He at of Mixture of Substances. 537 



It is necessary, therefore, to investigate first of all this 

 point. 



The molecules in a liquid or mixture of liquids are un- 

 doubtedly in rapid motion, and the distance between any 

 pair of molecules therefore continually changiug. The term 

 relative distribution of molecules has therefore at first sight 

 no definite meaning. But consider the work at successive 

 small intervals of time required to move a molecule in the 

 centre of a mass of liquid to the surface and then to infinity. 

 It is obvious that the average work approximates to some 

 constant as the number of intervals is increased. We may 

 therefore suppose, when we are concerned with the potential 

 energy of the molecules, that they are not in motion but fixed 

 in space in such a way that the work required to bring each 

 molecule to infinity is equal to the above defined average 

 work which corresponds to the molecule. This distribution in 

 space is obtained when it satisfies the following conditions : — 



(1) The forces on a molecule by the surrounding molecules 

 must neutralize one another. 



(This follows directly from the fact that the distribution is 

 to represent an average effect.) 



(2) The distribution must be such that keeping the density 

 of the matter constant the potential energy due to molecular 

 attraction is a minimum. 



(3) In the case of a mixture of substances it is further 

 necessary that conditions of symmetry are satisfied ; in other 

 words, the different molecules must be distributed as nearly 

 as possible evenly throughout the volume of the mixture. 



It will be easily seen that knowing the law of attraction 

 between molecules and given the density of a mixture of 

 substances and the numbers of different kinds of molecules 

 it contains per c.c, it should be possible to calculate the 

 relative distribution of the molecules subject to the above 

 conditions. But the calculations in the majority of cases 

 would be exceedingly difficult. 



There are a few cases of mixture in which the relative 

 distribution of the molecules, supposing no new molecules 

 are formed, is at once obtained. The simplest case is that in 

 which equal numbers of two different kinds of molecules, or 

 masses proportional to their gram-molecules, are mixed. The 

 distribution is in that case as follows. Suppose the mixture 

 cut into a large number of equal cubes by three systems of 

 parallel equidistant planes which are at right angles to one 

 another. And suppose that the molecules of the mixture 

 are situated at the various points of intersection of three 

 planes, one at each point, but in such a way that each ed^re 

 Phil. Mag. S. 6. Vol. 21. No. 124. April 1911, :' N 



