﻿Theory of Contact Electromotive Force. 275 



if P is the pressure of the internal free electrons at the point 

 whose temperature is 6 and Y x is the value of the same 

 quantity at a point whose temperature has a fixed value, 

 say di. Since P oc nO, the value of a may also be written 



This formula differs from those given by both Drude and 

 J. J. Thomson in the articles referred to. In Drude's case 

 the logarithmic term differs by a factor of 2, which arises in 

 the same way as the difference in the expression he finds for 

 the Peltier effect, There also seems to be a confusion of 

 sign in the expression for the heat generated by the internal 

 electric forces. When these changes are made his formula 

 reduces to that of J. J. Thomson. Both writers seem to 

 neglect the energy required to push the electrons against 

 their own pressure as they flow along the unequally heated 

 conductor. The formula which I have found may be deduced 

 after the manner of J. J. Thomson's calculations if this is 

 taken into account. For, consider the electrons present in 

 the region between two isothermal (and also equipotential) 

 surfaces whose temperatures are 6 and 6 + dQ respectively. 

 The internal (kinetic) energy of the electrons on entering 

 at the surface 6 is G v 0, and on leaving at the surface 0-\-d0 

 is Q v {0-ydO). The work done by the electrons at entrance 

 is (pv) q = H0, and on the electrons at leaving is 



The work done on the electrons by the electric forces within 

 the surfaces is 



E^(logP)^. 



Thus the net loss of energy by the metal comprised within 

 the surfaces, owing to the passage of this amount of electrons, 

 is 



so 



that 



|a + R-Rtf^(IogP)|^, 



in agreement with the previous result. 



The value of y lies between lrj and 1, so that the 

 minimum value of the first term on the right-hand side is 



