Molecules of a Gas in a Field of Force. 635 



exerted by a given electromagnetic radiation has twice the 

 frequency or! that radiation ; and (5) that the velocity or! 

 the elastic vibrations is proportional to the square root of 

 the energy of the corresponding vibration. 



The last assumption should be a valid approximation at 

 reasonably high temperatures. Its validity at low tempe- 

 ratures might possibly be capable of experimental investi- 

 gation. The other hypotheses have been introduced by 

 different writers on the quantum theory in connexion with 

 its various applications. Some support for Keesom's con- 

 clusions has been obtained from the equation of state of 

 helium at very low temperatures and in some other directions. 

 I shall therefore take equations (2) to (4) as the basis of 

 the discussion which follows. It is to be remembered that 

 these equations involve all the assumptions which have just 

 been outlined. However, the same treatment could be 

 applied to any form of quantum theory } and, in all 

 probability, would lead to somewhat similar results. 



Consider a gas which is in equilibrium in a field of force 

 at a constant temperature T. Let the resultant force 

 acting on a molecule at any point be R ( = X, Y, Z). For 

 equilibrium, 



x = re &c -> w 



and the differences of the potential-function of R for any 

 two points satisfy the equation 



I*!— w 2 = - \ Xdx+Ydy+2dz = — | ^dp. 



(10) 



Since p can be expressed as a function of V and T, 

 equation (10) shows that p is a function of w and T only, 

 and the results will be independent of the geometrical 

 distribution of the field of force. 

 From equation (3) we sec that 



whence, from (9) or (10) and (4), 



= U..-^fu-^mT(| + jV^)} 



o->; 



2 X - 



