e
indeed, say 8000 miles across, you cannot tell a small piece of it from
a true plane. Level water is part of such a surface, and you know that
still water in a basin appears perfectly flat, though in a very large
lake or the sea you can see that it is curved. We have seen that in
large bubbles the pressure is little and the curvature is little, while
in small bubbles the pressure is great and the curvature is great. The
pressure and the curvature rise and fall together. We have now learnt
the lesson which the experiment of the two bubbles, one blown out by the
other, teaches us.

[Illustration: Fig. 23.]

[Illustration: Fig. 24.]

A ball or sphere is not the only form which you can give to a
soap-bubble. If you take a bubble between two rings, you can pull it
out until at last it has the shape of a round straight tube or cylinder
as it is called. We have spoken of the curvature of a ball or sphere;
now what is the curvature of a cylinder? Looked at sideways, the edge of
the wooden cylinder upon the table appears straight, _i. e._ not curved
at all; but looked at from above it appears round, and is seen to have a
definite curvature (Fig. 24). What then is the curvature of the surface
of a cylinder? We have seen that the pressure in a bubble depends upon
the curvature when they are spheres, and this is true whatever shape
they have. If, then, we find what sized sphere will produce the same
pressure upon the air inside that a cylinder does, then we shall know
that the curvature of the cylinder is the same as that of the sphere
which balances it. Now at each end of a short tube I shall blow an
ordinary bubble, but I shall pull the lower bubble by means of another
tube into the cylindrical form, and finally blow in more or less air
until the sides of the cylinder are perfectly straight. That is now done
(Fig. 25), and the pressure in the two bubbles must be exactly the same,
as there is a free passage of air between the two. On measuring them you
see that the sphere is exactly double the cylinder in diameter. But
this sphere has only half the curvature that a sphere half its diameter
would have. Therefore the cylinder, which we know has the same curvature
that the large sphere has, because the two balance, has only half the
curvature of a sphere of its own diameter, and the pressure in it is
only half that in a sphere of its own diameter.

[Illustration: Fig. 25.]

I must now make one more step in explaining this que