Nov. 15, 1925 
Growth-Equation Constants in Crop Studies 
975 
Equation (2) is in form for application to observed data. The 
approximate application of the equation to growth data is compara¬ 
tively simple. Figure 1 shows the general form of the curve. It has 
a lower asymptote of 0 and an upper asymptote of the value of A. 
If the growth observations are plotted as ordinates against time as 
abcsissas, a reasonable value can be chosen by inspection as repre¬ 
senting the upper asymptote, and this value is taken as A. A line 
is then drawn at and the point where the growth curve 
seems to cut this line is taken as ti. Time may be taken from any 
point of origin and reckoned in any unit. In the present data the 
date of planting has been used as a convenient origin, and the day 
as a natural and convenient unit of time. For direct comparison 
between constants of different growth curves it is of course necessary 
that time be reckoned in the same unit. Having chosen values for 
(t-tj 
■ X 
Fig. 1.—Showing form of the curve to the equation log A _ X =K ( t—h) for 3 values of K, 0.03, 0.06, 
and 0.09. (Note that a higher value of K means a shorter “grand period” of growth. The values of K 
in this paper lie within the range 0.03 to 0.09.) 
A and t ± the value of E required to satisfy each observation may be 
computed, and the average of the several values thus obtained is 
used as the value of K. Robertson’s Table LX 5 facilitates the 
computations. The curve is then drawn, and if necessary slightly 
different values for the constants are chosen. The curve may be 
changed bodily to right or left by changing t u Its general slope 
may be increased or decreased by changing K . A better fit of the 
theoretical curves to the observed data may be obtained by correcting 
the constants as thus approximated by the method of least squares. 
For the present purpose the writers have considered this refinement 
as unnecessary. 
The question, from the present standpoint, is, what significance 
may be attached to the constants of the equation when applied to the 
observational growth data. According to Robertson’s view, A, 
Robertson. T.B. Op. cit 
