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.