1144 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1952 



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value of xi which satisfies the boundary conditions for the given values 

 of the other parameters. If additional accuracy is wanted, it is then not 

 too difficult to refine this approximate value by desk computation. The 

 results of quite a number of exploratory calculations which were made 

 on the Laboratories' general purpose analog computer will be shown 

 later in this section. 



The fields of the principal mode in the main dielectric of a Clogston 

 cable are given approximately by equations (46) of Section II, namely 



^P^V^/-^-^ (371) 



E. 



Zl . P2 . Z2 , Pi 



— log - + — log 



2ir log {pi/pi) \_pi p Pi p J ' 



for pi ^ p ^ P2 , where / is an amplitude factor equal to the total current 

 flowing in the positive 2-direction in the inner stack, and Zi and Z2 are 

 given by writing xi for x in (362) and (363) respectively. The fields in 

 the inner stack are 



H, 



I Ni(xia)Ji{xip) - JiixicQNiixip) -1 

 27rpi Ni(xia)Jiixipi) - Ji(xia)Ni{xiPi) 



(372) 



E r^ a/E -1^ Nl{xia)Jl{Xlp) - Jl(xiCi)Nl(xip) -7Z 



" '^ y e 2xpi iVi(xia)^i(xiPi) - /i(xia)A''i(xiPi) ' 



^ ^ XI _^ NiixicQJoixip) - '/i(xia)iVo(xip) g-7. 

 ' ^ g 2tpi iVi(xia)J'i(xipi) - /i(xia)iVi(xiPi) 



for a ^ p ^ pi ; while in the outer stack we have 



H^^-l- ^^(xib)J,(xip) - Ji{xih)N,(xip) ^-y. 

 '^ 2-KP2 N i{xih)J i{xip2) — Jiixib)Ni{xip2) 



"'^ y -e 2-Kp, N^(xih)Ji{xiP2) - Mxib)Nr{xiP2) ' ^ ^ 



^ ^ XI _i_ Ni(xib)Jo{xip) - Ji{xib)No(xip) g-T. 

 ' '^ g 27rp2 Ni(xib)Ji{xip2) - Ji{xib)NiixiP2) 



for P2 ^ p S b. The potential and current distributions may be calcu- 

 lated in the usual way from the fields. 



As numerical examples we have plotted in Fig. 14 the fields of the 

 principal mode in two Clogston coaxial cables. Fig. 14(a) shows a 



