280 Mr. Nicholson on Legendres Functions and the 

 for 



v- ±lV P u)- l ( e (^-^)# 

 \(fr+T? r ' w 32J0 / 2 * ,<> 



V cos i— °° s 2 



- 8 • J 32 J„ / cos2 £~ os2 6>' 

 substitution V s 2 2 



Bat by previous 



7 



J^/co4-co4 L ^ ^=° 



6 (k' 



,!-i' ^A,^ Sill A, Ulll 



16 



iFWsinXtanltan- 1 /! cosxW 



Jo l+tan 2 £cos 2 X 



" F' (X) sin X tan" 1 ( -r cos X ) dX 



= 16M' ' 79 „, V * J ~~ ; 



Jo £ 2 + £' 2 cos 2 X 



•-. ^^(X)tan-gcosx)sinX,/X^ ^_^ 



J o "7" F + k" 2 cos 2 X " *# o (2n + 1) "^ 



and if ^ (4tt 2 -c/> 2 )# 



l( )= Jo / 2 * ,*' 



V C0S 2 C ° S 2 



G?Wsm^^=(32) 2 fp^ T y 7 



= 2x(32) 2 .^ 7 (l^J) 



= 2032<r 7 , (63) 



and _ _ /k'oosX" 





^(-) n . (-)'- 1 . 

 2(2« + l) 2 (2re + l) 



.. • (64) 



