Of all the surfaces which we have been describing, the sphere is the
only one which can enclose space; the others can only help to do so, in
combination with one another or with the sphere itself. Thus we have
seen that, in normal equilibrium, the cylindrical vesicle is closed at
either end by a portion of a sphere, and so on. Moreover the sphere is
not only the only one of our figures which can enclose a finite space;
it is also, of all possible figures, that which encloses the greatest
volume with the least area of surface; it is strictly and absolutely
the surface of minimal area, and it is therefore the form which will be
naturally assumed by a unicellular organism (just as by a raindrop),
when it is practically homogeneous and when, like Orbulina floating
in the ocean, its surroundings are likewise practically homogeneous
and symmetrical. It is only relatively speaking that all the rest are
surfaces _minimae areae_; they are so, that is to say, under the given
conditions, which involve various forms of pressure or restraint. Such
restraints are imposed, for instance, by the pipes or annuli with the
help of which we draw out our cylindrical or unduloid oil-globule or
soap-bubble; and in the case of the organic cell, similar restraints
are constantly supplied by solidification, partial or complete, local
or general, of the cell-wall.
Before we pass to biological illustrations of our surface-tension
figures, we have still another preliminary matter to deal with. We have
seen from our description of two of Plateau’s classical experiments,
that at some particular point one type of surface gives place to
another; and again, we know that, when we draw out our soap-bubble into
and then beyond a cylinder, there comes a certain definite point at
which our bubble breaks in two, and leaves us with two bubbles of which
each is a sphere, or a portion of a sphere. In short there are certain
definite limits to the _dimensions_ of our figures, within which limits
equilibrium is stable but at which it becomes unstable, and above which
it {226} breaks down. Moreover in our composite surfaces, when the
cylinder for instance is capped by two spherical cups or lenticular
discs, there is a well-defined ratio which regulates their respective
curvatures, and therefore their respective dimensions. These two
matters we may deal with together.
Public-domain text, read in full here on John Shaqi.
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