574 BELL SYSTEM TECHNICAL JOURNAL 



and that of the corresponding reflected wave has the same value. 

 It should be noted that by the "reflected" cylindrical wave in the 

 space enclosed by a shield, we mean the sum total of an infinite number 

 of successive reflections. Each of the latter waves condenses on the 

 axis and diverges again only to be re-reflected back ; in a steady state 

 all these reflected waves interfere with each other and form what 

 might be called a "stationary reflected wave." Not being interested 

 in any other kind of reflected waves we took the liberty of omitting 

 the qualification. 



In conductors the attenuation of a wave due to energy dissipation 

 is much greater (except at extremely low frequencies) than that due 

 to the cylindrical divergence of the wave. Hence, in the shield we 

 can regard the wave as plane and write (108) in the following approxi- 

 mate form: 



f = - -''^- "f - - «^- (128) 



In form, these are exactly like ordinary transmission line equations. 

 Hence, in a shield the radial impedance is simply the intrinsic im- 

 pedance of the metal, 



Zp = r? = J^ohms, (129) 



and the propagation constant, 



0- = \'zco/ig = ^irfiigi]. + i) nepers /cm. (130) 



The exact value of the radial impedance in metals can be found by 

 solving (108). Thus, we can obtain 



for diverging waves, and 





for the reflected waves. 



Cylindrical waves of the electric type can be treated in the same 

 manner. It turns out that the transmission laws in metals are identical 

 with those for magnetic waves. The radial impedance in perfect 

 dielectrics, on the other hand is given by 



Zp = ^ . (133) 



