﻿of the Electron Theory of Matter. 603 



p is the pressure outside the potential filter. It is not the 

 vapour-pressure p of the electrons just outside the surface 

 of A. By the gas laws the relation between p and p is 



\ogp = logp ^g— , (17) 



where e is the charge on an electron. The N electrons are 

 then caused to expand adiabatically to the temperature 0\ 

 The expansion is continued isotherinally at 0' to the pressure 

 p', which is the equilibrium pressure of the electrons outside 

 of A'. They are then allowed to condense in A', and finally 

 to run down the connecting conductor to A. Since the 

 conductor varies in temperature from point to point, they 



will absorb heat in it to the amount N eJ odd, where a is the 

 specific heat of electricity. 



The equation \ —~ = gives us 



where w and w r are the internal latent heats of evaporation 

 of the electrons at 6 and 6' respectively, and y is the ratio of 

 their specific heats at constant pressure and at constant 

 volume. 



Substituting from (17), 



- to ' + R{lo gio -log / /-^ I (log^ + log^)}+«j'J^=0, 



or 



^P-^o g e + ^ + 0^d0 = A, . (19) 



where A is independent of 6. 



The exact relation between the equilibrium pressure of the 

 external electrons and the temperature is therefore 



p = A 1 6y- 1 e R* aJo * , (20) 



where A 1 does not involve 6. 



In the case of lead cr is extremely small, so that we may 

 put 



y ID 



p = K l d^e~ lie (21) 



In fact, in the case of all the commoner elements a is 



