536 Dr. R. D. Kleeman on the 



shown, however, that $ 2 must be a function of both z and T*, 

 and that it probably varies very little with T or z\. Since 

 the attraction between two molecules is equal to the product 

 of their powers of attraction the function 4> 2 must consist of 

 two factors of the same form, th;it is 



When the molecules are not of the same kind the attraction 

 would be given by the expression 



Although the form of the function </> 2 is not yet exactly 

 known, yet it will be of interest to deduce the general formulae 

 for the heat of mixture of substances. It will be found that 

 in special cases useful information can be obtained from 

 experimental data without an exact knowledge of the form 

 of <j) 2 being necessary. 



We are quite justified in using the above law of attraction, 

 as the distances of separation of the molecules in a mixture 

 are not of a smaller order than those of the molecules in a 

 pure liquid. When a new kind of molecule is formed by the 

 combination of two molecules, these are probably after com- 

 bination separated by a much smaller distance than the 

 average distance of separation of the molecules of the mixture, 

 but the above law of attraction probably holds down to dis- 

 tances of this magnitude. But other changes then happen, 

 thus the total kinetic energy is not the same after as before 

 combination. The heat of mixture might thus in some cases 

 be appropriately divided into two parts, one due to the 

 change of potential energy of the molecules that combine to 

 form new molecules, supposing the molecules to be in the 

 gaseous state at low pressure during the process, and the 

 other part due to the change in potential energy in rendering 

 into the gaseous state the molecules that combine to form 

 new molecules, and then forming a mixture of these molecules 

 and the remaining parts of the liquids. 



Relative Distribution of the Molecules in a Mixture. 



Im order to be able to calculate the change in the potential 

 energy of two quantities of matter on being mixed, we must 

 know the relative distribution of the molecules in the mixture. 



* PhiL Mag. Jan. 1911, pp. 91-94. 



f Phil. Mag. May ]910, pp. 795-798 ; Oct. 1910, pp. 6G7-670. 



