﻿of the Electron Theory of Matter. 609 



each characterized by constant values v 1 (o x r 1 . . . v p co p r p . 

 Then if v co t are the values of the corresponding variables 

 just outside the conductor, we have 



v o _ ir _ "l _ . __*V___ _ n ^98 ci\ 



where n is the total number of electrons which can become 

 free which are present in the system. In general it will 

 only be possible to regard o> as having a constant value over 

 a region of infinitesimal volume, so that 



V Q - K- ^~ — - (28b) 



g-oWR* ~ ^ - e -»' R9 dT " X e -"f B *dr. ' ' 



where the integral is taken throughout the entire volume of 

 the system. If we regard co as a fixed constant, 



v = n/§e-< w - w J' R6 dT (28 c) 



If we consider a system containing more than one body in 

 a state of equilibrium, the steady (contact) differences of 

 potential will be given by equations of the type 



e(V m -Y p ) = a) 0m — ©op, .... (29) 



where &>o»* denotes the potential energy of an electron just 

 outside the mih body. 



The next step is to calculate the absorption of heat when 

 electrons are allowed to evaporate from a conductor. Con- 

 sider the conductor to be surrounded by an insulating^ 

 boundary such that the volume of the space between the 

 conductor and the boundary is v. If the boundary is dis- 

 placed so that the volume increases by dv, work pdv will be 

 done by the equilibrium pressure, p, of the atmosphere of 

 electrons. The increment d$ in the entropy of the system 

 will be 



dS=^(dU+pdv), (30) 



Where U = n(fR0+J), (31> 



J =§ a >e-<*fx°dTl§e-»WdT, . . (32> 



and p= vliO (33) 



n is the total number of electrons in the system which can 

 become free, and the integrals in J are extended throughout 

 the system. Since n is constant it follows that when the 

 Phil. Mag. 8. 6. Vol. 23. No. 13G. April 1912. 2 S 



