The case we have dealt with is of little practical importance to the biologist, because the cases in which a cubical, or rectangular, cell divides unequally, and unsymmetrically, are apparently few; but we can find, as Berthold pointed out, a few examples, for instance in the hairs within the reproductive “conceptacles” of certain Fuci (Sphacelaria, etc., Fig. 139), or in the “paraphyses” of mosses (Fig. 142). But it is of great theoretical importance: as serving to introduce us to a large class of cases, in which the shape and the relative dimensions of the original cavity lead, according to the principle of minimal areas, to cell-division in very definite and sometimes unexpected ways. It is not easy, nor indeed possible, to give a generalised account of these cases, for the limiting conditions are somewhat complex, and the mathematical treatment soon becomes difficult. But it is easy to comprehend a few simple cases, which of themselves will carry us a good long way; and which will go far to convince the student that, in other cases {352} which we cannot fully master, the same guiding principle is at the root of the matter. ―――――――――― The bisection of a solid (or the subdivision of its volume in other definite proportions) soon leads us into a geometry which, if not necessarily difficult, is apt to be unfamiliar; but in such problems we can go a long way, and often far enough for our particular purpose, if we merely consider the plane geometry of a side or section of our figure. For instance, in the case of the cube which we have been just considering, and in the case of the plane and cylindrical partitions by which it has been divided, it is obvious that, since these two partitions extend symmetrically from top to bottom of our cube, that we need only consider (so far as they are concerned) the manner in which they subdivide the _base_ of the cube. The whole problem of the solid, up to a certain point, is contained in our plane diagram of Fig. 138. And when our particular solid is a solid of revolution, then it is obvious that a study of its plane of symmetry (that is to say any plane passing through its axis of rotation) gives us the solution of the whole problem. The right cone is a case in point, for here the investigation of its modes of symmetrical subdivision is completely met by an examination of the isosceles triangle which constitutes its plane of symmetry.