794 . Mr. R. H. Fowler on the 



The total work %(V) done by the attractions of all slabs when 

 a molecule is brought from positive infinity in the gas to 

 the distance z from the boundary of the gas, which may be 

 supposed to be the plane £ = 0*, is therefore given by the 

 equation 



Jo 



§ (7) . The effect of variation of v with f. — So far our 

 arguments are quite general, provided only that the molecular 

 density in the neighbourhood of a selected molecule is 

 adequately given by (5 a). This expression must fail at 

 sufficiently great concentrations, for the gas may for 

 example be so dense that no excess concentration in the 

 neighbourhood of any molecule is physically 'possible. It is 

 easily seen that the necessary correction can be introduced 

 in the usual way by taking account of the presence of one 

 molecule in affecting the chances for the presence of a 

 second etc., and that such corrections must result in terms 



of order 1/v, 1/v 2 , , compared to the leading terms in W. 



They are therefore irrelevant in the calculation of B from 

 equation (12). 



To proceed further with (12) we require the molecular 

 density v(f) as a function of/ the distance from the boundary. 

 It turns out that the effect of this variation is also of order 

 1/v and irrelevant for our present purposes. This may be 

 seen as follows. It is well known f that v(f) depends on/ 

 (a) because of the existence of the field of force of potential 

 %(°° )""%(/)> an d Q>) because the molecules are of finite 

 size. Jeans gives an expression for v(0) which takes, account 

 of the first-order correction for the size of the molecules 

 and of the complete effect of the field of force. It is easy 

 to extend the method so as to calculate not only v(0) but 

 also v(f) to the same order of accuracy. 



Ignoring details we may write this expression for v(/) in 

 the form 



v(f) = ve- 2j(x{x) - x(f)) {l + ve-W x{<a) - x(f)) <l>(f,j, a)}, (13) 



where the function <j> depends only on those variables which 

 are explicitly mentioned. If we combine together (12) and 



* The strict meaning of this statement is that when the centre of the 

 molecule lies in the plane z=0, the molecule is in contact with the 

 rigid boundary of the vessel (supposed plane). 



t Jeans, loo. cit. pp. 154-164. Jeans denotes our v(0) by v h . 



