Nov. 15, 1925 
Growth-Equation Constants in Crop Studies 
979 
represent the vegetative phase, but they also include certain portions 
of the plant directly concerned with the reproductive phase. It is 
reasonable, therefore, to treat the data as representing two cycles of 
growth. Such treatment is suggested also by the fact that growth in 
animals in many cases occurs in two or three distinct cycles. 
In Figure 4, the observational data for crude fiber in the stalk of the 
sunflower are repeated. Two curves of growth (designated x' and 
x") are given, together with the sum of these two as representing 
the observed data. It will be observed at once from Figure 4 that 
the theoretical curve as thus derived agrees better with the observa¬ 
tions than does the single-cycle curve of Figure 2. The root mean- 
square error for the single-cycle curve is 66 pounds, and for the 
double-cycle curve 40 pounds. 
Fig. 4.—Growth of crude fiber in stalk per acre of sunflower crop. Time (t) is reckoned in days from 
date of planting. Growth Or) is expressed as a percentage of 2,680 pounds. Observations same as Fig¬ 
ured, treated as a two-cycle phenomenon. Equations to curves: 
log ^^,=0.042 0-72.5) 
x" 
l °9 435 ,^ =0.082 (*- 110 ) 
Reed and Holland 9 studied the growth of the sunflower plant in 
height (cm.) and from their data derived the equation 
l0g 254.5 -s = - 042 (<_34 ' 2) 
time being counted in days from a date following planting not defi¬ 
nitely stated. K of their equation agrees exactly with K for the first 
cycle equation of Figure 4, a value considerably different than K of 
the single-cycle curve of Figure 2. Since growth in height of the 
plant is not accelerated by seed development, the relation between the 
K’s of the three equations may be taken as further evidence that the 
crude-fiber data represent a two-cycle growth process. 
9 Reed, H. S., and Holland, R. H. the growth rate of an annual plant helianthus. Proc. 
Nat. Acad. Sci. 5: 135-144, lllus. 1919. 
