360 Mr. W. H. L. Russell on [June 21, 



Continuing the process, we find 



(4o.) 1 : - — , and more generally (49.) 1 — • 



v 'Jo l + ^ 2 cos 2 fl' 6 J K J J l+# 2 cos 2 



<:?0sin 2 a0 tt e 2a — 1 e a 



/-»oo 



^ 50 * Jo (C 1 + / 1 + M 2 ) cos ad + M cos 3 a0)) (1 + 2 ) ~ 2 -2/x ' e 2 «+ 1 * e 2a +/I 



(51.) \ 2 d6e <""> cos cos (cos "6 sin nB) = ^J. 

 Jo 2 



(52.) r ^sin|e°°^sm(e+g) g 



l-2«cos0+a 2 _ 21 + a 



+ e CO30 cos sinQ) tt 1 



(1 - 2a cos 6 + a 2 ) (1 + 2/x e cos 6 cos sin + jjl 2 e 2 008 *) ~" 1-a 2 " 1 + /ue a ' 



003 co s sin 0) _ tt 1 



( J (1 + 2 )(1 + 2 cos e cos sin^r^ e * cos fl) ~ 2 " x + ^ 



f e cosg s j n (gin 0)^0 s in9 tt f e a 1 



^° J (l-2acos0 + a 2 )(l + 2 / ie cos0 cossin0 + / x 2 € 2cos0 )~2a|l+/ze a ~r+^ 



f* log e (l-2acos0+a a ) 2t , 71 



J 00 C? Q 

 — — — — ; 

 (l + d i )(l-2acosd + a 



and more generally (58.) ^ 



dd 



Q (1 + 6 2 ") (I -2a cos + a 2 )' 



(59.) f — 



J 



(60 



2aeos0 + a 2 )(l+2,rcos0 + <) 2 2(1 -a? 2 ) (l + oo?) 8 

 sin Odd tt e 



/loo 



^ J Q (T+0 2 ) (1 + 2a; cos + <) 2 ~ 2(1-^)' ( e +^) 2 * 



m . C cosine ( e -l)( e -a- 2 ) 



^ J (0 + 3 )(l + 2a?cos0+a? a ) a 2(l-a; 2 ) (l + a7) 3 (e + ^) a ' 



