From the simple fact that the sphere is of all surfaces that whose
surface-area for a given volume is an absolute minimum, we have already
seen it to be plain that it is the one and only figure of equilibrium
which will be assumed under surface-tension by a drop or vesicle, when
no other disturbing factors are present. One of the most important of
these disturbing factors will be introduced, in the form of complicated
tensions and pressures, when one drop is in contact with another drop
and when a system of intermediate films or partition walls is developed
between them. {241} This subject we shall discuss later, in connection
with cell-aggregates or tissues, and we shall find that further
theoretical considerations are needed as a preliminary to any such
enquiry. Meanwhile let us consider a few cases of the forms of cells,
either solitary, or in such simple aggregates that their individual
form is little disturbed thereby.
Let us clearly understand that the cases we are about to consider
are those cases where the perfect symmetry of the sphere is replaced
by another symmetry, less complete, such as that of an ellipsoidal
or cylindrical cell. The cases of asymmetrical deformation or
displacement, such as is illustrated in the production of a bud or
the development of a lateral branch, are much simpler. For here we
need only assume a slight and localised variation of surface-tension,
such as may be brought about in various ways through the heterogeneous
chemistry of the cell; to this point we shall return in our chapter on
Adsorption. But the diffused and graded asymmetry of the system, which
brings about for instance the ellipsoidal shape of a yeast-cell, is
another matter.
If the sphere be the one surface of complete symmetry and therefore
of independent equilibrium, it follows that in every cell which is
otherwise conformed there must be some definite force to cause its
departure from sphericity; and if this cause be the very simple and
obvious one of the resistance offered by a solidified envelope, such as
an egg-shell or firm cell-wall, we must still seek for the deforming
force which was in action to bring about the given shape, prior to the
assumption of rigidity. Such a cause may be either external to, or may
lie within, the cell itself. On the one hand it may be due to external
pressure or to some form of mechanical restraint: as it is in all our
experiments in which we submit our bubble to the partial restraint of
discs or rings or more complicated cages of wire; and on the other
hand it may be due to intrinsic causes, which must come under the head
either of differences of internal pressure, or of lack of homogeneity
or isotropy in the surface itself[296]. {242}
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