534 GROWTH 



growth of Protozoa. Robertson (1923) believed that the growth of an 

 organism, or of a population of organisms, was autocatalytic, because the 

 growth curves were sigmoid and could be fitted by the equation for a 

 monomolecular, autocatalytic, chemical reaction. The slowest chemical 

 reaction in the growth process was believed by Robertson to be the con- 

 trolling master reaction for the process which established the form of the 

 growth curve, and this could be discovered from the shape of the 

 growth curve. His particular choice of chemical reaction was not sat- 

 isfactory, and later he and other investigators have found difficulties 

 which have, for the most part, led to the abandonment of the autocata- 

 lytic theory. Cf. Robertson (1923), Snell (1929), Jahn (1930), Kava- 

 nagh and Richards (1934). 



The sigmoid nature of the growth curve is the inevitable result of the 

 regular geometrical increase during the time that the environment is 

 favorable, and the slowing of this increase when the environment be- 

 comes unfavorable as a result of the growth in it (decrease of foodstuffs 

 and accumulation of excretion products). As long as the environment is 

 maintained effectively constant, the rate of growth is constant and the 

 growth curve is exponential. However, it eventually becomes impossible 

 to maintain this constancy, and the growth is thus ultimately arrested. 

 In this sense Bernard's "milieu interieur" is part of the environment. 

 The granular material which Faure-Fremiet believes to limit the growth 

 of some colonial Protozoa is one of the few reported examples of limita- 

 tion in growth which apparently follows the appearance of a single 

 substance. Such a substance might be considered a catalyst in the Robertson 

 sense. Teissier (1937) has questioned this conclusion, and Snell's (1929) 

 objections are also applicable. Such substances, however, are rare. 



Allelocatalysis, according to Robertson (1924a), is "the acceleration 

 of multiplication by the contiguity of a second organism in a restricted 

 volume of medium." Robertson reported (1921b) that two Enchelys 

 farcimen, or two Colpidium colpoda in a drop of culture medium divided 

 more rapidly than twice the division rate of one individual in an en- 

 vironment of equal volume. It was shown later that his Colpidium was 

 Colpoda cucullus. Other publications followed, reporting that some un- 

 known substance, the allelocatalyst, stimulated cell division, and Robert- 

 son believed this was formed during nuclear division and effected the 

 permeability of the cells. 



