ELECTROMAGNETIC THEORY OF LINES AND SHIELDS 553 



may be provided either outside the given conductor or inside it or 

 partly inside and partly outside. We designate by Zaa the surface 

 impedance with internal return, and by Z^b, that with external return. 

 These impedances are equal only at zero frequency; but if the con- 



d|o 



3.5 R 



::J|c\j 



Fig. 2 — The skin effect in solid wires. The upper curve represents the ratio of 

 the a-c. resistance of the wire to its d-c. resistance and the lower curve the ratio of 

 the internal reactance to the d-c. resistance. 



ductor is thin, they are nearly equal at all frequencies. If the return 

 path is partly internal and partly external, we have in effect two 

 transmission lines with a distributed mutual impedance Zah due to 

 the mingling of the two currents in the hollow conductor common to 

 both lines. However, since this quantity Zah is not the total mutual 

 impedance between the two lines unless the hollow conductor is the 

 only part of the electromagnetic field common to them, it is better to 

 call Zah the transfer impedance from one surface of the conductor to 

 the other. 



In order to determine these impedances, let us suppose that of the 

 total current /„ + lb flowing in the hollow conductor, the part /„ 

 returns inside and the rest outside. Since the total current enclosed 

 by the inner surface of the given conductor is — /„, and that enclosed 

 by the outer surface is h, the magnetomotive intensity takes the values 

 — (/a/27ra) and (h/lirb), respectively, at these surfaces. This infor- 

 mation is sufficient to determine the values of the constants A and B 

 in the equation (59) governing current distribution. In fact, we 



