354 Blackman . — The Compound Interest Law and Plant Growth. 
and his pupils. 1 The application of the compound interest law to the 
growth of the higher plants, though of fundamental importance to a right 
understanding of the plant’s rate of increase, has, however, been over- 
looked by most botanists, 2 and its recognition is sadly lacking in the text- 
books both of plant physiology and general botany. Chodat in his 
‘ Principes de Botanique ’ (2nd edit., p. 133) appears to be the only text-book 
writer who even refers to the relation of growth to a geometric series, and 
his treatment of the subject appears under the section of the book which 
deals with the growth of the cell, and it is confined to pointing out the 
similarity of the growth of the cell to a process resembling autocatalysis. 
Apart from any question of autocatalysis it is obvious that the increase 
in size of the assimilating surface of the young plant must constantly 
accelerate the rate of growth, and that the consideration of this acceleration 
is essential for the proper comparison of the final weight of different plants 
and of the same plants grown for different periods. 
When money accumulates at compound interest, the final amount 
reached depends on (1) the capital originally employed, (2) the rate of 
interest, (3) the time during which the money accumulates. In the case of 
an annual plant the ultimate dry weight attained will depend on (1) the weight 
of the seed, since that determines the size of the seedling at the time that 
accumulation of new material begins ; (2) on the rate at which the material 
present is employed to produce new material, i. e. the percentage increase 
of dry weight per day or week or other period ; (3) the time during which 
the plant is increasing in weight. 
It is clear then that some simple equation is required to relate these 
three factors to the final, weight attained ; such an equation does not appear 
to have been hitherto put forward by those few workers who have considered 
the growth relations of the whole plant from this aspect. Before dealing, 
however, with this attention may be drawn to the work of Noll and his pupils, 
who have provided the data of the growth relations of a number of plants 
during various stages. 
Noll seems to have been the first to formulate the view that in the case 
of an annual plant the successive dry weights taken at regular periods 
follow a geometric series. In 1906 Noll read before the Niederrheinische 
Gesellschaft fiir Natur- und Heilkunde zu Bonn a paper (which appears only 
1 There can be no doubt that the development of an increasing number of rapidly enlarging 
cells which occurs in the development of most plant organs will cause a rapid acceleration of growth, 
producing a curve of growth which is very similar to that of an autocatalysed reaction. A process 
of autocatalytic nature does not, however, explain the rapid fall in the rate of growth in the later 
stages of development of the human body, or the fall in the rate of growth of a plant organ which 
has passed its ‘ grand period ’ of growth. The growth of an annual body of a plant organ of limited 
size is clearly dominated by factors other than those that play their part in a simple autocatalytic 
process. 
2 Since the above was written I have seen the proof of a paper (to appear in the Annals of 
Applied Biology) by Dr. F. Kidd and Dr. W. West in which they point out the importance of the 
compound interest law. 
