of the triangle of forces. Such lenses are often seen
formed by drops of fat floating on the surface of hot water, soup or
gravy. But when the surface-tension of A exceeds the sum of the tensions
of the surfaces of contact of B with air and with A, it is impossible to
construct the triangle of forces; so that equilibrium becomes
impossible. The edge of the drop is drawn out by the surface-tension of
A with a force greater than the sum of the tensions of the two surfaces
of the drop. The drop, therefore, spreads itself out, with great
velocity, over the surface of A till it covers an enormous area, and is
reduced to such extreme tenuity that it is not probable that it retains
the same properties of surface-tension which it has in a large mass.
Thus a drop of train oil will spread itself over the surface of the sea
till it shows the colours of thin plates. These rapidly descend in
Newton's scale and at last disappear, showing that the thickness of the
film is less than the tenth part of the length of a wave of light. But
even when thus attenuated, the film may be proved to be present, since
the surface-tension of the liquid is considerably less than that of pure
water. This may be shown by placing another drop of oil on the surface.
This drop will not spread out like the first drop, but will take the
form of a flat lens with a distinct circular edge, showing that the
surface-tension of what is still apparently pure water is now less than
the sum of the tensions of the surfaces separating oil from air and
water.

The spreading of drops on the surface of a liquid has formed the subject
of a very extensive series of experiments by Charles Tomlinson; van der
Mensbrugghe has also written a very complete memoir on this subject
(_Sur la tension superficielle des liquides_, Bruxelles, 1873).

When a solid body is in contact with two fluids, the surface of the
solid cannot alter its form, but the angle at which the surface of
contact of the two fluids meets the surface of the solid depends on the
values of the three surface-tensions. If a and b are the two fluids and
c the solid then the equilibrium of the tensions at the point O depends
only on that of thin components parallel to the surface, because the
surface-tensions normal to the surface are balanced by the resistance of
the solid. Hence if the angle ROQ (fig. 4) at which the surface of
contact OP meets the solid is denoted by [alpha],

T_(bc) - T_(ca) - T_(ab) cos[alpha