630 Dr. J. E. Mills on 



II. Theoretical Derivation of the Fundamental Equation. 



The equation was deduced theoretically (see sixth paper 

 above cited) from certain assumptions which may be stated 

 as follows : — 



1. The total energy per se of a molecule must be the same 

 in the liquid as in the gaseous state^ the temperature being 

 the same. If at a given temperature a given weight o£ gas 

 represents more energy than the same weight of the substance 

 as a liquid, the extra energy of the gas must be energy of 

 position only (assuming no intramolecular change). 



Expressing the above belief in a different form, it may be 

 said that the energy necessary to change a liquid into a gas 

 must be spent solely in overcoming the external pressure 

 and in altering the distance apart of the molecules. (Unless 

 the molecule breaks apart also or nears the point of dis- 

 ruption.) Hence the internal heat of vaporization must be 

 spent solely in overcoming the molecular attraction as the 

 molecules move further apart. 



2. The molecular attraction between two molecules varies 

 inversely as the square of the distance apart of the 

 molecules. 



3. The molecular attraction does not vary with the 

 temperature. 



4. The molecules in the liquid and in the gaseous condition 

 are evenly distributed throughout the volume occupied by 

 them and the number of molecules does not change. 



5. The molecular attractive forces are definite in amount. 

 If this attraction is exerted upon another particle, the 

 amount of: the attraction remaining to be exerted upon other 

 particles is diminished by an exactly equivalent amount. 



The above assumptions are, none of them, purely gratuitous 

 assumptions made to fit the case in hand. The evidence in 

 their favour cannot be given and discussed fully in the 

 present paper, but a few comments are warranted by the 

 general importance of the assumptions. 



2 he first assumption followed from a study of the kinetic 

 theory of gases, the specific heat of gases, and the application 

 of the gas law, PV = RT, to solutions. If the gaseous 

 pressure was produced by the motion of the molecules and 

 a similar pressure (as osmotic pressure) was produced in 

 solution, it seemed reasonable to suppose that the osmotic 

 pressure was in some way due to an equal molecular motion. 

 The molecules of the dissolved substance could not have an 

 average kinetic energy of translational motion different from 

 the molecules of the solvent. Hence the conclusion that 



