DO MOLECULES ATTRACT COHESIVELY INVERSELY 

 AS THE SQUARE OF THE DISTANCE? 



BY ALBERT p. MATHEWS 



In a very interesting and valuable recent paper in this 

 journal by Mills, 1 the conclusion was drawn that the cohesional 

 attraction of molecules varied inversely as the square of the 

 distance. Besides this conclusion, which was founded on the 

 interesting discovery that the internal latent heat of vaporiza- 

 tion divided by the difference of the cube roots of the densities 

 of the liquid and vapor was a constant, a most valuable part 

 of the paper was the reopening of the question whether the 

 field of molecular attraction is delimited by the surrounding 

 molecules, or whether it owes its small size to the very rapid 

 decrease of the attraction with the distance. This question 

 raised a century ago by Laplace, 2 was answered by him 

 in the latter sense without any convincing reason for his 

 conclusion, and has not been reopened since, the opinion 

 being almost universal that the shortness of the radius of 

 action is due to the attraction diminishing with the distance 

 at a rate far more rapid than the square; the fourth, fifth, 

 seventh and even higher powers having been suggested. 

 In thus reopening the question Mills has rendered a valuable 

 service. That his conclusion is correct, that the molecular 

 field is delimited by the surrounding molecules, is clearly 

 indicated by Einstein's 3 calculation of the radius of action, 

 showing that the radius is proportional to the distance be- 

 tween the molecular centers. The conclusion that the at- 

 traction is inversely as the square of the distance, however, 

 I believe to be erroneous for the reasons which will be pre- 

 sented in this paper. 



1 Mills: Jour. Phys. Chem., 15, 417 (1911). 



a Laplace: "Traite" de me"canique celeste," Supp. an Livre 10, p. 351. 



3 Einstein: Drude's Ann., 34, 165 (1911). 



