[GARVER] POLYMERIZATION OF LIQUID SUBSTANCES 99 
then we have in liquids exactly the same law of force—except as to 
sign—that holds for a perfect gas. Then in order to determine the 
proportion of the heat of vaporization that is due to the action of forces 
and that due to polymerization, it will merely be necessary to compare 
the experimentally found heat of vaporization with the heat equivalent 
of the work required to produce the same change in density in the given 
substance on the assumption that the force varies directly as the density. 
Hence if the preceding statements can be established as legitimately 
deducible from undoubted experimental facts, then it follows as a con- 
sequence that during an isothermal change in the density of any fluid 
substance accompanying a change in the volume, the heat given out or 
absorbed during such process will exceed the heat given out or absorbed 
by a perfect gas of the same molecular weight by an amount exactly equiva- 
lent to the polymerization or change in the number of molecules. This 
statement may be expressed mathematically by the equation 
2 
Hee pa, 
1 
where H represents the heat of polymerization, L the experimentally 
determined heat of vapourization, and the integral, f,? Pdv represents 
the work in calories required to produce isothermally the same change 
in density in a perfect gas of the same molecular weight and tempera- 
ture. For from Maxwell’s law the internal kinetic energy of a fluid is 
proportional to the absolute temperature and is independent of the 
volume provided the number of molecules remains constant. Hence also, 
the amount of heat given out or absorbed in an isothermal change in 
volume, or change in density, must be independent of whether the force 
be an external pressure or an internal attraction or both combined 
so long as there is no change in the number of molecules,—the only 
effect of internal attractions being to reduce the amount of external 
pressure required. Otherwise expressed, the work 
2 2 
W = [+ y) dv = [.P dv 
1 1 
if (p + y) = P, where P is a force equivalent to the externally ap- 
plied pressure p, and the internal attraction y. It has been shown 
that we may substitute an ideal gas pressure for the actual, combined, 
pressure and attraction because the pressure exerted by a molecule as a 
vapour is numerically equal to the attraction of a molecule of the liquid 
quite independently of whether a vapour molecule constitutes the whole, 
or only a part, of a liquid molecule. It is then immaterial whether we 
assume all the forces to be external pressures or internal attractions, 
