AGRICULTURE: REED AND HOLLAND 
135 
THE GROWTH RATE OF AN ANNUAL PLANT HELIANTHUS* 
By H. S. Reed and R. H. Holland 
Graduate School of Tropical Agriculture and Citrus Experiment Station, 
University or California 
Communicated by R. Pearl, February 28, 1919 
If we assume that growth is a dynamic process and that the organism is 
produced as its end-product, certain relations ought to exist between the size 
of the organism at any given time and the final size attained in time, T. 
Growth begins at a slow rate, but as the reaction proceeds it goes on at an 
increasingly rapid rate until it reaches a maximum velocity, then the rate de- 
creases until the reaction comes to a stop. This is precisely what happens in 
autocatalytic processes in which the reaction is catalyzed by one of its own 
products. It therefore becomes of interest to inquire whether the growth rate 
of an organism, or group of organisms, approximates the rate of autocatalysis. 
As will be shown in this article, the equation of autocatalysis expresses 
admirably the growth rate of plants studied. 
Growth may be considered as a function of two variables. The first of these 
is the genetic constitution of the individual. The second is the resultant of 
all those factors that make up what is commonly called the environment of 
the organism. The factors of the first group are essentially internal; those of 
the second group, essentially external. In analyzing the growth process it is of 
interest to separate so far as possible the results of these two classes of factors. 
If the growth rate follows approximately the course of an autocatalytic reac- 
tion, it is safe to assume that it is controlled by some internal factor resident 
in the organism. If it departs from the theoretical course more widely and 
uniformly than might be expected upon the basis of pure chance, we may 
believe that some other, presumably external, factor is of sufficient weight 
to control or, at least, influence the growth rate. 
The studies embodied in the present paper are based on measurements of a 
group of fifty-eight sunflowers, grown for the purpose on the grounds of the 
Citrus Experiment Station, Riverside, California. They were grown on a 
small piece of tolerably uniform soil to which water sufficient to maintain 
satisfactory soil-moisture conditions was applied every seven days. The 
plants grew from the middle of May to the middle of August during a time 
when heat and light were ample for plant growth. As soon as the plants had 
reached an average height of more than 10 centimeters, sixty of the normal, 
appearing plants were selected at random throughout the small plot and 
marked with suitable labels. (During the course of the observations, two 
plants had to be eliminated on account of accidents) . Each plant was marked 
with India ink at a distance of 10 centimeters below the growing tip. This 
mark served as a point from which further measurements were made. The 
