Vol. 7, 1921 
PHYSIOLOGY: H. S. REED 
311 
A METHOD FOR OBTAINING CONSTANTS FOR FORMULAS 
OF ORGANIC GROWTH* 
By H. S. Reed 
University op California 
Communicated by R. Pearl, October 8, 1921 
The growth of many organisms may be computed from the equation 
in which x represents the size of the organism at time t, A represents the 
size of the organism at maturity or at the end of a particular cycle of 
growth, h is the time at which x — A/2 t and K is a constant. This is the 
equation for an autocatalytic reaction and we are indebted to Robertson 
(1908) for showing its applicability to growth processes. 
While the equation expresses the growth of plants with a high degree 
of accuracy, it often fails to fit the observed data in the early life of the 
organism. In other words, the computed values of x are too large when t 
is small. Recently this feature of the equation has been discussed by 
Mitscherlich (1919) and Rippel (1919). 
The present paper intends to show how a simple graphic method may 
be used to overcome the difficulty just stated. 
Let us assume that the true state of affairs is represented by the equation 
This is merely assuming that the exponent of (t — h) may or may not be 
unity. We may write 
l0g ( l0g X^) = 1 ° g K+ C log ( * " k) 
This is the equation of a straight line if log (log — — ) be used as 
\ A—x/ 
ordinate and log (t — h) as abscissa. The intercept on the y-axis will 
be log K and the slope of the line c. 
When t < h the values of (t — h) are negative in sign, as t approaches 
the value of h the value of (t — £i) decreases to zero. As / increases 
beyond *i the values of (t — h) are positive. However the sign of the 
quantity it — 2i) does not affect the logarithm. The result is that we 
actually get two lines on the chart, one for values of the equation when 
t < h and another for values when t > h. These lines as determined 
from the" observations, are seldom superimposed. With them as guides the 
