§ 13. Hitherto we have confined ourselves entirely to examination of stems in one plane. We must glance--though only to ascertain how impossible it is to do more than glance--at the conditions of form which result from the throwing out of branches, not in one plane, but on all sides. "As your fingers divide when they hold a ball," I said: or, better, a large cup, without a handle. Consider how such ramification will appear in one of the bud groups, that of our old friend the oak. We saw it opened usually into five shoots. Imagine, then (Fig. 51), a five-sided cup or funnel with a stout rod running through the centre of it. In the figure it is seen from above, so as partly to show the inside, and a little obliquely, that the central rod may not hide any of the angles. Then let us suppose that, where the angles of this cup were, we have, instead, five rods, as in Fig. 52, A, like the ribs of a pentagonal umbrella turned inside out by the wind. I dot the pentagon which connects their extremities, to keep their positions clear. Then these five rods, with the central one, will represent the five shoots, and the leader, from a vigorous young oak-spray. Put the leaves on each; the five-foiled star at its extremity, and the others, now not quite formally, but still on the whole as in Fig. 3 above, and we have the result, Fig. 52, B--rather a pretty one. [Illustration: FIG. 52.] § 14. By considering the various aspects which the five rods would take in Fig. 52, as the entire group was seen from below or above, and at different angles and distances, the reader may find out for himself what changes of aspect are possible in even so regular a structure as this. But the branchings soon take more complex symmetry. We know that next year each of these five subordinate rods is to enter into life on its own account, and to repeat the branching of the first. Thus, we shall have five pentagonal cups surrounding a large central pentagonal cup. This figure, if the reader likes a pretty perspective problem, he may construct for his own pleasure:--which having done, or conceived, he is then to apply the great principles of subjection and resilience, not to three branches only, as in Fig. 49, but to the five of each cup;--by which the cups get flattened out and bent up, as you may have seen vessels of Venetian glass, so that every cup actually takes something the shape of a thick aloe or artichoke leaf; and they surround the central one, not as a bunch of grapes surrounds a grape at the end of it, but as the petals grow round the centre of a rose. So that any one of these lateral branches--though, seen from above, it would present a symmetrical figure, as if it were not flattened (A, Fig. 53)--seen sideways, or in profile, will show itself to be at least as much flattened as at B. [Illustration: FIG. 53.]