OF TWO LEGENDRE'S COEFFICIENTS. 371 



Now tan0V(-l) = - - T - = ---, if 



-L IV _L ~~ ill 



COS 



cos 6 + J( 1) sin 8 l + 7( l)tan# 1 h- 





Take logarithms of both sides and change signs ; 



x 4 + ^y + l'/^ f 



O D 





fi a -, 



Vdp.=- - ; = - - T -{/i 4 (a; i -x" 4 ) + &c., &c., &c.} 

 h sin 7i-lsin 



= 2 1 1 + J /i [2 cos <^ + 1 ] + \ fc [2 cos 2^ + 2 cos ^ + 1 ] + &c. \ , 

 ( 3 J 



where the law is manifest. 



47 S 



