leaves sometimes occurs as in Bryophyllum, and many plants of the
order Gesneraceae. The leaf of Venus’s fly-trap (Dionaea muscipula)
when cut off and placed in damp moss, with a pan of water underneath
and a bell-glass for a cover, has produced buds from which
young plants were obtained. Some species of saxifrage and of
ferns also produce buds on their leaves and fronds. In Nymphaea
micrantha buds appear at the upper part of the petiole.
Leaves occupy various positions on the stem and branches, and have received different names according to their situation. Thus leaves arising from the crown of the root, as in the primrose, are called radical; those on the stem are Phyllotaxis. cauline; on flower-stalks, floral leaves (see Flower). The first leaves developed are known as seed leaves or cotyledons. The arrangement of the leaves on the axis and its appendages is called phyllotaxis.
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Fig. 29.—A stem with opposite leaves. The pairs are placed at right angles alternately, or in what is called a decussate manner. In the lowest pair one leaf is in front and the other at the back; in the second pair the leaves are placed laterally, and so on. |
Fig. 30.—A stem with alternate leaves, arranged in a pentastichous or quincuncial manner. The sixth leaf is directly above the first, and commences the second cycle. The fraction of the circumference of the stem expressing the divergence of the leaves is two-fifths. |
In their arrangement leaves follow a definite order. The points on the stem at which leaves appear are called nodes; the part of the stem between the nodes is the internode. When two leaves are produced at the same node, one on each side of the stem or axis, and at the same level, they are opposite (fig. 29); when more than two are produced they are verticillate, and the circle of leaves is then called a verticil or whorl. When leaves are opposite, each successive pair may be placed at right angles to the pair immediately preceding. They are then said to decussate, following thus a law of alternation (fig. 29). The same occurs in the verticillate arrangement, the leaves of each whorl rarely being superposed on those of the whorl next it, but usually alternating so that each leaf in a whorl occupies the space between two leaves of the whorl next to it. There are considerable irregularities, however, in this respect, and the number of leaves in different whorls is not always uniform, as may be seen in Lysimachia vulgaris. When a single leaf is produced at a node, and the nodes are separated so that each leaf is placed at a different height on the stem, the leaves are alternate (fig. 30). A plane passing through the point of insertion of the leaf in the node, dividing the leaf into similar halves, is the median plane of the leaf; and when the leaves are arranged alternately on an axis so that their median planes coincide they form a straight row or orthostichy. On every axis there are usually two or more orthostichies. In fig. 31, leaf 1 arises from a node n; leaf 2 is separated from it by an internode m, and is placed to the right or left; while leaf 3 is situated directly above leaf 1. In this case, then, there are two orthostichies, and the arrangement is said to be distichous. When the fourth leaf is directly above the first, the arrangement is tristichous. The same arrangement continues throughout the branch, so that in the latter case the 7th leaf is above the 4th, the 10th above the 7th; also the 5th above the 2nd, the 6th above the 3rd and so on. The size of the angle between the median planes of two consecutive leaves in an alternate arrangement is their divergence; and it is expressed in fractions of the circumference of the axis which is supposed to be a circle. In a regularly-formed straight branch covered with leaves, if a thread is passed from one to the other, turning always in the same direction, a spiral is described, and a certain number of leaves and of complete turns occur before reaching the leaf directly above that from which the enumeration commenced. If this arrangement is expressed by a fraction, the numerator of which indicates the number of turns, and the denominator the number of internodes in the spiral cycle, the fraction will be found to represent the angle of divergence of the consecutive leaves on the axis. Thus, in fig. 32, a, b, the cycle consists of five leaves, the 6th leaf being placed vertically over the 1st, the 7th over the 2nd and so on; while the number of turns between the 1st and 6th leaf is two; hence this arrangement is indicated by the fraction 25. In other words, the distance or divergence between the first and second leaf, expressed in parts of a circle, is 25 of a circle or 360° × 25 = 144°. In fig. 31, a, b, the spiral is ½, i.e. one turn and two leaves; the third leaf being placed vertically over the first, and the divergence between the first and second leaf being one-half the circumference of a circle, 360° × ½ = 180°. Again, in a tristichous arrangement the number is ⅓, or one turn and three leaves, the angular divergence being 120°.
By this means we have a convenient mode of expressing on paper
the exact position of the leaves upon an axis. And in many cases
such a mode of expression is of excellent service in enabling us
Fig. 31.—Portion of a branch of a Lime
tree, with four leaves arranged in a distichous
manner, or in two rows. a, The branch with
the leaves numbered in their order, n being
the node and m the internode; b is a magnified
representation of the branch, showing
the points of insertion of the leaves and
their spiral arrangement, which is expressed
by the fraction ½, or one turn of the spiral
for two internodes.
readily to understand
the relations of the
leaves. The divergences
may also be represented
diagrammatically on a
horizontal projection of
the vertical axis, as in
fig. 33. Here the outermost
circle represents a
section of that portion
of the axis bearing the
lowest leaf, the innermost
represents the
highest. The broad
dark lines represent the
leaves, and they are
numbered according to
their age and position.
It will be seen at once
that the leaves are arranged
in orthostichies
marked I.-V., and that
these divide the circumference
into five equal
portions. But the
divergence between leaf
1 and leaf 2 is equal to
25ths of the circumference,
and the same
is the case between 2
and 3, 3 and 4, &c. The divergence, then, is 25, and from this
we learn that, starting from any leaf on the axis, we must pass
twice round the stem in a spiral through five leaves before reaching
one directly over that with which we started. The line which, winding
round an axis either to the right or to the left, passes through the
points of insertion of all the leaves on the axis is termed the genetic
or generating spiral; and that margin of each leaf which is towards
the direction from which the spiral proceeds is the kathodic side, the
Fig. 32.—Part of a branch of a
Cherry with six leaves, the sixth
being placed vertically over the
first, after two turns of the spiral.
This is expressed by two-fifths.
a, The branch, with the leaves
numbered in order; b, a magnified
representation of the branch,
showing the points of insertion of
the leaves and their spiral arrangement.
other margin facing the point
whither the spiral passes being
the anodic side.
In cases where the internodes are very short and the leaves are closely applied to each other, as in the house-leek, it is difficult to trace the generating spiral. Thus, in fig. 34 there are thirteen leaves which are numbered in their order, and five turns of the spiral marked by circles in the centre (513 indicating the arrangement); but this could not be detected at once. So also in fir cones (fig. 35), which are composed of scales or modified leaves, the generating spiral cannot be determined easily. But in such cases a series of secondary spirals or parastichies are seen running parallel with each other both right and left, which to a certain extent conceal the genetic spiral.
The spiral is not always constant throughout the whole length of an axis. The angle of divergence may alter either abruptly or gradually, and the phyllotaxis thus becomes very complicated. This change may be brought about by arrest of development, by increased development of parts or by a torsion of the axis. The former are exemplified in many Crassulaceae and aloes. The latter is seen well in the screw-pine (Pandanus). In the bud of the screw-pine the leaves are arranged in three orthostichies with the phyllotaxis 13, but by torsion the developed leaves become arranged in three strong spiral rows running round the stem. These causes of change in phyllotaxis are also well exemplified in the alteration of an opposite or verticillate arrangement to an alternate, and vice versa; thus the effect of interruption of growth, in causing alternate leaves to become opposite and verticillate, can be distinctly shown in Rhododendron ponticum. The primitive or generating spiral may
