98 THE ROYAL SOCIETY OF CANADA 
pressure per unit area will remain constant although the aggregate 
volume may be steadily diminished because there is a corresponding 
decrease in the average molecular volume, either by supersaturation, 
(i.e. polymerization) or liquefaction. 
This view of the function performed by polymerization as a pre- 
liminary to change of phase from the vapour to the liquid furnishes a 
rational explanation of the experimentally observed rectilinear portion 
of an isothermal curve and eliminates two of the three values for the 
volume in the reflexed theoretical portion of a van der Waals’ isothermal. 
This cubic curve arises from the theoretical assumption that the lque- 
faction takes place in consequence of the action of molecular forces 
which are proportional to the square of the density. But from equation 
(A) for the surface-tension, if 7 is the thickness of the superficial layer, 
it is evident that the attraction in the film is proportional to the density 
and not to the square of the density, so that van der Waals’ assumption 
that the molecular attraction may be represented by a/v? cannot be 
maintained as in accordance with the laws of molecular attraction. 
If the force function be directly proportional to the density, and a poly- 
merized molecule occupies the same volume as a simple molecule, then 
both density and surface-tension are linear functions of the polymeriza- 
tion. If molecular volumes are limited to a minimum value then the 
only remaining way the density can be increased is by the union of 
molecules. But from Maxwell’s law a union of molecules implies that, 
when the temperature is constant, internal molecular energy must leave 
the system; and from Clausius’ virial, an equal amount of molecular 
potential energy must escape from the system with the molecular kinetic 
energy. If, then, it be found that the heat given out during the change 
of phase from vapour to liquid is in excess of the equivalent of the work 
done by all the forces, external or internal or both combined, we must 
conclude, if the process be isothermal, that a portion of the internal 
molecular energy has left the system as heat because the actual number 
of molecules has decreased. 
It is evident, then, that if we can determine experimentally the 
total heat given out during an isothermal process and can otherwise 
estimate how much of that heat is equivalent to the action of any forces 
concerned, then the excess of the heat over that which can be attributed 
to work done by forces, external, internal or both combined must be 
due to a decrease and consequent union of the molecules concerned, 
i.e., to polymerization. 
Theoretical Summary 
If the molecular forces are directly proportional to the density— 
and the evidence seems incontrovertibly to prove that such is the case— 
