Leaf Surface of Cucumis sativus. 105 
in leaf surface were collected, their work throws no light on the changes in 
the assimilatory activity of the leaf surface. 
Figs. 6 and 7 show the curves of increase with time of the total leaf 
surface of the ‘average’ plant of the sets of experiments carried out in 
March and June respectively. These curves approximate closely to 
exponential curves of the type A = ae rt , (1) where A is total area after 
time t , and a and r are constants, which may also be written in the form 
A = ax 1 , (2) where # = log e r. 
Hence we see as far as these experiments go the surface area of the 
plant increases according to a compound interest law. Further reference to 
this will be made later. 
G. The Effect of External Conditions on the Expansion of the 
Leaf Surface . 
It has been established by the experiments of Koppen on root growth 
in maize, and those of Miss Leitch on root growth in Pisum sativum , that 
the relation of growth to temperature closely approximates to an exponential 
one ; hence, on the assumption that temperature is the controlling factor in 
leaf expansion, the logarithms of the ‘ average leaf areas ’ 1 should bear 
a linear relation to the average temperatures (geometric mean). This 
linear relation, however, does not hold, while,' on the other hand, the 
proportionality between the total radiation falling on unit area during the 
experiments and the ‘ average leaf area ’ developed by the plants in 
the various experiments is very close. The following tentative suggestion 
was put forward as a result of the Cheshunt experiments in the Third Annual 
Report, Experimental and Research Station, Cheshunt, 1917 : The ‘average 
leaf area ’ attained by a cucumber plant is proportional to the total 
radiation falling on unit area during the period of growth. 
The following table summarizes the results of the experiments performed 
at Cheshunt : 
1 By the term ‘ average leaf area ’ is meant the mean ordinate of the curve of increase with time 
of the total leaf surface (Figs. 6, 7, 10, 13), and the numerical value can be found approximately by 
summing the leaf areas for each day and dividing by the total number of daily observations. By 
‘ total leaf area ’ of a single plant is meant the sum total of the areas of individual leaves of one 
plant on a particular day. 
It is obvious that the * average leaf area ’ is the area of the leaf surface of a hypothetical plant 
which will in a given time produce the same dry weight of material as a real plant, but without 
increasing in leaf area. This presupposes the same rate of carbon-assimilation per unit area for all 
the leaves of the plant 
