4o6 
PHYSIOLOGY: H. S. REED 
Proc. N. a. S. 
Putting this into terms of the tree, we may say that the growth of the 
apricot branches was, in the first 6 weeks, accelerated by amounts which 
diminished from 19.1 cm. at the outset to 3.0 cm. in the 6th week. From 
the 7th to the 21st week the growth was retarded by regularly varying 
amounts, and from then on, there was an acceleration, amounting at the 
most, to 4.2 cm. 
The Dynamical Basis for Growth. — Our attention next passes to the 
question of the rate of growth. Since equation (6) represents the length 
of the apricot branches at successive intervals, we should obtain an equa- 
tion by differentiating it, which will represent the rate at which they 
grow. Clearly, this relationship is of considerable physiological im- 
portance. By differentiating equation (6) we obtain the following 
1^ = 19.95 <'-'»] -19.1 If "'" (.055 cos / + sin j-^t) \ (7) 
This expression will be more easily grasped if we obtain the values of the 
equation which correspond to different values of / and compare them with 
the rate per week (increments) actually observed as shown in table 4. 
The dotted line in figure 2 shows the graph obtained by plotting these values 
along with the observed values of the increments for the same intervals. 
The agreement between the two is good, with few exceptions. Better 
agreement might have been obtained had there been more frequent 
observations during the first two weeks; as it is, the number of observa- 
TABLE 4 
Values of the Weekly Increments in Length of Apricot Branches, Compared 
WITH the Rate of Growth Calculated from the Formula 
- = 19.95 [^--095 a- D] - 19.1[e-055^(.055 cos -/ + - sin-0] 
dt 14 14 14 
t 
OBSERVED 
CM. 
CALCULATED 
CM. 
d 
t 
OBSERVED 
CM. 
CALCULATED 
CM. 
9 
0 
20 
9 
15 
7 
6 
6 
1 
1 
5 
1 
15 
8 
18 
1 
-2 
3 
16 
6 
4 
6 
0 
0 
4 
2 
25 
7 
15 
6 
10 
1 
17 
3 
6 
5 
7 
-2 
1. 
3 
13 
0 
13 
5 
-0 
5 
18 
2 
9 
5 
4 
-2 
5 
4 
14 
1 
11 
8 
2 
3 
19 
5 
5 
5 
1 
0 
4 
5 
9 
4 
10 
4 
-1 
0 
20 
6 
6 
4 
7 
1 
9 
6 
7 
6 
9 
3 
-1 
7 
21 
6 
0 
4 
3 
1 
7 
7 
8 
3 
8 
4 
-0 
1 
22 
4 
8 
3 
9 
0 
9 
8 
3 
3 
7 
7 
-4 
4 
23 
3 
8 
3 
4 
0 
4 
9 
2 
4 
7 
3 
-4 
9 
24 
2 
1 
3 
0 
-0 
9 
10 
7 
1 
6 
9 
0 
2 
25 
1 
8 
2 
5 
-0 
7 
11 
11 
8 
6 
7 
5 
1 
26 
1 
9 
2 
1 
-0 
2 
12 
8 
9 
6 
6 
2 
3 
27 
1 
8 
1 
7 
0. 
1 
13 
7 
9 
6 
4 
1 
5 
28 
1 
4 
1 
5 
-0. 
1 
14 
5 
5 
6 
3 
-0 
8 
