and the Formation of L 'quid Films. 99 



an instructive example. Whatmough's results, plotted with 

 the concentration, are shown in curve I. (fig. 1). The curve 



FJcr. 1. 





7 8 — - Curves ImdUL^ 



6 -7 •%-*CuffV£2L 



Curve I. Surface Tension (dynes/cm.) with concentration (gm.-mol./litre). 

 „ II. „ ., „ ,, „ loprarith in of concentration. 



„ III. Surface Excess (o-rn. mol./sq. cm.) with concentration. 



is very approximately logarithmic, as is better seen in curve II,, 

 where the same results are plotted with the logarithms of 

 the concentrations. In acetic acid the molecular depression 

 o£ the freezing-point, throughout the range o£ concentration 

 included in the curves, is very approximately constant and 

 has the value 2° per gm.-mol. per litre. The factor i is thus 

 1*08, and consequently 



_ _1 dr _ _1__ dr 



a ~ i-08RT C dc l-08RT7nog e e* 



The second form of this equation shows that if the surface 

 tension vary linearly with the logarithm of the concentration, 

 the surface excess will be constant. Curve II. shows that 

 this must be very nearly the case in acetic acid. There is 

 perhaps a slight curvature in the direction which implies 

 that a increases a little with the concentration, as shown in 

 curve III., which represents its magnitudes at the different 

 concentrations as determined from the differences of the 



H2 



