﻿2G6 Prof. 0. W. Richardson on the Electron 



Now suppose that there are two conductors of different 

 materials present in the enclosure. As in the previous case, 

 they are to be of considerable size, so that the electrons 

 which they emit are s?nall in number compared with those 

 which are retained. For the present we shall also suppose 

 that the two bodies are not in contact with each other. As 

 before, the electrons in the two conductors and in the sur- 

 rounding enclosure will ultimately reach a condition of 

 statistical equilibrium, and the conductors will acquire de- 

 finite potentials, which we may denote by Y x and V 2 . Let 

 W be the work done in taking an electron from the first to 

 the second conductor when equilibrium has been established. 

 Then 



n A _ e -w/ue 



^n 2 

 But this work is also equal to 



w 1 + e(V 2 -Y 1 )-w 2 , 



where the suffixes refer to the values of the different quan- 

 tities for the two conductors. Hence 



tv 1 — eY 1 — R0 log n x = iv 2 — e V 2 — R# log n 2 . 



Similarly, if there are r conductors, 



w-l — eVi — R0 \ogn 1 = w 2 — eV 2 — R0 log n 2 

 = =w ?— e Y r — R# log n r . 



Thus the final state of equilibrium is characterized by the 

 invariance of w — eV— R# log n. This holds both for the 

 internal and the external electrons, since w = for the latter. 

 The steady difference of potential Y TO — V ? between any 

 two conductors m and q is evidently 



V w - Y g = - { w m - w q + R6> log Hi } . 



So far we have supposed all the bodies to be separate from 

 each other, but the results are equally true if any number of 

 them are in contact. To prove this it is necessary to consider 

 the conditions which determine the state of equilibrium of 

 the system more fully than we have done. Disregarding 

 the electrons present in the surrounding space, which may 

 be done here on account of the smallness of the external 



