﻿Attraction of Unlike Molecules. 189 



a later one on the Laws of Molecular Force (Phil. Mag. 

 March 1893, [5] vol. xxxv. p. 211), there is given the esta- 

 blishment of an expression for the surface-tension of a liquid 

 whose molecules attract one another with a force inversely as 

 the fourth power of the distance between them. If 3Am 2 /V 4 

 denotes the molecular attraction between two molecules of 

 mass m at distance r apart in a liquid of density p, then it is 

 shown that the surface-tension 



a<xAp 2 e, (1) 



where e is a length of the order of magnitude of the average 

 distance of a molecule from its nearest neighbours and pro- 

 portional to that distance ; for it represents the distance to be 

 left between two continuous distributions of matter on op- 

 posite sides of a plane in order that the attraction between 

 them may be the same as that between two molecular distri- 

 butions, the density and law of attraction in the continuous 

 and molecular distributions being the same. 



Suppose we have a gramme of a mixture of which a frac- 

 tion pi is a liquid of density pi and molecular mass m ly and 

 the fraction p 2 a liquid of density p 2 and molecular mass m 2 , 

 producing a liquid of density p ; if there is no shrinkage on 

 mixing the liquids 1 and 2, then 



l / o=p 1 /p 1 +ps/p 2 (2) 



Now in the mixture p 1 grammes of liquid 1 are distributed 

 through a volume 1/p, and by themselves form a medium of 

 density 



p x p, to be denoted by p/; 



similarly the other liquid 2 has in the mixture a density 



p 2 p, to be denoted by p/. 



Thus, then, if we draw a plane in the mixed liquid and seek 

 to represent the attraction between the molecules on the 

 opposite sides of the plane, the problem reduces itself to that 

 of finding the attraction between a liquid 1 of density p/ on 

 one side (say the left side) on the liquid 1 of density p/ on 

 the right side, and the similar attraction between the parts of 

 liquid 2 of density p/ on the left and right sides, and the 

 attraction of liquid 1 of density p/ on left on liquid 2 of 

 density p/ on right, and the attraction of liquid 2 of density 

 p/ on the left on liquid 1 of density p/ on the right. The 

 last two attractions are equal ; thus in place of the expression 

 kp 2 e in the surface-tension of a single liquid we shall have for 

 the mixture 



1 A 1 p' 1 2 ./ + 2 A 2 pV 2 +2 1 A 2 p 1 'p 2 ' 1 ^ ... (3) 



