In the horse-chestnut, as we have already observed, the leaves are in pairs, each one of the pair standing opposite its partner, while the pair just below or above stand across the stem at right angles to the position of the former pair. In other cases (the common bed-straw) the leaves are in whorls, that is, several stand at the same level on the axis, distributed around the stem. By far the larger number of plants have their leaves arranged alternately. A simple example of alternate leaves is presented by the elm, where the leaves stand successively on alternate sides of the stem, so that the distance from one leaf to the next, as one would measure around the stem, is exactly one half the distance around the stem. This arrangement is one half, or the angle of divergence of one leaf from the next is one half. In the case of the sedges the angle of divergence is less, that is one-third. By far the larger number of those plants which have the alternate arrangement have the leaves set at an angle of divergence represented by the fraction two fifths. Other angles of divergence have been discovered, and much stress has been laid on what is termed a law in the growth of the stem with reference to the position which the leaves occupy. Singularly by adding together the numerators and denominators of the last two fractions gives the next higher angle of divergence. Example: 1 + 2 3 2 + 3 5 —- —- = —-; —- —- = —-; 3 + 5 8 5 + 8 13 and so on. There are, however, numerous exceptions to this regular arrangement, which have caused some to question the importance of any theory like that of the “spiral theory” of growth propounded by Goethe and others of his time. =749. Adaptation in leaf arrangement.=—As a result, however, of one arrangement or another we see a beautiful adaptation of the plant parts to environment, or the influence which environment, especially light, has had on the arrangement of the leaves and branches of the plant. Access to light and air are of the greatest importance to green plants, and one cannot fail to be profoundly impressed with the workings of the natural laws in obedience to which the great variety of plants have worked out this adaptation in manifold ways.