694 



CAVALLIN, SECULAR PBRTURBATIONS. 



Let e denote a function, whose value is for r = q and 

 + 1 for r=l, 2 , . . . , q — 1, q + l, • 

 dition can be written 



|A|>2«'M'I 



n] then this con- 

 (33) 



We have 



E 



lid 



i dt 



log 2 ^r 



1 j "V " 



i dt 



= — ^ + it — -^ log 

 711 i dt ^ { 



^\ Er -Aj 



1 + 



(34) 



But in consequence of the condition (33) is 



2 e,-Are'~' 



in„ 11 



1. 



Consequently the logarithni in (34) can be developed in a 

 convergent series in the manner that we get instead of (34) 



m^ ^ 22^ — — ^ 

 m i Aq dt \ 



. ^1 1 d 



<i 

 + . . . , 



where the series in the right meniber, dependent on the symbol 

 R, after the differentiations are performed only contains terms 



i 



involving dignities of e~ '" ' 



Hence according io the definition before given to M and 

 by (18) and (19) it foUows in the present case 



m 



n 

 r = \ ■ 



.£A.f 





. 



7nq 



n 





m,. 





m 



'2^ 



.A 



,e"^ 



i 



M = '^ 



(35) 



