towards a Dynamical Theory of Solutions. 21 



neighbours of a supposed cubical arrangement. If the 

 arrangement were strictly and permanently cubical, then 

 the axial lines of force would run on in continuous straight, 

 lines from molecule to molecule, as perhaps they do in 

 crystals. But there would be no detectable free charge at a 

 surface, because as many axial lines are directed in one way 

 as in the opposite. In liquids it is better to imagine the 

 axial lines at any instant not running far as nearly straight 

 lines, but as closing their circuits by all sorts of interlaced 

 paths. From this point of view it appears that if a few 

 molecules of a liquid 1 are evenly distributed amongst many 

 of liquid 2, the cohesive force between the molecules of 

 liquid 1 cannot come into play, because the six immediate 

 neighbours of a molecule of 1 are always molecules of 2. But 

 experiments on the surface-tension of mixtures show that in 

 this case the cohesional forces between the molecules of 

 liquid 1 do come into operation. Hence we conclude that 

 the molecules of liquid 1 are not evenly distributed, at any 

 instant, amongst the molecules of 2, though they are evenly 

 distributed on the average for a large number of instants. 

 The most natural explanation of this fact is that the motion 

 of the molecules causes a molecule of 1 to have another 

 molecule of 1 for an immediate neighbour for a time which 

 is a function of the properties of the two sorts of molecules. 

 Thus we have a kinetic principle applying to all those 

 properties of mixtures which depend on the relations of a 

 molecule to its immediate neighbours, such as cohesion, 

 density, viscosity, and the like. Let U\ be the amount of 

 some property of unit mass of a pure liquid 1, u 2 that of 

 pure liquid 2, and let u ]2 be the amount for liquid 1 when a 

 molecule of 1 is in contact with molecules of 2, and u 2 \ the 

 amount for liquid 2 when a molecule of 2 is in contact with 

 molecules of 1. In general, u 12 and w 2 i are functions of 

 the concentrations, though they may become constants. 

 Consider a mixture containing n x molecules of 1 per unit 

 volume and n 2 of 2, /z 01 and ?i 02 being the numbers for the pure 

 substances. Then in the mixture a molecule of 1 may be 

 assumed to be in contact with another of 1 as an immediate 

 neighbour for the fraction ni/n 01 of its time : so being of 

 mass nil ^ carries the amount ??i 1 w 1 ?i 1 />j 01 of the property 

 into the mixture, and the n^ molecules contribute ?» 1 u 1 ?z 1 2 //?oi. 

 Thus for the whole amount pit of the property in unit volume 

 of the mixture we get 



pU = >«i?'i»i 2 /^01 + ^l1l20 n l v 12j n Q2 + " ? 2 ? '21, ;i 0l) + '^2 7 '2 r? 2 2 / "02- (1) 



q£356 



