Wave Propagation over Parallel Wires. 607 



therefore be such as to satisfy the two equations : 



V 4 ^ = 



and V 2 ^=/W, 



where / is arbitrary, along with the appropriate boundary 

 conditions. Such problems, of course, give a system of 

 stream-lines in virtue of V 4/ ^, which are not changed when 

 the direction of motion of the body is reversed. The only 

 known solutions of this type so far obtained are those of 

 the steady motion of a fluid between the walls of a channel 

 and the steady relative rotation of two concentric cylinders. 

 It may be remarked, in conclusion, that certain classes 

 of problem, although violating the ordinary condition of 



steadiness, viz. ^- and =- - = everywhere, can still be 

 ot of 



reduced to that of a steady-motion case by the super- 

 position of a uniform linear velocity or angular velocity 

 upon the axes of reference. For example, if every point of 

 a cylinder of any given shape describe a circular path inside 

 and concentric with a given circular cylinder, ihe motion may 

 be reduced to that of a steady case. 



LI V. Wave Propagation over Parallel Wires: The Proximity 

 Effect. By John R. Carson, Department of Development 

 and Research, A merican Telephone and Telegraph Company*. 



I. Introduction. 



THE importance of the problem dealt with in the 

 present paper — wave propagation along a conducting 

 system composed of two similar and equal parallel wires — 

 has been emphasized by modern developments in telephonic 

 transmission such as the carrier wave system of the 

 American Telephone and Telegraph Company, and the 

 utilization of loaded cable circuits in which the wires are 

 in very close juxtaposition. For such systems, where the 

 frequencies employed are relatively high and the wires very 

 close together, considerable theoretical work has been 

 found necessary to reduce the solution to a form available 

 for immediate engineering use, in spite of the previous 



* Communicated bv the Author. 



