THE NATURE OF PHOTOSYNTHESIS 97 



"The light energy available fixes an upper limit to the carbon dioxide 

 that can be decomposed, and when that amount is attained, which even for 

 direct sunlight could be provided with a current of air containing less than 

 1 per cent, if the current were sufficiently fast, the limit of effect of 

 carbon dioxide is reached : any more provided is wasted, and has no 

 further effect till many times that concentration is reached and a general 

 depressing effect comes in. . . ." 



Similarly, any of the other factors can act as the limiting one. It is 

 evident that in all experimental work all of these factors must be taken 

 into account and that it is essential to determine that no other factor 

 beside the one under consideration is acting as the limiting one. 



The principle of limiting factors has its analog in the step-reactions 

 of chemistry. Here if a reaction is made up of a number of steps, the 

 rate of the total reaction will be determined by the rate of that step which 

 is proceeding at the lowest rate. 



Also, as early as 1843, in his book, "Chemistry in its application to 

 Agriculture and Physiology," Liebig had formulated his well-known Law 

 of Minimum which stated : "by the deficiency or absence of one necessary 

 constituent, all the others being present, the soil is rendered barren for 

 all those crops to the life of which that one constituent is indispensable." 

 At the time, of course, Liebig was not familiar with all the factors which 

 affect the growth of plants and it required a great deal of experimental 

 work by many investigators before this principle found an approximate 

 mathematical expression. It is of interest here on account of the fact that 

 the problem of crop yield is very similar to that of photosynthetic activity 

 and has been dealt with in much the same way. Liebig's law of minimum 

 has undergone many modifications and the facts which this law endeavored 

 to express have finally been put into mathematical form though there still 

 exists some controversy regarding it. It can be dealt with here but very 

 briefly. ^^ 



There are five soil factors which influence the growth of plants : 

 (1) Water supply, (2) Air supply, (3) Temperature, (4) Supply of min- 

 eral nutrients, (5) Injurious factors. The effect of these factors may 

 be determined by the total amount of dry matter formed by the plant under 

 definite conditions. The effect of the fourth factor, the supply of mineral 

 nutrients can be most easily determined. When then, the weights of dry 

 matter formed under conditions in which but one essential factor is varied, 

 are determined, there are obtained smooth curves which are amenable to 

 mathematical expression. Mitscherlich has done this on the basis of many 

 crop experiments. From these results it is evident that in the law of 

 minimum we are dealing with a logarithmic function. The crop yields 

 obtained with a single varying factor can be expressed in curves which are 

 asymptotic to a maximum. This maximum would be attained if all condi- 

 tions were ideal and there is a shortage in yield corresponding to the 



™ Russell, E. J., Soil Conditions and Plant Grou'th. London, 1921. Pfeiffer, T.. 

 Der Vegetationsversuch. Berlin, 1918. 



