6o 



GROWTH 



Time 



Figure 40. Time curves of oxidation of lin- 

 seed oil under various conditions (after 

 Genthe). 



of the growth-inhibiting substances have been used up on 

 reaching this stage, and the process is necessarily approaching a 

 standstill, or, to use a physico-chemical term, growth is ap- 

 proaching a state of equilibrium. 



Indeed, the situation is exactly as that taking place in a 

 physico-chemical system undergoing a so-called autocatalytic 



reaction. Thus Figure 40 in- 

 dicating the course of oxida- 

 tion of linseed oil is an ex- 

 ample of an autocatalytic re- 

 action, and it is very similar in 

 general shape to the Figure 

 30, the growth curve of the 

 rat. The work of Bray sug- 

 gests the possibility that curves 

 of inorganic chemical reaction 

 in vitro are not as uneventful 

 as might be inferred from Fig- 

 ure 40, but on the contrary they are pulsating in nature and 

 probably pass through fluctuations in velocity comparable to the 

 fluctuations indicated by the growth curves in Figure 36. 



The general explanation for the shape of the time curve of 

 chemical reactions is applicable for explaining the shape of the 

 age curve of growth. In both cases the time curves of trans- 

 formation are shaped, first, by the tendency of the reacting sub- 

 stances (substrates) to give rise to the products of the reaction j 

 second, by the "back pressure" of the products of the reaction, 

 caused by the finite nature of the "universe," inhibiting the 

 speed of transformation ; and, third, the effect of catalysts on 

 the speed of transformation. 



These general mechanisms appear to hold true, not only for 

 growth of individuals, but also for the growth of populations. 

 Indeed, we are concerned with populations in all cases. In 

 chemical reactions we are concerned with populations of mole- 

 cules j in growth of multicellular organisms, we are concerned 



