72 THE ROYAL SOCIETY OF CANADA 
supposition, for the film is found to grow thinner at higher temperatures. 
If we have to admit that the equation 
applies whether the liquid is polymerized or not then = is not af- 
fected by a variation in the molecular weight due to ploymerization, 
or p and m do vary proportionally. If this be admitted, then it seems 
necessary to conclude that a polymerized molecule exerts only the same 
attraction that a simple one does. Thus we are led to the apparent 
contradiction that the attraction is not proportional to the mass. How 
is it possible to reconcile the apparent contradiction? 
In the first place let us consider the application of Avogadro’s 
rule to vapours and gases. Here it is evident, the temperature being 
the same, that a heavy substance exerts exactly the same pressure per 
molecule that is exerted per molecule by a substance of lower molecular 
weight. This is really the basis of the law, for when the statement of 
the law is analyzed it is seen to be equivalent to asserting that at equal 
temperatures the pressure exerted by a molecule is independent of its 
weight. Then when the pressures are equal the number of molecules 
must be equal. 
If then the tension in a liquid film is numerically equal to the pres- 
sure the substance would exert if it were a perfect gas we must conclude 
that the tension per molecule in a liquid film is independent of the mole- 
cular weight of the molecule if the molecular weight is in part due to 
polymerization. I can see no escape from this conclusion. It remains 
to show that the conclusion is not necessarily inconsistent with mole- 
cular mechanics. 
If we apply to molecules the laws of Newton we must conclude 
that molecules proceed in straight lines unless acted on by some de- 
flecting force. If then at any instant a molecule describe a curved path 
of radius of curvature r we may represent the deflecting force by f. 
Since the molecule of mass m and velocity u moves in a curve of radius 7, 
the deflecting force is a centripetal force and its instantaneous value 
m u? 
may be represented by .- =f. If we represent different mole- 

= 
cules by numerical subscripts we shall have 

