Growth in General 



17 



The essential feature of this growth equation is that the rate of growth 

 is determined by the amount of growth which is yet to occur. This im- 

 plies that the final size is established at the start of growth, either by the 

 amount of available building material or in some other way. If only one 

 "master reaction" were concerned, the course of growth might well fol- 

 low Robertson's equation, but there are evidently many substances in- 

 volved and many processes going on simultaneously which probably 

 make the growth process too complex to be analyzed by any one reac- 

 tion. 



Growth curves for certain organs and organisms fit Robertson's equa- 

 tion fairly well (Reed, 1927). For others the fit is not so close. In a struc- 

 ture which in its growth fits the equation perfectly, the rate of exponential 



E 



-3i 



Fig. 2-4. Growth of large and of small fruits in Cucurhita. Log of fruit volume plotted 

 against time in days. Early growth in all races is at a constant rate (straight line) the 

 slope of which here is the same in large and small races. Solid circle, time of flowering. 

 ( From Sinnott. ) 



growth will constantly decrease (since it is proportional to the amount 

 yet to grow, which is decreasing) so that the curve of the logarithm of 

 size against time will be convex from the beginning. When the rate is 

 relatively low the difference between this and the straight line of con- 

 stant exponential growth at first is not great, since the absolute amount 

 of growth in these early time intervals is slight. In many growth curves, 

 such as those of fruits of various races of cucurbits presented by Sinnott 

 ( 1945b ) , the early growth is at a constant exponential rate and shows no 

 indications of convexity of line (Fig. 2-4). Furthermore, large and small 

 fruits which are here compared grow at essentially the same rates but 

 for very different durations. Under these conditions, Robertson's formula 

 would require that the length of time between half size and maturity 



