[Illustration: Fig. 428.—Shoot of butternut showing leaf-scars, axillary buds, and adventitious buds (buds coming from above the axils).] [Illustration: Fig. 429.—Shoot and bud of white oak.] =733. Phyllotaxy.=—Investigation of a horse-chestnut or willow twig will show that the leaf-scars occupy definite positions which are constant for each plant but different for the two species. The arrangement of the leaves on the stem in any plant is termed phyllotaxy. In the horse-chestnut we find two scars placed at the same node, but on opposite sides of the stem. Somewhat higher up we find two more similarly placed, but in a position perpendicular to that of the first pair. Such phyllotaxy is termed opposite. If in any plant several leaves occur at a node, the phyllotaxy is whorled. If but one at each node, as in the willow, the phyllotaxy is alternate. The opposite and alternate types are very commonly met with. Closer observation will show that in the willow, if a line be drawn connecting the successive leaf-scars, it will pass spirally up the twig until at length a scar is reached directly over the one taken as a starting-point. Such spiral arrangement always accompanies alternate phyllotaxy. The section of the spiral thus delineated is termed a cycle. We express the nature of the cycle by the fractions ½, ⅓, ⅖, ⅜, ⁵/₁₃, etc., in which the numerator denotes the number of turns around the stem in each cycle, and the denominator the number of leaf-scars in the same distance. In a general way we find in plants only such arrangements as are represented by the fractions given above. These fractions show the curious condition that the numerator and denominator of each is equal to the sum of the numerator or denominator of the two preceding fractions. Much speculation has been indulged in regarding the significance of these definite laws of leaf arrangement. In part they may be due to the desire that each leaf receive the maximum amount of light. Only certain definite geometrical conditions will insure this. More likely it is due to the economy of space allotted to the leaf-fundaments in the bud. Here, again, geometrical laws govern this economy. The phyllotaxy is nearly constant for a given species. =734. Buds.=—The growing point of the stem or branch together with its leaf or flower fundaments and protective structures is termed a bud. Winter buds on woody plants are terminal when inclosing the growing point of the main axis of the twig; lateral when the growing point is that of a branch of the main axis. Lateral buds are always axillary, i.e., situated on the upper angle between a leaf and the main axis.