560 Proceedings of the Royal Irkh Academy. 



Each. Satellite's contribution to (i). 



m r m' 

 ■^ = -7^ cos (v -v)- , ^j 



= m' (i^o + ^1 cos (y - v') + A. cos {2v - 2v') ). 

 First, consider the contribution of ^mAq to the periodic terms 



^i? ^ , dAo 

 (it ~ dr 



Retaining the periodic teiins, we have 



m' ( dAo d^Ao\ 

 2 \ da da- j 



To find the contribution of 



, mA,, cos {kv - lev'). 



2 --^ = m' , Aj, cos (h - lev'), 



I dt n - n 



dR , dA^ 



r —— = ma — — cos [kv - kv). 

 dr da 



Uniting these terms, Tre hare for each satellite's contribution to (i) 

 (retaining of course only periodic terms), 



m' ( dAo d-Ao\ „ 



,f 2n . dAA ^ ,^ 



+ m' ■ Ai + a — — cos (v - v') 



yn - n' da J 



,( 2n , dA.\ 



-f m' , A. + a -^ 1 cos {2v - 2v') 



\9i -n' ~ da ' ^ 



,( 2ti , dAi^ 



+ m'i , A3 + a — — cos (ov - 3v). 



\)i - n da ' 



