reached. The corresponding bubble curves are
produced by a gradually increasing pressure, and, as the diagram shows,
these bubble curves are at first wavy (C), then they become straight
when a cylinder is formed (D), then they become wavy again (E and F),
and at last, when the cutting plane, _i. e._ the black line in the upper
figure, passes through the vertex of the cone the waves become a series
of semicircles, indicating the ordinary spherical soap-bubble. Now if
the cone is inclined ever so little more a new shape of section is seen
(G), and this being rolled, draws a curious curve with a loop in it; but
how this is so it would take too long to explain. It would also take too
long to trace the further positions of the cone, and to trace the
corresponding sections and bubble curves got by rolling them. Careful
inspection of the diagram may be sufficient to enable you to work out
for yourselves what will happen in all cases. I should explain that the
bubble surfaces are obtained by spinning the dotted lines about the
straight line in the lower part of Fig. 31 as an axis.

As you will soon find out if you try, you cannot make with a soap-bubble
a great length of any of these curves at one time, but you may get
pieces of any of them with no more apparatus than a few wire rings, a
pipe, and a little soap and water. You can even see the whole of one of
the loops of the dotted curve of the first figure (A), which is called a
nodoid, not a complete ring, for that is unstable, but a part of such a
ring. Take a piece of wire or a match, and fasten one end to a piece of
lead, so that it will stand upright in a dish of soap water, and project
half an inch or so. Hold with one hand a sheet of glass resting on the
match in middle, and blow a bubble in the water against the match. As
soon as it touches the glass plate, which should be wetted with the soap
solution, it will become a cylinder, which will meet the glass plate in
a true circle. Now very slowly incline the plate. The bubble will at
once work round to the lowest side, and try to pull itself away from the
match stick, and in doing so it will develop a loop of the nodoid, which
would be exactly true in form if the match or wire were slightly bent,
so as to meet both the glass and the surface of the soap water at a
right angle. I have described this in detail, because it is not
generally known that a complete loop of the nodoid can be made with a
soap-bubble.

[Illustrati