Taking for our broadest division among forms, the regular and the irregular, we may divide the latter into those which are wholly irregular and those which, being but partially irregular, suggest some regular form to which they approach. By slightly straining the difference between them, two current words may be conveniently used to describe these subdivisions. The entirely irregular forms we may class as asymmetrical—literally as forms without any equalities of dimensions. The forms which approximate towards regularity without reaching it, we may distinguish as unsymmetrical: a word which, though it asserts inequality of dimensions, has been associated by use rather with such slight inequality as constitutes an observable departure from equality.
Of the regular forms there are several classes, differing in the number of directions in which equality of dimensions is repeated. Hence results the need for names by which symmetry of several kinds may be expressed.
The most regular of figures is the sphere: its dimensions are the same from centre to surface in all directions; and if cut by any plane through the centre, the separated parts are equal and similar. This is a kind of symmetry which stands alone, and will be hereafter spoken of as spherical symmetry.
When a sphere passes into a spheroid, either prolate or oblate, there remains but one set of planes that will divide it into halves, which are in all respects alike; namely, the planes in which its axis lies, or which have its axis for their line of intersection. Prolate and oblate spheroids may severally pass into various forms without losing this property. The prolate spheroid may become egg-shaped or pyriform, and it will still continue capable of being divided into two equal and similar parts by any plane cutting it down its axis; nor will the making of constrictions deprive it of this property. Similarly with the oblate spheroid. The transition from a slight oblateness, like that of an orange, to an oblateness reducing it nearly to a flat disc, does not alter its divisibility into like halves by every plane passing through its axis. And clearly the moulding of any such flattened oblate spheroid into the shape of a plate, leaves it as before, symmetrically divisible by all planes at right angles to its surface and passing through its centre. This species of symmetry is called radial symmetry. It is familiarly exemplified in such flowers as the daisy, the tulip, and the dahlia.
From spherical symmetry, in which we have an infinite number of axes through each of which may pass an infinite number of planes severally dividing the aggregate into equal and similar parts; and from radial symmetry, in which we have a single axis through which may pass an infinite number of planes severally dividing the aggregate into equal and similar parts; we now turn to bilateral symmetry, in which the divisibility into equal and similar parts becomes much restricted. Noting, for the sake of completeness, that there is a sextuple bilateralness in the cube and its derivative forms which admit of division into equal and similar parts by planes passing through the three diagonal axes and by planes passing through the three axes that join the centres of the surfaces, let us limit our attention to the three kinds of bilateralness which here concern us. The first of these is triple bilateral symmetry. This is the symmetry of a figure having three axes at right angles to one another, through each of which there passes a single plane that divides the aggregate into corresponding halves. A common brick will serve as an example; and of objects not quite so simple, the most familiar is that modern kind of spectacle-case which is open at both ends. This may be divided into corresponding halves along its longitudinal axis by cutting it through in the direction of its thickness, or by cutting it through in the direction of its breadth; or it may be divided into corresponding halves by cutting it across the middle. Of objects which illustrate double bilateral symmetry, may be named one of those boats built for moving with equal facility in either direction, and therefore made alike at stem and stern. Obviously such a boat is separable into equal and similar parts by a vertical plane passing through stem and stern; and it is also separable into equal and similar parts by a vertical plane cutting it amidships. To exemplify single bilateral symmetry it needs but to turn to the ordinary boat of which the two ends are unlike. Here there remains but the one plane passing vertically through stem and stern, on the opposite sides of which the parts are symmetrically disposed.
These several kinds of symmetry as placed in the foregoing order, imply increasing heterogeneity. The greatest uniformity in shape is shown by the divisibility into like parts in an infinite number of infinite series of ways; and the greatest degree of multiformity consistent with any regularity, is shown by the divisibility into like parts in only a single way. Hence, in tracing up organic evolution as displayed in morphological differentiations, we may expect to pass from the one extreme of spherical symmetry, to the other extreme of single bilateral symmetry. This expectation we shall find to be completely fulfilled.
CHAPTER VII.
THE GENERAL SHAPES OF PLANTS.
§ 217. Among protophytes those exemplified by Pleurococcus vulgaris are by general consent considered the simplest. As shown in Fig. [1], they are globular cells presenting no obvious differentiation save that between inner and outer parts. Their uniformity of figure co-exists with a mode of life involving the uniform exposure of all their sides to incident forces. For though each individual may have its external parts differently related to environing agencies, yet the new individuals produced by spontaneous fission, whether they part company or whether they form clusters and are made polyhedral by mutual pressure, have no means of maintaining parallel relations of position among their parts. On the contrary, the indefiniteness of the attitudes into which successive generations fall, must prevent the rise of any unlikeness between one portion of the surface and another. Spherical symmetry continues because, on the average of cases, incident forces are equal in all directions.
Figs. 1, 2, 3.