99 
Leaf Surface of Cucumis salivus. 
centimetres could be calculated, and so a curve of errors was drawn from 
which the error of calculation for leaves of any size could be read off direct. 
For areas less than 80 sq. cm. formula i tends to give values which are too 
high, while for greater areas negative errors are introduced. Formula 2 
tends always to give positive errors, which decrease relatively in magnitude 
as the area of the leaf increases. 
Utilizing all the data available, and considering the percentage errors 
in the calculated areas as the differences, the probable error for a single 
determination by either formula, within the range of areas measured, was 
estimated. These errors were found to be as follows : 
P.E. for single determination by formula I = +5*7 per cent. 
„ „ „ „ „ „ 2 = +4*7 per cent. 
Each value for the leaf area is based on the average dimensions of ten 
corresponding leaves on separate plants, hence the value for the probable 
error of a single determination as stated above must be divided by V io, 
i. e. the probable error of each value for the total leaf area of a single plant 
is in the neighbourhood of + i-6 per cent. In the case of the June data 
the calculated area of the leaf surface per plant was 1,684 sq. cm. ; the 
actual area measured with the planimeter was 1,659 sc b cm -> giving a positive 
error of 1 -5 per cent., which lies within the range of the probable error. 
Errors introduced by failure to measure angles of leaf during the course 
of the experiment. From the leaf tracings taken at the end of Expt. Ill 
the angles a, / 3 , y were measured for each leaf of all the plants. The 
averages for angles of corresponding leaves are set out below in Table III. 
Table III. 
Leaf A T o. 
2 a. 
218. 
27. 
1 
80.4° 
132.6° 
162-9° 
2 
8o.8° 
152-6° 
146-4° 
3 
93 - 8 ° 
162*5° 
138-4° 
4 
95 -°° 
1 7 ** 5 ° 
137 - 7 ° 
5 
94.6° 
162.1° 
142.4° 
6 
98-1° 
176*1° 
i 35 -i° 
7 
101-5° 
1 79.0° 
135 - 0 ° 
8 
1 01. 4 0 
180.2° 
133 - 4 ° 
9 
99 - 5 ° 
180.9° 
130.6° 
io 
101*7° 
182-7° 
— 
Average 
excluding 1 and 2 
98.2° 
174 * 4 ° 
136.1° 
Leaves 1, 2, 3 were full grown at the end of the experiment, but the 
remainder were in various stages of development. Leaving the first two 
leaves out of account, there is among the remainder a fairly regular 
gradation in the angular magnitudes ; a and (3 continually increasing, and 
y decreasing. The maximum variations in 2 a, 2 / 3 , and 2y are 4 0 , 10-5°, 
PI 2 
