HYPER-FREQUENCY TRANSMISSION 315 



For the very high frequencies with which we shall be concerned in the 

 following analysis, a physically very thin cylindrical metallic sheath 

 behaves electrically as though it were infinitely thick. This fact 

 greatly simplifies the mathematical treatment; its real importance, 

 however, is that external interference is entirely eliminated. 



As stated at the outset, this paper will not attempt to deal with the 

 problem of the reflection phenomena which occur at the terminals of 

 the system and at points of discontinuity. For a discussion of the 

 general character of the boundary problem the reader is referred to 

 "Guided and Radiated Energy in Wire Transmission."^ It maybe 

 remarked here, however, that the simple engineering boundary 

 conditions (continuity of current and potential) are entirely inadequate. 



IB. Transmission Through Dielectric Guides 



The greater part of this paper deals with transmission in thin hollow 

 conducting cylinders; the last section, however, discusses briefly 

 transmission along the dielectric wire.^ Theoretically this type of 

 transmission is extremely interesting and the mathematical theory 

 resembles to a considerable extent that of hollow cylinder transmission. 

 Unfortunately, however, dielectric losses are usually high. Hence our 

 discussion of dielectric waves will be limited to a development of the 

 fundamental equation from which the critical frequencies and the 

 phase velocities can be determined. 



II. NoN-DissiPATivE Hollow Conducting Guides 



In dealing with the propagation of hyper-frequency electromagnetic 

 waves inside a long hollow conducting cylinder parallel to the 2-axis, 

 it is convenient to write the field equations in the appropriate cylindrical 

 coordinates (p, 6, z) in the form,^^ 



ixlw p ad op 



P-Kj) op p otf 



X^Ej = — - ^ Ez -\- f^i(^ ^ liz, 

 p dd op 



div E = 0, div // = 0. 



" In this form the field is expressed explicitly in terms of liic axial electric and 

 magnetic intensities and their spatial derivatives. This is highly advantageous for 

 the purposes of this paper. 



