IN THE MOTIONS OF THE EARTH AND VENUS. 
87 
Section 8. 
Selection of the coefficients of cos (13 — 8) in the development of 
— m . — r f 2 • cos (v 1 -j- v — 2 0). 
{V 2 — 2 r 1 r . cos ( v ' — tt) + r 2 } T 
(t) 
24. The general term of the expansion is — m . T 3 . cos (kv 1 — kv ) .f 2 . cos 
T 
(v' + v — 2 0). The expression for cos (k v — kv) .f 2 . cos ( v ' + v — 2 0) we 
(*) 
have just found ; and the expression for — T 3 will be in all respects similar 
(Jc) (k) (fc) 
to that for — I\ in (18), putting C ± for Ch . Observing that k cannot be 
less than 9 or greater than 12, and selecting for the different values of k the 
terms whose combination produces (13 — 8), we get the following coefficients : 
m X 
{- 
k = 9. 
(°»°) + iH (i.o) - tb ( 2 >°) + us ( 3 >°) } c f - e ' 3 / 2 • • (M 19 ^ 3 / 2 ) 
k = 10. 
m X l ^ (0,0) - ^ (1,0) + 5 -§ (0,1) + ^ (2,0) 
l 16 
16 (M) 
(M m .e'* ef‘) 
k= 11 . 
»> X { - ~ (0,0) + ^ (i )0 ) _ f (0,1) + || (1,1) - | (0,2) 
1 4 (H) (11) 
+ r2 ( 1 ,2)jc; .e'effi 2 (M \e'e 2 f 2 ) 
k = 12 . 
* X (0,0) + ^ (0,1) + | (0,2) + gg (0,3) J Cf . effi 2 . . (M° 2) .e 3 /^ 
