xm, 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" 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. 

 •Hooker, D. H., Liebig's law of the minimum in relation to general 

 biological problems, Science N. S. 46: 197-204, 1917. 



