The Compound Interest Law and Plant Growth. 
BY 
V. H. BLACKMAN. 
I N many phenomena of nature we find processes in which the rate of 
change of some quantity is proportional to the quantity itself. Since 
money put out at compound interest increases in this way — the rate of 
increase being clearly proportional to the amount of capital at any time — 
Lord Kelvin called the law which such processes follow ‘ the compound 
interest law The rate at which a body cools follows the compound 
interest law, for the hotter the body relative to its surroundings the more 
rapidly it loses heat. Again, the variation of atmospheric pressure with 
height above sea-level follows this law, as does also the velocity of a chemical 
reaction. Wilhelmy’s law, discovered as long ago as 1850, that ‘ the amount 
of chemical change in a given time is directly proportional to the quantity 
of reacting substance present in the system ’, is simply a restatement of the 
compound interest law. 
The importance of this law for the proper appreciation of the growth of 
.a plant was brought home to the writer in 1917 in connexion with the 
results of some experiments on the growth of cucumbers carried out in 
association with Mr. F. Gregory at the Cheshunt Experimental Station. 
It is clear that in the case of an ordinary plant the leaf area will increase 
as growth proceeds, and with increasing leaf area the rate of production of 
material by assimilation will also increase ; this again will lead to a still 
more rapid growth, and thus to a greater leaf area and a greater production 
of assimilating material, and so on. If the rate of assimilation per unit area 
of leaf surface and the rate of respiration remain constant, and the size of 
the leaf system bears a constant relation to the dry weight of the whole 
plant, then the rate of production of new material, as measured by the dry 
weight, will be proportional to the size of the plant, i. e. the plant in its 
increase of dry weight will follow the compound interest law. 
The fact that the increase in number of unicellular organisms, when 
not limited by external conditions, follows a regular geometric series has 
long been recognized. The resemblance also of the growth processes of 
animals and plants to an autocatalysis has been pointed out by a number 
of workers, as J. Loeb, W. Ostwald, Robertson, F. F. Blackman, Chodat 
[Annals of Botany, Vol. XXXIII. No. CXXXI. July, 1919.] 
