﻿Mechanism of Electrical Conduction, fi5 



scopical vision, we shall find the conduction-potential constant 

 from point to point throughout the mass of metal on either 

 side of the surface of separation; but as we approach that 

 surface from the left, the conduction-potential begins to 

 diminish, changing very rapidly by a finite amount as we pass 

 through the boundary. 



We now come to a theorem which is certainly true for our 

 model, and which seems to me as certainly true for any 

 mechanism which could be devised to represent the Peltier 

 effect ; but for the sake of avoiding questions of too con- 

 troversial a character, the statement may be made in this 

 conditional form : 



Theorem IV. 



In our model, the contact -difference of conduction-potent'^ 

 between two metals is equal to the coefficient of the Peltier effect. 

 For when a molecule at the junction is moving backwards 

 and forwards between places of different potentials, provided 

 no current flows through the junction, as much electrification 

 is carried from the lower to the higher potential as from the 

 higher to the lower, and on the whole there is no transforma- 

 tion of electric energy into heat, or vice versa. But when a 

 current flows across the junction from the metal of lower to 

 that of higher conduction-potential, the molecules at the 

 junction are persistently carrying more electrification from 

 the lower to the higher potential than they bring back with 

 them on their return, and thus on the whole the movements 

 of the molecules at the junction are systematically opposed 

 by electrostatic forces. It is evident from elementary con- 

 siderations that the quantity of electricity which has crossed 

 the junction, multiplied by the step of (conduction-) potential 

 up which it has passed, is the measure of the total work done 

 by the molecules against electrostatic forces, and is therefore 

 the measure of the heat absorbed. Similarly, when a current 

 has been flowing from the metal of higher to that of lower 

 conduction-potential, the quantity of electricity which has 

 crossed the junction, multiplied by the (negative) step of 

 conduction-potential, is the measure of the (negative) heat 

 absorbed; that is, numerically, of the heat given out. Hence, 

 in our model, the coefficient of the Peltier effect is equal to 

 the contact- difference of conduction-potential. 



Again, generally speaking, we may expect a difference of 

 conduction-potential between a hotter and a colder portion of 

 the same metal, owing to the increase of molecular distances 

 which rise of temperature produces ; and it is evident that (on 

 our model) the specif c heat of electricity for any metal is equal 

 to the rise of conduction-potential for one degree rise of tem- 

 perature. 



Phil. Mag. S. 5. Vol. 38. No. 230. July 1894. F 



