9 8 Gregory. — - The Increase in Area of Leaves and 
leaf was calculated direct from its dimensions and then compared with the 
area of its trace computed with the planimeter. In tjiis way a series of 
nearly one hundred figures for leaf area was obtained by planimeter 
measurement, and by calculation from the two formulae. Table II shows 
the calculated and actual areas for the leaves of a single plant. 
Table II. 
Leaf No. 
Area by calculation. 
Area by 
Error. 
ist forniuld. 
2rtd formula. 
Planimeter . 
ist f dr Mill a. 
2nd formula. 
1 ( 9 ) 
78-0 
89.9 
86.4 
- 9 - 8 % 
+ 4 ‘i% 
2 ( 9 ). 
163.8 
192.4 
184-9 
+ 4 *o% 
3 ( 9 ) ' 
235*6 
266-2 
259*2 
- 9 -i% 
+ 2-7 % 
4 ( 9 ) * 
236.4 
26 1 .6 
252-6 
- 6 - 3 % 
+ 3-5 % 
5 ( 9 ) 
208.9 
226*8 
214.1 
- 2 - 4 % 
+ 6.0% 
6 ( 9 ) 
185-7 
208-8 
I 95*9 
- 5 * 2 % 
+ 6-6% 
7 ( 9 ) 
* 44 * r 
1 59.0 
1 50.0 
'- 3 - 9 % 
+ 6.0% 
8 ( 9 ) 
117.8 
129.9 
r 1 3*3- 
+ 4--0 % 
+ * 4 -o% 
9 ( 9 ) 
844 
— 
79*5 
+ 6-2% 
10(9) 
56.2 — 53.0 + 6.0 % 
Mean errors — 3*3 % 
Error by first formula frorii regression equation =• 
„ second „ i> » — 
+'6.0% 
~ 5 * T % 
+ 4 -- 8 % 
These figures include areas of leaves in all stages of development. It 
will be seen at once that formula i gives both positive and negative errors, 
and that, as was to be expected, negative erfors are associated with large, 
and positive with small, leaf areas. Formula 2, on the other hand, gives 
consistent positive errors related inversely in magnitude to the areas of the 
leaves. 
To investigate the matter more thoroughly a statistical method was 
employed. A correlation table was drawn up with ‘Area of Leaf’ and 
‘ Percentage Error ’ as the arrays and the correlation Coefficient was 
calculated for estimations by either formula. 
Formula i gives r Y — — 0-74, 
>> 2 ,, r 2 = — Oil 20. 
The negative sign of the coefficient shows a tendency, as anticipated, 
for errors to decrease as the area increases. The high value of the coefficient 
for formula 1 indicates that there is marked negative correlation between 
percentage errors, and area as calculated from this formula ; on the other 
hand, the correlation in the case of formula 2 is very low and barely 
significant. 
The regressions of error on area in the two cases are as follows : 
1. F = — 0-047X4- 3-62 ; 
2. Y=— 0-007X4-6-37. 
where Y is the percentage error, and X the area of the leaf. From the 
regression- equations were derived equations from which the error in square 
