134 THE KATE OF GROWTH [ch. 



and specialised functions that of cell-multiplication tends to fall 

 into abeyance*. 



It would seem to follow, as a natural consequence, from what 

 has been said, that we could without much difficulty reduce our 

 curves of growth to logarithmic formulae | akin to those which 

 the physical chemist finds apphcable to his autocatalytic reactions. 

 This has been diligently attempted by various writersj ; but the 

 results, while not destructive of the hypothesis itself, are only 

 partially successful. The difficulty arises mainly from the fact 

 that, in the life-history of an organism, we have usually to deal 

 (as indeed we have seen) with several recurrent periods of relative 

 acceleration and retardation. It is easy to find a formula which 

 shall satisfy the conditions during any one of these periodic 

 phases, but it is very difficult to frame a comprehensive formula 

 which shall apply to the entire period of growth, or to the whole 

 duration of fife. 



But if it be meanwhile impossible to formulate or to solve in 

 precise mathematical terms the equation to the growth of an 

 organism, we have yet gone a very long way towards the solution 

 of such problems when we have found a "qualitative expression," 

 as Poincare puts it; that is to say, when we have gained a fair 

 approximate knowledge of the general curve which represents the 

 unknown function. 



As soon as we have touched on such matters as the chemical 

 phenomenon of catalysis, we are on the threshold of a subject 

 which, if we were able to pursue it, would soon lead us far into 

 the special domain of physiology ; and there it would be necessary 

 to follow it if we were dealing with growth as a phenomenon in 

 itself, instead of merely as a help to our study and comprehension 

 of form. For instance the whole question of diet, of overfeeding 

 and underfeeding, would present itself for discussion §. But 

 without attempting to open up this large subject, we may say a 



* Cf. Enriques, Wachsthum und seine analytisohe Darstellung, Biol. Centralbl. 

 1909, p. 337. 



f Cf. (int. al.) Mellor, Chemical Statics and Dynamics, 1904, p. 291. 



t Cf. Robertson, I.e. 



§ See, for a brief resume of this subject, Morgan's Experimental Zoology, 

 chap. xvi. 



