﻿Electrodynamic Phenomena suggested by Gauss. 451 



which, neglecting the higher members, gives 

 A , r r dr 



At = ITS 



a or at 

 In accordance with this the expression for the potential should be 



In the further course of Riemann's calculations there occurs 



another very essential oversight. To prove this I will follow his 



own developments further, merely remarking that wherever in 



v 

 the sequel the fraction - occurs, the somewhat altered value 



d a 



,-— should be inserted. 



a. oC l at 



In order to deduce from the potential of the individual elec- 

 trical masses s and e' the potential of the entire electrical cur- 

 rents S and S', he considers the summations executed in reference 

 to all the quantities of electricity in the two conductors. Hence 

 from this the potential of S upon S' would be 



-SSee'F^- -, t). 



But, for the transformations which he intended, it was necessary 

 to have the time in the formula differently from the manner in 

 which it occurs ; and he therefore considers the potential not 

 merely at the time t, but during an interval of time from to t ; 

 and the expression thus formed he considers to be the potential of 

 the forces exerted from the time to the time t. If this poten- 

 tial be denoted by P, we get 



V=-( t 2Zee , Y(r- r -,Tyh. ... (6) 



To calculate this magnitude P, it would have been simplest to 



v 



develope the function occurring in the expression according to -. 



Then, neglecting higher members, there would have been obtained 



P--£*SSrf[ier; t)- ZVt, t) + ^ F'(r, T )]*i 

 or, otherwise written, 



P-.TsSee'r 1 '' *(r) , > S ^(r)l 



Jo 1/ « ~ W^-} dT - 



This expression, in which occur only differential coefficients which 

 refer to the motion of e, becomes equal to zero if the summation 



