222 



PIERCE. 



Substituting these various integrations (67), ((38), (69), and (70) 

 in (66), we have « 



P = 



12 n hn n l.yi 



4c |_ n!n n -\- 11 



n hn ~ V 9 



+ 2 COS 52: (- 1)2 



+ 2 sin 52: (- 1)2 



Jn+l{B)- 

 2 



(71) 



n = 2, 4,6,- •• 00 



„ 2irb . , ,^ , TT 



B = - IS between () and -• 

 A. 2 



This result may be expessed in a power series by expanding the 

 Bessel's Functions by equation (6), Art. 120 of Byerly's Fourier's 

 Series, giving 



n-l 



B 2 



Jn-i (B) = -„rr-7-^ ^ 



1 - 



52 



92 



+ 



54 



w+ 1 



fi« 



w+ 1\ A?, + 3 



2!2^ 



3!2« 



n + 1 \ Ai + 3\ //t + o 



+ 



(72) 



J„+i (5) 

 2 



+ 



n+l 

 52 



2 2 p 



B' 



n + 3 



1 - 



B'- 



,.f>L±l 



B« 



.,,94'^^+'^^" + -^ 



3; 2*5 



n -\- 3\ fti -\- 5 



/' + 7 

 9 



+ • 



(73) 



