IN THE MOTIONS OF THE EARTH AND VENUS. 
87 
Section 8. 
Selection of the coefficients of cos (13 — 8) in the development of 
—f 2 . cos (v 1 -j- v — 2 0). 
— m 
[r 12 — c 2r' r. cos (v 1 — v) + r 2 } T 
,(*) 
24. The general term of the expansion is — m . T 3 . cos (kv 1 — kv) .f 2 . cos 
T 
(v' + v — 2 6). The expression for cos (k v — kv) .f 2 . cos (v 1 + v — 2 6) we 
(k) 
have just found; and the expression for — T 3 will be in all respects similar 
(0 (/<) (*) 
to that for — r\ in (18), putting C 3 for C* . 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 
{- 
2815 ( 0 , 0 )+ ^( 1 , 0 ) 
24 
1c = 9. 
- IS (2.0) + ^ (3,0) } <>. e*/ 2 • • (M ( V/ 2 ) 
k = 10. 
» X { || (°>°) - IT (*.°) + IF (0.1) + h (2,0) 
+ S |(2.1)}C. 
re (U) 
m 
k — 11 . 
X { - ~ (0,0) + ^ (1,0) - f (0,1) -4-11(1,1) 
+ i (1,2) } C™. eV/ 2 . 
T (0,2) 
( 11 ) 
(M .e'e 2 f 2 ) 
k = 12. 
»*x{f (0,0) + f (0,1) + 1 (0,2) + i (0,3)] 4' 2) . e 2 / 2 . . (M (,2> .e s / 2 ) 
