252 Mr. W. Sutherland on Molecular 



consists of evaporation into the vacuum, but for the moment 

 we may neglect the effects of this. The main part of the 

 adjustment consists in a changed arrangement of the mole- 

 cules in the surface layer, involving a change of density 

 which is often small compared with the density because of 

 the small compressibility of liquids and solids. To a first 

 approximation we may say that a molecule in the surface 

 layer has only 5/6 of the potential energy of a molecule in 

 the body. If then we regard the potential energy of the 

 whole mass as being due to compression brought about by 

 the attractive forces between neighbours, then we must say 

 that each molecule on the surface has superposed on this 

 compressional energy a tensional supply which is 1/6 of the 

 potential energy of a molecule in the body. So the surface 

 energy per molecule is 4<?V/3R 3 = 4n£ 2 s 2 /3, and the surface 

 energy per unit surface often denoted by a is 4^V/3R 5 . 

 This will apply to a liquid in contact with its vapour whose 

 density is small enough to be neglected. The case in which 

 t l ie ell'ect of the vapour becomes appreciable can be treated 

 as a special one of the following. 



5. Surface energy at the contact of two substances. 



Here the attraction between unlike molecules enters. Let 

 the one substance be called 1, and have quantities assigned 

 to it by the subscript 1, the other substance being 2. Then 

 the average attraction between a molecule of 1 and a neigh- 

 bouring molecule of 2 is 4£ 1 s l £ 2 .? 2 / 1 R 2 4 , where iR 2 has still to 

 be defined. It is the average distance between the surface 

 layer of molecules of 1 and the surface layer of molecules 

 of 2. Thus the representative cubical arrangement of six 

 molecules of 1 round a central molecule in the body of 1 is 

 to be replaced for a central molecule in the surface layer by 

 five molecules of 1 in cubical order round it, and one mole- 

 cule of 2 at distance iR 2 in the sixth direction. So the 

 surface energy of a molecule in the surface of 1 is 4(<? ] 2 s 1 2 /R 1 3 



— e ] s 1 e 2 Sf/iR 2 & )/^i an d for a molecule in the surface of 2 it is 

 4(<? 2 2 s 2 2 /R 2 3 — eiSie 2 s 2 l\ R 2 3 . Per unit surface the energies are 

 4(£ 1 V/Ri 3 -*iW 2 /iR2 3 )/3Ri 2 and 4(> 2 V/R 2 3 



— e x s l e 2 s 2 \~ [ R 2 z )\ , d'R 2 2 , so for the total surface energy or tension 

 a we have 



3*/4 = *! V/V - e lSl e 2 s 2 ( 1/Ri 2 + 1/R 2 2 )/ 1 R 2 3 + £ 2 V/R 2 5 . (4) 



The conditions of statical equilibrium are not provided by our 

 definition of iR 2 and placing of molecules in the sixth direction. 

 An adjustment takes place, whose effects are neglected. 



