97 
Leaf Surface of Cucnmis sativus. 
areas for successive leaves the mean total leaf surface for each day of the 
experiment is obtained. It is obviously less laborious to calculate the 
mep areas of the leaves from the mean dimensions than to take the average 
of the areas of the single leaves of each plant ; also the value so obtained is 
more trustworthy, as it is less liable to error from irregularities in growth 
and from errors in measurement. In these experiments the angles were not 
measured each day, but assumed to remain constant during the course of 
development of the leaf, and the values obtained from the leaves on the last 
day of the experiment were utilized. The magnitude of the error introduced 
in this way will be considered below. 
At the end of each experiment the leaves were removed from the 
plants, and their areas ascertained in the following manner. Tracings of 
the leaves were made on thin ground glass sheets immediately after 
removal from the plants. The pressure of the glass was adjusted so that 
the leaves were flattened out but not crushed, and this was done by raising 
the glass slightly at the edges. The only precaution necessary is to avoid 
parallax during tracing. In the case of certain leaves it is necessary to cut 
the leaf into portions in order to ensure its flatness. 
By suitably illuminating the plate from below, the traces can be redrawn 
on tracing-paper, and the areas can then be measured with a planimeter. 
In this way the leaf area of each plant can be obtained on the last day of 
the experiment, and, by comparing the average of these with the mean 
area calculated from the mean dimensions of the leaves on the last day an 
estimate of the error of calculation is found. 
D. The Errors of the Method. 
From the nature of the method employed, the calculated values of the 
leaf areas will differ more or less from the real area. 
Examining Figs. 2 and 3 once more, it is clear that the area calculated 
is that of the rectilinear figure A B C O E D, and this will equal the area of 
the leaf only when the areas of the irregular portions of the polygon 
external to the leaf happen to be equal to the irregular portions of the leaf 
excluded. The; calculated areas are thus liable to chance errors, and it 
becomes important to estimate the effect of these errors on the trust- 
worthiness of the results. From a priori considerations it is obvious that 
the negative discrepancies given by formula 1 will increase in magnitude as 
the areas of the basal lobes of the leaves become proportionately greater. 
On the other hand, formula 2 may give results which are too high for small 
leaves when the bights between the points of the leaf are great. 
In order to investigate this point the areas of the leaves of the plants 
in Expt. Ill were compared at the end of the experiment with the actual 
area obtained with the planimeter. In this case, of course, the area of each 
H 
