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.