1892.] in the neighbourhood of a planet. 317 



S being very large compared with M and m, p will be small 

 compared with r. 



Then since r = R 2 + p 2 + 2Rp cos 0, 



-K 3 -. o P a 3 P 2 , 15 P 2 ia 



Therefore approximately 



^=-l4l(i-l- 



3p - 3 p 2 15 p 2 j _ 



"i cos ^~2fe + Ti 2COS * lcos 



1 _ 3 C os 2 0_?^cos0+y^ cos 3 e\ 



and 



l 2 - + ^- 2 |(l-3cosW 



+ 3 cos (5 cos 2 $ - 3) (1 - 3 cos 2 0) -gj 



Asfain 



and 



^ 2 = + ^ 2 {9cos 2 ^(l-cos 2 ^) 



- 9 cos (5 cos 2 - 1) (1 - cos 2 0) £j , 

 whence 



^ 2 = ^{ 1 + :1C0S ^- 12c0sS ^}- 

 Now 



CD 



P" 

 And 



) 2 ^{l + 3cos^-12cos^|} 



QL 2 \M+.m 



We now have to introduce a similar approximation into the 

 value of F 2 /C 2 . 



25—2 



