140 AGRICULTURE: REED AND HOLLAND 
the mass of the plant is half the final mass, etc. Obviously it would be better 
to weigh the sunflower plants, but as this would require severance between 
the plant and the soil, it would not have been practicable to use the same plants 
for subsequent measurements. In the case of a straight unbranched stalk 
(such as most of these sunflowers were), it seems sufficiently accurate to use 
the height of the plant as an index of the amount of growth, at least up to the 
time of flowering. 
In the case of these sunflowers, A is 254.5 cm., h is 34.2 days, then 
Substitution of the various values of x and corresponding values of t gives 
the corresponding values of K which are shown in the third column of table 2. 
TABLE 2 
Constants for the Mean Height of Sunflowers at Successive Intervals 
/ 
X 
(observed) 
K 
X 
(calculated) 
6 
days 
cm. 
cm. 
cm. 
7 
17.93 
0.04128 
17.05 
-0.88 
14 
36.36 
0.03851 
31.43 
-4.93 
21 
67.76 
0.03341 
55.35 
-12.41 
28 
98.10 
0.03274 
90.09 
-8.01 
35 
131.00 
0.03250 
132.21 
+ 1.21 
42 
169.00 
0.03794 
173.06 
+4.06 
49 
205.50 
0.04196 
205.64 
+0.14 
56.... 
228.30 
0.04312 
227.01 
-1.29 
63 
247.10 
0.05295 
239.74 
-7.36 
70 
250.50 
0.04997 
246.87 
-3.63 
77 
253.80 
0.05892 
250.56 
-3.24 
84 
254.50 
252.46 
-2.04 
The average value of K determined in this way is .0421 . Using this value of K 
we proceed to find the values oiK {t — h), and from these, with the assistance 
of Robertson's tables, a series of calculated values of x were obtained. These 
were the theoretical heights of the plants at the successive intervals provided 
the orginial equation was a correct expression of the growth rate. The diver- 
gence, 6 J between the observed and the theoretical values is shown for each in- 
terval in the last column of the table. On the whole, the correspondence be- 
tween the observed and the theoretical values is very satisfactory. The 
observed and calculated heights of the plants are shown graphically in figure 3. 
More accurate comparison of these values was made by testing the good- 
ness of fit of the theoretical to the observed curve. Employing the method 
given by Elderton (1902), it was found that P = .9256, which is taken to in- 
dicate a satisfactory fit, since in approximately ninety-two cases out of one 
