Growth in General 13 



In organs which (unlike the axes) have a limited or determinate 

 growth, such as leaves, flowers, or fruits, the meristems are usually not 

 localized but are diffuse, so that the whole organ, or most of it, is grow- 

 ing throughout and not at any particular point. Such structures have a 

 growth cycle of their own, much as does an animal body, and when they 

 reach maturity all their tissues stop growing and there is no embryonic 

 region set apart by which further growth may be accomplished. 



Graphical and Mathematical Analysis of Growth. One of the most 

 obvious facts which a study of growth reveals is that it does not proceed 

 at a constant rate. Many factors influence this rate, but under normal 

 and favorable conditions a growing organ or organism undergoes a 

 characteristic course of increase, first growing slowly, then with increas- 

 ing speed, and finally slowing down again until growth stops entirely. 



It is possible to picture this graphically in various ways. In Table 2-1 

 are presented the data for the increase in diameter of a gourd fruit from 

 its early state as a small ovary primordium until maturity. If these diam- 

 eters are plotted as ordinates against time in days, the growth curve 

 shown in Fig. 2-1 results. This is an S-shaped, or sigmoid, curve and is 

 typical of most growing organisms, both plant and animal, though it is 

 subject to much variation. It presents the changing size of the growing 

 organ throughout its course but does not give a very clear picture of the 

 changing amounts of daily growth. If daily increments are plotted in the 

 same way against time, the curve in Fig. 2-2 results. These increments 

 are small at first, then progressively larger, and then smaller again. 



Such graphical representations of growth have long interested biol- 

 ogists and mathematicians, who have endeavored to analyze them in 

 mathematical terms and thus obtain clues as to the character of the 

 growth process itself. In many cases such analyses have proved helpful 

 in providing a simple statement of the course of growth, but there are so 

 many variables involved in growing organisms that one can hardly expect 

 to express their increase completely in an equation. 



Table 2-1. Growth of a Gourd Fruit from a Small Primordium to Maturity 



Diameter, Diameter, 



Date mm. Date mm. 



July 30 2.4 Aug. 9 30.0 



" 31 3.1 " 10 35.2 



Aug. 1 3.9 " 11 40.0 



" 2 5.1 " 12 43.8 



" 3 6.5 "13 46.0 



" 4 8.4 " 14 47.0 



" 5 11.0 " 15 47.5 



" 6 14.0 " 16 47.9 



" 7 18.0 " 17 48.0 



" 8 23.5 " 18 48.0 



