and the Properties of Liquids. 579 



previous papers that a. better agreemernVwith the facts is often 

 obtained by using 2C a instead of 2\A n i> the values C a being 

 deduced from the experimental d;ita. But the values of C a 

 thus found differ little from those of V^i- It appears there- 

 fore that 2 \/m 1 should strictly be written 2 y/otm^ where a 

 denotes a constant depending on the nature of the atom. A 

 better agreement of the law of attraction with the facts would 

 obviously now be obtained on deducing the average values of 

 a corresponding to each atom from all the available data. 

 But it is probable that a still better agreement would be 

 obtained by dealing with substances in groups, for it is very 

 probable that the values of a are constant for the atoms of 

 substances belonging to the same chemical group, but differ 

 from group to group, or generally that the properties of a run 

 parallel with the purely chemical properties of the substances. 



The fifth power of z in the law might perhaps in some cases 

 be replaced by some other power giving a better agreement 

 with the facts. But the application of the law to the facts 

 shows that the modified powers of z would differ very little 

 from the fifth. 



The form of the arbitrary function in the law very probablv 

 also depends somewhat on the nature of the substances under 

 consideration. Since the law of corresponding states follows 



. T z 



if the function is one of the ratios ™- and — , and is the same 



for all substances *, a deviation from the law would indicate 

 a change in the form of the arbitrary function. It will very 

 probably be found when sufficient reliable data for comparison 

 are available, that the substances which have a very low critical 

 temperature do not fit in very well with the other substances 

 in respect to the law of corresponding states. 



A more general expression for the law of attraction between 

 two molecules is therefore 



Ml £) • 



T Z\ (Sy/ttTpQ' 



r?5 



where a, 7, and ty are quantities which depend to a certain 

 extent on the nature of the substance under consideration, 

 but which as a rule differ very little from unity. The 

 quantities a, 7, and i/r are probably each the same for each 

 group of substances possessing similar chemical properties, 

 and otherwise are intimately connected with the chemical 

 constitution of substances. 



It should be observed that when a good agreement of the 



* Phil. Mag-. March 1911, pp. 336-341. 



