SLOW AND RAPID GROWTRi 
H. S. Reed 
The growth rate of plants and of plant organs resembles the rate of a 
monomolecular chemical reaction (Reed, 1920 a). Having obtained a 
mathematical expression of the growth rate, it should be possible to analyze 
the process into some of its main components. It has been found that 
the growth rate of certain organisms may be expressed by the differential 
equation 
■ — - k(a — X), 
dt 
where x represents the size of the organism at time /, a represents the final 
size attained, and ^ is a constant of the reaction. The rate at any given 
time is, therefore, proportional to the amount of growth yet to be made. 
It is accordingly rapid at the outset and becomes slower as the end of the 
growth period is reached. 
The integral form of this equation is 
X = a{i — e"^^), 
from which the size of the organism at any time may be calculated. If the 
above assumption is correct, the calculated value of x should not be widely 
divergent from the observed value for the same time. As a matter of fact, 
the two values have been found to agree very well. It seems profitable 
to extend this method of inquiry into different phases of the problem of 
growth, in the attempt to gain further information on the dynamics of 
growth. 
Measurements of a selected number of shoots on young apricot trees were 
made throughout the growing season. The mean length of the shoots at 
each interval of measurement was taken as the observed length at that 
particular time. 
The shoots were of two sorts, and measurements were separately made 
upon each. The first were on trees which received no pruning; the second 
were on trees which received, annually, a severe pruning, with the result 
that the new shoots grew very much more rapidly than those on the un- 
pruned trees. Both classes of trees are in adjoining rows in the orchard 
and receive the same cultural treatments with the exception of pruning. 
At the outset, 50 shoots were selected for each class, but the number 
was reduced by various accidents during the summer, with the result 
1 Paper 70, University of California, Graduate School of Tropical Agriculture and 
Citrus Experiment Station, Riverside, California. 
327 
