the phenomenon which we are now studying is a velocity (whose ãdimensionsã are ÿ£¢ Space ÿ£¢ãÿ£¢ Time or ÿ£¢ L ÿ£¢ãÿ£¢ T ); and this phenomenon we shall speak of, simply, as a rate of growth.
In various conventional ways we can convert a two-dimensional into a three-dimensional diagram. We do so, for example, by means of the geometrical method of ãperspectiveã when we represent upon a sheet of paper the length, breadth and depth of an object in three-dimensional space; but we do it more simply, as a rule, by means of ãcontour-lines,ã and always when time is one of the dimensions to be represented. If we superimpose upon one another (or even set side by side) pictures, or plane projections, of an organism, drawn at successive intervals of time, we have such a three-dimensional diagram, which is a partial representation (limited to two dimensions of space) of the organismãs gradual change of form, or course of development; and in such a case our contour-lines may, for the purposes of the embryologist, be separated by intervals representing a few hours or days, or, for the purposes of the palaeontologist, by interspaces of unnumbered and innumerable years1.
Such a diagram represents in two of its three dimensions form, and in two, or three, of its dimensions growth; and so we see how intimately the two conceptions are correlated or inter-related to one another. In short, it is obvious that the form of an animal is determined by its specific rate of growth in various directions; accordingly, the phenomenon of rate of growth deserves to be studied as a necessary preliminary to the theoretical study of form, and, mathôÙeôÙmatôÙiôÙcally speaking, organic form itself appears to us as a function of time2.
At the same time, we need only consider this part of our subject somewhat briefly. Though it has an essential bearing on the problems of morphology, it is in greater degree involved with physiological problems; and furthermore, the statistical or numerical aspect of the question is peculiarly adapted