books usually figure the root tip in longitudinal section with various regions marked off: root cap, meristematic zone, zone of elongation, and zone of differentiation or maturation. Such descriptive demarcations fail to give quantitative information concerning the absolute or even the relative rates at which the various developmental processes, which are supposed to be occurring in these regions, are actually taking place. The nature of the transitions between one zone and the next are often completely ignored. 1Received for publication July 14, 1914. Growth rate measurements were made by the junior author, who is now serving with the armed forces. In 1939, Sinnott pointed out the suitability of certain species of small-seeded grasses for, studies of the growing root tip. In these species the transparency of the fine roots and the rudimentary character of the root caps permit unobscured microscopic observation of the surface of the living meristems. Brumfield (1942) has made some interesting experimental studies on one of these species, Phleum pratense L., in which rates of elongation of roots at various distances from the root apex were measured. In this paper methods are developed for determining rate of elongation of a root, cell elongation, rate of transverse cell division, and rate of increase in cell wall area, each expressed as a function of distance from the root apex. These methods are then applied to roots of Phleum pratense. The resulting data give a graphic picture of the above-mentioned developmental processes which are taking place within the growing region of a root and of the complex interrelations between them. Some further observations on the differentiation of vascular elements are correlated with these findings. THEORETICAL METHODS.-Rate of elongation.Seedlings of grasses such as Phleum pratense may be grown in vertical culture chambers so constructed as to allow examination of the root meristems under high magnifications with a compound microscope. It is possible to measure the amount of growth occurring during short time intervals between the root apex and characteristically-shaped epidermal marker cells. When such growth increments in unit time (r) are plotted against the initial distance (x) of the marker cells from the root apex, sigmoid curves, representing the rates of displacement of x from the root apex, are obtained (fig. 2). It should be pointed out that the time interval must be sufficiently short to prevent undue displacement of the marker cell from its original position, x units of distance from the root apex. The first derivatives of these sigmoid curves, dr/dx (the slope of the tangent to the curve at any point), give the rates of elongation of the roots as a function of distance from the tip (fig. 3). Average length of epidermal cells.-The length (1) of epidermal cells at various distances from the root apex may be readily determined. Camera lucida drawings of the surface of actively-growing roots cannot be made with sufficient rapidity to serve for this purpose. If large numbers of cells are to be measured, it may be convenient to make such measurements upon roots killed in fixatives which do not appreciably distort the cell dimensions, although measurements from photographs of living roots should be preferable. The length of cells in the subepidermal layers may be studied from longitudinal sections. Figure 4 shows the average length of epidermal cells with their basal ends at x.