Do Molecules Attract, Etc. 521 



Mills 1 discovered the empirical relationship that the 

 quotient of the internal latent heat of vaporization divided 

 by the difference of the cube roots of the densities of the 

 liquid and vapor was a constant, except in the neighborhood 

 of the critical temperature. If I/ is the total latent heat, 

 and E is the part of it used in doing external work, then 

 IY - - E would be the part of the heat used in doing internal 

 work. He found that (L - - E)/(^ /3 - - D 1/3 ) = /*' '. He 

 assumed that this internal heat was all used in overcoming 

 molecular cohesion, and he ascribed the fall of the^constant 

 near the critical temperature to the inaccuracy of^the data. 

 He then reasoned that since for u/ /3 D^ /3 the expression 

 i/V| /3 -- i/V^ /3 might be substituted, the molecules must 

 attract each other inversely as the square of the distance; 

 since it is only on such a supposition that the difference in 

 potential energy of the molecules in the liquid and the vapor 

 can be given by an expression of this kind. The similarity 

 of his expression: I, -- E -= /(i/V; /3 -- i/V^ /3 ) to Helm- 

 hoi tz's formula for the heat given off by the contraction of 

 the sun seemed significant, the Helmholtz formula being 

 W == 3 / 5 M 2 K 2 (i/R-- i/CR). From this similarity Mills 

 reasoned that molecular attraction, like gravitational, must 

 follow the inverse square law. Since it is impossible that 

 molecules should attract each other cohesively according to 

 this law, if the cohesional attraction penetrated matter, he 

 concluded that Cohesion did not penetrate matter, but was 

 delimited by the surrounding molecules. 



There is, however, another relationship expressing the 

 latent heat consumed in overcoming molecular cohesion or 

 the internal pressure, which has been given by van der Waals 

 and is derived from his expression for cohesive pressure of 

 a/V 2 . This relationship is: Iv E = a(i/V, i/VJ, 2 where 



1 Mills: Jour. Phys. Chem., 15, 417 (1911); Comptes rendus, 153, 193 

 (1911); Phil. Mag., [6] 22, 84 (191;!); [6] 23, 484 (1912). 



2 This formula should, in my opinion, be written: L - E X = a (i/Vj- 

 i/Vy) where X represents heat used in any other internal work than the separa- 

 tion of the molecules. See van der Waals: "Condensation of Gases," Encyclo. 

 Britannica, xi edition. Also .Sutherland: Phil. Mag., [5] 22, 83 (1886). 



