Origin of Molecular Attraction. 667 



energy must be largely a mutual affair, and its localization 

 in a molecule is only a convenience and not a necessity. 

 When we expand the collection o£ molecules to density D in 

 such a way that each always attracts its six nearest neigh- 

 bours through the electrization, the mutual potential energy 

 per molecule is proportional to — e 2 s 2 /(m/D) and may be 

 written — 27n?V/3(m/D) . If the total potential energy is 

 — 27n? 2 /3(m/D)^, then the internal or self-energy is 



_!£{(5Y_d,j (5) 



3 L\m/ m J 



Thus, then, for any density p we divide the potential energy 

 per molecule up into two parts, the mutual — 2ire 2 s 2 /S{m/p) 7 

 and the internal — 27re 2 {(p/m) l ' i — s 2 (p/m)}/?). At absolute 

 zero this scheme makes the internal energy nil, the whole 

 potential energy being mutual of amount — 27re 2 s 2 /3(m/p ). 

 The total electrostatic energy — 27r<? 2 ( / o/m) 1 '' 3 /3 does not appear 

 in the equation of the virial or in the corresponding charac- 

 teristic equation of gases, liquids, and solids, wherein the 

 mutual relations of molecules are discussed. In these charac- 

 teristic equations the mutual potential energy — 27re 2 s' 2 p/3m 

 appears by itself or in association with other expressions for 

 mutual potential energy during molecular collisions. The 

 discovery of Mills may be stated as the following principle: — 

 The total potential energy of a number of like molecules is the 

 same as if each caused its own domain to he uniformly electrized 

 with an electric moment proportional to the linear dimension of 

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

 general any molecule attracts its six immediate neighbours. 

 Once again we are face to face with the difficulty in a gas of 

 satisfying the condition that a molecule and its six immediate 

 neighbours may have their electric axes related as in figs. 2 

 and 3. We seem to be led to the conclusion that in the 

 molecules of a gas the electric axes change their direction 

 with sufficient rapidity and in such a manner that as nearly 

 as possible each molecule is attracting its six immediate 

 neighbours. Thus we can apply fig. 3 to a gas, each of the 

 four-sided regions corresponding with a six-faced region of 

 space forming the domain of a gaseous molecule, the molecule 

 being centrally situated. In this way then we trace cohesion 

 in a gas to electric polarity, avoiding the difficulty of re- 

 pulsions by the consideration that under a sort of mutual 

 induction between neighbours and in accordance with the 

 principle of minimum potential energy the polarities of 

 neighbour molecules are related to one another according to 

 the scheme of figs. 2 and 3. The same explanation applies 



