524 Albert P. Mathews 



"a" is van der Waals' constant. According to Sutherland 1 

 the latter expression indicates that the attraction of the mole- 

 cules is inversely as the fourth power; whereas Mills has 

 interpreted the former as meaning that it is inversely as the 

 square. 



To show how constant Mills' constant is, I have given, 

 in Table i, the results of the calculations by his formula of a 

 number of substances from Young's data. The figures re- 

 present ergs for gram molecular quantities. It will be seen 

 that the constancy is good for a considerable range of tem- 

 perature, but that in all cases there is a more or less pro- 

 nounced drop close to the critical temperature, and in some, 

 as in ether and ethyl acetate, there is a pretty steady fall 

 in the constant throughout. The fall near the critical tem- 

 perature might be ascribed to errors of observation, or calcula- 

 tion. There is no doubt, therefore, that for most substances 

 the expression (L -- E)/( 3 v / ^ 1 - 8 VD W ) closely approximates 

 a constant except near the critical temperature, as Mills has 

 pointed out. 



The conclusion that this relationship shows that the 

 molecules attract inversely as the square of the distance is, 

 I believe, sound, if the premise is correct. The premise, or 

 assumption, is that the internal latent heat of vaporization, 

 or Iy E, represents only the work done in separating the 

 molecules against their molecular cohesion. While Mills 1 

 states in a recent paper that not all the internal heat may be 

 used in doing this work, and attempts to show that this is 

 not incompatible with this conclusion, the conclusion never- 

 theless depends on the assumption that it is so used and that 

 there is no change in the internal energy of the molecules on 

 passing from the liquid to the vapor. It is clear that if this 

 premise be not true, then the conclusion does not follow. 



This premise I believe to be certainly erroneous. It 

 could only be true if the molecules remained of the same 



1 Mills: Phil. Mag., [6] 22, 97 (1911); 23, 499 (1912). 



