﻿2()4 Prof. 0. W. Richardson on the .Electron 



with that of a molecule of a gas at the temperature of the 

 metal. By an application of the principles of the kinetic 

 theory of gases it follows that the same statements are true 

 of the free electrons inside the metal at the same temperature. 

 Finally, the existence of the work w has been put on a firm 

 basis by the discovery of the corresponding heating and 

 cooling effects when electrons pass into and out of a metal. 



Several of the calculations which follow have been given 

 by the writer in a course of lectures on the electron theory 

 of matter, in the past few years. It seems desirable to 

 publish them apart as the results which have been obtained 

 by other investigators in this subject are not in complete 

 accordance, and a discussion of the differences sheds some 

 light on the nature of the phenomena concerned. The 

 strength of the present method lies in the fact that it is 

 completely independent of the idea of free paths, and of the 

 assumptions about the nature of collisions which play a 

 prominent part in most forms of the electronic theory of 

 conductors. 



We shall suppose that all the free electrons are alike and 

 negatively charged in order to simplify the calculations ; 

 although the method is equally applicable to the case in 

 which different kinds of electrons, both positive and negative, 

 are considered to be present. The view that there are several 

 kinds of free electrons to be reckoned with can hardly be 

 considered to have had much success so far in reducing the 

 apparently rather considerable inconsistencies of the electron 

 theory of conduction. In what follows very considerable 

 use will be made of the theorem that in any system in equi- 

 librium at a constant temperature 0, if n-i is the concentration 

 of the electrons at a point A and r> 2 that at a point B then 



-1 — g-W/Efl 



"l 



where W is the work done in taking an electron from A to 

 B and Ris the gas constant in the equation pv = YL0, reckoned 

 for a single electron. This theorem * has been proved by 

 writers on the kinetic theory of matter with a degree of 

 generality which covers all the conditions contemplated in 

 the electron theory of conductors. 



We shall suppose each metal to be characterized by the 

 possession of a number n of free electrons per unit volume. 

 The value of n is different for different metals, and for a 

 given metal it is a function of the temperature 6 only. In 



* Cf. Jeans, ' Dynamical Theory of Gases/ p. 78. 



