478 PROCESSES INFERRED FROM INDIRECT OBSERVATION 



The answer to this question is undoubtedly to be sought in the fact 

 that in any system of interdependent chemical transformations the 

 slowest reaction in the series governs the velocity of the whole. On the 

 hither side of the slowest reaction all the raw materials for subsequent 

 processes must accumulate and await the elaboration of the products 

 which they utilize, while on the far side of the slowest reaction the 

 subsequent processes are retarded to its pace by the consumption of 

 their substrates. The slowest reaction in any chain of chemical 

 processes is the Master-reaction which determines from moment to 

 moment the quantitative relations of the product to the time. Now 

 in the complex of events which constitutes growth not a single sig- 

 nificant transformation is independent of the rest; each must evidently 

 use some product of other transformations and contribute some product 

 to get another series of processes. We can therefore understand how 

 the whole phenomenon, notwithstanding its complexity and the multi- 

 plicity of the chemical reactions involved in it, may nevertheless be 

 governed, as to its quantitative outcome, by the rate at which a single 

 reaction occurs. This reaction, as we have seen, is autocatalytic. 



We are thus led to inquire whether the growth-diagram, which is so 

 similar in form to the curve which represents the progress of an auto- 

 catalyzed chemical reaction, may properly be regarded as establishing 

 the existence of Catalyzers of Growth which are numbered among the 

 products of the growth-process, or Endogenous Catalyzers, as Hopkins 

 has termed them, and also the existence of Impeding Factors, attribut- 

 able either to the exhaustion of an essential constituent of the reaction, 

 or to the accumulation of growth-products. 



The problem becomes somewhat clearer when we consider the simple 

 case of Bacteria, growing on a limited amount of a given culture-medium. 

 In this case, as McKendrick has shown, precisely analogous phenomena 

 are exhibited to those which characterize the growth of higher organ- 

 isms. The growth of the bacterial culture, measured by the total 

 mass or number of bacteria produced at given time-intervals, is at 

 first extremely slow; it increases in velocity, however, and at first 

 almost in proportion to the number of bacteria produced. At a later 

 stage growth is impeded and finally comes to a standstill when the 

 density of the population of the culture-medium has attained a certain 

 maximum. 



These phenomena are interpreted by McKendrick in the following 

 manner: Each bacterium is capable of giving rise to a certain number 

 of daughter-cells in a certain interval of time under constant nutritive 

 conditions. This potentiality is transmitted to its offspring, so that 

 were the nutritive constituents of the culture-medium inexhaustible, 

 the velocity of reproduction would always be proportionate to the 

 number of bacteria previously produced, or, in other words, the density 

 of the bacterial population would increase in geometrical, while the 

 time increased in arithmetical progression. In practice, however, the 

 ability of the culture-medium to supply nutritive materials to the 



