LIMITING FACTORS 9 



to F. F. Blackman * who enunciated the axiom that when 

 a process is conditioned as to its rapidity by a number of 

 separate factors, the rate of the process is limited by that of 

 the slowest factor. The limiting factor in any definite in- 

 stance may be identified by the experimental application of 

 the principle that " when the magnitude of a function is 

 limited by one of a set of possible factors, increase of that 

 factor, and of that one alone, will be found to bring about an 

 increase of the function." f 



The principle may be illustrated by one of Matthsei's $ 

 many experiments on the effect of temperature on carbon 

 assimilation in conditions constant except for temperature 

 and illumination. In Prunus laurocerasus there was a gradual 

 increase in the assimilation as the temperature was raised ; 

 at about n°C. a maximal assimilation of 22 mg. of carbon 

 dioxide per 50 square cm. per hour obtained and was not 

 increased even by raising the temperature to 25 C. By 

 doubling the light intensity, however, the maximal assimi- 

 lation was equivalent to 37-5 mg. of carbon dioxide per 50 

 square cm. per hour and again there was no increase on raising 

 the temperature. This means that light intensity was a 

 limiting factor and only by its increase could a greater carbon 

 assimilation be obtained. In his original illustration of the 

 principle of limiting factors, Blackman graphically represented 

 the reaction as linear up to the point of limitation and then 

 abruptly horizontal ; and it is this abruptness in the course of 

 the graph which has led to some controversy and has resulted 

 in an accretion of knowledge. But before dealing with this, 

 it must be pointed out that the graph originally presented was 

 an illustration of a principle, not necessarily a precise repre- 

 sentation of a reaction : " It is not claimed that a limiting 

 factor curve always adheres rigidly to a typical form with a 

 sharp angle at the point of change of the limiting factor. It 



* Blackman : " Ann. Bot.," 1905, 19, 281. 



f Blackman and Smith : " Proc. Roy. Soc," B, 191 1, 83, 389. 



J Matthjei : " Phil. Trans. Roy. Soc," B, 1904, I97» 47- For the 

 application of the principle to the growth of field crops see Balls and Holton : 

 '* Phil. Trans. Roy. Soc," B, 1915, 206, 103, 403 ; and Balls : id., 1917. 

 208, 157. 



