IQO 



BELL SYSTEM TECHNICAL JOURNAL 



The physical system contemplated is shown in Fig. 1. The out- 

 going and return systems of conductors, each comprising a cyhndrical 

 wire with insulated cylindrical sheath, are assumed to be identical 

 in all respects. For the sake of generality, it is assumed that the 

 magnetic sheaths may be insulated from the wires, as shown. The 

 interesting practical case where wire and sheath are contiguous, form- 

 ing a bi-metallic conductor, then appears as the limiting case of 

 infinitesimally thin insulation. 



WIRE 



•E'; 



DIRECTION 



OF PROPAGATION I 



MAGNETIC SHEATH 



3L| bg cl2 



INSULATION (ADMITTANCE Yg) 

 MAGNETIC SHEATH (X2,|J.2) 



^\ E" *i XV, + 4^ dz \— INSULATION (ADMITTANCE Y,) 



— ^ » 7 — 1- 



iHl'+^'dz (I) ^Ii Y WIRE(X,.|I,) 

 * oz ^ 



Fig. 1 — Illustrating various quantities involved in the analysis. 



The problem consists in finding a solution for the propagation con- 

 stant of the system from Maxwell's equations. If the magnetic 

 sheaths are in contact with the wires, the propagation constant is 

 given in the usual form, V = \ Y^Z, where Y2 is the admittance across 

 the insulation between the sheaths and Z is the series impedance 

 of the system. The admittance is, in general, either a known, or 

 an experimentally determined, quantity; so that for this case the 

 theoretical problem resolves itself into that of finding the series im- 

 pedance. 



An important part of the investigation is, however, to determine 



