136 Mr. 0. Heaviside on Electromagnetic Waves, and the 



terminate upon them, whilst those of magnetic force go round 

 the wires. We shall still have these plane electromagnetic 

 waves w r ith curved lines of force propagated undistorted and 

 unattenuated, at the same speed v. If V be the line-integral 

 of E across the dielectric from one wire to the other, and 47rC 

 be the line-integral of H round either wire, we shall have 



-'^ = L/>C, (34) 



-§ = S„V, ...... (35) 



(34) taking the place of (29), and (35) of (28), with k and g 

 both zero. Here L and S are the inductance and per- 

 mittance of unit length of the circuit of the parallel wires, 

 and r=(LS) _ *. 



Next let the wires have constant resistance R per unit 

 length to current in them, and let the medium between them 

 be conducting (to a very low degree), making K the con- 

 ductance per unit length across from one wire to the other. 

 We then turn the last equations into 



"f=(R+W .... (36) 



-g=(K + S/>)V, .... (37) 



and have a complete imitation of the previous unreal problem. 

 The two dissipations of energy are now due to R in the 

 wires, and to K in the dielectric, it being that in the wires 

 which takes the place of the unreal magnetic dissipation. 

 The relation R/L = K/S, which does not require excessive 

 leakage when the wires are of copper of low resistance, 

 removes the distortion otherwise suffered by the waves. I 

 have, however, found that when the alternations of current 

 are very rapid, as in telephony, there is very little distortion 

 produced by copper wires, even without the leakage required 

 to wholly remove it, owing to R/L?i becoming small, n/27r 

 being the frequency ; an effect which is greatly assisted by 

 increasing the inductance (see Note A, p. 151). Of course there 

 is little resemblance between this problem and that of the long 

 and slowly-worked submarine cable, whether looked at from 

 the physical side or merely from the numerical point of view, 

 the results being then of different orders of magnitude. A 

 remarkable misconception on this point seems to be somewhat 

 generally held. It seems to be imagined that self-induction 



