Our full formula of equilibrium, or equation to an elastic surface, is _P_ = _p_{e}_ + (_T_/_R_ + _T′_/_R′_), where _P_ is the internal pressure, _p_{e}_ any extraneous pressure normal to the surface, _R_, _R′_ the radii of curvature at a point, and _T_, _T′_, the corresponding tensions, normal to one another, of the envelope. Now in any given form which we are seeking to account for, _R_, _R′_ are known quantities; but all the other factors of the equation are unknown and subject to enquiry. And somehow or other, by this formula, we must account for the form of any solitary cell whatsoever (provided always that it be not formed by successive stages of solidification), the cylindrical cell of Spirogyra, the ellipsoidal yeast-cell, or (as we shall see in another chapter) the shape of the egg of any bird. In using this formula hitherto, we have taken it in a simplified form, that is to say we have made several limiting assumptions. We have assumed that _P_ was simply the uniform hydrostatic pressure, equal in all directions, of a body of liquid; we have assumed that the tension _T_ was simply due to surface-tension in a homogeneous liquid film, and was therefore equal in all directions, so that _T_ = _T′_; and we have only dealt with surfaces, or parts of a surface, where extraneous pressure, _p_{n}_, was non-existent. Now in the case of a bird’s egg, the external pressure _p_{n}_, that is to say the pressure exercised by the walls of the oviduct, will be found to be a very important factor; but in the case of the yeast-cell or the Spirogyra, wholly immersed in water, no such external pressure comes into play. We are accordingly left, in such cases as these last, with two hypotheses, namely that the departure from a spherical form is due to inequalities in the internal pressure _P_, or else to inequalities in the tension _T_, that is to say to a difference between _T_ and _T′_. In other words, it is theoretically possible that the oval form of a yeast-cell is due to a greater internal pressure, a greater “tendency to grow,” in the direction of the longer axis of the ellipse, or alternatively, that with equal and symmetrical tendencies to growth there is associated a difference of external resistance in {243} respect of the tension of the cell-wall. Now the former hypothesis is not impossible; the protoplasm is far from being a perfect fluid; it is the seat of various internal forces, sometimes manifestly polar; and accordingly it is quite possible that the internal forces, osmotic and other, which lead to an increase of the content of the cell and are manifested in pressure outwardly directed upon its wall may be unsymmetrical, and such as to lead to a deformation of what would otherwise be a simple sphere. But while this hypothesis is not impossible, it is not very easy of acceptance. The protoplasm, though not a perfect fluid, has yet on the whole the properties of a fluid; within the small compass