150 THEORY OF JUPITER'S SATELLITES. [7 



the coefficient of e cospt in this is 



1 Q^ 1 8Q \ 



1 - 4/+ G/c> + 1 2f - 1 J2/V + i|= / V J 



8 /- 



JC 



_ _ __ _ _ . 



2 p(2q-p) _ 12 p(2q~p) 2p (2q+p) 



' 



-- - - - _ 



12 p(2q+ I >) 



the coefficient of e cos (2ry p) t in the same is 



_ _ _ r ^._ _ 



12- p(2q- 2 )) 2p(2q+ 2 >) 



" " 



2 



16 ^ (2</ +p) 4 (2 2 -p) (4<7 -_p) 4 



the coefficient of e cos (2</ + p} t is 



e'-6/v+f A'] 



3 .,,. <f 2 T ,._U / . _ (/ f ., 7 



"12 /C 2+> J * 2 



*f "_ ^ 2 



'IG 6 - 7 p(2q-p) q " 4 C/ 



the coefficient of c cos (4^ p) t is 



16" p (2q-p) ' 

 and the coefficient of ecos^g + pji is 



i 21 /-y g* g 2 f 3 | 



7 q 



- _ _ 



l6p(2q+p) 



If for the sake of simplification we first confine our attention to the 

 term in the above found coefficients which involves the first power of f, 



