Voi<. 6, 1920 
PHYSIOLOGY: H. S. REED 
amount of catalyst is in some way proportional to values of dx/dt, there 
would be in the present instance a progressive decrease during the growing 
season. If the initial excess of catalyst is unfavorable to growth then the 
effect of Y (which is negative during the first part of the season) would 
accelerate the reaction because it operates to cause a more rapid decrease 
in the amount of the catalyst. The amount of this acceleration is actually 
indicated by the values of 19.1 [e~'^^^^ cos 7r/14] in equation (6). 
If the assumptions made in this study have any basis, it would seem 
that some light has been thrown upon the process of growth. It appears 
that growth proceeds at a definite rate, and is capable of mathematical 
expression. The growth rate appears to be proportional to the amount 
2i 
0 
\\ 
[ 
? - nr 
1 ° D 
0 5 10 15 20 Z5 Z8 
Time in weeks 
FIG. 3 
Growth rate of apricot shoots. 
— (A), curve calculated from ake~^^ ~ 
, (B), curve calculated {rom — he~^'^^ [^2 cos at -\- a sin at] 
, (C), curve calculated from sum of values of (A) and (B). 
□ □ □ observed increments. 
of a hypothetical catalyst and the intra-seasonal cycles of growth may be 
indicative of fluctuations in the amount of active catalyst in the organism. 
Summary. — 1. The growth of shoots on a selected sample of young 
apricot trees, followed a definite, though fluctuating rate. The maximum 
growth rate was exhibited soon after the growth of the season began, and 
declined with some regularity to the end of the season, though three 
distinct intra-seasonal cycles of growth were apparent. 
2. The growth in each cycle closely resembled the rate of an auto- 
catalytic reaction. The growth rate for the entire season conforms to 
that of a reaction consisting of two unimolecular reactions, one of which 
at first accelerates and subsequently retards the other. 
3. If growth be assumed to be proportional to the amount of active 
catalyst present, a method is available for studying the dynamics of the 
growth process. 
