THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOUENAL OF SCIENCE. 



[SIXTH SEME 



NO V EMBER 1911. 



LXVII. The Distribution of the Molecules of a Gas in a Jfield 

 of Force, with Applications to tJie Theory of Electrons. B;j 

 Professor 0. W. Richardson, F.R.S.* 



§ 1. A CCORDING to the results of the classical dynamics, 

 J\. the concentration of the molecules of a perfect 

 gas in equilibrium in a field of force at the uniform tempe- 

 rature T is governed by the relation 



ni / tl2 = e --^r\ (1) 



where n ] and n 2 are the concentrations of the molecules at 

 points where the potential energies of a molecule are ivi 

 and ic 2 respectively, and R is the gas constant reckoned for 

 one molecule. According to the quantum theories, equa- 

 tion (1) merely expresses a limit which a more general law 

 approaches when the temperature becomes sufficiently high. 

 If this position is correct, the discovery of the general law 

 of which equation (1) is an asymptotic limit becomes a 

 matter of great importance in a number of branches of 

 theoretical physics. 



In considering this question it is necessary to adopt 

 some definite form of quantum theory. In a recent paper 

 W. H. Keesom f has found that the heat-energy U of 

 a gram-molecule of a perfect gas at constant pressure and 



* Communicated by the Author. 



t Comm. Pliys. Lab. Leiden, Supplement No. 30 to Nos. 133-144 

 (Leiden, 1913). 



Phil. Mag. S. 6. Vol. 2S. No. 167, JSTov. 1914. 2 T 



