﻿446 Prof. R. Clausius on the new Conception of 



guished mathematicians, by pursuing three different methods of 

 investigation, have obtained what is virtually the same result, 

 would seem to furnish a guarantee for the accuracy of the inves- 

 tigation ; and perhaps many physicists will thereby be led to con- 

 sider the matter settled. Under these circumstances a publication 

 of the reasons on the other side can only have a useful effect, by 

 giving rise to further investigations made probably from other 

 points of view. 



The most complete of the above investigations is that of C. 

 Neumann, which appeared, under the title "Principles of Electro- 

 dynamics/'' as a publication on the occasion of the Jubilee of the 

 University of Bonn, after a preliminary notice of the results had 

 been published in the Proceedings of the Gottingen Royal Aca- 

 demy of Sciences. I will first discuss this. 



Neumann starts from the consideration of two points, which 

 move under their reciprocal action. If the potential of one of 

 these points, (for greater accuracy we will at once say) the point 

 m v is to be determined in reference to the point m, the time ne- 

 cessary for the propagation of the action must be taken into 

 account, which is done by Neumann in the following manner. 



The potential which the point m x exerts at the time t he calls 

 the emissive potential, and denotes it by it. Assuming Newton's 

 law in reference to the reciprocal action of the two points, namely 

 that the force is inversely as the square of the distance, we have, 

 according to Neumann, for the determination of the emissive 

 potential the equation 



mm 



7T= -) 



r 

 in which r denotes the distance of the two points at the time /. 



This potential requires some time to reach the point m, and 

 hence arrives there not at the time t, but somewhat later. If, 

 on the contrary, we want the potential arriving at the time t in 

 the point m, which Neumann calls the receptive potential, we 

 must take for it that potential which the point m x emitted at a 

 certain earlier time t — At. Denoting the distance which the 

 two points had at this previous moment by r — Ar, and choosing 

 for the receptive potential the sign co, according to Neumann we 

 must put 



mm, 



o) = T^' 



r — Ar 



Replacing the denominator by a series progressing by powers of 

 At, we have 



mm, ,,, 



Atdr_ APtfr 

 1 dt + T7<ldt 



+ 1— ,-7^-&C 



