Molecules of a Gas in a Field of Force. 611 



The last equation agrees with Keesom's formula for the 

 thermoelectric power at low temperatures. 



It is easily verified that the values (18), (19), (22), and 

 (24) satisfy the equations 



c>F P 12 . T B/Ti 2 \ 



— == _and,r 1 -^=T^ ir j 5 



given by Kelvin's thermodynamic theory, both when x is 

 large and when x is small. 



It will be noticed that these relations satisfy the condition 

 required in any case of reversible heat-production that the 

 rate of absorption or evolution of heat should approach the 

 value zero at the absolute zero of temperature more rapidly 

 than the heat capacity of the matter whose temperature is 

 affected approaches zero. Otherwise it would be possible 

 to maintain a finite quantity of matter at a temperature below 

 the absolute zero, a state of affairs which would involve a 

 contravention of the laws of thermodynamics. This con- 

 dition is satisfied in the present case because on the hypotheses 

 adopted the specific heats are proportional to T 3 , whilst the 

 Peltier effect varies as T 4 at low temperatures. 



§ 3. The Emission of Electrons from Hot Bodies. 



The formulae for the number of electrons emitted by hot 

 bodies furnished by the present theory differ in important 

 respects from the corresponding formulae calculated on the 

 basis of the ordinary dynamics. One might therefore expect 

 to find in these phenomena a satisfactory test of the validity 

 of the hypotheses under consideration. Unfortunately the 

 data are far from being as decisive as one could desire. 



If n 2 is the number of electrons per c.c. outside a metal 

 which are in equilibrium with it at temperature T, if v 2 is 

 the number emitted from unit area in unit time, and if we 

 neglect electron reflexion which will only affect the results 

 by a factor not very much different from unity, then 





This result involves the kinetic theory which is valid in the 

 present instance. The thermionic saturation-current per unit 

 area is therefore 



2 */lto/3e\i MR 2 _. acS + ft» 



by substituting from (16). However, an examination of the 

 probable value of some of the quantities entering shows that 



