84 THE ROYAL SOCIETY OF CANADA 
The formula (A) expresses purely geometrical relations and should 
hold for al] valuesof r where there is no appreciable change in the density 
of the liquid. A change in the liquid density would change the ratio 
n, / (a— /\a) by also changing the value of n,. If there should be an 
appreciably greater density in the superficial film than in the rest of 
the drop, then the average density of small drops will be greater than 
the average density of large drops where the surface film is a smaller 
proportion of the whole drop. Conversely,—if the function (A) satis- 
fies the dynamic conditions, then the variations in vapour density ac- 
companying variations, in the sizeof drops may be attributed exclusively 
to the influence of curvature; but if it fails for small drops, the fail- 
ure may be attributed to the varying influence of the density of the 
superficial film on the average density of the active portion of the drops. 
By a parity of reasoning we may conclude that the degree of departure 
of the geometric function from the requirements of the dynamic func- 
tion 1s a measure of the degree of increase in density in the superficial 
film as compared with the average density of the active portion of the 
liquid. 
We shall find that the foregoing considerations have an important 
bearing on the interpretation of the results of the analysis. The first 
impression is that the superficial density is just twice the normal; but 
a closer view of the matter does not permit of this sweeping conclusion, 
for the film may be of gradually changing density and 2¢ thick, in which 
ease all change in density observed would be merely change in the 
average density of the film itself. 
In accordance with the theory outlined above let it be assumed 
that the active portion of the vapour molecules lie on a spherical surface 
of average raidus r + /\r and that the active portion of the liquid mol- 
ecules acting normally through the same spherical surface of radius r 
occupy a spherical surface of average radius r — Ar. Those mole- 
cules outside of the average range of action, either of liquid or of vapour, 
will be in homogeneous equilibrium and will take no active part in the 
phase equilibrium, unless there should be some other source of dis- 
turbance than curvature. 
Poynting and Thomson’s equation, referred to above, showing the 
relation of the vapour-pressure, w' in equilibrium with a drop of radius 
r, and the vapour-pressure, ©, of the same vapour in equilibrium with 
a plane liquid surface, is 

