[GARVER] POLYMERIZATION OF LIQUID SUBSTANCES 97 
of molecules per unit mass is different in the two phases, liquid and 
R : are 
vapour, and p — T = PF RT then it must be true that any variation 
m m : 
in the numerical value of m, the molecular weight, merely changes 
the density p in the same proportion. This peculiarity in turn becomes 
explicable and consistent with the experimental facts if we assume the 
applicability to both liquids and gases of Maxwell’s law of distribution 
of molecular energies. This is, that 
9 
2 
CRE NS 
ym, UW, = FM, Wy, = FM; Wy = 
or, that the translational energy of the molecule is independent of the 
mass of the molecule and of the phase of the substance, but is propor- 
tional to the absolute temperature. An interesting experimental 
verification of Maxwell’ s law is given by Philip Blackman! who uses 
it to determine the relative molecular weights of dissolved substances. 
If Maxwell’s law holds, and it seems necessary to assume its truth 
in order to understand the above mentioned characteristics, then when 
two or more molecules coalesce to form one there is a change in the 
total volume with a corresponding change in the density but no change 
(if the temperature be kept constant) in the average energy of transla- 
tion per molecule, while there is a change in the aggregate molecular 
kinetic energy, 2 4 m wu? because the total number of molecules has changed. 
The effect of the change in the number of molecules by polymeriza- 
tion during an isothermal process involving an increase in the density 
would, with a given volume of a gaseous substances, be to diminish 
the outwardly directed pressure per unit area to something less than 
would have been found with the original number of molecules. Or, we 
should infer that the external pressure necessary to compress a gas or 
vapour would increase more slowly when there is polymerization than 
‘when there is no polymerization, but molecular attractions only. 
For suppose polymerization in a vapour to take place at a certain 
definite minimum molecular volume which we will assume is a function 
of the temperature; then any decrease in the aggregate vloume at that 
temperature must necessarily bring about a decrease in the number of 
molecules instead of an increase in pressure, for the pressure could not 
be increased without diminishing the average molecular volume of the 
vapour which we have supposed to have reached a definite minimum. 
This is exactly what we observe in the so-called saturated vapours— 
there is a definite maximum pressure and minimum volume correspond- 
ing to each temperature. Hence at this particular temperature the 

! Jour. of Phys. Chem. 15, 866 (1911). 

