I I 2 
Gregory. — The Increase in Area of Leaves and 
Discussion of the Results. 
The growth in area of leaf surface. The curves of increase in area of 
the total leaf surface, obtained by plotting the daily leaf area data for 
March and J une, are very approximately represented by a function of the form 
A = ™ r \ ( 9 ) 
where A is area at any time, t after germination, a , r are constants. Differ- 
entiating this function with respect to time gives the relation between rate of 
increase in area and time. This operation gives 
dA 
Tt 
(10) 
i. e. the rate of increase of leaf surface at any time is determined first by the 
area of leaf surface already present, and secondly by the value of the 
constant r. 
If relation (9) were strictly true the leaf surface should go on increasing 
in a geometric ratio indefinitely, which certainly is not the case with annual 
plants, though taking the year as a time unit perennial plants may approxi- 
mate to such a condition. The expression given above is therefore limited 
in its application to early stages in growth. 
The curve of increase in area of the leaf surface throughout a growing 
season has been determined roughly by Kreusler and his co-workers for 
a number of crop plants, and is of the ubiquitous S form. Thus two facts 
are clear from the author’s and Kreusler’s results: (1) during the early 
stages of growth the leaf surface increases in geometric ratio ; (2) the rate 
of increase gradually declines and finally becomes zero. Comparing the 
Cheshunt results for increase in area of total leaf surface during March and 
June, we find that the value of r, or what might be termed the ‘ rate of 
interest is 0*159 and 0*196 in the two cases. It is clear, therefore, that the 
magnitude of r depends on external factors. 
It has already been pointed out that the ‘ average leaf areas ’ in the 
Cheshunt experiments are proportional to the total radiation per unit area 
during the period of the experiments, i. e. proportional to the product of 
light intensity and light duration, which must accordingly regulate the rate 
of increase. 
Now these factors are varying during the periods of the experiments, 
particularly so in March, at which time the altitude of the sun goes through 
its period of most rapid increase, and hence it is not surprising that the 
curve of closest fit, calculated on the assumption that r is a constant, falls 
short of the experimental values for leaf area from the 19th to 24th days of 
the March experiment, and that for June the fit is much closer. Hence we 
1 A similar term r has been introduced by V. H. Blackman as a measure of the rate of 
production of dry matter, and the name ‘ efficiency index of dry weight production ’ was suggested. 
By analogy, this term r might be called the £ efficiency index ’ of leaf-surface increase. 
