EQUATION AND THE NATURE OF COHESION. 5 



phatic, etc. These various values are also quite unexplained. They 

 help us not at all in understanding the real nature of cohesion. 

 But the real point at issue between van Laar and myself is not 

 whether a is additive or not, for I had already shown that it 

 was additive before the publication of his' work. The question is 

 as to the real value of a. Van Laar computes a by applying a 

 correction to the ordinary method of computing from van der 

 Waals' equation, which has been solved on the basis of the con- 

 stancy of a and b. The values of a he secures by this method 

 agree with mine in only a few instances and in the more complex 

 substances. In general they are 10 — L 20 °/ lower than the values 

 computed by the methods 1 have found. They differ from my values 

 particularly in the simpler substances where for example in hydrogen 

 his value is about 150 °/ lower than the value I assigned to a 

 of hydrogen. They differ from my values in such a way that if van 

 Laar is right then the law correlating cohesion with the valences 

 and molecular weight, the law 1 have announced, cannot be true. 

 And it follows, also, that if my values of a are correct, then 

 his empirical rule, even with the secondary assumptions he has 

 made, can no longer be applied. Van Laar' s work and mine are 

 entirely incompatible. The whole question at issue between us is, 

 therefore, the real value of a in all these different substances. 

 I have sought, therefore, to determine this constant accurately. 



I have found several different methods of computing a some 

 of which are quite independent of van der Waals' equation. These 

 methods give at least an approximate determination of the constant. 

 I shall present them in a moment. They show indubitably, in my 

 opinion, that the law I have announced is a true law, and that 

 the values of a computed by the method of van Laar are in 

 error in nearly all cases by from 10 — 30 °/ and in some cases 

 by 100 °/ . Only exceptionally do they happen to be approximately 

 in harmony with the values computed from the latent heat of vapori- 

 zation, the latent heat of expansion, from the surface tension, or 

 in other ways. Before discussing these methods in detail, however, 

 I -wish to answer briefly a few of the criticisms van Laar has 

 made of my work 1 ). 



!) In a foot note on page 1229 of his paper van Laai; gives the impression that the 

 law correlating cohesion, or rather the value of a 'of van der Waals' equation, with 

 the number of valences in the molecule, hail also been suggested by Walden and Swinne. 

 He says „Walden and Swinne, Zeit. f. phys. Chem., Si'. 289(1913) cursorily mention the 

 partial additivity of the specific molecular cohesion, that is of a —like 



Mathews — seek connection between the values of ,, and the sum of the effective valencies." 



