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C. West , G. E. Briggs, and F. Kidd. 
measured by the size of the population or its dry-weight, is found to 
increase exponentially with time, but the rate per unit of population 
or per unit of dry-weight is constant throughout (14). We may, 
therefore, legitimately take the dry-weight at any moment as a 
measure of the material actually engaged in growth at that moment 
and proceed at once to the determination of a growth constant. 
In this simple case the method of expressing the rate of growth 
is physiologically sound in so far as the rate remains constant under 
constant conditions, and changes in rate would be expressions of 
changes in environment. The soundness of the method depends 
upon the fact that all the material is equally active in forming new 
growth by cell-division and by assimilation of new material, and 
hence the dry-weight of any time is a measure of the material 
responsible for dry-weight increment and growth. 1 
In the higher plants the state of affairs is more complex. The 
material of the plant is not all equally active in forming new growth 
by cell-division and by assimilation, and moreover we do not know 
that the relation of the amount of material actually engaged in 
growth to the total material (dry-weight) is constant: in fact the 
evidence from morphological considerations and from analyses of 
growth data carried out by the present writers (4) is that the 
relation undergoes a definite type of variation. Consequently, 
in relating growth to dry-weight in the higher plants we are not 
relating growth to the amount of actual “ growing material.” The 
growth-rate expressed per unit of dry-weight does not remain 
constant under constant external conditions and we cannot 
therefore, on this basis alone, determine constants for the plant, 
nor can we evaluate the effect of environmental factors. 
Previous Attempts to evaluate Constants for Plant Growth. 
In practically all previousattemptsto evaluateconstantsfor plant 
growth the rate, i.e., increase in dry-weight per unit time, has been 
dx 
expressed per unit of dry-weight. The formula ^-=Kx (A—x), or 
^ 
in its integrated form log —-—=K (t—t'), which is the autocatalytic 
formula put forward by Robertson (12 & 13) as expressing the 
growth of an organism, and which Reed (8 & 9) and Rippel (10 & 11) 
apply to the growth of the plant organism, involves the assumption 
that since K is constant, 2 x, the dry-weight, is a measure of the “grow- 
1 The result is actually a statistical one, assimilation preceding cell 
division in the individual, but at any moment both processes are going on 
when the population as a whole is considered. 
* Reed goes as far as to assume that K is a constant apart from A. 
