Leaf Surface of Cucumis sativus . 121 
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these optimal relations through a study of efficiency of plants under various 
conditions. 
In concluding this part of the subject one may bring forward additional 
evidence for the compound interest law of leaf-surface increase. If the rate 
of increase of the leaf surface is determined by the leaf area already in 
existence, then the plant with large cotyledons should gain a start over the 
plant with smaller cotyledons, and this extra start should persist throughout 
the development of the plant. 
For 100 cucumber seedlings the correlation coefficients have been 
worked out between 
(1) the maximum area of cotyledons and maximum area of first leaf, 
(2) the maximum area of cotyledons and the dry weight after 30 days. 
These are as follows : 
(1) r= +0-54, 
(2) r == +0-36. 
Furthermore, it was noticed by the author that plants with highest growth- 
rate later produced the largest crop of fruit, and in the Fourth Annual 
Report of the Cheshunt Experimental Station are published the growth- 
rate and crop weight for the average plants of eighteen batches of four plants 
each. From these data the author has worked out the correlation coefficient 
between growth-rate and crop weight, and finds that 
r — +073. 
The coefficient is high and certainly suggests that the whole future activity 
of the plant is correlated with the area of the cotyledons of the seedling. 
Finally, it must be borne in mind that the results of this investigation 
apply only to plants grown under similar conditions, when the actions of 
limiting factors other than light intensity are excluded ; and the results 
obtained cannot be applied directly to plants grown under other conditions 
of soil moisture and soil fertility. 
Summary. 
A method is described for ascertaining the areas of leaves without 
detaching them from the plant. The errors of the method are discussed, 
and it is shown that a single determination of the total area of the leaf 
surface is significant to 5 per cent. 
The growth in length and breadth and in area of leaves in daylight is 
shown to follow the same law as the growth in length of axial organs, 
displaying a grand period of growth. Under continuous electric light, 
however, the rate of increase falls off from the first measurement of area 
onwards. 
The curves of increase in area and in linear dimensions for a single leaf 
in daylight are of S form, and can be fairly represented by the formula of an 
