462 The Theory of Aether and Electrons in the 



open circuit in which there is no conduction of heat or electricity 

 .(so that i and da/dx are zero). Integrating the equation 



= m a 2 clN 

 " 2eNdx 



.across the junction of the metals, we have 



Discontinuity of potential at junction = -^ log - ; 



or since f ma 2 , which represents the average kinetic energy of an 

 electron, is by Drude's assumption equal to q/T, where gr denotes 

 a universal constant, we have 



2 q N 



Discontinuity of potential at junction = ^ - T log ~- 



O > J\ A 



This may be interpreted as the difference of potential con- 

 nected with the Peltier* effect at the junction of two metals ; 

 the product of the difference of potential and the current 

 measures the evolution of heat at the junction. The Peltier 

 discontinuity of potential is of the order of a thousandth of a 

 volt, and must be distinguished from Volta's contact-difference 

 of potential, which is generally much larger, and which, as it 

 presumably depends on the relation of the metals to the medium 

 in which they are immersed, is beyond the scope of the present 

 investigation. 



Eeturning to the general equations, we observe that the flux 

 of energy JFis parallel to the axis of x, and is given by the 

 equation 



W = \m HI ur i f(u, v, iv) du dv dw, 



where the integration is again extended over all possible values 

 of the components of velocity ; performing the integration, we 

 have 



or, substituting for E from the equation already found, 



TT _ ma 2 . 4ml da 



W = ^ - -rr Na z -7- 



e 871-2 dx 



* Cf. p. 264. 



