M. B. Riemarm on Electrodynamics. 371 



the sums being extended over the entire masses of both con- 

 ductors. 



Since the motion for opposite electrical masses is opposite in 

 each particle of the conductor, the function Y(t, t 1 ) by derivation 

 with respect to t acquires the property of changing its sign with 

 e, and by derivation with respect to t' the property of changing 

 its sign with e 7 . Hence on the supposed distribution of the 

 electricities, if derivation with respect to t be designated by upper, 

 and derivation with respect to t 1 by lower accents, 2)2ee'F ( w n) (T,T) 

 distributed over all the electrical masses only becomes infinitely 

 small as compared with the sum extended over the electrical 

 masses of one kind when n and n l are both odd. 



Let it now be assumed that during the time occupied in the 

 transmission of the force from one conductor to the other the 

 electrical masses pass over a very small space, and let us con- 

 sider the action during a length of time compared with which 

 the time of transmission vanishes. In the expression for P, 



F K") 



can be replaced by 



r 

 F ( T - V -, t)-F(t, T) = - pF(<7— <7, T)d<7, 



since X 2 e dF(r, t) may be neglected. 

 There is thus obtained 



r 



P= r^rSSee' IF(t-<t, T)<&r; 



•Jo Jo 



or if the order of the integrations be inverted and r-f cr put 

 for t, 



vo •) - 



P = 22ee' d<r\ <?tF(t,t + «t) 



— cr 



h 



If the limits of the inner integral be changed to and t, at the 

 upper limit the expression 



%J o *J -<r 



will be thereby added, and at the lower limit the value of this 

 expression for £ = will be taken away. We have thus 



= CdrZlee' f 

 Jo «Jo 



ee' ) daWir, r + a) - H (t) + H (0). 



