IOO 
Gregory . — The Increase in Area of Leaves and 
and 5-5° respectively. The average magnitudes of the angles over the 
whole series are as follows : 
a = 49 * 1 °, 
#= ^ 7 * 2 °, 
y = 68-1°. 
Assuming dimensions a — b — c = ioo, d = 50, and also the above angles, 
a hypothetical leaf area is calculated, and this is compared with the area 
of a leaf of same linear dimensions but with angles differing from the 
average dimensions by half the maximum variation noted above. In this 
way two areas are obtained differing by %. per cent, in area. We may thus 
assume that errors of this order are introduced into the daily estimate of 
leaf area by utilizing end values for the dimensions of the angles, instead 
of measuring these each day. The foregoing considerations of the sources 
of error make it clear that the method is capable of yielding results 
significant to 5 per cent. 
E. Growth of Leaves under Greenhouse Conditions. 
In Fig. 4 is represented graphically the increase in time of the three 
dimensions, a , £, c, of an ‘ average ’ leaf, based on figures obtained by taking 
the geometric means of the daily average dimensions of the first five leaves ; 
in Fig. 5, the increase in area in time of the third leaf. 
The curves are of the S form which frequently occurs in graphical 
representations of growth phenomena. Robertson, and Ostwald have shown 
that such curves can be represented by the equation of an autocatalytic 
reaction, and values calculated from an equation of this type are placed in 
Table IV, together with the geometric means of the dimensions of the first 
five ‘average ’ leaves on successive days. 
Table IV. 
Days . 
a (cm.). b (cm-.). c (cm.). 
Calculated. Observed. Calculated. Observed. Calculated. Observed. 
Area (cm. 2 ). 
From From 
dimensions, equation. 
I 
1.63 
1.76 
I *44 
1.66 
I.2S 
1-26 
i*9 
4.6 
2 
2.28 
2-40 
2.08 
2.49 
i*95 
1.98 
3-8 
7-3 
3 
3-09 
3.20 
2.94 
3*35 
2.67 
2.76 
8.2 
11.4 
4 
4*°9 
4-16 
4*13 
4*3i 
3-7 3 
3*84 
20-0 
19.7 
5 
5 -.2 6 
5 ,r 4 
5*59 
5*74 
5.04 
5-oo 
31.6 
26-7 
6 
5.55 
6.39 
7* 2 5 
7.08 
6.48 
6*41 
44*5 
39-8 
7 
7-87 
7.60 
9-00 
8.51 
8*23 
8.07 
59*2 
57*6 
8 
9-i 1 
8-85 
10-53 
10-00 
9-86 
9-61 
70.8 
79*6 
9 
10-24 
10-18 
n-86 
11.31 
11.34 
11.17 
89-9 
10 5 *° 
10 
n-1-8 
11-13 
! 2-95 
12.40 
12-60 
1 2-60 
1 16-0 
132-0 
1 r 
12-94 
n- 8 i 
13-82 
13.48 
i3"5 8 
13*45 
146-0 
158-0 
1 2 
12-51 
1 2 *47 
14.30 
14-01 
M’33 
14*36 
i860 
1820 
13 
12.95 
12-95 
14-66 
14.52 
14-85 
14-96 
199.0 
i97-o 
14 
13.26 
13.48 
14-97 
15-07 
15*22 
15-58 
211-0 
2 ICO 
15 
13*50 
13.80 
I 5’ 1 3 
15.28 
15.48 
15*80 
2200 
217-0 
16 
13*64 
14*02 
J 5* 2 5 
15.46 
15*65 
16.00 
226o 
2240 
The observed and calculated values agree very well, showing that the 
