experiment which any one can easily perform.

[Illustration: Fig. 50.]

Then again, if a wire frame is made in the shape of the edges of any of
the regular geometrical solids, very beautiful figures will be found
upon them after they have been dipped in soap-water. In the case of the
triangular prism these surfaces are all flat, and at the edges where
these planes meet one another there are always three meeting each other
at equal angles (Fig. 50). This, owing to the fact that the frame is
three-sided, is not surprising. After looking at this three-sided frame
with three films meeting down the central line, you might expect that
with a four-sided or square frame there would be four films meeting each
other in a line down the middle. But it is a curious thing that it does
not matter how irregular the frame may be, or how complicated a mass of
froth may be, there can never be more than three films meeting in an
edge, or more than four edges, or six films, meeting in a point.
Moreover the films and edges can only meet one another at equal angles.
If for a moment by any accident four films do meet in the same edge, or
if the angles are not exactly equal, then the form, whatever it may be,
is unstable; it cannot last, but the films slide over one another and
never rest until they have settled down into a position in which the
conditions of stability are fulfilled. This may be illustrated by a very
simple experiment which you can easily try at home, and which you can
now see projected upon the screen. There are two pieces of window-glass
about half an inch apart, which form the sides of a sort of box into
which some soap and water have been poured. On blowing through a pipe
which is immersed in the water, a great number of bubbles are formed
between the plates. If the bubbles are all large enough to reach across
from one plate to the other, you will at once see that there are nowhere
more than three films meeting one another, and where they meet the
angles are all equal. The curvature of the bubbles makes it difficult to
see at first that the angles really are all alike, but if you only look
at a very short piece close to where they meet, and so avoid being
bewildered by the curvature, you will see that what I have said is true.
You will also see, if you are quick, that when the bubbles are blown,
sometimes four for a moment do meet, but that then the films at once
slide over one another and settle down into their only possi