﻿of the Electron Theory of Matter. 619 



volume) of the electrons in the atmosphere inside an en- 

 closure, bounded by any single material substance, and its 

 temperature, may be determined in the following manner. 

 Imagine a cylindrical box made of the material substance. 

 The sides and top of the box are covered with a layer of the 

 ideal transparent non-emitting substance, but the bottom 

 surface is exposed to the interior. A piston made of the 

 ideal transparent substance works up and down the cylinder 

 and is initially at the bottom. The enclosure then contains 

 asthereal radiation alone. Its walls are externally in thermal 

 and electrical contact with an indefinitely large mass of 

 conducting matter at the same temperature. As the piston 

 moves up the amount of sethereal radiation in the enclosure 

 remains constant, but the space below the piston becomes 

 filled with the electrons emitted by the substance. These 

 exert a pressure p on the piston. There is no work done by 

 the pressure arising from the radiation as the density of this 

 is always the same on both sides. By moving the piston up 

 and down, the electrons may be pumped out of and into the 

 material in a reversible manner. 



Let v be the volume below the bottom face of the piston- 

 head, n the number of electrons per unit volume in the same 

 space, e the charge on an electron, <£ the difference in the 

 energy of the system due to the escape of a single electron, 

 then the change in U, the energy of the system, produced 

 by a motion of the piston, is 



The corresponding increment of entropy is 



d&=Q{dU+pdv)=~{(p+n<l>)dv + vd(n<l>)}. 



Since S is a perfect differential when v and 6 are the 

 independent variables 



0^=p + n<j> + v~ v (n<l>)=p + nw, . . (50) 



where iv is the latent heat of evaporation reckoned for a 

 single electron, and since p = nl&0, 



(' IV 



n = Ae , (51) 



wl ere A is a constant, characteristic of the material but 

 independent of 6. 



Equation (51) expresses the relation between the equi- 

 librium concentration of the electrons in the atmosphere 



