and Electronic Potential Energy. 



253 



6. Surface energy of a liquid in contact with its vapour. 



Here there is more difficulty in specifying an artificial 

 arrangement which will represent the average case of Nature. 

 A molecule of the surface layer of the vapour in a cubical 

 scheme has five nearest neighbours amongst the vapour 

 molecules and one nearest amongst the surface molecules of 

 liquid, but there are many surface molecules of the liquid 

 which are almost as near as the nearest, half of these re- 

 pelling and half attracting. But it seems to me that it is 

 right to assume that the electrical adjustments to minimum 

 potential energy which cause a molecule of vapour not at a 

 surface to attract its six immediate neighbours, w T ill likewise 

 cause it, when it is in a surface layer, to determine in all the 

 near molecules of the liquid surface such a total electric 

 moment as attracts it as if the sixth vapour molecule were 

 present alone in the place of the nearest liquid molecule. 

 In Nature the surface molecule of vapour is not stationary 

 in the average position, but it moves right up to the liquid 

 surface, establishing for itself there liquid conditions, it may 

 retreat, or its place may be taken by a molecule leaving the 

 liquid. Our assumption averages the values of the force 

 experienced during this motion, and supposes it to be equal 

 to the force between two vapour molecules whose distance 

 apart is the average distance of a surface molecule of vapour 

 from the liquid surface. On this supposition there is no 

 reason to expect any appreciable perturbation of the vapour 

 density except in the layer quite close to the liquid. It leads 

 to somewhat different results from those obtained in my 

 paper " The Principle of Dynamical Similarity in Molecular 

 Physics" (Boltzmann Festschrift, 1904, A. Earth, Leipzig) 

 from similar considerations. By suitably changing the 

 symbols in the last section with subscript 2 for vapour we 

 get for the tensional surface energy of a molecule in the 

 liquid 4<?V(1/B 1 3 — l/-[B 2 3 )/3, and for the compressional sur- 

 face energy or a molecule in the vapour 4^V(l/E 2 3 "-l/i-^2 3 )/3, 

 the total per unit surface being 



a = 4eV{ 1 /Ri 5 - (1/IV + lfRflliBf + l/E 2 5 }/3. . (5) 



It has been assumed here that es remains constant during 

 the change from liquid to vapour. It is possible that two 

 molecules approaching one another might alter one another's 

 electric moments by a process of induction or otherwise. 

 This is a very important matter in connexion with the elec- 

 trization of molecules. In section 10 we shall be investigating 

 a change of equal importance within each molecule due to 



I 



