400 
PHYSIOLOGY: H. S. REED 
Proc. N. a. S. 
log — =i^(^-« (2) 
which is the integral form of the equation (1), in which a is the length 
of the -shoot at the end of the cycle, x is the length at any given time, 
t, K = ak, and h is the time at which the cycle is half completed, i.e., 
when X = a/2. 
The computations may be followed by the aid of table 1. Since the 
new shoots were marked at the commencement of observations at a uni- 
form distance of 10 cm. from the tip, we may take the value of rx; as 10 
when ^ = 0. The successive length of shoots in each cycle was com- 
puted from the equation (2). For convenience the time was computed 
in days instead of weeks. Data for the three cycles are given in table 1. 
For the computation of the second and third cycles the axes were moved 
to AOB and A'O'B' (fig. 1). For the second cycle the observed values of 
X are diminished by 100 cm, and for the third cycle by 165 cm. Having 
obtained the mean value of K for each cycle, the calculated values of x 
were obtained from the equation stated above. 
The observed and calculated values of this kind of a reaction are apt 
to show more divergence in the initial stages than after the reaction gets 
under way. The growth rate is apparently no exception to this rule. 
However, the divergence is not excessive when one considers the nature 
of the material and the observational errors involved in making measure- 
ments. The graph in figure 1 shows the nature of the curves and their 
agreement with observed values. It is thus apparent, not only that the 
growth process followed the course of a definite reaction, but that the 
individual cycles which made up the growth period also follow a definite 
course which conforms to certain quantitative relationships. 
It will be noted that there is very good agreement between the ob- 
served and computed values of these three cycles and that each in itself 
appears to follow the course of an autocatalytic reaction. The root- 
mean-square deviations of the values of the three cycles are 5.15 cm., 
2.15 cm., and 2.52 cm. 
It will be further noted that the mean value of K in the three cycles is 
successively less in each case, being, 0.0380, 0.0355, and 0.0277 respec- 
tively. Reference to the graph in figure 1 shows that the mean slope of 
the three curves is also successively less. 
This analysis of the growth rate of the apricot shoots is taken to indi- 
cate that their seasonal growth was made up of three distinct cycles of 
approximately 9 weeks each. In the first cycle growth was more rapid 
than in any other. Growth goes on at a more rapid rate during ap- 
proximately the first third of each cycle and then "fades away" toward 
the end of that cycle. 
While this analysis affords some interesting insight into the growth 
