200 Messrs. M. N. Shaha and S. N. Basu on Influence of 



proposed all relate to the influence of the cohesive forces ; 

 the part of the argument dealing with the finiteness of 

 molecular volumes is generally left untouched. 



But it has been found that the results of experiments 

 do not agree with the predictions of theory if we regard a 

 and b as absolute constants. Accordingly it has been pro- 

 posed to regard both a and b as functions of volume and 

 temperature *. 



But before proceeding to these considerations, it is neces- 

 sary to scrutinize whether the influence of finite molecular 

 volumes is properly represented by the term b. From 

 theoretical considerations, the conclusion has been reached 

 that this is not the case. The argument is as follows : 

 According to Boltzmann's theory, 



the entropy S = K log W + C, 



where K = Boltzmann's gas-constant, W = probability of the 

 state. Let us now calculate the probability that a number 

 .N" of molecules originally confined within the volume V 

 and possessing finite volumes, shall be contained in a volume 

 "V . Neglecting the influence of internal forces, the pro- 

 bability for the first molecule is =^r, for the second molecule 



V — 8 ° 



the probability is ^ — ^, where /3= 8 X volume of a single 



molecule, for when the first molecule is in position, the 



space enclosed by a concentric sphere of double the radius 



of the molecule will not be available for the second molecule. 



The available space is therefore V — /3, whence the pro- 



V—R 

 bability is ^ -. Introducing similar considerations for the 



rest of the molecules, we have 



y y-ff y-2/3 V-N-l/3 



V o -V -/3-V -^ • ' • Vo-N^l/S -- (> 



We are, of course, neglecting those cases in which partial 

 overlapping of the regions occupied by two or more mole- 

 cules occurs ; for the number of such cases can at best be a 

 small fraction of the total number. Even cases of actual 

 association do not include these, for in that case, two discrete 

 molecules become merged into one, without their outer 

 surfaces being actually in contact. 



* Compare van der Waals, Proc. Amst. 1916 ; Van Laar, Proc. Amst. 

 toI. xvi. p. 44. 



