GROWTH, TIME, AND FORM

Summary 1. The equation, log w = k. log (2 t + 1) + C is a peculiar modification of the compound interest law. It is derived from growth in fresh weight of chick embryos, and applies to fresh weights of the domestic fowl and of the smaller as well as larger domestic mammals. For the dairy cow, weights are calculable from time, with an error of less than 1 per cent. 2. The circumstances under which k can remain constant are analysed. A period of constancy is called a stanza of growth. Stanzas for the whole and the part or for different parts, may or may not be synchronized. The conditions under which a particular category terminates a stanza of growth can be foreseen from the circumstances that assure the constancy of k. 3. In the category of fresh weight, water is the quantitatively dominant entity. The equation describes also other categories: ( a ) when dominated by specific entities; ( b ) when their quantitative organization is constant; ( c ) when applied to specific isolated chemical substances. This and the relatively independent behaviour of unit categories or entities makes it possible to calculate the amount of calcium moved from the shell by the developing embryo; and to account for the upward swing of dry substance after the ninth day of incubation. The only specific postnatal category dealt with, is “antlers” in deer. Such analysis is possible since, under certain conditions, the time “lost” in intermittent growth, becomes irrelevant. 4. The effects of temporal errors introduced by faulty timing are discussed and illustrated. According to the equation, any finite value of k automatically provides for the termination of growth at infinity. Actual cessation is mathematically precocious, and implicates heterogony. 5. By means of y = bx k , the functional relation between organic mass and time can be extended to include also form, since the heterogonic constantor6. Heterogonous growth may be considered as imposed on a system in certain respects practically or actually isogonous at origin. Parallel rates whether limited to a single stanza or surviving several are designated according to the number of rates involved, as isogonic diads, triads, etc., and are responsible for the maintenance of the compatibilities during heterogonic growth. 7. Among the heterogonic relationships is one that cannot at all times conform to y = bx k , since it involves the mixture “dry substance”. Excepting the frog tadpole prior to metamorphosis, the ratio of water to dry substance falls during growth and stabilizes at maturity. Where growth is indeterminate, stabilization occurs at a level higher than for determinate growth. 8. Certain kinetic implications of the water to dry substance ratio suggest that growth, maintenance, and senility, are related to changes in the rates of the several metabolic transactions. This hypothesis is tested by an appeal to data on the frog, the white rat, man, and a variety of crop plants. In all the plants the onset of senility demonstrably associates with a fall of the water to dry substance ratio below the maintenance level of maturity.