[3] Fig. 11 is a shoot of the line, drawn on two sides, to show its continuous curve in one direction, and alternated curves in another. The buds, which may be seen to be at equal heights in the two figures, are exquisitely proportioned in their distances. There is no end to the refinement of system, if we choose to pursue it. CHAPTER IV. THE LEAF. § 1. Having now some clear idea of the position of the bud, we have next to examine the forms and structure of its shield--the leaf which guards it. You will form the best general idea of the flattened leaf of shield-builders by thinking of it as you would of a mast and sail. More consistently with our classification, we might perhaps say, by thinking always of the arm sustaining the shield; but we should be in danger of carrying fancy too far, and the likeness of mast and sail is closer, for the mast tapers as the leaf-rib does, while the hand holding the uppermost strap of the buckler clenches itself. Whichever figure we use, it will cure us of the bad habit of imagining a leaf composed of a short stalk with a broad expansion at the end of it. Whereas we should always think of the stalk as running right up the leaf to its point, and carrying the expanded, or foliate part, as the mast of a lugger does its sail. To some extent, indeed, it has yards also, ribs branching from the innermost one; only the yards of the leaf will not run up and down, which is one essential function of a sailyard. § 2. The analogy will, however, serve one step more. As the sail must be on one side of the mast, so the expansion of a leaf is on one side of its central rib, or of its system of ribs. It is laid over them as if it were stretched over a frame, so that on the upper surface it is comparatively smooth; on the lower, barred. The understanding of the broad relations of these parts is the principal work we have to do in this chapter. § 3. First, then, you may roughly assume that the section of any leaf-mast will be a crescent, as at _a_, Fig. 17 (compare Fig. 7 above). The flat side is the uppermost, the round side underneath, and the flat or upper side caries the leaf. You can at once see the convenience of this structure for fitting to a central stem. Suppose the central stem has a little hole in the centre, _b_, Fig. 17, and that you cut it down through the middle (as terrible knights used to cut their enemies in the dark ages, so that half the head fell on one side, and half on the other): Pull the two halves separate, _c_, and they will nearly represent the shape and position of opposite leaf-ribs. In reality the leaf-stalks have to fit themselves to the central stem, _a_, and as we shall see presently, to lap round it: but we must not go too fast. [Illustration: FIG. 17.] [Illustration: FIG. 18.] [Illustration: FIG. 19.]