PROCEEDINGS 
OF THE 
NATIONAL ACADEMY OF SCIENCES 
Volume 6 JULY 15, 1920 Number 7 
THE DYNAMICS OF A FLUCTUATING GROWTH RATE^ 
By H. S. Rekd 
Graduate Schooiv of Tropical Agriculture; and Citrus Experiment Station, 
University oe California 
Communicated by R. Pearl, April 17, 1920 
Quantitative studies of growth phenomena should lead to a considera- 
tion of the energy relationships involved. We cannot but believe, in the 
absence of contrary evidence, that the life processes of living organisms 
are manifestations of the same principles of energy relationships which 
exist in other parts of the universe. The study of these energy relation- 
ships ought not, therefore, to be disregarded. Our aspirations for such 
knowledge, which have received so much encouragement from the dis- 
covery of the principle of the conservation of energy, can never be entirely 
suppressed. 
This quantitative study of the rate of growth of shoots on a perennial 
plant, has been attempted in order to gain an insight into some kinetic 
aspects of the problem of growth. Growth, in one form or another, is 
the end product of most of the energy transformations of a tree. Not all 
forms of growth are readily measured. Increase in length is the most 
readily measured and its determination is fairly free from error. Increase 
in weight might be better, but where one wishes to study identical shoots 
through the season, weighing is impossible because it requires removal of 
the shoots from the tree. 
The present study is based upon measurements of 70 selected shoots 
of Royal apricot trees which grew on the grounds of the Citrus Experi- 
ment Station at Riverside, California. The observations were made 
during the growing season of 1918. At the time the observations began, 
the trees had been growing two years in the orchard. The trees on which 
shoots were selected for measurement were scattered over the entire 
orchard in such a way that a fairly random distribution was obtained. 
Shortly after the new shoots appeared, two were selected on each tree 
which had been pruned according to the "Winter- vase" type (a tree which 
is pruned every winter to produce a vase type). The type of pruning 
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