On the Motion of Growth. VII. Fundamental Relations and Quantities of Growth and Metabolism

Abstract

This paper affords, in extension of work already reported, 1 a further description of the fundamental relations and quantities by means of which a dynamical connection between growth and metabolism has been established.

Definition of Growth. Many writers have regarded growth, in the broadest sense, as a matter of increase in size. One of the best expressions of this view has been given by Julian Huxley, who states that growth is “a process of self-multiplication of living substance.” 2 For analytical purposes, however, it is better to surrender the position that growth must necessarily or by implication consist substantially only of an increase in size. It is, in fact, useful to approach the problem in more general terms and thus to conceive of growth as involving a change rather than exclusively an increase in size. Yet mere change alone cannot itself characterize growth, for this denotes a difference simply, and above all, a difference without respect to the quantity responsible for generating the resulting surplus or deficit as the case may be. Hence, the essence of growth is held to be change in size per unit size; and, since the process has been shown subject to dynamical constraints we have proposed to consider growth a mode of motion defined in practical terms as change in mass per unit mass. Length and cell number may also serve, where suitable or convenient, as valid measures of size and so of growth as well. The significance of the preceding definition is best brought out by comparing, as in Table I, what may, for the purpose in view, be called true growth and ordinary gain.

Minot 3 was among the first to recognize this “relativity of growth” because he laid great stress upon methods designed to approximate the relative rate of gain and clearly perceived that the latter should be called the “rate of growth”.