146 THEORY OF JUPITER'S SATELLITES. [7 



Also the coefficient of 8z in the second differential equation is /x/a 8 

 multiplied by 



+ cos 2qt ft - ^ /V + f ./V + \ /V - 1 5/c* + 



+ cos 4<7 -/V+ 15/c 2 . 



or 



- 1 - 3/+ Y /<? + f /V + cos 2<jt [ - 7/c^ + 1 / V - ^ / VJ + cos 4ry [^ / VJ ; 

 the coefficient of r8r in the second equation is /A/a 4 multiplied by 



sn 



7 , 3 203,, 2a 2131 ,, 5 55 ,., , . f j 1 9 ,, 2 3 



' 





[ 



or 



sin qt \3c + 1 5/c - 25/c 3 + ~ f'c 3 - 7 J^ f*c 



. 63 127 ... , , 2909 -,."!,. T 1171 



+ sm 90 - yc- - - yv + -/Vj + sm 5 ? [ - 



Now we have seen that 



whence 



