Leaf Surface of Cucumis sativus . 1 1 5 
and will remain so until the relation of the change of r with time has been 
established, but as such it has the advantage over the conception of an 
autocatalytic reaction in that it is independent of any theory of the ultimate 
mechanism of growth. 
Returning once more to the curves of increase in total leaf surface 
(Figs. 6 and 7), it is seen that the experimental values lie on a sinuous curve 
which fluctuates round the curve of closest fit. This is brought out more 
clearly in Fig. 11, where the logarithms of areas are plotted against time. 
This sinuosity is due to the fact that each leaf in its development goes 
through a grand period of growth, and that the number of developing leaves 
at each moment is small, so that periods of greater and lesser increase 
alternate. It is also seen that towards the end of the experiments the rate 
Days - — >- 
Fig. 12. 
of increase markedly falls off. This can readily be accounted for by a study 
of Fig. 12, which shows for each day the actual areas of successive leaves 
from the cotyledons onwards, and it is evident that up to the eighth leaf the 
development is normal, but after this the later formed leaves go through 
their cycle of development in a shorter time and fail to attain the same 
maximum area as their predecessors. This inhibiting effect is due to the 
fact that the pots in which the plants are growing are more and more 
restricting root development. For this reason the last figures for leaf area 
are untrustworthy and fall short of the areas calculated from the compound 
interest formula. In corroboration of this conclusion it will be noticed that 
in March, where development is less rapid, the effect does not appear until 
the 28th day, while in June it is evident on the 24th. 
The action of light as a limiting factor. The curve of increase in area 
of the total leaf surface of the ; average ’ plant in the December experiment 
(Fig. 13) is apparently of the same form as for March and June, but on 
