790 Mr. R. H. Fowler on the 



It appears, however, to be generally assumed * that under 

 the same conditions W, and therefore a, is independent also 

 of the temperature, and that a is therefore, theoretically at 

 least, a true constant. When one looks into this assumption 

 more closely it is easy to convince oneself that it has no 

 justification whatever, however great the dilution. The 

 ordinary kinetic theory of gases really demands an a which 

 is a function of the temperature whose variations for most 

 gases are appreciable at ordinary and even at fairly high 

 temperatures. It is the more unfortunate that this theoretical 

 result is so often overlooked, since the independence of a of 

 the temperature is not borne out by experiment. In point 

 of fact, both theory and experiment demand variations of a 

 with the temperature which are, qualitatively at any rate, in 

 full agreement with one another. 



As we shall see directly in calculating a, the error arises 

 from regarding the gas molecules in the interior of the gas 

 as uniformly distributed through its volume. But if there 

 are attractive forces sufficient to create a boundary field, 

 these attractive forces must also make it correspondingly 

 more probable that any pair of molecules will be close 

 together than far apart. This alters the calculated value of 

 W by an amount which may be called the clustering correction. 

 It appears on calculation that this clustering correction 

 depends on the temperature, and at ordinary temperatures is 

 in fact of the same order as the whole boundary field itself. 



§ (5). The dependence of a on the nature of the inter- 

 molecular forces. — We have stated above that a is independent 

 of the volume in the circumstances we contemplate here. 

 It seems necessary even now to insist that this independence 

 holds good whatever the nature of the intermolecular 

 forces, and is in no way dependent on obedience to any 

 special law of variation with distance such as for example 

 the inverse 4th power law. It is still frequently stated f 

 that if van der Waals' a is to be independent of the volume 

 the law of attraction must be the inverse 4th power. This 

 is quite untrue. As we shall see, the law of variation with 

 the distance affects and only affects the form of a as a 

 function of the temperature. 



In the case of spherically symmetrical attractions following 

 inverse 5th power laws generally we can go further, for we 

 find that the integrals that occur do not converge unless 

 s>4. The physical meaning of this failure is easily seen to 



* Jeans, loc. cit. 



f E. g., Lewis, ' A System of Physical Chemistry/ vol. i. p. 8 (1918), 

 and many recent papers in the Phil. Mag. 



