Further, cj)(6) is an odd function of 6 of average value 0. 

 Hence 



m=l 



Here 



974 Dr. G. Breit on the Effective Capacity of 



an odd function of ( 



00 



(f)(6) = X.a m smm0. 



377 



dm = - 1 6(6) sin md dd. 



2 



This gives 'IfJ 5 4 



a, ?l = ( — 1) ' 2 , o — r-pr if ??i is odd 



V y 7r(wr— 4) 



and a m = if m is even (m = 2 included). 

 Hence 





-^[/W+W]§ 



7T 



(Consequently at the boundary (i. e., r = a) 



Or 



or by (7) and (8) 



(Vo) r= a=- 



By virtue of (5) and (6) 



rv v 16L^z g (->-i s j n (2?z+l)<9 



(V Jr=a- ^ ^.J (2n + l; 2 (2n-f 3)(2«-l) 



us 



°~ it 2 dt n Z (2n + iy\2ni-'3)(2n-l) " ^ 

 The quantity -^— ° in (2) is now simply ( —~ I . Th 



0?1 \ LIT I r=a 



3n " 7r 2 a^ M io(2n-fl)(2n + 3)(2n-l)* * l Uj 

 This solves the first part of the problem. It now remains 

 to find the quantities ^-, -j~Y' 



The first of these is obtained from (3) as 



£V fdV\ .a 2L di /-« g . . - , 1t * 



and similarly ^ ^ y ^ , ^ ^ 



<fy 2 7ra 2 rf« ,^/V 



