570 BELL SYSTEM TECHNICAL JOURNAL 



When the ratio of the impedances is very large by comparison with 

 unity, the formula becomes 



i? = 20 1ogio-^, (115) 



and when k is very small, then 



i? = 20 1ogioj|^. (116) 



In the next section we shall see that to all practical purposes, the 

 wave in the shield is attenuated exponentially. If a. is the attenuation 

 constant in nepers and if t is the thickness of the shield, then the 

 attenuation loss is 



A = 8.686«^ decibels (117) 



and the total reduction in the magnetomotive intensity due to the 

 presence of the shield is 



S = R-\-A. (118) 



The electromotive intensity is reduced in the same ratio. 



But if the shield is not electrically thick, a correction term has to 

 be added to the reflection loss. This correction term can be shown 

 to be 31 



{k - 1)2 ^_ 



C = 20 logi 



1 



decibels, (119) 



{k + 1)2^ 



and if k is very large or very small by comparison with unity then 



C = 3 - 8.686a/ + 10 logio (cosh 2at - cos 2/3/). (120) 



Equation (120) does not hold down to / = 0; when Tt is nearly zero, 

 then 



{k - 1)2 



. C = 20 logi 



1 



{k + 1)^ 



(121) 



So far we Supposed that the shields were coaxial with the source. 

 If this is not so, it is always possible to replace any given line source 

 within the shield by an equivalent system of line sources coaxial with 

 the shield and emitting cylindrical waves of proper orders. Mathe- 

 matically this amounts to a change of the origin of the coordinate 

 system. In the next section we shall see that the shielding effective- 

 ness is not the same for all cylindrical waves. This means, of course, 

 that if the shield is not coaxial with the source, the total reduction in 



^1 Here, r = a -\- ip \s the propagation constant in the shield. 



