316 BELL SYSTEM TECHNICAL JOURNAL 



In these equations the symbols have the following significance: 



£p, Eb, Eg = components of electric force, 

 lip, He, H- = components of magnetic force, 



X2 = -y,2 _ h\ 



y = propagation constant, 



V = cjyjefx = velocity of light in the medium, 

 c = velocity of light in air, 



H = permeability of the medium in electromagnetic units, 

 a = conductivity of the medium in electromagnetic units, 

 e = dielectric constant of the medium in electrostatic units, 

 co/Itt = frequency, 

 i = V^L 



The solutions of these equations for the axial components of electric 

 and magnetic force, E^ and //j respectively, in the region, 0~p=a, a 

 being the internal radius of the conductor, are of the form 



00 



E^ — Y. /„(pX)(^n cos nd + B„ sin nd) exp. (icot ± 72), 



no (2) 



II. = X] /„(pX)(C„ cos nd + Dn sin nd) exp. {iwt ± 72), 



n=0 



where An, Bn, C„ and Dn are arbitrary constants to be determined by 

 boundary conditions and /„ is the Bessel function of the first kind or 

 the internal Bessel function. The components of the transverse 

 electromagnetic field may then be expressed by introducing (2) in (1). 

 We shall first discuss the simplest case, that in which there is no 

 dissipation. The current will then be in a sheet on the surface, p = a, 

 of the perfectly conducting cylinder. But the axial current density 

 u^ and the circulating current density Ue are given by 



u^ = J- He, p = a (3) 



and 



Wfl = y- H^, p = a. (4) 



Thus it follows that Hz and He are discontinuous at the surface p = a 

 and the boundary conditions are simply E^ = Ee = 0. These con- 

 ditions can be fulfilled by two types of waves: (1) a wave for which //; 



