﻿452 Prof. E. Clausius on the new Conception of 



be effected of the quantities of electricity 

 the current S ; , which are so distributed that there is everywhere 

 the same quantity of positive and of negative electricity. It 

 follows thence that the expression (6), proposed by Eiemann 

 for the potential, is not fitted to explain the action of two cur- 

 rents upon each other. 



An expression which is to fulfil this object must necessarily 

 contain a member in which a differentiation in respect to the 

 motion of e as well as one in reference to the motion of e f 

 occurs — a member, that is, which contains either the product 



ifi) d< 1 - 



— ; — , or the differential coefficients of the second order, 



(It dr 



dd' 



c-) 



drdr 



To introduce such a member into his expression, Eiemann effects 

 a peculiar operation. 

 He first writes 



r 



K Z ~ ~a! T ) = F ^ T ) "" f "~ P '( T - (r > T ) d(T ' 



If we introduce the difference which stands here on the right- 

 hand side into the expression (6), it divides into two members, 

 the first of which, containing F(r, r), becomes zero by summing 

 all the quantities of electricity e and e', owing to the uniform distri- 

 bution of positive and negative electricity. Hence there remains 



r 



P=frfT22ee' yW(T-<r,T)d(r (7) 



Jo Jo 



Eiemann now changes the order of the integrations by writing 



r 



P=^e ? fVo-f^TF(T-(r,T). ... (8) 



Jo Jo 



In this he puts r + a for t, by which he gets 



P = SSee'f Vo-P'^tF'Ot, t + o). 



Jo J-a- 



If in this expression the limits — a and t—ct of the second in- 

 tegral are to be replaced by the limits and t, to the integral 

 thus changed another must be added which goes frcm — a to 0, 

 and another from t— a to t subtracted from it. But Eiemann 

 shows subsequently that the members resulting from these two 



