284 THE RATE OF GROWTH [ch. 



In this discussion of growth, we have left out of account a vast 

 number of processes or phenomena in the physiological mechanism 

 of the body, by which growth is effected and controlled. We have 

 dealt with growth in its relation to magnitude, and to that relativity 

 of magnitudes which constitutes form; and so we have studied it 

 as a phenomenon which stands at the beginning of a morphological, 

 rather than at the end of a physiological enquiry. Under these 

 restrictions, we have treated it as far as possible, or in such fashion 

 as our present knowledge permits, on strictly physical lines. That 

 is to say, we rule "heredity" or any such concept out of our present 

 account, however true, however important, however indispen- 

 sable in another setting of the story, such a concept may be. 

 In physics "on admet que I'etat actuel du monde ne depend que du 

 passe le. plus proche, sans etre influence, pour ainsi dire, par le 

 souvenir d'un passe lointain*." This is the concept to which the 

 differential equation gives expression; it is the step which Newton 

 took when he left Kepler behind. 



In all its aspects, and not least in its relation to form, the growth 

 of organisms has many analogies, some close, some more remote, 

 among inanimate things. As the waves grow when the winds strive 

 with the other forces which govern the movements of the surface 

 of the sea, as the heap grows when we pour corn out of a sack, as 

 the crystal grows when from the surrounding solution the proper 

 molecules fall into their appropriate places: so in all these cases, 

 very much as in the organism itself, is growth accompanied by 

 change of form, and by a development of definite shapes and 

 contours. And in these cases (as in all other mechanical phenomena), 

 we are led to equate our various magnitudes with time, and so to 

 recognise that growth is essentially a question of rate, or of velocity. 



The diiferences of form, and changes of form, which are brought 

 about by varying rates (or "laws") of growth, are essentially the 

 same phenomenon whether they be episodes in the life-history of 

 the individual, or manifest themselves as the distinctive charac- 

 teristics of what we call separate species of the race. From one 

 form, or one ratio of magnitude, to another there is but one straight 

 and direct road of transformation, be the journey taken fast or 



* Cf. H. Poincare, La physique generale et la physique mathematique, Rev. 

 gin. des Sciences, xi, p. 1167, 1900. 



