Ponderomotive and Electromotive Forces. 271 



or, the sign of summation being employed, 



n=2H,J- (17 a) 



This changes equation (13) into 



ggg dx BH y dy ~d~E z dz _ dR x n „. 



d# dt + ~dx dt + ~dx dt dt > ' ^ } 



or, with the aid of the symbol of summation, 



*=|^£-^ w 



According to the fundamental laws of Biemann and "Weber, 

 the electrodynamic potential of two moved quantities of elec- 

 tricity e and e / J supposed concentrated in points, upon each 

 other is represented by the expressions 



2 r Z \dt dt)' 

 __k ee r /dr\ 2 



From these are obtained for the potential of a closed current 

 / upon a unit of electricity, consequently for the potential 

 function of the closed current, which according to these laws 

 may be denoted by Hi and U 2 , the expressions : — 



The latter expression can be transformed in the following 

 manner. From 



*--£[ 



J»=V/.«— iK^a 



is obtained 



Br 



9 1 — 



dt 



%{x-xj 



=^ x - x Ait~^r) 



= %(x-x / )-£-%(x-x r )-^; 



and from this we get, further, by differentiation with respect 

 to /, 



^yr'dr dV dx B^ 3_ -. _ ,xB^ 



6* 5? d*^ ~ ~ dt -ds' W Z ^ x } §T 



