﻿Electron Tlieory of Metallic Conduction. 175 



of Thomson and Wilson are consistent with Lorentz\s 

 general theory. It is perhaps necessary to add that Wilson 

 gives two independent deductions of his formula, one 

 following Jeans and the second following Thomson. It is 

 the second deduction with which I shall here concern myself, 

 the first, being more concerned with the optical side of the 

 question, will be discussed in the future communication. 



With each of the aforementioned authors we shall consider 

 that the phenomenon of electrical conduction in the metal 

 arises entirely from the motions of a swarm of electrons 

 moving about in a perfectly irregular manner in the free 

 space between the atoms of the metal, which are presumed 

 to be of such comparatively large mass that their energy 

 and motion may be neglected. The electrons and atoms 

 are presumed to be perfectly elastic spheres so that the 

 velocity of an electron is not altered by collision, the atom 

 being at rest. 



The general principles underlying the determination of 

 the conductivity (V) to ~be here reviewed, depend essen- 

 tially on the fact that the energy dissipated by a steady 

 current, driven by the electric force E, is presumed to be 

 the same as the energy acquired by the electrons on account 

 of the action on them of the electric force during their 

 otherwise free motion between the collisions, and which is 

 dissipated on the collision of the electron at the end of this 

 path. The rate of dissipation is known to be o\E 2 , and it 

 can be calculated by statistical considerations of the motions 

 of the electrons. 



We shall first make the calculation on the assumption 

 that a steady field of constant strength E is in action 

 parallel to a fixed direction. This is not precisely the 

 problem discussed by Thomson and Wilson, but the analysis 

 is much easier and has the additional advantage of bringing 

 out very clearly the correction which it is necessary to 

 introduce into the original analysis of these authors. The 

 extension to rapidly alternating fields will be given in a 

 subsequent paragraph. 



Analysis for steady fields. 



We choose a definite system of rectangular axes with the 

 ct'-axis parallel to the direction of the electric force. Referred 

 to these axes the velocity of the typical electron at time t 

 has components which we shall denote by (ft, V t , £), so that 

 the resultant velocity is r t where 



