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 equiôÙlibôÙrium 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 conôÙsiôÙdeôÙraôÙtions 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 equiôÙlibôÙrium, 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 itself33.
Our full formula of equiôÙlibôÙrium, or equation to an elastic surface, is P =ã₤ pÿ£¢ e ã₤+ã₤( Tã₤ãã₤R ã₤+ã₤ Tÿ£¢ãýã₤ãã₤Rÿ£¢ãý ), where P is the internal pressure, pÿ£¢ e any extraneous pressure normal to the surface, R , Rÿ£¢ãý the radii of curvature at a point, and T , Tÿ£¢ãý , the corôÙreôÙsponôÙding tensions, normal to one