Relationship between Molecular Cohesion 499 



Finally, if it is true that the surrounding molecules de- 

 limit the field of cohesion in any way whatever, and that 

 only six molecules really take part in this delimitation, we can 

 derive the value a/V 2 of van der Waals' at once and very 

 simply. 



Suppose that each molecule has a certain mass of cohes- 

 ion, M, and that two molecules attract each other directly 

 as the product of their cohesive masses and inversely as the 

 fourth power of the distance between their centers, then the 

 attraction between two molecules would be M 2 K/V /3 , where 

 v is the space at the disposal of a single molecule. Since 

 each molecule attracts only the one above, below and to each 

 side, the pressure per square centimeter of a double layer of 

 molecules will be M 2 K/V /3 multiplied by the number of mole- 

 cules in i sq. cm or i/z> 2/3 , making M 2 K/7; 2 . Since the at- 

 traction extends only a single molecular diameter, we may 

 multiply both numerator and denominator by N 2 , where N 

 is the number of molecules in the volume, V, and we obtain, 

 N 2 M 2 K/NV -= M 2 N 2 K/V 2 == a/V 2 . M 2 K has already been 

 shown to be 2.98 X io~ 37 (Mol. Wt. X Valences) 2/3 . 



We have, as yet, no proof that only the six surrounding 

 molecules are attracted, although Sutherland 1 has made a 

 similar supposition. But such may be the case nevertheless. 

 Einstein, in his calculation, computed that each molecule 

 could be considered as lying at the center of a cube and that 

 it attracted the 26 other molecules of the cube. Of course 

 the fact that the value a/V 2 may be so easily derived in this 

 way does not furnish any proof that the attraction is inversely 

 as the fourth power of the distance. But I know of no other 

 derivation of a/V 2 which involves so few, or less radical, 

 assumptions. 



The general conclusion of the paper is then, that cohesion, 



1 Sutherland : Phil. Mag., [6] 17, 667 (1909). "The total potential 

 energy of a number of like molecules is the same as if each caused its own domain 

 to be uniformly electrized with an electric moment proportional to the linear 

 dimensions of the domain, the direction of electrization being such that in general 

 any molecule attracts its six immediate neighbors." 



