to the Motion of Electrification through a Dielectric. 333 



break up if the charge were stopped. But if perfectly- 

 conducting: surfaces be given on which to terminate the dis- 

 placement, the natural motion of the wave will itself carry the 

 electrification along them. In fact we now have the rudi- 

 mentary telegraph-circuit, with no allowance made for absorp- 

 tion of energy in the wires, and the consequent distortion. 

 If the conductors be not coaxial, we only alter the distribution 

 of the displacement and induction, without affecting the pro- 

 pagation without distortion *. 



If we now make the medium conduct electrically, and 

 likewise magnetically, with equal rates of subsidence, we shall 

 have the same solutions, with a time-factor e~P* producing 

 ultimate subsidence to zero ; and, with only the real electric 

 conductivity in the medium the wave is running through, it 

 will approximately cancel the distortion produced by the 

 resistance of the wires the wave is passing over when this 

 resistance has a certain value f. We should notice, however, 

 that it could not do so perfectly, even if the magnetic retar- 

 dation in the wires due to diffusion were zero ; because in 

 the case of the unreal magnetic conductivity its correcting 

 influence is where it is wanted to be, in the body of the 

 wave ; whereas in the case of the wires, their resistance, 

 correcting the distortion due to the external conductivity, is 

 outside the wave ; so that we virtually assume instantaneous 

 propagation laterally from the wires oii their correcting influence 

 in the elementary theory of propagation along a telegraph- 

 circuit which is symbolized by the equations 



-^=(R + Lp)C, -f^=iK + Sp)Y, . (32) 



where E., L, K, and S are the resistance, inductance, leakage- 

 conductance, and permittance per unit length of circuit, C the 

 current, and V what I, for convenience, term the potential- 

 diff'erence, but which I have expressly disclaimed | to represent 

 the electrostatic ditFerence of potential, and have shown 

 to represent the transverse E.M.F. or line-integral of the 

 electric force across the circuit from wire to wire, including 

 the electric force of inertia. Now in case of great distortion, 

 as in a long submarine cable, this V approximates towards 

 the electrostatic potential-difference, which it is in Sir W. 

 Thomson's diffusion theory ; but in case of little distortion, as 



* ' Electrician,' Jan. 10, 1885. Also "Self-induction of Wires," part iv. 

 PHI. Mag. Nov. 1886. 



t " Electromagnetic Waves," § 6, Phil. Mag. Feb. 1888. ' Electrician,' 

 June 1887. 



X " Self-induction of Wires," part ii. Phil. Mag. Sept. 1886. 



