700 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 195G 



3 



0.5 



1.0 



1.5 



2.0 



2.5 



3.0 



Fig. 5 — The function (j(co) of equation (67). 



Analysis 

 We denote 





r = 



no 

 rii 



From (11) and (67) 



/p(co) = Ips^ , ln(0) = Ins^ 



(68) 



(69) 



By means of (62) and (64) Ave eliminate /„ and Ip and obtain the equa- 

 tions 



(b + l)Ipsf = / - Ir{^ cosh ic - t) 

 (b + l)RIpsf = hi + Iri^ - r cosh co) 

 where Ir is a (particle) current density 



2Dnni 



Ir = 



L sinh CO 



(70) 



(71) 



In principle we could solve (70) for ^ and f as functions of I with R and 

 oj as parameters; this would determine ^V through (58) and (65) and 

 complete the problem. First we shall rewrite these equations in terms 

 of 7 as in the analysis of the second section. 



