§ 4 The Arrangement of Leaves
181. Phyllotaxy, meaning leaf-arrangement, is the study of the position of leaves, or parts answering to leaves, upon the stem.
182. The technical name for the attachment of leaves to the stem is the insertion. Leaves (as already noticed, 54) are inserted in three modes. They are Alternate (Fig. 181), that is, one after another, or in other words, with only a single leaf to each node;
Opposite (Fig. 182), when there is a pair to each node, the two leaves in this case being always on opposite sides of the stem;
Whorled or Verticillate (Fig. 183) when there are more than two leaves on a node, in which case they divide the circle equally between them, forming a Verticel or whorl. When there are three leaves in the whorl, the leaves are one third of the circumference apart; when four, one quarter, and so on. So the plan of opposite leaves, which is very common, is merely that of whorled leaves, with the fewest leaves to the whorl, namely, two.
183. In both modes and in all their modifications, the arrangement is such as to distribute the leaves systematically and in a way to give them a good exposure to the light.
184. No two or more leaves ever grow from the same point. The so-called Fascicled or Clustered leaves are the leaves of a branch the nodes of which are very close, just as they are in the bud, so keeping the leaves in a cluster. This is evident in the Larch (Fig. 184), in which examination shows each cluster to be made up of numerous leaves crowded on a spur or short axis. In spring there are only such clusters; but in summer some of them lengthen into ordinary shoots with scattered alternate leaves. So, likewise, each cluster of two or three needle-shaped leaves in Pitch Pines (as in Fig. 185), or of five leaves in White Pine, answers to a similar extremely short branch, springing from the axil of a thin and slender scale, which represents a leaf of the main shoot. For Pines produce two kinds of leaves,—1. primary, the proper leaves of the shoots, not as foliage, but in the shape of delicate scales in spring, which soon fall away; and 2. secondary, the fascicled leaves, from buds in the axils of the former, and these form the actual foliage.
185. Phyllotaxy of Alternate Leaves. Alternate leaves are distributed along the stem in an order which is uniform for each species. The arrangement in all its modifications is said to be spiral, because, if we draw a line from the insertion (i. e. the point of attachment) of one leaf to that of the next, and so on, this line will wind spirally around the stem as it rises, and in the same species will always bear the same number of leaves for each turn round the stem. That is, any two successive leaves will always be separated from each other by an equal portion of the circumference of the stem. The distance in height between any two leaves may vary greatly, even on the same shoot, for that depends upon the length of the internodes, or spaces between the leaves; but the distance as measured around the circumference (in other words, the Angular Divergence, or angle formed by any two successive leaves) is uniformly the same.
186. Two-ranked. The greatest possible divergence is, of course, where the second leaf stands on exactly the opposite side of the stem from the first, the third on the side opposite the second, and therefore over the first, and the fourth over the second. This brings all the leaves into two ranks, one on one side of the stem and one on the other, and is therefore called the Two-ranked arrangement. It occurs in all Grasses,—in Indian Corn, for instance; also, in the Basswood (Fig. 181). This is the simplest of all arrangements, and the one which most widely distributes successive leaves, but which therefore gives the fewest vertical ranks. Next is the
187. Three-ranked arrangement,—that of all Sedges, and of White Hellebore. Here the second leaf is placed one third of the way round the stem, the third leaf two thirds of the way round, the fourth leaf accordingly directly over the first, the fifth over the second, and so on. That is, three leaves occur in each turn round the stem, and they are separated from each other by one third of the circumference. (Fig. 186, 187.)
188. Five-ranked is the next in the series, and the most common. It is seen in the Apple (Fig. 188), Cherry, Poplar, and the greater number of trees and shrubs. In this case the line traced from leaf to leaf will pass twice round the stem before it reaches a leaf situated directly over any below (Fig. 189). Here the sixth leaf is over the first; the leaves stand in five perpendicular ranks, with equal angular distance from each other; and this distance between any two successive leaves is just two fifths of the circumference of the stem.
