289 
Blackman . — Optima and Limiting Factors. 
tion of the separate factors that are involved in growth to see whether 
or not in some simple case it is merely the inadequate working of a single 
one of them that is checking growth. Peradventure food reserves cannot 
be translocated fast enough, or oxygen cannot quickly penetrate to the 
deep-lying growing cells. 
This analytical attitude brings us naturally to the second part of this 
study, to the consideration of those influences which I propose to call 
‘ limiting factors.’ 
II. 
We start this section with the following axiom. 
W hen a process is conditioned as to its rapidity by a number of separate 
factor s, the rate of the process is limited by the pace of the 1 slowest' factor. 
I think one may fairly express surprise at the extent to which this 
principle has been overlooked by those who have proposed to work out the 
relation between a function and some single one of the various factors that 
control it. 
This desirable end often cannot be really accomplished without taking 
deliberate thought to the other factors, lest surreptitiously one of them, and 
not the factor under investigation, becomes the real limiting factor to an 
increase of functional activity. 
We will consider in some detail the application of this axiom to 
assimilation, and briefly its application to respiration and growth. 
Carbon assimilation furnishes the most instructive case for the con- 
sideration of the inter-relation of conditioning factors, because these factors 
are largely external ones, whereas in growth they are internal and less 
under control. 
Let us then consider first the case of assimilation. We can recognize 
five obvious controlling factors in the case of a given chloroplast engaged 
in photosynthesis. 
(1) The amount of C 0 2 available, 
(2) the amount of H 2 0 available, 
(3) the intensity of available radiant energy, 
(4) the amount of chlorophyll present, 
(5) the temperature in the chloroplast. 
In theory any one of these five might be the limiting factor in the 
total effect, and it is comparatively easy to experiment with (1), (3), or (5) 
successively as limiting factors. 
Many experimenters have indeed done this without premeditation. 
The experiments of Reinke T , in which with increasing light the rate of 
assimilation (as measured by the bubbling of Elodea) suddenly ceased its 
proportional increase and remained stationary while the light increased yet 
1 Bot. Zeit., 1883. 
