SLOW AND RAPID GROWTH 
From these results, it is plain that the quantitative difference between 
the two classes of shoots existed from the very outset, and that the greater 
total growth of shoots on the pruned trees was due to their faster growth 
in the early part of the period. This conclusion accords with the results 
of Pearl and Surface (191 5), who showed that the superior plants in a 
population are, as a rule, superior from the seedling stage, and that the 
inferior members of the population are likewise inferior from the beginning. 
This raises an important physiological question, viz., How did the pruning 
of one lot affect the g'rowth process in such a way that they made so much 
more rapid growth as soon as activity began in the spring? In other words, 
what happened to cause one lot to grow three times as fast as the other in 
the second week? 
Referring to the differential equation expressing the rate, it will be seen 
that the rate in unit time is equal to the product of two quantities. The 
first quantity is k, the constant of the reaction, and the other is (a — x), 
the difference between a constant and the length of the shoots at time /. 
The rate of growth of the two classes of shoots differs, then, only by the 
value of the second factor, i.e., (a — x). From the data, it seems probable 
that k, the constant of the reaction, is determined by the genetic constitution 
of the tree. It is well known that its value is determined from 
The quantity a — x is, therefore, the one whose value was altered. Now, 
from the integral equation 
X = a(i — e-^^) 
it is easy to see that 
a — X = ae~^\ 
which means that the values oi a — x are equal to the product of a by an 
exponential function of the time. Since in both the unpruned and the 
pruned trees the value of e~^*' was the same, it is, therefore, plain that the 
value of a — X is dependent upon the value of a. While the value of a 
must be, in a measure, determined by hereditary factors, it seems also 
subject to the influence of outer environmental factors such as those here 
operative. 
In short, the rate of growth of the shoot appears to depend upon its 
final length. Whatever, therefore contributes to the production of the 
ultimate length of the shoot influences the rate of growth from the beginning 
of the season. 
The close correspondence between the growth of the shoots and the 
equations above stated is evidence that their growth is some sort of a 
catalytic process. According to this view, the organism is the end-product 
of a process in which a catalyst acts upon a substrate. 
