Kinetic Theory of Gases. 789 



The existing discrepancies in S and a are qualitatively such 

 as should be properly accountable for by such an extension 

 of the theory; to this point I hope to return in a later 

 paper. 



Elementary calculations of van der Waals' a. 



§ (3). My immediate object in the rest of this paper is to 

 present two simple proofs of the exact formula for B, and so 

 for van der WaaJs' a. Keesom has calculated B in terms of 

 the intermolecular field by a somewhat elaborate method 

 based on Boltzmann's expression for the entropy, a method 

 which can be used when the molecules are not spherically 

 symmetrical. But Keesom's own work shows that molecules 

 with spherical symmetry give the best representation of 

 experimental facts for the simplest (monatomic) gases. 

 Such molecular models are therefore of the first importance, 

 and for such it is possible to calculate B directly by very 

 simple arguments — (1) By a direct calculation of the 

 boundary field, measured by W, the work to be done in 

 bringing a molecule from the interior to the boundary of the 

 gas ; or, (2) By a calculation of the Virial of Clausius. 



Method (1) has moreover this advantage over all other 

 methods, that it enables adequate account to be taken of 

 surface effects, which is not possible, or at least far less 

 simple, by the entropy and virial methods. In calculating 

 B all the terms in pv of order l/t> 2 are of course to be 

 omitted. 



§(4). Hie meaning of a. — The so-called constant a of 

 van der Waals' or Dieterici's equation of state can be 

 specified in various ways. The most satisfactory physical 

 meaning can be attached to it, by first recognizing * that 

 intermolecular attractions must result in the production of a 

 permanent field of force near any boundary of a gas, and 

 then connecting a to the work that must be done against 

 this boundary field in bringing one molecule from the 

 interior to the actual boundary of the gas. At sufficiently 

 great dilutions this work W must obviously be proportional 

 to the molecular density v, and it is easily proved that t 



a = N 2 W/^, (5) 



where N is the total number of molecules in the body of gas 

 considered. Thus a will be independent of the volume. 



* Jeans, loc. cit. p. 159. 

 t Jeans, loc. cit. 



