548 BELL SYSTEM TECHNICAL JOURNAL 



importance.'^ The second and third equations, on the other hand, 

 give 



^log^' = E/'(a)-E;(^)-i^, (52) 



1 «" 



27r(g + icoe) dz 



But, upon substituting (45), (47) and (51) in the first of these equations 

 and (43) in the second, we get 



where Z and Y are to be interpreted respectively as the distributed 

 series impedance and shunt admittance. 



Current Distribution in Cylindrical Conductors 



So far, we have been dealing with electromagnetic intensities in 

 dielectrics. We now turn our attention to conductors and determine 

 their current distributions with the ultimate view of calculating their 

 surface impedances. One of our sources of information is the familiar 

 set of equations (12). In these equations, however, we now let e = 

 since the displacement current in conductors is negligibly small by 

 comparison with the conduction current. From these equations, we 

 eliminate electromotive intensities and thus obtain a differential 

 equation for the magnetomotive intensity. The latter is in fact 

 equation (6) with only one difference: the exponential factor e~^^ has 

 been explicitly introduced and cancelled so that the equation has 

 become 



or (54) 



where 



This 0- will be called the intrinsic propagation constant of solid metal. 



1^ Our standard practice of neglecting the longitudinal displacement currents 

 has given us the general rule that 2-irpH^ = / is independent of p. Using this relation 

 in the first of equations (2.2), we get 



(g + i(jie)Ez == 0; 



but this merely reflects the fact that g + zwe is very small. 



