — 7 - ■ - - 1 \« + u ) C ^+1 “ 
* pp- 1 ) 
S C s+1 
k + s 
Q s (*) 
A- +5 — 1 ^ + 1 
(4 - 1) 
Eliminating C J+1 , 
^( 0 . 2 (k + s — 1 ) 
^S+l— c 
2 
'(T-) 
5 c 
(A) 
(4) (4-1) (4 + 1) 
If in this we substitute the value of C in terms of C s and C s , given 
by the relation above, 
