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BELL SYSTEM TECHNICAL JOURNAL 



together, then between the interiors of the metals across the weld 

 there must be a potential-difference of 4.2 voltSj^" potassium being 

 negative. This figure is calculated by the formula (135); the classical 

 formula gives a value considerably lower, about 0.04 volt. This 

 contrast is characteristic. Both the new and the old statistics associate 

 an internal or intrinsic potential-difiference with a difTerence in electron- 

 concentration, and vice versa; but the amount of the P. D. associated 

 with a given pair of concentrations is by no means the same by the 

 two theories; and in actual cases, the new statistics gives much the 

 larger amount. 



Though it is not actually possible to measure the potential in the 

 interior of a metal, there are phenomena which indicate that between 



Fig. 2. 



two metals touching one another, or between two parts of a metal 

 maintained at different temperatures, there is a difference of potential. 

 These are the thermoelectric phenomena— Peltier effect, Thomson 

 effect, thermal electromotive force. The internal potential-gradient 

 reveals itself through the fact that when an electric current is sent 

 through the region where it exists, the rate of generation of heat 

 departs from that which is calculated by Joule's law. We must 

 therefore apply the statistics — this will be the last application which 

 I shall consider — to the problem of evaluating the transport and the 

 generation of heat in an electron-gas, in which the distribution- 

 function is perturbed by an electric field and simultaneously by either 

 of the two other influences — varying temperature, varying concen- 

 tration of electrons — which we have heretofore considered separately. 



2« Sommerfeld originally computed 5.7 volts, having put G = 1; the value 4.2 

 corresponds to G = 2. 



