Middle of the Nineteenth Century. 257 



this shows that any harmonic disturbance, and therefore any 

 disturbance whatever, is propagated along the wire with 

 velocity (CL}~\ The difference between propagation in an 

 aerial wire and propagation in an oceanic cable is, as Thomson 

 remarked, similar to the difference between the propagation 

 of an impulsive pressure through a long column of fluid in a 

 tube when the tube is rigid (case of the aerial wire) and when 

 it is elastic, so as to be capable of local distension (case of the 

 cable, the distension corresponding to the effect of capacity) : 

 in the former case, as is well known, the impulse is propagated 

 with a definite velocity, namely, the velocity of sound in the 

 fluid. 



The work of Thomson on signalling along cables was followed 

 in 1857 by a celebrated investigation* of Kirchhoff's, on the 

 propagation of electric disturbance along an aerial wire of 

 circular cross- section. 



Kirchhoff assumed that the electric charge is practically all 

 resident on the surface of the wire, and that the current is 

 uniformly distributed over its cross-section; his idea of the 

 current was the same as that of Fechner and Weber, namely, 

 that it consists of equal streams of vitreous and resinous elec- 

 tricity flowing in opposite directions. Denoting the electric 

 potential by V, the charge per unit length of wire by e, the 

 length of the wire by I, and the radius of its cross-section by a, 

 he showed that Fis determined approximately by the equationf 



V = 2e log (I/a). 



* Ann. d. Phys. c (1857), pp. 193, 251 : Kirchhoff's Ges. Abhandl., p. iai ; 

 Phil. Mag. xiii (1857), p. 393. 



t His method of obtaining this equation was to calculate separately the effects of 

 (1) the portion of the wire within a distance e on either side of the point con- 

 sidered, where e denotes a length small compared with J, but large compared with o, 

 and (2) the rest of the wire. He thus obtained the equation 



where the integration is to be taken over all the length of the wire except the 

 portion 2e : the equation given in the text was then derived by an, approximation ,. 

 which, however, is open to some objection. 



S 



