the Electron Theory to Induction Currents. 709 



If 



S = cross-section of conductor, 



p = rS = the specific resistance, 



n 

 v = ^ = number of negative electrons per cub. cm., 



we g et v = 2»V/A P , 



the numerical result given by Thomson, i Corpuscular 

 Theory,' p. 54. 



The idea of relative motion naturally gives the same 

 expression for the E.M.F. when the circuit is fixed and the 

 field varying. But the force acting is no longer the electro- 

 magnetic force in the ordinary understanding of the term, 

 but an electric force. I will consequently show, next, that 

 the equation 



curl E = jr 



at 



leads to the same numerical result as before. 



If E is the electric force at any point of the conductor, the 

 acceleration of an electron along the conductor is 



— r E . ds, 

 m as 



and the E.M.F. generated in the element between collisions 

 r ne 2 



m 



and the total E.M.F. 



dt E . ds, 



- dt I E . ds 



m 

 r n i j 



- dt \\ curl E . dA 

 m 





dt \\ - . dA 



~'-Sr*'ij]|*-» 



r n e' 2 7 dN 



dt j* ' 



m dt 



The same result as for the case of the moving circuit. 



