442 BELL SYSTEM TECHNICAL JOURNAL 



In (31) the a's and 6's are given by: 



a\h = 



(l2{h-k) 



bih = 



rp+Zh 



{r^-\-Zh){:rp + ~Zk)(rp-\-Zh-k) 



M Zh 

 V rp-\-Zh 



[ 1 

 2 



h2(h-k)—- 



,(v)( 



''■^{h-k) 



+ 



rg-fx-ZhZk 



dE^ 



(rp-\-Zh){rp+Zk. 



n 



)(32) 





Discussion of General Equations 



Equations (31) and (32) contain the general solution of the prob- 

 lem. The formulas are too long to consider all effects at one time 

 but if we separate (31) into components and consider each component 

 separately, useful applications may be secured. 



First taking the component that gives rise to amplification effects, 

 we get 



ipih) =aih{l — bihqh)eih 



\rp-hzj\ 



, /. M Zh \ 



;-g + g,,(l--— — J 



\ V Tp+Zh/ 



[eih. 



(33) 



The point to be noted in this relation is that when gi,< <rg we have 

 the well-known relation 



*/>(/!) = 



rp+Zh 



e\h- 



(3-4) 



