260 The Mathematical Electricians of the 



magnetic effects of the current produced by discharging the jar. 

 The resulting value was nearly 



c = 3*1 x 10 10 cm./sec.; 



which was the same, within the limits of the errors of measure- 

 ment, as the speed with which light travels in interplanetary 

 space. The coincidence was noticed by Kirchhoff, who was thus 

 the first to discover the important fact that the velocity with 

 which an electric disturbance is propagated along a perfectly- 

 conducting aerial wire is equal to the velocity of light. 



In a second memoir published in the same year, Kirchhoff* 

 extended the equations of propagation of electric disturbance 

 to the case of three-dimensional conductors. 



As in his earlier investigation, he divided the electromotive 

 force at any point into two parts, of which one is the gradient 

 of the electrostatic potential </>, and the other is the derivate 

 with respect to the time (with sign reversed) of a vector- 

 potential a ; so that if i denote the current and k the specific 

 conductivity, Ohm's law is expressed by the equation 



i = k (c 2 grad < - a). 



Kirchhoff calculated the value of a by aid of Weber's formula 

 for the inductive action of one current element on another; 

 the result is 



where r denotes the vector from the point (x, y, z), at which a is 

 measured, to any other point (x, y, z") of the conductor, at which 

 the current is i' ; and the integration is extended over the whole 

 volume of the conductor. The remaining general equations are 

 the ordinary equation of the electrostatic potential 



V 2 < + 4irp = 



(where p denotes the density of electric charge), and the equation 

 of conservation of electricity 



| + div i = 0. 

 ot 



* Ann. d. Phys. cii (1857), p. 529 : Ges. AbhandL, p. 154. 



