528 Mr. G. H. Livens on the Electron Theory 



direction by the vector product of v by H, reduced, however,, 

 by the usual radiation velocity constant c, if the Hertz- 

 Heaviside system of units is adopted. The statistical effect 

 of these forces on all the electrons comprising the current is 

 exactly the same as that of a general impressed electromotive 

 force in the same direction. Again, when the ends of a 

 metal bar are kept at different temperatures so that there is 

 no flow of heat along the bar, there will on the average be 

 no drift of the electrons from one end of the bar to the other^ 

 but the electrons which are travelling from the hot end to 

 the cold end possess a greater kinetic energy and greater 

 velocity on the average than those which are travelling in 

 the opposite direction. And since the force on an electron 

 travelling in a magnetic field tending to deflect it at right 

 angles to its direction of motion is proportional to its velocity, 

 the force tending to deflect the electrons travelling from the 

 hot end to the cold end will be greater than that tending to 

 deflect (in the opposite direction) those travelling from the 

 cold end to the hot end. There will thus, on the whole, be 

 a differential drift of the electrons in the direction in w Inch 

 the electrons moving from the hot end to the cold are 

 deflected by the magnetic field. 



If this explanation or its more detailed equivalent to be 

 given in the following pages were a complete representation 

 of the action of the magnetic field on the current, the various 

 effects would be of the same sign in all metals and would 

 always be proportional to the magnetic force, whereas neither 

 of these statements is rigorously true in all cases. In all 

 ferromagnetic metals it appears, for instance, that the effects 

 are proportional to the magnetization produced in the metal 

 rather than to the actual magnetic force. This and the 

 other discrepancies which have been found will be discussed 

 in their proper places in a future paragraph with the expla- 

 nations which have been suggested by them. 



The main object of the present paper is to provide a re- 

 discussion and generalization of the detailed analysis of the 

 explanation offered by Thomson and Drude and roughly 

 sketched above. The method to be followed is essentially 

 the same as that introduced by Lorentz but with the genera- 

 lization, which seems to be necessitated by the facts, that the 

 electrons and atoms act on one another like point centres of 

 force, the latter being of such comparatively large mass that 

 their motion and energy may be neglected. A detailed 

 discussion of the present theory for the case in which the 

 electrons and atoms are hard elastic spheres has been given 



