360 Blackman.— T he Compound Interest Law and Plant Growth. 
representing the initial capital with which the plant starts ; (%) the average 
rate at which the plant makes use of the material already present to build 
up new material : this represents the rate of interest on the capital (material) 
employed ; (3) the period of growth. 
The plant is continually unfolding its leaves and increasing its assimi- 
lating power. Successive increases in the weight of the plant cannot there- 
fore be treated as a discontinuous geometric series, as if the new material 
(interest) were added at the end of daily or weekly periods. New material 
is added continuously during daylight, and during rapid growth the plant is 
continuously, or nearly continuously, unfolding its leaves and increasing its 
assimilating rate. The growth of the plant more nearly approximates to 
money accumulating at compound interest where the interest is added 
continuously. The simple equation which best expresses the growth rela- 
tions of active, annual plants is W 1 = W 0 e rt , where W 1 = the final weight, 
W 0 — the initial weight, r — rate at which the material already present is 
used to produce new material, and t = time. 
The term r is an important physiological constant, for it is a measure 
of the efficiency of the plant in the production of new material ; the greater 
r is, the higher the return which the plant obtains for its outlay of material. 
The rate of interest, r. may thus be termed the * efficiency index ’ of dry 
weight production, for not only is it a measure of the plant’s efficiency but 
it is also an exponential term in the equation expressing the growth of the 
plant. In some forms of Helianthus the average efficiency index for the 
period up to the formation of the inflorescence may reach 0-1763 (i e. 17-63 
per cent.) per day. 
It is suggested that in all experiments (such as water cultures, pot 
experiments) dealing with the production of vegetative material the efficiency 
index be calculated. The relative efficiency of different plants and of the 
same plant at different stages can thus be determined ; also the effect on 
the efficiency index of various external conditions. 
A small difference in the ‘ efficiency indices ’ of two plants (resulting, for 
example, from a slightly greater rate of assimilation or a more economical 
distribution of material between leaves and axis) may lead to a large 
difference in final weight. In oats, for example, an increase of 6 per cent, 
in assimilation might lead to an increase of 50 per cent, in dry weight at the 
end of joo days. 
The data of earlier workers show that the ; efficiency index ’ is highest in 
the early stages of growth, and then falls slightly. In Helianthus , Cannabis , 
and Nicotiana it falls sharply at the beginning of the reproductive period 
when the inflorescence first appears. 
There is evidence that annual plants at the end of their period of 
growth may lose considerably in dry weight. 
Imperial College of Science and Technology, 
London. 
