[GARVER] POLYMERIZATION OF LIQUID SUBSTANCES 101 
the difference in behaviour between gases and vapours and accounts for 
the fact that less external work is required to produce a given increase 
in density in a vapour than in a gas, and that a larger quantity of heat 
is given off by the former than can be accounted for by the work done 
on the assumption that the number of molecules remains unchanged. 
Again, consideration based on the relation of potential to kinetic 
energy in such a molecular system must lead to a revision of the concep- 
tion of intrinsic or molecular pressure. When two or more molecules 
unite to form a single molecule there is no physical thing’ remaining 
that can be made to represent, or be interpreted as, a pressure. The 
pressure per molecule exerted by a vapour and the attraction per mole- 
cule in the liquid seem to be unaffected by the polymerization although 
the polymerization increases the density. So long as forces exist be- 
tween molecules pressure may be used to represent the force relation; 
but when two molecules unite to form one single molecule one-half the 
sum of the two energies in an isothermal change must leave the system 
as the molecular energy of heat. There remain, then, no forces to 
represent a pressure,—the molecular kinetic energy of the vanished 
molecule with its complement of potential energy having left the system 
as heat nothing remains but an increased density to represent the de- 
crease in the number of molecules. In a fluid system of discrete flying 
corpuscles there is nothing corresponding to a static pressure. If the 
molecules are close enough together to be held partially by the mole- 
cular forces the external pressure required is merely diminished; but 
when two molecules unite the internal tension or force acting between 
them disappears simultaneously with the distance as the molecular 
energy of heat. The hypothetical distance between molecules involv- 
ing, mathematically, an infinite force when the distance becomes van- 
ishingly small, simply does not exist when molecules unite because 
they then both possess the same centre of mass without leaving anything 
to be represented by the force function except the change in density 
and the heat that is dissipated when they unite. A careful considera- 
tion of the experimental evidence will show that the use of the pv 
function to represent the energy changes caused by the changes in the 
number of molecules due to polymerization is as impossible to interpret 
in terms of p v as the union of hydrogen and chlorine in terms of p v 
where there is no change in the volume of the constituents, since in the 
case of polymerization we do not know what aggregate amount of vol- 
ume change is introduced by the polymerization. In each case the 
energy takes the form of heat and leaves the system; hence all expres- 
sions of such energy changes in terms of changes in p and v must be 
more or less illusory. However, since energy in whatever way expressed 
must have the same dimensions in the fundamental units, p v may 
