CH. Ill] CONCERNING DIMENSIONS 51 



length against time, as the phrase is), we get that kind of vector 

 diagram which is commonly known as a "curve of growth." We 

 perceive, accordingly, that the phenomenon which we are now 



studying is a velocity (whose " dimensions" are ^t or ^ J ; 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 "perspective" 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 "contour-lines," 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 

 (hmited to two dimensions of space) of the organism's 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 years*. 



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 iriter-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, mathematically speaking, organic foym itself appears 

 to us as a function of titnei. 



* Sometimes we find one and the same diagram suffice, whether the intervals 

 of time be great or small; and we then invoke "Wolff's Law," and assert that 

 the life-history of the individual repeats, or recapitulates, the history of the race. 



f Our subject is one of Bacon's "Instances of the Course," or studies wherein 

 we "measure Nature by periods of Time." In Bacon's Catalogue of Particular 

 Histories, one of the odd hundred histories or investigations which he foreshadowed 

 is precisely that which we are engaged on, viz. a "History of the Growth and Increase 

 of the Body, in the whole and in its parts." 



4—2 



