ELECTROMAGNETIC THEORY OF LINES AND SHIELDS 573 



Cylindrical Waves in Dielectrics and Metals 



In good dielectrics g is small by comparison with we and the first 

 term on the right in (109) very nearly equals (lirp/xy where X is the 

 wave-length. But we are interested in wave-lengths measured in 

 miles and shields with diameters measured in inches;, thus we shall 

 write (109) in the following approximate form: 



When n ^ there are two independent solutions 



El = p-« and E^ = p""; (123) 



and when w = 0, 



El = log p and £2 = 1. (124) 



The corresponding expressions for H are, by (108), 



Hi = "^^ and H2= - ^ . (125) 



in the first case, and 



Hi = J— and Hi = 0, (126) 



Iwfxp 



in the second. 



The second case in which Ei and Hi are the electromotive and mag- 

 netomotive intensities in the neighborhood of an isolated wire carrying • 

 electric current is of interest to us only in so far as it helps to interpret 

 (123) and (125). If we were to consider 2n infinitesimally thin wires 

 equidistributed upon the surface of an infinitely narrow cylinder, the 

 adjacent wires carrying equal but oppositely directed currents of 

 strength sufficient to make the field different from zero, and calculate 

 the field, we should obtain expressions proportional to Ei and Hi. 

 An actual cluster of 2n wires close together would generate principally 

 a cylindrical wave of order n; the strengths of other component waves 

 of order 3w, 5w, etc. rapidly diminish as the distance from the cluster 

 becomes large by comparison with the distance between the adjacent 

 wires of the cluster. For the purposes of shielding design we can 

 regard a pair of wires as generating a cylindrical wave of the first 

 order (w = 1). The radial impedance of an wth order wave is 



^^ Hi~ n ' ^^^^^ 



