558 Proceedi)igs of tlie Royal Irish Academy. 



Substitute for r its equivalent « + Sa + S/- and 



Id-r _ 1 d^r 

 rd^~a 'W' 



r^ a* \ a a J 



1 dR 1 dF 1 fdR dF\ 



+ 



r dr a da a \ da da j ' 



whence, since (/x = n'^d^), 



dv" 

 df 



, i S« , dF 



«.M 1 - 3 — + rr — 

 t a da 



Taking the square root 

 dv 



-dr'' 



+ Periodic Terms. 



3 la a? dF 

 ~ 2 7 ^ 2 la 



+ Periodic Terms, 

 but if 7i be the real mean motion of the disturbed satellite, then 

 dr 



dt 



whence, finally. 



n + Periodic Terms 



ha =- a^ -~-. 

 3 da 



Perturhations in Radius Vector ichich are independeni of the Fccentri- 

 cities and Inclinations. 



AVe first compute 



^'f^-(f 



(i) 



Oraittiug the inclinations, we have 



inJr m' 



^^7^^°^^^-^^- (.^-2./eos(.'-.)^0 ^ 





(1 + 3 cos (2^7- 2(0) 





