ressions, and dividing the second member by S, we
obtain for the tension of the surface of contact of the two liquids
_ _
/ [epsilon]1 / [epsilon]2
T1.2 = | ([chi]1 - [chi]01) [rho]1 d[nu]1 + | ([chi]2 - [chi]02) [rho]2 d[nu]2. (10)
_/0 _/0

If this quantity is positive, the surface of contact will tend to
contract, and the liquids will remain distinct. If, however, it were
negative, the displacement of the liquids which tends to enlarge the
surface of contact would be aided by the molecular forces, so that the
liquids, if not kept separate by gravity, would at length become
thoroughly mixed. No instance, however, of a phenomenon of this kind
has been discovered, for those liquids which mix of themselves do so
by the process of diffusion, which is a molecular motion, and not by
the spontaneous puckering and replication of the bounding surface as
would be the case if T were negative.

It is probable, however, that there are many cases in which the
integral belonging to the less dense fluid is negative. If the denser
body be solid we can often demonstrate this; for the liquid tends to
spread itself over the surface of the solid, so as to increase the
area of the surface of contact, even although in so doing it is
obliged to increase the free surface in opposition to the
surface-tension. Thus water spreads itself out on a clean surface of
glass. This shows that
_
/ [epsilon]
| ([chi] - [chi]0) [rho] d[nu]
_/0

must be negative for water in contact with glass.

_On the Tension of Liquid Films._--The method already given for the
investigation of the surface-tension of a liquid, all whose dimensions
are sensible, fails in the case of a liquid film such as a soap-bubble.
In such a film it is possible that no part of the liquid may be so far
from the surface as to have the potential and density corresponding to
what we have called the interior of a liquid mass, and measurements of
the tension of the film when drawn out to different degrees of thinness
may possibly lead to an estimate of the range of the molecular forces,
or at least of the depth within a liquid mass, at which its properties
become sensibly uniform. We shall therefore indicate a method of
investigating the tension of such films.

Let S be the area of the film, M it