[GARVER] MOLECULAR ATTRACTION IN LIQUIDS 73 
Since from Maxwell’s law the average energy of translation per molecule 
is independent of the mass (at the same temperature) the numerators 
of the above fractions are equal on the average. Hence 
> (mu) = Z (rf) on the average. 
But the sum Z (m u?) is the total molecular energy, kinetic and potential 
of the molecules of the substance and 2 (rf) may be regarded as a quan- 
tity which is proportinal to the produce of a force and a displacement 
produced by the foree—a quantity which is also of the dimensions of 
energy. As in the case of gases the velocity « may be resolved into 
three rectangular components, or u?:= x? + y?+ 2. In a homo- 
geneous substance in equilibrium the three component -parts are equal 
or, x? = 4.u°, where x represents some given direction. 
This view of the action af attracting forces in a liquid enables us to 
regard them as being numerically equal but opposite in sign to the pres- 
sure the substance would exert if there were no attractions. Now if 
we are to consider the forces as independent of the mass of the molecule, 
then the average 7’s are also equal, for the numerators of the fractions 
and the forces having equal values the average volumes as represented 
by the 7’s must also be equal. 
Whilst the above analysis cannot be regarded asa proof of the law 
of action it is at least sufficient to show that the assumption of a force 
function not directly proportional to the mass of individual molecules 
is not necessarily in opposition to all rational explanation of the observed 
facts and deductions'. From the above outline it is evident that to 
separate two adjacent portions of a film a force proportional to the X(f) 
would have to be exerted, or the force required would be proportional 
to the number of molecules, in the cross-section of the film and thus 
fulfils the requirement that the tensile strength of a film is numerically 
equal to the intrinsic pressure of the liquid in the film. 
State College, Pa., 
> April 24, 1912. 

*An alternative hypothesis is that there is no polymerization in the film itself, 
only in the interior of the liquid. In that case the above reasoning would not be 
applicable, and the attraction might still be assumed to be proportional to the mass. 
Sec. III., 1912. 6 
