154 THEORY OF JUPITER'S SATELLITES. [7 



Hence to the second order in f 



8 - 



>V4. n 



C + T2 



or 



Next in the second equation make the same substitutions, and in the 

 coefficient of e l put 



( 2fy _ p y _ r/ = (? _ 7 ,) (37 _ p ) = (r/ _^) to 

 Hence 





- s 



t', 9 , 2 54 

 so that J = -y c - ; 



4 

 5 

 it' 17 c' 2 = 0, the approximation becomes insufficient, and the terms in the 



denominator of eje must be carried to one order higher in f\ and eje 

 becomes finite, that is, contains a term which is independent of f. 



We have already found e,/e= fc 1 to the first order in f, and by 



again substituting in the third equation we may find e 2 /e to the second 

 order. 



