connected with its Surface Tension. 153 
‘The Influence of the Curvature of Surface of a Inqud on its 
| Surface Tension in Connexion with the Radius of the Sphere 
of Action of a Molecule. 
Since the surface tension of a liquid is due to the existence 
of molecular forces we should expect that it should depend on the 
curvature of the liquid surface. But the effect of curvature of 
surface on the surface tension becomes appreciable only when the 
radius of curvature becomes comparable with the radius of the 
sphere of action of a molecule. The latter quantity may be 
defined as the distance that two molecules in a liquid must be 
separated in order that the energy expended in overcoming their 
attraction on one another during the process is approximately 
equal to that expended in separating them an infinite distance 
from one another. 
Consider a sphere of liquid in the centre of which is a tiny 
spherical air bubble whose diameter is equal to the radius of the 
sphere of action of a molecule. Suppose the air bubble increased 
slightly in size by forcing an additional quantity of air into it. Now 
it will be easily seen that during the increase of the liquid surface 
in contact with the bubble the molecules in and near the surface 
do not get out of each other's range of molecular action for an 
increase of surface ds to such an extent as if the surface were 
plane. The amount of work done per unit increase of surface 
is therefore less than in the case of a plane surface, and the 
surface tension therefore decreases with increase of the curvature 
of the surface when it is concave with respect to a point outside 
the liquid. 
In a similar way it can be shown that if the diameter of a 
sphere of liquid is equal to the radius of the sphere of action 
of a molecule, less energy would be expended in producing an 
increase of surface area ds than if the surface were plane. The 
surface tension will therefore also decrease with increase of 
curvature of the surface when it is convex. It will be observed 
that these results should also hold if a liquid is incompressible 
and no transition layer is formed. 
Properties of Plane Inqud Films. 
It can be easily shown that the average external work done 
im evaporating by a reversible process a film of liquid of constant 
mass, and expanding the vapour till its density is equal to a given 
density, increases with a decrease of the thickness of the film. 
Thus let W, denote the external work done in one case. Next 
let the process of evaporation be carried out in a different way. 
Thus let the area of the film first be considerably increased by 
stretching it out, and let w, denote the work done against the 
