xiii, c, 6 Brown: Theory of Limiting Factors 349 
An examination of Blackman and Smith’s curve for Fontinalis 
shows that it might just as well have been drawn to indicate 
an optimum as to demonstrate the operation of a limiting factor. 
If the theory of limiting factors as expounded by Blackman 
held rigidly for all physiological processes, we would expect 
it to be a well-known and generally applied law in physical 
chemistry dealing with such things as pressure, temperature, 
and concentrations. Such, however, is not the case, as two 
very simple examples will illustrate: 
First, we may take the case of the solution of carbon dioxide 
in water. If carbon dioxide is in an atmosphere in the pro- 
portion of 1 per cent and under a pressure of one atmosphere, 
it will go into solution at a given rate. If now we indepen- 
dently increase either the concentration of carbon dioxide to 2 
per cent or the pressure to two atmospheres, the rate at which 
the carbon dioxide will be dissolved will increase. Clearly in 
this case there is no single limiting factor. 
Another example is afforded by the action of hydrochloric acid 
on calcium carbonate. We will suppose that a 10 per cent so- 
lution of hydrochloric acid is acting on a given amount of 
calcium carbonate at a temperature of 15°. If now we increase 
independently the concentration of the acid to 15 per cent, or 
the temperature to 20°, the rate of the reaction will be increased. 
In this case also there is clearly no single limiting factor. 
If the rates of such simple chemical processes as those just 
mentioned do not show the operation of a limiting factor, it is 
hardly to be expected that physiological processes in general 
would do so. It might be mentioned that, if Blackman’s the- 
ory did hold, we would expect to find instances frequently re- 
ported. But such does not seem to be the case. That one 
factor should have much more influence than another under 
certain conditions is entirely reasonable and, in fact, such is 
known to be the case; but this does not prove that changes in 
other factors are without effect. 
Crocker 8 in a review mentions quite a number of reasons 
why the theory of limiting factors cannot be regarded as gen- 
erally applicable to physiological processes. He says : 
Hooker 9 gives an interesting discussion on the application of the law 
of the minimum, or limiting factors, to biological problems. He is perhaps 
fortunate, in so far as rigid application of the law is concerned, in drawing 
’Crocker, W., Law of the minimum, Bot. Gaz. 65 (1918) 287-288. 
9 Hooker, D. H., Liebig’s law of the minimum in relation to general 
biological problems, Science N. S. 46: 197-204, 1917. 
