Let 

 Also let 



Royal Astronomical Society. 



aP=r° cos v°—p + 2(p m cos mM) 

 y°=sr° sin v° = 2 (<7 m sin mM) . 



1_ 1 _ r -. 



379 



rp, — % fx Sfx — i fi 



then the coefficient of cos (iM— i'M') in the integral will have the 

 following form : — 



<rl I p_ 1( i_ 2 ]Mi-M! + p ( ,-_3]Mi+ p+ i,,-_4]£l£i±M< 



+ [i + 2,i-5]«4M+[i + 3,i-6]«4M. \ 



4 4 J 



i 



+ a ±± { ft i-2]M?+ p + 1 ,^3]MltM + p + 2,,-4]Mi±M* 

 Wjj I J 2 TL J 4 4 



+p + 3,,'-5]M+M j 



/c-v/p 12 4 4 



+ p-f 8, j-4]Ml±fefc + [t + 4, ,--6jMi+fcil } 



+ii_/p+l,«-l]Ml+p+2,i-2]^+p+8 i i-S]M! 



+ P+4,i-4]Ml } 



+i^/p + i > qMi + p+2,«-i]afe^+p+3,.--2]M4^ 



ft\/» 12 4 4 



+ p + 4,^S]Mi+Mi + p+5,.--4]Ms+M* J 



A;V» 12 4 4 



+ [i+5,t-3]M*±M» I 



kVpl J 4 L 2 4 



+ p>5,i-2]Md^^+[H6,e-3]M£+M3 < _ #> J 



2C2 



