708 Mr. K. J. A. Barnard on Direct Application of 



If r — resistance per unit length, the E.M.F. generated in 

 the element 



= rds . C 



r n' e' 2 

 m 



where ^N' = (dcrx H) . ds = number o£ lines of force cut by 

 the element in its motion. 



Similarly, on account of the negative electrons the E.M.F. 

 generated is 



m 

 undashed letters referring to negative electrons. 



Now — j is very small, while n and n f and also e and e r 



are of the same order of magnitude; hence the E.M.F. due to 

 the effect on the negative electrons is very much greater than 

 that due to the positive. (V may be numerically a multiple 

 of e and may not be the same multiple for all positive 

 electrons, but the argument will not be affected.) If, then, 

 we neglect the positive electrons we have the total E.M.F. 

 generated in the whole circuit 



me 2 7AT 



= dN, 



m 



where ^N = total number of lines of force cut by the whole 

 circuit in time dt. 



To take the collisions into account we proceed as in 

 J. J. Thomson, fc Corpuscular Theory/ p. 53. The average 



time between two collisions is ^, where X is the mean free 



path and V the mean velocity of an electron treated as a 

 gaseous molecule, and we have to replace dN by 



ldNX 

 2 dt V 



We thus get, finally, 



_ 1 r n e 2 X ^N 

 2^n~ V dt' 



This is the ordinary law of induction currents provided 



me 2 \ = 2m V. 



