﻿Theory of Contact Electromotive Force. 273 



temperature, if P x Pi' P 2 and P 2 ' are the pressures o£ the free 

 electrons iuside A A' B and B', we find that 



showing that this expression or its equivalent HO log — is 

 the true value of the cooling effect at the junction. Wl 



The Legitimacy of Applying the Gas Equation. 



Objection to the results of the foregoing discussion may 

 be urged on the score of the propriety of applying the 

 equation of a perfect gns pv = NR6 to the electrons. At 

 any rate the legitimacy of the application is not obvious 

 without further consideration. It might be thought, for 

 instance, that the pressure arising from the mutual repulsion 

 of the electrons would seriously modify the simple equation, 

 and that corrections would have to be introduced somewhat 

 after the manner of Van der Waals's treatment of a real gas. 

 It will be noticed, however, that the equation pv=U0 has 

 only been applied to the external electrons, and the concen- 

 tration of these is alwaj^s exceedingly small at moderate 

 temperatures. Now the correction for the work done by the 

 mutual repulsion of the electrons depends upon the square of 

 the concentration, and thus vanishes, in comparison with the 

 external work, in the limit when the concentration is small. 

 On the other hand, the size of the electrons is very much 

 less than that of a molecule, so that the correction for the 

 finite size of the particles will be infinitesimal. It seems, 

 therefore, that at small concentrations a collection of electrons 

 will exhibit a closer dynamical approximation to the ideal 

 gas than will any real gas under comparable conditions. 



The Thomson Effect. 



The expression for Lord Kelvin's specific heat of electricity 

 may be deduced by means of a thermodynamic cycle, similar 

 to that already considered, but not quite so complicated. It 

 is now necessary to consider only two conductors, A and A', 

 of the same material but with different temperatures, 6 and 

 6'. They are joined by a thin conductor of the same 

 material, down which there is, of course, a constant stream 

 of heat. Let the potential outside A be Y x and that outside 

 A x Vi, and let eVY be >eV!. As before we surround A by 

 a potential filter maintained at V/. The reversible cycle 

 consists in evaporating the electrons from A through the 

 potential filter, bringing them by reversible processes to the 



