﻿598 The van der Waals Formula. 



(1) For the vapour-pressure formula, Mills* has chosen 

 Biot's form 



logjt^A+Ba' + QS*, {a) 



involving five arbitrary constants. 



Applebey and Chapman prefer to use a form such as 

 van der Waals' equation (J. C. S. 1914, p. 734), 



(p+$)(v-b)=Bt, 



but treat b as a variable (p. 735). Later (p. 736) they find that 



-J— is a constant, and is to be chosen to suit the data (see 



method p. 737). 



This is equivalent to employing the three-constant formula 



fr+SH-S*)-*' • • •> 



where a, b, and j.-are adjustable constants and R is the gas 



constant, b is the value of the van der Waals' constant at the 

 critical temperature, and Bt the difference between the critical 

 temperature and the absolute temperature considered. 



The constants of the formulae [a) and (b) are chosen so as 

 to suit the same series of measurements — that is to say, so 

 that their graphs may agree as closely as possible with the 

 experimental graph. They are, therefore, the same relation 

 expressed in different forms. 



(2) By differentiating to obtain -£ } and substituting its 



value in the Clausius-Clapeyron relation, Mills gets 



L = t(v 2 - Vl ){B log a . «« + log£ . £'}, 



while Applebey and Chapman by an ingenious but mathe- 

 matically similar process (pp. 735-6) obtain 



These two formulae are derived from relations which 

 approximately represent the same experimental results, by 

 means of the same mathematical processes ; and should, 

 therefore (if the approximation is good), give concordant 

 values of L. 



* Journal of Physical Chemistry, 1902, 1904, &c. 



