RECENT STATISTICAL THEORIES 743 



Before undertaking this I had better dispel any notion that the 

 "contact" or "Volta" potential-difference between a pair of metals 

 is the measure of the P. D. between their interiors for which we have 

 just been deriving theoretical expressions. It is in fact a measure of 

 something else, as one sees by examining an arrangement like that of 

 Figure 2, where A and B signify pieces of two metals which are in 

 contact at 1, and face one another across a gap between 2 and 3. 

 Consider an electron anywhere inside A, and estimate the potential- 

 barriers which it must cross in order to arrive at the point P^ just 

 outside of the boundary 2, and also those which it must cross in 

 order to pass through the metal B and reach the point Pz just outside 

 of the boundary 3. Recalling the symbols and the relations introduced 

 in the section on thermionics, one sees that there is a potential- 

 difference between P^ and Pz given by the expression 



{WaA - WaB) " {WiA " Wis) = Ba' B B. (137) 



This is the contact potential difference; and we see that if the new 

 statistics is correct, it is equal (at the absolute-zero limit) to the 

 difference between the values, for the two metals in question, of that 

 quantity b which appears in Richardson's equation and used to be 

 regarded as the surface work-function. By the old statistics, it differs 

 from (bA — bB) by the amount of the internal potential-difference 

 between the metals across the junction 1. Perhaps this difference 

 between the consequences of the two theories could be tested by 

 experiment. 



Theory of the Thermoelectric Phenomena 



We turn now to the problem of evaluating the rate of generation of 

 heat in a metal through which an electric current is flowing, and in 

 which (according to these theories) there is an intrinsic electric 

 potential-gradient due to a temperature-gradient, or to a gradient of 

 electron-concentration, or both together. The process leads to 

 formulae which can be tested by experiment, furnishing thus some 

 additional ways of finding out whether these ideas of the new statistics, 

 of the perturbed distribution-function and of the internal electric 

 field are justifiable. 



The expression for the rate of generation of heat per unit volume 

 in a conductor traversed by currents of electricity and heat flowing 

 along the axis of x and having current-densities / and W respectively, 

 is {JE — dW/dx). Here E stands for the electric field — not in general 

 for the applied electric field alone, but for the sum of this and the 

 hypothetical internal field. I denote the corresponding acceleration 



