914 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1952 



given by 



J. = gE. = ±gZo{yo)Hoe-'' . (124) 



The total current per unit width carried by the stack is just J^s, where 

 s is the thickness of the stack; there will also be small currents in the 

 sheaths unless we assume the sheath impedance to be infinite. The 

 potential difference between any two points i/i and 2/2 in the same trans- 

 verse plane may easily be found from 



V{y2) 



rV2 



F(2/i) = - 



''Vl 



Eydy. 



(125) 



For a Clogston 1 line of the proportions which we have been considering, 

 the potential difference across the stacks will be small compared to the 

 potential difference across the main dielectric. 



In a coaxial Clogston 1 with infinitesimally thin laminae, the fields in 

 the main dielectric are given to a good approximation by equations 

 (46) of Section II, namely 



Ha 



E. 



E. 



2irp 



€0 2irp 



/ 



2t log (p2/pi) 



(126) 



?i^log^^ + ?^logei 

 L Pi P P2 P J 



where / is an arbitrary amplitude factor and ^1(70) and ^2(70) are ex- 

 pressed by (113). In the inner stack we have 



Hd 



E. 



Ziiyo)! Vgip' - a~) 



2irpi _ 

 e 2xpi 



+ 



2p ' pZa(yo)_ 



gip' - a) 



2p 



+ 



P^a (70) _ 



(127) 



E. 



Zi{yo)I 

 2irpi 



while in the outer stack, 



