﻿Electrodynamic Phenomena suggested by Gauss. 447 



As regards the difference of time At, it is the time which the 

 potential requires to traverse the distance between the two points; 

 and denoting by c the velocity of propagation of the potential, 

 Neumann puts 



At=, c ( 2 ) 



The previous equation thereby passes into 

 mm x 



C0 ~ ~ F7v ~ ( 8 ) 



r -cdt + 2?aW-^' 



Developing this expression in a series, and, inasmuch as c is 

 very great, neglecting all members which have in their denomi- 

 nator higher powers of it than the second, we obtain 



r L ^ celt + c«W 2c 2 dt*Y ' ' [ } 



From this expression Neumann separates that part which may 

 be represented in the form of a differential coefficient according 

 to the time, viz. 



(I 1 dr 1 d*r\ 

 mm Ac'rdt-2?'dFh 

 and calls it the ineffective potential. The other members form 

 then the effective potential. Denoting this by w, he finally ob- 

 tains the equation 



mm x T_ 1 /drVl 



In this statement I think I have accurately reproduced that 

 part of Neumann's investigations with which we are concerned 

 for our present purposes, and we will now inquire whether this 

 reasoning can be allowed to be correct in all points. 



If the action of the point m } on the point m is presupposed to 

 be momentary, both the emissive and the receptive potential of 



m 1 in reference to m must be represented by the fraction ^ > 



in which r is the distance which the two points possess at the 

 time t. In order to express that a duration of time is needed 

 for the propagation of the potential, and that thus the potential 

 which arrives at the time t on the point m was exerted from the 

 point m x at an earlier time t— At, Neumann puts in the receptive 

 potential the value r — Ar as the denominator of the fraction 

 instead of r, by which he understands that distance which the 

 points had at the time *— A*. But if we assume that the 

 action is propagated similarly to light from the point m v to 



