﻿Electrodynamic Phenomena suggested by Gauss. 449 

 Hence, instead of the previous equation, we must put 



m- c 



or if we take for r(t— At, t) the above-mentioned expression, 

 AJ 1/ Atd x r At 2 (fir \ 



From this equation we get for At l the following series, 



*-;-?$ +&c (2a) 



Reverting to equation (la), if we replace At by the series just 

 found, we obtain instead of (3) the equation 



mm \ to \ 



°>= ; -rri — sr* J • ( 3fl ) 



r d*r 



c dt + c*K 



Adt) + 2c*dt* &c " 

 and from this we get the following equation instead of (4), 



mm-if. 1 d,r r d A r\ .. . 



This expression for the receptive potential is distinguished from 

 that in (4), not only by the complete differential coefficients of 

 r being replaced by partial differential coefficients, but" also by 

 the fact that the principal member of Neumann's formula (that 

 containing the square of the first differential coefficient) is wanting. 



It appears to me to follow indubitably that Neumann's ana- 

 lysis, by means of which he deduces his potential formula from 

 the assumption mentioned in the introduction to his paper (that 

 the potential, like light, is propagated through space with a cer- 

 tain constant velocity), cannot in all respects be admitted as con- 

 clusive. Whether perhaps that formula may be arrived at by 

 different assumptions as to the mode of propagation of the po- 

 tential, or by the help of other points of view, is, of course, 

 still undecided. 



I turn now to Niemann's paper, which appeared in Poggen- 

 dorff's Annalen, vol. cxxxi. p. 237*, after it had been presented 

 to the Gottingen Royal Society in 1858, but subsequently with- 

 drawn by Riemann. 



Riemann endeavours to deduce an expression for the potential 

 of a constant galvanic current S, in reference to another constant 

 galvanic current S'j from the same assumption, namely, that the 

 potential requires time for its propagation through space. 



He first of all considers two small quantities of electricity, e 



* Phil. Mag. S. 4. vol. xxxiv. p. 368, 



