However we shall require to deal more fully with this matter in our discussion of the rate of growth, and we may leave it meanwhile, in order to deal with other matters more or less directly concerned with the magnitude of the cell.
The living cell is a very complex field of energy, and of energy of many kinds, surface-energy included. Now the whole surface-energy of the cell is by no means restricted to its outer surface; for the cell is a very heterogeneous structure, and all its protoplasmic alveoli and other visible (as well as invisible) heterogeneities make up a great system of internal surfaces, at every part of which one “phase” comes in contact with another “phase,” and surface-energy is accordingly manifested. But still, the external surface is a definite portion of the system, with a definite “phase” of its own, and however little we may know of the distribution of the total energy of the system, it is at least plain that {35} the conditions which favour equilibrium will be greatly altered by the changed ratio of external surface to mass which a change of magnitude, unaccompanied by change of form, produces in the cell. In short, however it may be brought about, the phenomenon of division of the cell will be precisely what is required to keep approximately constant the ratio between surface and mass, and to restore the balance between the surface-energy and the other energies of the system. When a germ-cell, for instance, divides or “segments” into two, it does not increase in mass; at least if there be some slight alleged tendency for the egg to increase in mass or volume during segmentation, it is very slight indeed, generally imperceptible, and wholly denied by some[56]. The development or growth of the egg from a one-celled stage to stages of two or many cells, is thus a somewhat peculiar kind of growth; it is growth which is limited to increase of surface, unaccompanied by growth in volume or in mass.
In the case of a soap-bubble, by the way, if it divide into two bubbles, the volume is actually diminished[57] while the surface-area is greatly increased. This is due to a cause which we shall have to study later, namely to the increased pressure due to the greater curvature of the smaller bubbles.
An immediate and remarkable result of the principles just described is a tendency on the part of all cells, according to their kind, to vary but little about a certain mean size, and to have, in fact, certain absolute limitations of magnitude.
Sachs[58] pointed out, in 1895, that there is a tendency for each nucleus to be only able to gather around itself a certain definite amount of protoplasm. Driesch[59], a little later, found that, by artificial subdivision of the egg, it was possible to rear dwarf sea-urchin larvae, one-half, one-quarter, or even one-eighth of their {36} normal size; and that these dwarf bodies were composed of only a half, a quarter or an eighth of the normal number of cells. Similar observations have been often repeated and amply confirmed. For instance, in the development of Crepidula (a little American “slipper-limpet,” now much at home on our own oyster-beds), Conklin[60] has succeeded in rearing dwarf and giant individuals, of which the latter may be as much as twenty-five times as big as the former. But nevertheless, the individual cells, of skin, gut, liver, muscle, and of all the other tissues, are just the same size in one as in the other,—in dwarf and in giant[61]. Driesch has laid particular stress upon this principle of a “fixed cell-size.”
We get an excellent, and more familiar illustration of the same principle in comparing the large brain-cells or ganglion-cells, both of the lower and of the higher animals[62].
Fig. 1. Motor ganglion-cells, from the cervical spinal cord.
(From Minot, after Irving Hardesty.)
In Fig. [1] we have certain identical nerve-cells taken from various mammals, from the mouse to the elephant, all represented on the same scale of magnification; and we see at once that they are all of much the same order of magnitude. The nerve-cell of the elephant is about twice that of the mouse in linear dimensions, and therefore about eight times greater in volume, or mass. But making some allowance for difference of shape, the linear dimensions of the elephant are to those of the mouse in a ratio certainly not less than one to fifty; from which it would follow that the bulk of the larger animal is something like 125,000 times that of the less. And it also follows, the size of the nerve-cells being {37} about as eight to one, that, in corresponding parts of the nervous system of the two animals, there are more than 15,000 times as many individual cells in one as in the other. In short we may (with Enriques) lay it down as a general law that among animals, whether large or small, the ganglion-cells vary in size within narrow limits; and that, amidst all the great variety of structural type of ganglion observed in different classes of animals, it is always found that the smaller species have simpler ganglia than the larger, that is to say ganglia containing a smaller number of cellular elements[63]. The bearing of such simple facts as this upon the cell-theory in general is not to be disregarded; and the warning is especially clear against exaggerated attempts to correlate physiological processes with the visible mechanism of associated cells, rather than with the system of energies, or the field of force, which is associated with them. For the life of {38} the body is more than the sum of the properties of the cells of which it is composed: as Goethe said, “Das Lebendige ist zwar in Elemente zerlegt, aber man kann es aus diesen nicht wieder zusammenstellen und beleben.”
Among certain lower and microscopic organisms, such for instance as the Rotifera, we are still more palpably struck by the small number of cells which go to constitute a usually complex organ, such as kidney, stomach, ovary, etc. We can sometimes number them in a few units, in place of the thousands that make up such an organ in larger, if not always higher, animals. These facts constitute one among many arguments which combine to teach us that, however important and advantageous the subdivision of organisms into cells may be from the constructional, or from the dynamical point of view, the phenomenon has less essential importance in theoretical biology than was once, and is often still, assigned to it.