4o8 
PHYSIOLOGY: H. S. REED 
Proc. N. a. S. 
week the rate is fairly constant, only diminishing about 2.5 cm., but from 
that time on, the decline is considerably more rapid. At the end of the 
growing season the rate is less than one-tenth of the initial rate. 
From a biological point of view, our interest in any equation represent- 
ing the growth of organisms is not confined to evolving equations which 
shall represent their size at any given time. If we know the rate at which 
an organism grows and can express it quantitatively, we are in a position 
to analyze the processes by which it increases in size. 
To facilitate matters, we may write equation (6) in a general form 
X = a [l-e~^'^'- + be-^'-' cos at. 
When differentiated, this becomes 
1^ = ahe~'' hf^'' [ h cos at^- a sin at } 
which is the general form corresponding to equation (7). This can also be 
written in the form 
dx 7 r / \ \ ~ ! (^2 — ki) cos at -\- a sin at } 1 
ia-x) + 
For the sake of brevity let 
Y = -be'^'^ [{k2-ki) cos at + a sin at] 
We may then write 
J = h [{a-x) + Y/h] (8) 
In the case of the apricot data 
Y = 19.1 f ''"[ - .04 cos -t + - sin -t]. 
The advantage of this form of expression lies in the fact that Y may be 
expressed in terms of x, since equation (7) may be written 
Y = ^-ki (a-x). 
at 
It seems, therefore, that the growth of these apricot shoots in one 
season conforms to that of a unimolecular consecutive reaction, in which 
the main reaction is influenced by a secondary reaction product. The 
rate of the main reaction would follow the path of curve A in figure 3, if it 
were alone operative. The secondary reaction (represented by curve B) 
has an additive effect on the main reaction and gives the resultant course 
shown by curve C. In the first part of the season, B has a negative value, 
its effect, therefore, is to diminish A. In the latter part of the season, 
B has positive values and accordingly augments A. 
The writer is inclined to adopt the suggestion of Robertson (1913) 
concerning the progressive increase or decrease in the amount of growth- 
catalyst during a cycle. If we assume that in this sort of a reaction the 
TT TT TT 
