IN THE MOTIONS OF THE EARTH AND VENUS. 
95 
(A) (A) 
36. For the calculation of the terms C 3 , , &c., we shall adopt the general 
T T 
notation 
Jda. {4- 2cos Z + v} 
1 JS>) , _,(!) , _,( 2 ) 
= -o c s + c COS % + C 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 
(A+i) k /I , \ k~\+sJl<-') 
C 
And since 
_ k f 1 \ 1 +, . 
k + ] — s^ a y * & + 1 — s * 
' da - 2c°sx + - z } 
(*“ + a - 2 c °sx)x— — 
C a' a 1 *+1 
■ | « 2 cos z + v j 
we find on substituting the expansions and comparing the coefficients of cos k %, 
fA) /i . x _(A) _(A-1) ^(A+l) 
c; =(i +.) C rb -cr + r- c ; +1 
s k + o 
Removing C J + 1 by means of the relation just found (putting ^+1 for s ) 
A*) 
5 / 1 | \ pW . 
- - ;73- s + a ) C S + 1+ /7Z 
(*) . 2 s (A-i) 
s + i 
In nearly the same manner, 
_/J , \p(*“0 _2£__p« 
— 1 \ « ' / * + 1 & -f- S — 1 i_ M 
p(*“ l > £_ 
“ A + s 
(A- 1) 
Eliminating C s+1 , 
^(*). 2(Ar + s— 1) l 
C s+1 — S 
,(A-1) k _ 5 a + a (A) 
1 C s 
/ 1 Y 
2 '•'s 
S 
/ 1 \ 
1 
( — — « ) 
V « / 
\* ) 
(A) (A-l) (A + l) 
If in this we substitute the value of C in terms of and C s , given 
by the relation above, 
