158 Intelligence and Miscellaneous Articles, 



must then have a constant value for all points situated within one 

 and the same conductor. The function V, introduced into analysis 

 by Laplace, has been designated by Green under the name of the 

 potential function. 



If m and m' denote two masses of electricity of the same name 

 situated at a distance r, each of the masses is repelled by a force 



equal to — 2~; if the distance of the masses becomes r-\-dr, the 



sum of the elementary works of the repulsive forces is 



mm j , 



r 2 



Or) 



The sum of the elementary works of all the repulsive forces is 

 therefore equal to the increase of the function 



r 



in which the summation is extended to all the masses of electricity, 

 each of them being supposed to be affected by a sign. The func- 

 tion ~W is designated, according to a notation borrowed from Gauss, 

 by the name of the potential of electricity. 



The works of Helmholtz and Clausius have particularly called 

 attention to this function, which plays a considerable part in the 

 phenomenon of the electric discharge ; indeed the increase of the 

 potential represents the work done in the electric discharge. M. 

 Clausius has shown that the potential can be readily expressed by 

 means of the charges and potential functions relative to each of the 

 conductors. If V is the potential function on one conductor, and 

 Q its charge, 



W=i2VQ. 



If V , Q are the initial values, Y v Q x the final values relative to 

 one conductor, 



measures the work done in the partial discharge of the system of 

 conductors ; and when the conductors are restored to the neutral 

 state, the work of the complete discharge is 



isv Q„. 



The mechanical equivalent of the discharge is independent of the 

 manner in which the discharge is effected ; it depends only on the 

 initial and final values of the potential ; so that the sum of the 

 effects of the electrical discharge remains the same, whatever may 

 be the nature of the discharge. 



M. Helmholtz has already estimated the vis viva gained by the 

 electricity in passing from the surface of a conductor to an infinite 

 distance ; but he considered the potential of the electricity of a 

 conductor a constant quantity, while in reality the potential on the 

 conductor diminishes in proportion to the charge : this diminution 

 has the effect of modifying the expression of the work produced in 

 the discharge through air. 



