August 31, 1917] 



SCIENCE 



199 



sity of light and the supply of carbon di- 

 oxide. The temperature curve shows that 

 the rate of assimilation is an exponential 

 function of the temperature. In fact the 

 process of assimilation obeys van't Hoff's 



FiQ. 1. Effect of external factors on assimilation 

 in Elodea. (After Blackman and Smith.) 



law of reactions for temperatures under 

 30° C. Above this, the rate of assimilation 

 at first rises and then falls off, the process 

 being complicated at high temperatures by 

 a "time factor." The same effect has been 

 observed at high light intensities, and with 

 strong concentrations of carbon-dioxide 

 which have a narcotic effect. 



Disregarding these complications, we 

 will confine our attention to the first parts 

 of these curves. The ordinates of all three 

 curves are the same, namely, rates of carbon 

 assimilation, which can be measured in 

 terms either of CO, absorbed or of sugar 

 produced. The former happens to be the 

 more convenient measure. At any given 

 temperature, the rate of assimilation which 

 is a function of that particular temperature 

 can be determined directly by the curve and 

 is equal to a certain distance measured off 

 from the origin on the Y-axis. Similar dis- 

 tances are given for any definite supply of 

 carbon dioxide and for any degree of il- 

 lumination. In any actual environmental 

 complex, where the temperature, light and 

 carbon-dioxide supply are known, the rate 



of assimilation is equal to the shortest dis- 

 tance measured on the Y-axis. This is 

 stated as a general principle by Blackman 

 as follows: "When a process is conditioned 

 as to its rapidity by a number of separate 

 factors, the rate of the process is limited 

 by the pace of the 'slowest' factor." The 

 factor which gives the shortest distance on 

 the Y-axis — that is, the "slowest" factor, 

 he calls the limiting factor. 



As a matter of fact the carbon assimila- 

 tion of green plants is usually limited by 

 the seasonal variation in temperature and 

 the diurnal variation in light, the CO, con- 

 tent of the air being constant. Nothing has 

 been said of the other factors that effect 

 carbon assimilation — the water supply, 

 chlorophyll and enzymes. These so-called 

 "internal" factors, as well as the "exter- 

 nal" factors, are governed by the Law of 

 the Minimum. Of the internal factors, 

 water and chlorophyll are present in ex- 

 cess in healthy green plants, the amount of 

 assimilatory enzymes being the only prob- 

 able limiting factor. 



It is not necessary to adduce additional 

 examples to show that the Law of the Mini- 

 mum is a universal law, affecting not merely 

 the concentration of reacting substances, 

 but all factoi-s that in any way influence a 

 reaction or process. The law is applicable 

 to physical, chemical and geological as well 

 as biological problems.' An interesting in- 

 stance of its application to a problem in 

 physics is the determination of the magni- 

 tude of a thermionic current. This varies 

 with changes in temperature, and also with 

 changes in the voltage applied. The tem- 

 perature formula gives one value, the vol- 

 tage formula may give another; the lesser 

 value determines the current flowing. The 



7 A timely application may be made which is 

 worth bearing in mind. The efEciency of a nation 

 at war is subject to the Law of the Minimiun. 

 Defeat, in the last analysis, may be attributed to 

 the effect of some limiting factor. 



