1136 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1952 



For the odd modes, the fields in the main dielectric are 

 Hx = Hq sh Kay e"^', 



Ey= -Ho^sh Koij 6""% (335) 



Ez = —Ho -^ ch Koy e"'% 



for —\h ^ y ^ ^b, where Ho is again an arbitrary amplitude factor 

 and 7 and kq are defined as before in terms of F^ , which is now a root of 

 (332). The fields in the stacks are 



Hx = ±Ho %i^ sh rX^a T y) e-'\ 

 sh T(S 



Ey = ^Ho -^ '^|?5 sh r,(ia -F y) e''^ (336) 



?coe sh 1 (S 



E. = +Ho ^ '-^ ch T^{ha T y) 6''% 

 g sh TfS 



for |6 ^ \ y \ ^ ^a, where again the upper signs refer to the upper 

 stack and the lower signs to the lower stack. The continuity of E^ at 

 y = ±|6 is now a consequence of equation (325) or (332). 



The notation for the partially filled coaxial cable is shown in Fig. 6 

 of Part I, where as before we assume that the laminae are infinitesimally 

 thin, the boundary impedances are effectively infinite, and the main 

 dielectric satisfies Clogston's condition. The radius of the inner core is a 

 and that of the outer sheath is b, while the stack thicknesses are Si and S2 

 respectively; but no restrictions, other than obvious geometrical limita- 

 tions, are placed on the relative values of a, b, Si , and S2 . The inner and 

 outer radii of the main dielectric are denoted by pi (= a + Si) and po 

 (= b — S2) respectively. 



The boundary conditions at the surfaces of the main dielectric will 

 be satisfied, as in Section II, by matching radial impedances at the 

 stack-dielectric interfaces. If the impedance Za looking into the core at 

 p = a is effectively infinite, then the impedance looking into the inner 

 stack at pi is given by equation (98) of Section III to be 



^^ ^ Tj Ko(r,pi)/i(r,a) -f Kr{T(a)Io(Tcpi) ,33^. 



g Ki(r,a)7i(r,pi) - Ki(Tfp,)h{Tfa) ' 



Similarly, if the sheath impedance Zi is infinite, then looking into the 



