﻿Electron Theory of Metallic Conduction, 427 



with any definite velocity in the positive direction of the 

 #-axis than in the negative direction. By calculating the 

 transfer of electricity resulting from such a distribution 

 Lorentz is led to his well-known formula for the electrical 

 conductivity. 



On the other hand Drude, Riecke, Thomson, Wilson, and 

 others take rather a different view of the matter. According 

 to these authors the whole effect imparted by the electric 

 force on the electron during its free-path motion is oblite- 

 rated by the collision at the end of the path, so that each 

 free path is started with the velocity the electron would 

 have had throughout it, in the absence of any field of force : 

 the distribution of the initial velocities in the paths is thus 

 that specified by Maxwell's law given above. 



The object of the present paper is to show that these two 

 views, which at first sight appear to be rather contradictory, 

 are in reality probably the same, or at least that they are 

 consistent with one another. Although on a priori grounds 

 one would certainly prefer to accept Lorentz's view of the 

 situation, yet detailed consideration of the matter rather 

 inclines one towards the perhaps less general but certainly 

 more direct methods of Drude and Thomson. I will not, 

 however, presume to dogmatize on the relative merits of the 

 two forms of the theory. 



We shall consider the problem of conduction from the 

 point of view that the initial velocities at the beginning of 

 the free paths are distributed according to Maxwell's law, 

 each impact removing all effects imparted to the electron by 

 the electric field previous to it. The peculiarity of this 

 assumption is that it does not give the law of distribution of 

 the velocities of the electrons at any particular instant, but 

 rather the law of distribution of the initial velocities at the 

 beginning of the free paths being pursued at that instant, the 

 instant of beginning the free paths being, however, different 

 for the different electrons. The actual law for the distribu- 

 tion of the velocities at any particular instant can, however, 

 easily be deduced and in the following manner. 



Consider the electrons and their motion at any instant in 

 their free paths : the number of the electrons per unit volume 

 which started their current free paths with their velocity 

 components between (f, 97, f) and (£ + <•?£, y-'rdy, f+^f) is 

 given by Maxwell's law, and is thus equal to 



dK=T$x/Xe-<i**dPd v dZ .... (i.) 



V 7T° 



