88 THE ROYAL SOCIETY OF CANADA 
be true, then the ratio, ¢/p = n,/n, is simply the ratio of the number 
of molecules acting normally through unit area in one direction. Now 
comparing the two equations (F) and (G) we are forced to conclude 
that if p is the average density in the film, 2 € must be its cross-section. 
If on the other hand € is the cross-section then the density in the film 
is twice the usual density of the liquid. This latter supposition can 
hardly be reconciled with the close agreement, down to almost molec- 
ular range, of the geometric function with the dynamic function which 
differ fom each other, in the case of water, only three per cent for drops 
as small as 10° em. and in no case do they differ to exceed ten per cent 
for values of r greater than 2 €. In any event the thickness of the super- 
ficial film lies between € and 2 € as the limiting values. 
The thickness may be shown in another way as follows: In case of a 
liquid whose vapour-pressure is negligibly small, let us suppose that the 
molecular attractions are just sufficient to neutralize the pressure which 
the molecules would exert if there were no molecular attractions. That 
is, the molecular attractions in a liquid will be assumed to be numeri- 
rally equal, but opposite in sign, to the pressure the substance would 
exert if it were a perfect gas at the same temperature and density. As- 
suming the temperature to be the same in the two cases, we have to 
compare the two effects—attraction and pressure—on equal areas with 
equal densities. 
By Boyle’s law w/¢ = K (say). With 6 = 1, © will equal K at 
the same ratio. Now if + is the attraction in a liquid film 1 em. long 
and 7 em. thick in a film of density p, then y/7 is the attraction per 
unit area for unit density, or -y/te = K by hypothesis. Therefore 
or solving for T 
the negative sign indicating merely that y and & are opposite in sign. 
The result shows that the above assumptions are justified if the thick- 
ness of the film is 26€. But from equation (G) this thickness indicates 
that the density in the film is the same as the ordinary density of the 
liquid, unless the polymerization in the film is greater than in the rest 
of the liquid. 
The slight forces displayed in the surface films of liquids may in 
consequence of their extreme thinness, give us a totally inadequate 
conception of the magnitude of the molecular forces concerned.  Al- 
