﻿Theory of Contact Electromotive Force. 2Q7 



pressures, it is evident that the state of the system is com- 

 pletely determined by the n varhibles w-i w 2 . . . w n , the n 

 variables n x n 2 ... n„, and n — 1 o£ the variables V x V 2 ... V„, 

 one o£ which is arbitrary, together with the temperature 6. 

 Now the n — 1 equations of the type 



v:> 



— eV m — R# log n m — w p — eY p — TLd log 



are not the only equations connecting the 3n—l variables. 

 We have seen that the w's are functions of the n's and 0, so 

 that there are n equations of the type w p =f p (n P 6). In 

 virtue of the equilibrium between the negative electrons and 

 the positive remainder inside each conductor there are also 

 n equations of the type n p — ¥ p (6). There are thus 3n 

 variables and ?>n — 1 equations, so that when is given all 

 the n's and io's and the differences Y m — V q are determined. 

 This is true independently of the relative position of the 

 different conductors, and includes physical and electrical 

 contact as a particular case. It is clear that 



£ (. ^»i ) 



measures a true intrinsic difference of potential (contact 

 electromotive force) between the conductors m and p. 



The values of the electrical conductivity and some other 

 considerations indicate that the number n of free electrons 

 in unit volume is of the same order of magnitude for all the 



metallic conductors, and the term R#loo-~^- is found to lead 



to comparatively small electromotive forces of the order of 

 magnitude of those required to account for the Peltier effect. 

 So far no method has been devised for measurino; the values 

 of the w 9 8 except at high temperatures, and the relation 

 between any given w and the temperature is a matter of 

 much uncertainty, so it is rather risky to argue from the 

 values of the iv's at high temperatures to the values of these 

 functions at ordinary temperatures. Broadly speaking, how- 

 ever, there is no doubt that the more electropositive metals 

 have smaller values of w, and the differences which have 

 actually been observed are of the order of magnitude which 

 corresponds to the Volta effect. The fact that negative 

 electrons are emitted at much lower temperatures from the 

 alkali metals than from their more electronegative brethren 

 strongly supports this view, since the concentration of the 

 free electrons is much the same in all cases. It seems to 



T2 



