[ 605. ] 



L1X. On some Cases of Propagation of Electric Oscillations 

 along a .Number of Parallel Wires. By W. B. Mokton,' 

 M.A., Professor of Natural Philosophy, Queen's College, 

 Belfast *. 



§ 1. Introduction. 



WHEN simple harmonic electromagnetic waves are 

 guided along conducting wires of finite resistance, the 

 effect of the leads is to produce, first, a retardation of the 

 speed of propagation as compared with that in free space, and, 

 second, an attenuation of the amplitude of the waves as they 

 proceed. Both these effects are, in general, functions of the 

 frequency of the oscillations and of the constants of the con- 

 ducting system. Their determination is what is mainly 

 wanted in the solution of the problem. The complete solution,, 

 of course, involves in addition a knowledge of the distribution 

 of the electric and magnetic vectors inside and outside the 

 conductors. 



Let A, be the wave-length, k. the attenuation-factor, -~~ 



the frequency. Then, for waves travelling along the axis of 

 s iu the positive direction, the different vectors contain the 

 factor 



. rl-nz \ 



Replacing this by 



e z(ms—j)t) } where m— we, 



A. 



we see that a knowledge of the complex quantity m gives us 

 at once the wave-length (and therefore the speed of propaga- 

 tion) and the attenuation factor. The case of a single wire 

 surrounded by a sheath was worked out by Prof. J. J. 

 Thomson f; that of a single wire isolated in space has been 

 solved by Soniuierfeld |. In the latter case the return 

 currents are carried by the dielectric ; lines of force which 

 start from a positive section of the surface of the wire bend 

 round and end on an adjoining negative section, forming in 

 general very long loops. 



In experimental investigations on the subject the common 

 arrangement consists of two similar parallel wires. For slow 

 oscillations we have then Heaviside's well-known formula 



m?=-(R + ip~L)(S+ipV) 



* Communicated, in abstract, to the British Association at Bradford 

 ■f J. J. Thomson, Recent Researches, p. 262. 

 X Sommerfeld, Wied. Ann. lxvii. p. 233 (1899). 



