s 

 148 THEORY OF JUPITER'S SATELLITES. [7 



the first power of f, and also take into account the first powers of f in 

 the multiplier of r8r/a 2 , and we shall have 



: _ 3 ce (i + 2 /_ 29 ^ r - : 

 63 . ,- . 



-p) t + sin (3q +p) f] 



nr -- \ sin ('7 -p) t -- 7?r 

 LP (2q-p) P( 2 q 



sin 



T ^ ~ sin < + ' + sin 3 ~ 



' T * e f 



e 



- -r-1- - > /c 2 sin (a p)t 

 2 p(2q+p) J J 



-- f - -- , 

 6 J p(2q+p) J 



7 (f ~\ 



+ 1 \f c \ s (q+p)t 



2p(2qp) J 



sin (3 _ ) t 



sn 



Whence again, 



p(2q-p) 



6 J p 



^,2 "I 



in (q +p) t 