189. The five-ranked arrangement is expressed by the fraction 2/5. This fraction denotes the divergence of the successive leaves, i. e. the angle they form with each other: the numerator also expresses the number of turns made round the stem by the spiral line in completing one cycle or set of leaves, namely, two; and the denominator gives the number of leaves in each cycle, or the number of perpendicular ranks, namely, five. In the same way the fraction 1/2 stands for the two-ranked mode, and 1/3 for the three-ranked: and so these different sorts are expressed by the series of fractions 1/2, 1/3, 2/5. Other cases follow in the same numerical progression, the next being the
190. Eight-ranked arrangement. In this the ninth leaf stands over the first, and three turns are made around the stem to reach it; so it is expressed by the fraction 3/8. This is seen in the Holly, and in the common Plantain. Then comes the
191. Thirteen-ranked arrangement, in which the fourteenth leaf is over the first, after five turns around the stem. The common Houseleek (Fig. 191) is a good example.
192. The series so far, then, is 1/2, 1/3, 2/5, 3/8, 5/13; the numerator and the denominator of each fraction being those of the two next preceding ones added together. At this rate the next higher should be 8/21, then 13/34, and so on; and in fact just such cases are met with, and (commonly) no others. These higher sorts are found in the Pine Family, both in the leaves and the cones and in many other plants with small and crowded leaves. But in those the number of the ranks, or of leaves in each cycle, can only rarely be made out by direct inspection. They may be indirectly ascertained, however, by studying the secondary spirals, as they are called, which usually become conspicuous, at least two series of them, one turning to the right and one to the left, as shown in Fig. 191. For an account of the way in which the character of the phyllotaxy may be deduced from the secondary spirals, see Structural Botany, Chapter IV.
193. Phyllotaxy of Opposite and whorled Leaves. This is simple and comparatively uniform. The leaves of each pair or whorl are placed over the intervals between those of the preceding, and therefore under the intervals of the pair or whorl next above. The whorls or pairs alternate or cross each other, usually at right angles, that is, they decussate. Opposite leaves, that is, whorls of two leaves only, are far commoner than whorls of three or four or more members. This arrangement in successive decussating pairs gives an advantageous distribution on the stem in four vertical ranks. Whorls of three give six vertical ranks, and so on. Note that in descriptive botany leaves in whorls of two are simply called opposite leaves; and that the term verticillate or whorled, is employed only for cases of more than two, unless the latter number is specified.
194. Vernation or Præfoliation, the disposition of the leaf-blades in the bud, comprises two things; 1st, the way in which each separate leaf is folded, coiled, or packed up in the bud; and 2d, the arrangement of the leaves in the bud with respect to one another. The latter of course depends very much upon the phyllotaxy, i. e. the position and order of the leaves upon the stem. The same terms are used for it as for the arrangement of the leaves of the flower in the flower-bud. See, therefore, “Æstivation, or Præfloration.”
195. As to each leaf separately, it is sometimes straight and open in vernation, but more commonly it is either bent, folded, or rolled up. When the upper part is bent down upon the lower, as the young blade in the Tulip-tree is bent upon the leaf-stalk, it is said to be Inflexed or Reclined in vernation. When folded by the midrib so that the two halves are placed face to face, it is Conduplicate (Fig. 193), as in the Magnolia, the Cherry, and the Oak. When folded back and forth like the plaits of a fan, it is Plicate or Plaited (Fig. 194), as in the Maple and Currant. If rolled, it may be so either from the tip downwards, as in Ferns and the Sundew (Fig. 197), when in unrolling it resembles the head of a crosier, and is said to be Circinate; or it may be rolled up parallel with the axis, either from one edge into a coil, when it is Convolute (Fig. 195), as in the Apricot and Plum; or rolled from both edges towards the midrib,—sometimes inwards, when it is Involute (Fig. 198), as in the Violet and Water-Lily; sometimes outwards, when it is Revolute (Fig. 196), in the Rosemary and Azalea. The figures are diagrams, representing sections through the leaf, in the way they were represented by Linnæus.