ow almost able to see what the conic section has to do with a
soap-bubble. When a soap-bubble was blown between two rings, and the
pressure inside was varied, its outline went through a series of forms,
some of which are represented by the dotted lines in the lower part of
the figure, but in every case they could have been accurately drawn by a
pencil at the focus of a suitable conic section made to roll on a
straight line. I called one of the bubble forms, if you remember, by its
name, catenoid; this is produced when there is no pressure. The dotted
curve in the second figure B is this one; and to show that this catenary
can be so drawn, I shall roll upon a straight edge a board made into the
form of the corresponding section, which is called a parabola, and let
the chalk at its focus draw its curve upon the black board. There is the
curve, and it is as I said, exactly the curve that a chain makes when
hung by its two ends. Now that a chain is so hung you see that it
exactly lies over the chalk line.

All this is rather difficult to understand, but as these forms which a
soap-bubble takes afford a beautiful example of the most important
principle of continuity, I thought it would be a pity to pass it by. It
may be put in this way. A series of bubbles may be blown between a pair
of rings. If the pressures are different the curves must be different.
In blowing them the pressures slowly and _continuously_ change, and so
the curves cannot be altogether different in kind. Though they may be
different curves, they also must pass slowly and continuously one into
the other. We find the bubble curves can be drawn by rolling wheels made
in the shape of the conic sections on a straight line, and so the conic
sections, though distinct curves, must pass slowly and continuously one
into the other. This we saw was the case, because as the candle was
slowly tilted the curves did as a fact slowly and insensibly change from
one to the other. There was only one parabola, and that was formed when
the side of the cone was parallel to the plane of section, that is when
the falling grease just touched the edge of the candlestick; there is
only one bubble with no pressure, the catenoid, and this is drawn by
rolling the parabola. As the cone is gradually inclined more, so the
sections become at first long ellipses, which gradually become more and
more round until a circle is reached, after which they become more and
more narrow until a line is