CH. Ill] OF CHANGE OF MAGNITUDE 79 



a three-dimensional diagram. We do so, for example, when, by 

 means of the geometrical method of "perspective," we represent 

 upon a sheet of paper the length, breadth and depth of an object 

 in three-dimensional space, but we do it better by means of contour- 

 Hnes or "isopleths." By contour-lines superposed upon a map of 

 a country, we shew its hills and valleys; and by contour-Unes we 

 may shew temperature, rainfall, population, language, or any other 

 *' third dimension" related to the two dimensions of the map. Time 

 is always impHcit, in so far as each map refers to its own date or 

 epoch; but Time as a dimension can only be substituted for one of 

 the three dimensions already there. Thus we may superpose upon 

 our map the successive outlines of the coast from remote antiquity, 

 or of any single isotherm or isobar from day to day. And if in hke 

 manner we superpose on one another, or even set side by side, the 

 outhnes of a growing organism — for instance of a young leaf and 

 an old, we have a three-dimensional diagram which is a partial 

 representation (limited to two dimensions of space) of the organism's 

 gradual change of form, or course of development; in such a case 

 our contours may, for the purposes of the embryologist, be separated 

 by time-intervals of a few hours or days, or, for 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 we see how 

 intimately the two concepts are correlated or interrelated to one 

 another. In short it is obvious that the form of an organism is 

 determined by its rate of growth in various directions ; hence rate 

 of growth deserves to be studied as a necessary preliminary to the 

 theoretical study of form, and organic form itself is found, 

 mathematically speaking, to be di function of time'\. 



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

 be great or small; and we then invoke " Wolff's law" (or Kielmeyer's), and assert 

 that the life-history of the individual repeats, or recapitulates, the history of the 

 race. This "recapitulation theory" was alt-important in nineteenth -century 

 embryology, but was criticised by Adam Sedgwick {Q.J. M.S. xxxvi, p. 38, 1894) 

 and many later authors; cf. J. Needham, Chemical Embryology, 1931, pp. 1629-1647. 



t Our subject is one of Bacon's "Instances of the Course" or studies wherein 

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

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

 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." 



