7] THEORY OF JUPITER'S SATELLITES. 145 



lo^c r/ 7 \ / 7 \ . ~| 



= ~^~ (^-^a l }smqt + (c l + -a l }sm3qt 



U \_\ 4 / \ & J J 



- n sn 



a" 



3W 



~aT 



pj g -| 



[1 + 9cfj cos 2^^] - (3 sin qt sin 3qt) + - (1 - cos 2qt) c t sin 3gi 



|~1 + 9a, cos 2c/l ( --- c, ) sin (/<+(- + - c,) sin 3qt -CjSinSoi 

 L ^ J |_\4 4/ \ 4 2 / 4 J J 



35rc :1 r/3 8 \ / 1 3 



~ 4 7 Sm ^ + V~4 + 2 l 



27 9 ~| 



+ j ( sin qt + sin 3qt) ^^ (sin 5^ + sin 5^) 

 o o J 



9 3 1 27 3 



- 3 c- 9 



+ A 1 



5g< . 



* 



Hence the coefficient of rSr in the first differential equation is p,/a* 

 multiplied by 



or 



the coefficient of 82 in the same equation is /x/a 2 multiplied by 

 in qt [2/c + |/V] + sin 3 ? * [ - ^ / 



sn 

 A. II. 19 



