704 CAVALLIN, SECULAR PERTÜRBATIONS. 



where y2L^i and where, when y is not a wliole number, to 

 avoid ambiguousity the principal value is supposed to be taken. 



The series in the right member of (62) converges absohitely, 

 and swifter than the series in the right member of (53) when 

 y > 1. 



The series in (62) is of the same form as the series in 

 (58) and thus by Converting both merabers of the former in 

 accordance with (61) we arrive at the result 



%<^)m I 



^=1 V (63) 



. K .t . K . t , 



after having put ?/ = 1. 



But the value of F{x) is found according to (53) and (62) 

 to be 



m 



I7 ^ 2 <p(«^'^' "' ) - ^(«) j ' (63') 



and hence by (63) 





m 



s = \ 



Tf in this equation we put — t in stead of t and so add 

 the two equations, then cos— will be a factor in the second 

 member, which tlius disappears wnen t = —^ . 



In this manner we arrive at the relation 



11 I 



We can not solve this equation in respect to M{a)'., the 

 convergency of the series should be destroyed if we endeavoured 

 to separate M{a) from the connection in which it is situated. 



