1138 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1952 



where 



^ ^ ^/i('<:opi) + BKiJKopi) , 



7^i(r,a)/:(r,pO - /i(r,a)/Ci(r,pO • ^'^^^^ 



111 the outer stack, for p- ^ p ^ b, 



E, = — . Z)[A'i(r,6)A(r,p) - h{Vth)K,{T(p)]e"'% (343) 



?coe 



E. = ^4 D[lUVth)UVcp) + h{Vch)K,{Tcp)]e-'\ 

 9 



where 



_ ^/l('^0P2) + BKi(koP2) 



i^i(r,6)/i(r,p2) - /i(r,6)K:(r,p2) ' ^'^"^"^^ 



For the remainder of the present section we shall confine our attention 

 to the principal mode. In the parallel-plane line this mode corresponds 

 to the lowest root in r^ of equation (331), that is, 



tanh I V^W^ Tfh tanh T(S = -^a/^-^ . (345) 



Mo K Q 



We note that the right side of the equation is very small compared to 

 unity, being of the order of the square root of the ratio of displacement 

 current density in the insulators to conduction current density in the 

 conductors, and also that the coefficient of Vi in the first factor on the 

 left will under all ordinary conditions be much smaller than the coefficient 

 of r^ in the second factor. Hence in seeking the lowest root we are justi- 

 fied in replacing the first hyperbolic tangent on the left side of (345) by 

 its argument, so that the equation becomes 



(346) 



(347) 



(348) 

 Since the right side of (348) is a positive real constant, the equation has 



