320 Robertson, Explanatory Remarks concerning the Normal Rate of Growth etc. 



iii which he independently and almost simultaneously suggested 

 the same theory of growth as the author and adduced much evi- 

 dence of a qualitative kind in its support 6 ). But, in addition, 

 I contend that a comparison of curves, in the sense implied by 

 Pearl, is not the only kind of evidence adduced in my papers. 

 Perhaps the following recital of facts, which are quite independent 

 of the existence or non-existence of algebraic identity between the 

 theoretical curve of growth proposed by me and the curve of 

 growth which has been experimentally determined, may assist in 

 enlightening Pearl. The experiments of Peter 7 ) and of Loeb 8 ) 

 upon the temperature-coefficient of Growth have shown that the 

 velocity of growth is determined by the velocity of chemical reactions. 

 Now the growth of an organism, as the results of a very large 

 number of investigators have shown, undergoes, in the first part 

 of a growth-cycle, positive acceleration and, later, negative 

 acceleration with time; the curve of growth therefore possesses a 

 point of inflexion. Now, as I have pointed out elsewhere 9 ), only 

 two groups of chemical reactions are known which display 

 positive acceleration, the one group consists of the auto- 

 catalysed reactions and the other of certain catenary reactions. But 

 the curve expressing the extent of transformation with time, in a 

 catenary reaction, is almost invariably markedly assymetric about 

 its point of inflexion, whereas that expressing the extent of trans- 

 formation with time in an autocatalytic reaction is symmetrical 

 about its point of inflexion. Simple inspection of the numerous 

 published curves of growth is sufficient to assure us that the curve 

 of growth, in any given growth-cycle, is almost invariably notably 

 symmetrical about its point of inflexion. We cannot, I think, avoid 

 the conclusion, :om these considerations alone, that the growth of 

 living tissues and organisms is the expression of an autocatalysed 

 chemical reaction. 



are two or more catenary cycles of growth, the agreement between theory and experi- 

 ment which are cited by Pearl. As regards Donaldson's determinations of the 

 growth of the brain in Frogs, these measurements, as a cursory glance at Donald- 

 son's paper will suffice to show, were subject to very considerable error. 



6) Wo. Ostwald. ,,Uber die zeitlichen Eigeuschaften der Entwickelungs- 

 vorgange." Vortrage und Aufsatze u'ber Entwickelungsmechanik der Organismcn. 

 Herausgeg. von Wilh. Roux, Heft 5, Juli 1908. 



7) Karl Peter. ,,Der Grad der Beschleunigung tierischer Entwickelung durch 

 erhohte Temperatur." Arch. f. Entwickehingsmech. 20 (1906), p. 130. 



8) Jacques Loeb. ,,Uber den Temperaturkoeffizicnteu fur die Lebensdauer 

 kaltbliitiger Ticre und u'ber die Ursache des uaturlichen Todes." Arch. f. d. ges. 

 Phys. 124 (1908), p. 411. 



9) T. Brailsford Robertson. ,,Sur la dynamique chimiquc du systeme 

 ncrvcux central." Arch. Internat. de Physiol. G (1908), p. 388. 



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