AGRICULTURE: REED AND HOLLAND 
139 
An examination of the consecutive increases in mean height of the plants 
may help to give a clearer picture of the distribution of the growth increments 
of these plants. The mean growth increases observed at seven-day intervals 
have been plotted out in figure 2. The increases, starting from the day on 
which the plants were marked, show a general trend upward for the first forty- 
two days and a decline for the following forty-two days. Inspection of the 
graph shows that the line does not rise and fall smoothly, there being several 
abrupt changes. The mean height increased rapidly from the beginning to 
the twenty-first day. The rate fell off somewhat to the twenty-eighth day, 
then increased gradually until the maximum was reached on the forty-second 
day. From the forty-second to the forty-ninth day the rate fell off slightly 
and then declined abruptly to the fifty-sixth day. From the fifty-sixth to the 
sixty-third day there was only a slight decline in the rate, but from the sixty- 
third to the seventieth day there was a rapid decline followed by a halt until 
the seventy-seventh day, and then a descent to a point near the eighty-fourth 
day where growth ceased entirely. 
The Correspondence Between Growth and Autocatalysis. — It may next be in 
order to inquire concerning the nature and action of some of the internal 
factors which influenced the growth of these plants. Studies on the growth 
of animals made by Robertson (1908, 1915) and of bacterial activity made by 
Miyake (1916) have shown the similarity of these processes to that of auto- 
catalysis. In autocatalysis one of the products of the reaction catalyzes the 
reaction. Such reactions begin slowly, but as more of the catalyzing sub- 
stance is produced the reaction goes on at an increasingly rapid rate. As the 
supply of reacting substances is used up, the reaction begins to slow down and 
comes eventually to a stop. 
Brief mention will be made here to the formula used to express the course 
of an autocatalytic reaction. The reader who wishes more complete mathe- 
matical discussion should consult papers of Robertson (1915) and Miyake 
(1916). An autocatalytic reaction may be expressed by the differential 
equation 
dx 
-=KxiA-x), 
in which A is the initial quantity of material subject to transformation, x is the 
amount transformed at time /, and K is a, constant. The integral form of this 
equation is 
in which ti is the time at which the reaction has run half way to equilibrum; 
that is, the time at which x = A/2. 
Translating these functions into terms of growth, we let ^ represent the final 
mass of the plant; x, the size of the plant at any time, t; ti, the time at which 
