Between the form of a twig and that of the leaves which it bears we can generally at once perceive a relation. The little leaves of the birch are borne on twigs slender as a piece of twine. The oak and elm, with larger leaves, require a stouter twig for their support. The sycamore and ash have twigs which are stouter still. The large leaves of the horse chestnut are borne on very thick twigs, in which the principle of the hollow column is introduced. The arrangement of the leaves on the stem, or _phyllotaxis_, is a question of the first importance. The leaves must be so grouped that all may receive as much light as possible. So far as can be arranged, there should be no overlapping, nor should any of the available space be wasted. On the stem of the ash, or sycamore, or teazel, the large leaves are arranged in alternate pairs, the direction of the axis of each pair being at right angles to that of the next. Thus two spaces or _internodes_ separate any pair of leaves from the nearest pair which, being placed in the same position, might overshadow it. This is a very simple case, which we shall find to be the rule when we examine plants in which the leaves are borne in opposite pairs. When leaves are borne in whorls of three a similar rule will be found to hold good. The position of the leaves of any whorl is such that they are vertically below or above the _spaces_ between the leaves of the next whorl. It will be seen at once that the amount of light received by each leaf is materially increased by this arrangement. If in a theatre we can look between the heads of two people in the row immediately in front of us, the head of a person in the next row beyond, even though directly before us, does not much interfere with our view of the stage. In most cases, however, the arrangement of the leaves on the stem is much more complicated than this. The leaves usually emerge singly. If we join by a line the point of emergence of a leaf with that of the next leaf above it on a stem, and that again with the next, a spiral will be the result, along which at equal intervals we reach the _nodes_, or points where leaves are borne. And the distance between these nodes will be always found to bear some definite relation to the total length of the spiral line in making one complete revolution round the stem. If the distance from node to node is one-half of this whole distance, it signifies that the leaves are borne alternately on opposite sides of the stem, each leaf being vertically below the second one higher up the stem--a very common arrangement. Or the leaves may be borne three to each spiral revolution, so that the position of each leaf shifts one-third way round the stem as compared with the preceding leaf. If we look along such a stem, the leaves will appear to be borne in three vertical rows, with an equal angle between each. Examining some other plant, we may find that we have to go as far as the fifth leaf