256 THE RATE OF GROWTH [ch. 



in a chemical reaction. But the velocity-curve is not altered in 

 form ; for the amount of energy in the system is not affected by the 

 presence of the catalyst, the law of mass exerts its eifect, and the 

 rate of action gradually slows down. In certain cases we have 

 the remarkable phenomenon that a body capable of acting as a 

 catalyser is necessarily formed as a product, or by-product, of the 

 main reaction, and in such a case as this the reaction- velocity will 

 tend to be steadily accelerated. Instead of dwindhng away, such 

 a reaction continues with an ever-increasing velocity: always 

 subject to the reservation that limiting conditions will in time make 

 themselves felt, such as a failure of some necessary ingredient (the 

 "law of the minimum"), or the production of some substance which 

 shall antagonise and finally destroy the original reaction. Such an 

 action as this we have learned, from Ostwald, to describe as "auto- 

 catalysis." Now we know that certain products of protoplasmic 

 metabohsm — we call them enzymes — are very powerful catalysers, 

 a fact clearly understood by Claude Bernard long ago*; and we 

 are therefore entitled, to that extent, to speak of an autocatalytic 

 action on the part of protoplasm itself. 



Going a httle farther in the footsteps of Claude Bernard, Chodat 

 of Geneva suggested (as we are told by his pupil Monnier) that 

 growth itself might be looked on as a catalytic, or autocatalytic 

 reaction: "On peut bien, ainsi que M. Chodat I'a propose, considerer 

 I'accroissement comme une reaction chimique complexe, dans 

 laquelle le catalysateur est la cellule vivante, et les corps en presence 

 sont I'eau, les sels et Facide carboniquet-" 



A similar suggestion was made by Loeb, in connection with the 



* "Les diastases contiennent, en definitive, le secret de la vie. Or, les actions 

 diastatiques nous apparaissent comme des phenomenes catalytiques, en d'autres 

 termes, des accelerations de vitesse de reaction." Cf. M. F. Porchet, Rewie 

 Scientifique, 18th Feb. 1911. For a last word on this subject, see W. Frankenberger, 

 Katalytische Umsetzungen in homogenen u. enzymatischen Systemen, Leipzig, 1937. 



t Cf. R. Chodat, Principes de Botanique (2nd ed.), 1907, p. 133; A. Monnier, La 

 loi d'accroissement des vegetaux, Publ. de VInst. de Bot. de VUniv. de Geneve (7), 

 m, 1905. Cf. W. Ostwald, Vorlesungen iiber Naturphilosophie, 1902, p. 342; 

 Wo. Ostwald, Zeitliche Eigenschaften der Entwicklungsvorgange, in Roux's 

 Vortrdge, Heft 5, 1908; Robertson, Normal growth of an individual, and its 

 biochemical significance, Arch.f. Entw. Mech. xxv, pp. 581-614; xxvi, pp. 108-118, 

 1908; S. Hatai, Growth-curves from a dynamical standpoint, Anat. Record, v, 

 p. 373, 1911; A. J. Lotka, Ztschr. f. physikal. Chemie, Lxxn, p. 511, 1910; lxxx, 

 p. 159, 1912; etc. 



