Electron Theory of the Metallic Stair. 757 



§ 9. Ratio of Conductivities, 

 From equations (14) and (20) we get, as u = N, 



\ 1 v/2« 2 m 



^>" e 2 



(21) 



The ratio of conductivities is thus Found to be nearly 

 constant for all pure metals (law of Wiedemann and Franz) 

 and proportional to the absolute temperature (law of Lo.renz). 

 Also the numerical value of the constant is in good agree- 

 ment with experimental facts. We find for 18° C. 



-=-.6-9.10 lo e.m.u. 



K p 



The measurements of Jaeger and Diesselhorst * gave, as a 

 mean for eleven metals, 



- = 7-1.10 10 e.m.u. 



K 



The agreement is good if p is, as was predicted, nearly 

 equal to one. 



§ 10. Thermoelectric Phenomena. 



In the classical theory the thermoelectric phenomena are 

 referred to the variations of the energy of motion of the 

 electrons and the variations of their number with varying 

 temperature. We have assumed this number to be constant 

 in good conductors and thus without influence on their 

 thermoelectric properties. But our theory gives three other 

 origins for contributions to a specific heat of electricity or 

 the Thomson effect <r, from which the other thermoelectric 

 phenomena, thermoelectric power e ab and Peltier coefficient 

 Ylab-, of a couple of metals a and b are determined. By 

 Thomson's thermodynamic equations, 



_ n^ _ J T a a — a b ,—, 



- T - 1 T a±, 



<?ab 



in which, however, the lower limit of the integral is first 

 fixed by the theorem of Nernst or the quantum theory. 

 The three origins are : — 1st, the variations with the tempe- 

 rature of the kinetic energy of the electrons ; 2nd, the 

 variations of their potential energy by heating at constant 

 volume ; 3rd, the variations of their potential energy due to 



* W. Jaeger and IT. Diesselhorst, Abh. Phys. Techn. Reichens'alt, iii. 

 1>. 209 (1900). 



