brium at O for the
corresponding tensions R, P and Q is that the angle ROP shall be the
supplement of abc, POQ of bca, and, therefore, QOR of cab. Thus the
angles at which the surfaces of separation meet are the same at all
parts of the line of concourse of the three fluids. When three films of
the same liquid meet, their tensions are equal, and, therefore, they
make angles of 120 deg. with each other. The froth of soap-suds or
beaten-up eggs consists of a multitude of small films which meet each
other at angles of 120 deg.

If four fluids, a, b, c, d, meet in a point O, and if a tetrahedron ABCD
is formed so that its edge AB represents the tension of the surface of
contact of the liquids a and b, BC that of b and c, and so on; then if
we place this tetrahedron so that the face ABC is normal to the tangent
at O to the line of concourse of the fluids abc, and turn it so that the
edge AB is normal to the tangent plane at O to the surface of contact of
the fluids a and b, then the other three faces of the tetrahedron will
be normal to the tangents at O to the other three lines of concourse of
the liquids, and the other five edges of the tetrahedron will be normal
to the tangent planes at O to the other five surfaces of contact.

If six films of the same liquid meet in a point the corresponding
tetrahedron is a regular tetrahedron, and each film, where it meets the
others, has an angle whose cosine is -1/3. Hence if we take two nets of
wire with hexagonal meshes, and place one on the other so that the point
of concourse of three hexagons of one net coincides with the middle of a
hexagon of the other, and if we then, after dipping them in Plateau's
liquid, place them horizontally, and gently raise the upper one, we
shall develop a system of plane laminae arranged as the walls and floors
of the cells are arranged in a honeycomb. We must not, however, raise
the upper net too much, or the system of films will become unstable.

When a drop of one liquid, B, is placed on the surface of another, A,
the phenomena which take place depend on the relative magnitude of the
three surface-tensions corresponding to the surface between A and air,
between B and air, and between A and B. If no one of these tensions is
greater than the sum of the other two, the drop will assume the form of
a lens, the angles which the upper and lower surfaces of the lens make
with the free surface of A and with each other being equal to the
external angles