660 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1953 



Therefore the possibility of volume generation and surface recombina- 

 tion cannot be discarded. 



This case is somewhat more difficult. Assuming all sources to be un- 

 correlated and uniformly distributed throughout the interval { — a, +a), 

 we have to square expression (10) and integrate it from Xq = —atoxo = 

 -ha in order to find (Agl). (We suppose that all the sources are of equal 

 strength («/*)). Substituting the values of the A and B from 9 and 10, 

 we get, after some obvious cancellations 



th 



rixo) = 1^ [^0 + Se-^''^''^' + T] 



where 



S = 2a 



(-Kk+s)) 



«ie ^'^ + ^26 



*/2 



T = — 



$ aie 



-*/2 



0:26 



,+*/2 



ciia2 sinh 



$ 



L2 aie-*/2 + 0:26+*/' 



aie-*/^ -f a:2e*/2 



- 1 



Hence 



4a' 



{Agl)= (J) f rUx„)dx, 



J— a 



**Z)2 



-a -f 2r a + -— — sinh - 

 6 $ 2 



(14) 





cosh 



a> 



Before proceeding with this general case, we first consider the limiting 

 case ^, = ^2 = «>, when ai = -1, ag = +1. Then 



T = -acoth 



* 



and 



1^ tJ(xo) = 



8a^ 



5 



tt 



sinh I 



i+coth'l 



coth 



$ 



$ 



+ 



^ 



