114 GROWTH 



Robertson * concludes that in any particular growth cycle, 

 either of an organism or of a member of an organism, the 

 maximum increase in volume or in weight in a unit of time 

 occurs when the total growth due to the cycle is half completed. 

 Such a cycle of growth conforms to the formula 



A - x" 



where x is the amount of growth in weight or volume which 

 has been attained in time t. A is the total amount of growth 

 attained during the cycle, K is a constant and t is the time at 

 which growth is half completed. These relations are such as 

 would be expected to hold good were growth the expression 

 of an autocatalytic chemical reaction, and the growth of the 

 organism should, from the hypothesis, remain constant, having 

 once attained its maximum. But the contrary obtains, in old 

 age and senescence a loss of weight occurs ; this is supposed 

 to be due to the action of secondary factors which are imposed 

 on the phenomena of growth itself. 



An inspection of Robertson's figures, for example those 

 given for the oat,f or for Cucurbita, shows differences between 

 the observed and calculated growth values of varying magni- 

 tude, and these differences when expressed in percentages 

 sometimes appear too large to support the thesis ; but when 

 the observed and the calculated values are expressed in the 

 form of a curve (Fig. 9) their incidence is sufficiently close 

 to give support to the thesis, especially when allowance is 

 made for the experimental errors. 



To what extent and in what degree growth processes may 

 be correlated with this law is uncertain. The observations of 

 Gregory show that the curves of increase in the area of the 

 leaf surface of cucumber plants are of the S form and can be 

 represented by the formula of such a reaction. In the earlier 

 stages of growth this increase also is in accordance with a law 

 of compound interest. There is thus a choice between the 

 two expressions : the compound interest law is a conception 

 rather than a physiological constant, but even so Gregory con- 

 siders it to have the advantage over the law of autocatalytic 



* Robertson : "Arch. Entwicklungsmech. Org.," 1908, 25, 581. 

 [Id., 26, 108. 



