GROWTH UNDER CONSTANT EXTERNAL CONDITIONS. 
817 
for T, T, T3 T, T, T, 
we shall have < Ig < I3 < I4 > I5 > Ig > zero. 
This rule holds good for the separate zones of roots, internodes, and leaves, as well 
as for the entire organs from then- first formation to the time of their full maturity. 
This course of growth I have termed The Grand Period'^, or Grand Curve of Growth; 
since it is at once evident that if the values I^, I2 .... I„ are drawn as ordinates with 
the intervals of time as abscissae, a curve will be obtained which, starting from the 
axis of abscissae, reaches a maximum of elevation, and returns again to the axis. 
The following examples will render this more clear. 
Koppen^ found the following increase of length attained in periods of twenty- 
four hours with a nearly uniform mean temperature : — 
Roots ^ of Lupinus albus. 
Increase in length. Mean temperature. 
First three days : per diem 10 mm. i7'2°C. 
Fourth day 18 i6"6 
Fifth day 44 lyi 
Sixth day 32*6 16-9 
Seventh day 27*9 i7'i 
Eighth day 28 16-4 
In an internode of the flowering stem of Fritillaria imperialis I found the fol- 
lowing increase in length in each period of twenty-four hours * : — 
Normal plant 
Etiolated plant 
Mean temperature. 
in the light. 
in the dark. 
March 20 
2-0 mm. 
io-6° C. 
21 
5*3 
10-5 
. 22 
6-1 
11*4 
23 
6-8 
I 2*2 
24 
9'3 
7*5 mm. 
13*4 
25 
13-4 
125 
139 
26 
12*2 
12-5 
14-6 
27 
8-5 
15-0 
28 
io*6 
I4'2 
14-3 
29 
10-3 
I 2 '6 
I2'4 
30 
6-3 
15-9 
120 
31 
4-7 
i6-ö 
I I'2 
April I 
5-8 
18-2 
10-7 
2 
44 
15-5 
10*2 
^ ' Grand period,' in contrast to the small periodic oscillations of growth which, if represented 
graphically, would appear as smaller elevations and depressions on the grand curve. 
^ Koppen, I. c. p, 48. I have calculated the daily growth from the lengths given in his tables. 
3 That is, the root together with the hypocotyledonary portion of the stem. 
* A few irregularities in the course of the growth are explained by the temporary acceleration 
of the growth from the watering of the ground. Compare the curve in pi. i of the Arbeiten des bot. 
Inst, in Würzburg, vol. I, Heft II. p. 129. 
3 G 
