328 
H. S. REED 
that there were 33 shoots in the unpruned class and 28 in the pruned class. 
In either case the number of variants is large enough to give a satisfactory 
mean. 
Table i. Mean Length of New Shoots on Pruned and Unpruned Apricot Trees During one 
Season 
On Unpruned Trees 
On Pruned Trees 
X (Observed) 
X (Calculated) 
X (Observed) 
X (Calculated) 
weeks 
cm. 
cm. 
cm. 
cm. 
I 
9 
10 
13 
23 
2 
17 
20 
37 
43 
3 
25 
28 
60 
61 
4 
29 
36 
73 
78 
5 
34 
42 
88 
92 
6 
42 
48 
102 
105 
7 
50 
54 
113 
117 
8 
57 
59 
121 
128 
9 
63 
63 
132 
137 
10 
68 
67 
142 
145 
II 
71 
70 
148 
153 
12 
77 
73 
156 
160 
13 
79 
76 
163 
166 
14 
82 
79 
174 
171 
15 
83 
81 
177 
176 
16 
84 
83 
182 
181 
17 
85 
85 
186 
184 
18 
86 
86 
190 
188 
19 
87 
88 
194 
191 
20 
88 
89 
197 
194 
21 
89 
90 
200 
196 
22 
90 
91 
203 
199 
24 
25 
94 
94 
208 
204 
26 
27 
210 
207 
Table i contains the observed lengths of the two classes of shoots on the 
successive weeks of measurement. The mean final length of shoots on the 
unpruned trees was 94 cm., and that of shoots on the heavily pruned trees 
was 210 cm. We may let 100 represent the limiting value of X\ and 218 
that of X2. By a series of approximations the equation 
Xi = 100(1 — e~-^^ 0 
was found to be satisfactory for the values of the shoots on the unpruned 
trees, and 
x. = 218(1 - 0 
for the shoots on the pruned trees. A graphic comparison of these values 
is given in figure i. 
It will be seen that the only difference between the two integral equations 
is in the value of the constant a. The value of k, the constant of the re- 
action, is the same in both cases. The values of x calculated from these 
