In a budding yeast-cell (Fig. [60]), we see a more definite and restricted change of surface tension. When a “bud” appears, whether with or without actual growth by osmosis or otherwise of the mass, it does so because at a certain part of the cell-surface the surface tension has more or less suddenly diminished, and the area of that portion expands accordingly; but in turn the surface tension of the expanded area will make itself felt, and the bud will be rounded off into a more or less spherical form.
The yeast-cell with its bud is a simple example of a principle which we shall find to be very important. Our whole treatment of cell-form in relation to surface-tension depends on the fact (which Errera was the first to point out, or to give clear expression to) that the incipient cell-wall retains with but little impairment the properties of a liquid film[281], and that the growing cell, in spite of the membrane by which it has already begun to be surrounded, behaves very much like a fluid drop. But even the ordinary yeast-cell shows, by its ovoid and non-spherical form, that it has acquired its shape under the influence of some force other than that uniform and symmetrical surface-tension which would be productive of a sphere; and this or any other asymmetrical form, once acquired, may be retained by virtue of the solidification and consequent rigidity of the membranous wall of the cell. Unless such rigidity ensue, it is plain that such a conformation as that of the cell with its attached bud could not be long retained, amidst the constantly varying conditions, as a figure of even partial equilibrium. But as a matter of fact, the cell in this case is not in equilibrium at all; it is in process of budding, and is slowly altering its shape by rounding off the bud. It is plain that over its surface the surface-energies are unequally distributed, owing to some heterogeneity of the substance; and to this matter we shall afterwards return. In like manner the developing egg {214} through all its successive phases of form is never in complete equilibrium; but is merely responding to constantly changing conditions, by phases of partial, transitory, unstable and conditional equilibrium.
It is obvious that there are innumerable solitary plant-cells, and unicellular organisms in general, which, like the yeast-cell, do not correspond to any of the simple forms that may be generated under the influence of simple and homogeneous surface-tension; and in many cases these forms, which we should expect to be unstable and transitory, have become fixed and stable by reason of the comparatively sudden or rapid solidification of the envelope. This is the case, for instance, in many of the more complicated forms of diatoms or of desmids, where we are dealing, in a less striking but even more curious way than in the budding yeast-cell, not with one simple act of formation, but with a complicated result of successive stages of localised growth, interrupted by phases of partial consolidation. The original cell has acquired or assumed a certain form, and then, under altering conditions and new distributions of energy, has thickened here or weakened there, and has grown out or tended (as it were) to branch, at particular points. We can often, or indeed generally, trace in each particular stage of growth or at each particular temporary growing point, the laws of surface tension manifesting themselves in what is for the time being a fluid surface; nay more, even in the adult and completed structure, we have little difficulty in tracing and recognising (for instance in the outline of such a desmid as Euastrum) the rounded lobes that have successively grown or flowed out from the original rounded and flattened cell. What we see in a many chambered foraminifer, such as Globigerina or Rotalia, is just the same thing, save that it is carried out in greater completeness and perfection. The little organism as a whole is not a figure of equilibrium or of minimal area; but each new bud or separate chamber is such a figure, conditioned by the forces of surface tension, and superposed upon the complex aggregate of similar bubbles after these latter have become consolidated one by one into a rigid system.
Let us now make some enquiry regarding the various forms {215} which, under the influence of surface tension, a surface can possibly assume. In doing so, we are obviously limited to conditions under which other forces are relatively unimportant, that is to say where the “surface energy” is a considerable fraction of the whole energy of the system; and this in general will be the case when we are dealing with portions of liquid so small that their dimensions come within what we have called the molecular range, or, more generally, in which the “specific surface” is large[282]: in other words it will be small or minute organisms, or the small cellular elements of larger organisms, whose forms will be governed by surface-tension; while the general forms of the larger organisms will be due to other and non-molecular forces. For instance, a large surface of water sets itself level because here gravity is predominant; but the surface of water in a narrow tube is manifestly curved, for the reason that we are here dealing with particles which are mutually within the range of each other’s molecular forces. The same is the case with the cell-surfaces and cell-partitions which we are presently to study, and the effect of gravity will be especially counteracted and concealed when, as in the case of protoplasm in a watery fluid, the object is immersed in a liquid of nearly its own specific gravity.
We have already learned, as a fundamental law of surface-tension phenomena, that a liquid film in equilibrium assumes a form which gives it a minimal area under the conditions to which it is subject. And these conditions include (1) the form of the boundary, if such exist, and (2) the pressure, if any, to which the film is subject; which pressure is closely related to the volume, of air or of liquid, which the film (if it be a closed one) may have to contain. In the simplest of cases, when we take up a soap-film on a plane wire ring, the film is exposed to equal atmospheric pressure on both sides, and it obviously has its minimal area in the form of a plane. So long as our wire ring lies in one plane (however irregular in outline), the film stretched across it will still be in a plane; but if we bend the ring so that it lies no longer in a plane, then our film will become curved into a surface which may be extremely complicated, but is still the smallest possible {216} surface which can be drawn continuously across the uneven boundary.
The question of pressure involves not only external pressures acting on the film, but also that which the film itself is capable of exerting. For we have seen that the film is always contracting to its smallest limits; and when the film is curved, this obviously leads to a pressure directed inwards,—perpendicular, that is to say, to the surface of the film. In the case of the soap-bubble, the uniform contraction of whose surface has led to its spherical form, this pressure is balanced by the pressure of the air within; and if an outlet be given for this air, then the bubble contracts with perceptible force until it stretches across the mouth of the tube, for instance the mouth of the pipe through which we have blown the bubble. A precisely similar pressure, directed inwards, is exercised by the surface layer of a drop of water or a globule of mercury, or by the surface pellicle on a portion or “drop” of protoplasm. Only we must always remember that in the soap-bubble, or the bubble which a glass-blower blows, there is a twofold pressure as compared with that which the surface-film exercises on the drop of liquid of which it is a part; for the bubble consists (unless it be so thin as to consist of a mere layer of molecules[283]) of a liquid layer, with a free surface within and another without, and each of these two surfaces exercises its own independent and coequal tension, and corresponding pressure[284].
If we stretch a tape upon a flat table, whatever be the tension of the tape it obviously exercises no pressure upon the table below. But if we stretch it over a curved surface, a cylinder for instance, it does exercise a downward pressure; and the more curved the surface the greater is this pressure, that is to say the greater is this share of the entire force of tension which is resolved in the downward direction. In mathematical language, the pressure (p) varies directly as the tension (T), and inversely as the radius of curvature (R): that is to say, p = T ⁄ R, per unit of surface. {217}
If instead of a cylinder, which is curved only in one direction, we take a case where there are curvatures in two dimensions (as for instance a sphere), then the effects of these must be simply added to one another, and the resulting pressure p is equal to T ⁄ R + T ⁄ R′ or p = T(1 ⁄ R + 1 ⁄ R′)[*].
And if in addition to the pressure p, which is due to surface tension, we have to take into account other pressures, p′, p″, etc., which are due to gravity or other forces, then we may say that the total pressure, P = p′ + p″ + T(1 ⁄ R + 1 ⁄ R′). While in some cases, for instance in speaking of the shape of a bird’s egg, we shall have to take account of these extraneous pressures, in the present part of our subject we shall for the most part be able to neglect them.