On the Motion of Growth. II. Human Growth in Weight from Early Fetal to Adult Life

Abstract

The equation of energy previously set forth 1 has been applied to the case of human growth in weight but the steps necessary for this can only be briefly outlined here. We need first to know the nature and relations of the functions S, (V_c , E_c ) (t), which as already explained, pertain to energy at the source, to that in the form of cells, and to the energy of synthesis respectively. It can be shown that these several factors are connected in the case of “average” human weight by the relation,

E, E_o , β and θ being constants and . Certain other examples of human growth which depart from the “average” healthy trend, especially between 6-16 years of life have actually proven to be represented instead by an analogous circular function on the right of (2) though this exceptional case will not be treated in detail now. But it is of considerable interest that, whereas neither the hyperbolic nor the circular terms can be omitted in the human case, they vanish for all other examples of plant and animal growth we have so far studied.

The identity (2) is thus seen to symbolize merely the balance of energy after that which provides for the cells themselves, and that which is to do the work of synthesis has been deducted from the source. This balance must now suffice to perform three remaining fractions which, together with the energy of synthesis (already discounted), constitute the external work of growth.

Substituting, then, into the equation of energy (1), differentiating once with respect to t, and transposing terms we get an equation each term of which by these procedures figuratively denotes, per unit of weight, a component in the “forces” of growth: