﻿448 Prof. R. Clausius on the new Conception of 



the point m, it seems to me that we must take as denominator 

 of the fraction neither the distance which the points have at the 

 time t, nor that which they had at the time t—At, but must take 

 into account another quantity — that is, the distance between the 

 position where the point m l was at the time t — At (at the moment 

 of emission) and the position where the point m is at the time t 

 (the moment of reception). This distance may be denoted by 

 r(t—At, t). 



To determine this distance, it is convenient, besides the above- 

 used differential coefficients of the distance r, in which the mo- 

 tions of the two points are simultaneously taken into account, to 

 bring in two other kinds of differential coefficients of this mag- 

 nitude — those, that is to say, which only refer to the motion of the 

 point m, and those which only refer to the motion of m v We have 

 now to do with the latter, and will distinguish them by an index 



d r d^r 

 added to the d, thus, -jj-3 -—, &c. The distance in question may 



then be expressed by the following series, 



„ A . , N Atd Y r , At* d\r s 



Putting this value into the denominator of the fraction which is 

 to represent the receptive potential, we obtain instead the follow- 

 ing expression, 



. . . . (la) 



At d,r Afi d*r „ 



This expression is essentially different from Neumann's. If it 

 be applied to two constant currents, presupposing that in each of 

 the two conductors there is everywhere an equal quantity of posi- 

 tive and negative electricity, we obtain zero for the potential of 

 the two currents on each other. 



Besides what has here been said, there is another objection 

 which I think I must make against Neumann's analysis. To 

 determine the difference of time A^ which the potential requires to 

 pass from the point m x to the point m, Neumann uses equation (2), 



that is, he regards in this determination the distance r, which 

 the two points have at the time t, as the path traversed by the 

 potential. But this is obviously not the real path ; this we must 

 again consider to be the above-discussed distance — that is, the 

 distance of the position of the point m x at the moment of emission, 

 from the position of the point m at the moment of arrival. 



