GENERAL CHARACTERISTICS OF GROWTH -PROCESS 4?5 



processes one or more of the products of the reaction is endowed with 

 the property of facilitating the further progress of the reaction. Such 

 transformations are designated Autocatalyzed Reactions (Fig. 32). 



The fact that each growth-cycle begins slowly and progressively 

 increases in velocity until the moment of maximal growth-velocity is 

 attained at the center of the cycle is sufficient in itself to show that the 

 process of growth is autocatalyzed, whatever the mechanism of the 

 self-acceleration may be. The resemblance of the process of growth 

 to the transformations in an autocatalyzed reaction is not merely 

 superficial, however, but extends even to quantitative details. 



It will be recollected that the relationship between the extent of 

 transformation and the time in an ordinary Monomolecular Chemical 

 Reaction is expressed by the equation: 



Velocity = k(a x) 



where "a x" is the amount of the original material which is as yet 

 untransformed and "k" is a constant, specific for the particular reac- 

 tions under consideration. The effect of catalyzers upon such a reac- 

 tion is to multiply the value of "k" by a quantity which is proportional 

 to the amount of catalyzer present. Now in an autocatalyzed reaction 

 the amount of catalyzer which is present is proportional to the mass of 

 the product of the reaction, that is, to "x." The equation for an 

 Autocatalyzed Monomolecular Reaction becomes, therefore: 



Velocity = kx(a x) 



which, when integrated, yields the equation: 



Iog 10 - = ka(t - ti) 



where t is the time from the beginning of the measurements and ti is 

 the time at which the reaction is half completed, i. e., the center of the 

 autocatalytic curve. 



The applicability of this equation to the growth in numbers of 

 Bacteria in a limited quantity of culture medium has been established 

 by McKendrick. It is, however, not less applicable to relatively 

 complex phenomena of Human Growth. The juvenile and adolescent 

 cycles of growth in man are rather closely interfused, so that their 

 separation into individual cycles is a difficult and uncertain matter. 

 The infantile cycle, however, is rather definitely separated from the 

 remainder of the human-growth curve by a rather long period or " pla- 

 teau" of relatively slow growth. The Infantile Growth -cycle, therefore, 

 at any rate for the first ten months succeeding birth, presents the 

 relatively uncomplicated characteristics of a single cycle of growth to 

 which the above equations may be applied. In the following compari- 

 sons of the theoretical values calculated from the equation 



Iog 10 - = ka(t - ti) 



