98 PHOTOSYNTHESIS 



deficiency of any essential factor. The exact mathematical formula for 

 these curves is still a matter of controversy. •'° The important fact is that 

 they are logarithmic curves. 



In the problem of crop yield and the manner in which this is affected 

 by various factors, there has been obtained, through a great mass of 

 experimental data, a fairly accurate mathematical expression of the in- 

 fluence of the deficiency of one of these factors. This expression is un- 

 doubtedly an outgrov^rth of the original law^ of minimum, though in its 

 course of development it has undergone considerable change. 



In the principle of limiting factors the photosynthetic activity, as first 

 formulated by Blackman, vit have a state of affairs w^hich is in many re- 

 spects analogous to that of crop yield. Blackman's theory has been one 

 of the most helpful conceptions w^hich has been contributed to the study 

 of the problem of photosynthesis. Within the last few years there has 

 been some agitation regarding the general applicability of Blackman's 

 theory.*'^ Some of the writers have gone so far as to maintain that the 

 principle is entirely erroneous. It would seem, however, that these are 

 rather developmental phases such as occur in the evolution of any funda- 

 mental theory. In the more valid objections which have been raised, 

 the conflict centers about the graphic or mathematical expression to be 

 given to the theory rather than to the more general underlying principles. 

 With more refined methods and extensive data it is not surprising that 

 some modifications should come to light which may have escaped the origi- 

 nal propounders with their rather limited experimental methods and data. 



Benecke "^ has given a very good elucidation of the principle of limiting 

 factors. He points out that Blackman's theory is usually stated in such 

 a manner as to predicate that only one of the various factors is limiting, 

 while probably Jost's ^^ position is more tenable. The latter states that 

 it may happen that all factors but one have so high an intensity or con- 

 centration, that this single factor alone may determine the rate of photo- 

 synthesis. Benecke shows that the curve representing the rate of photo- 

 synthesis, when only one factor is varied, does not, when the intensity of 

 this factor is augmented, exhibit a straight line increase and then a sharp 

 turn when some other factor prevents the further increase in the photo- 

 synthetic rate. But rather, the curve is a logarithmic one as, for example, 

 is shown by Warburg's curve of the efifect of light intensity. Fig. 8. At 

 first this is practically directly proportional to the light intensity, then it 

 gradually bends to the horizontal. Here the photosynthetic rate is no 

 longer directly proportional to the intensity of a single factor. This is 

 the region where other factors interact and more than one factor limits. 

 Finally, the curve is almost parallel to the abscissa, and here some other 

 factor besides the one which was varied becomes the limiting one. As 



"Baule. Landtv. Jahrb., 54. 495 (1920). 



"Hooker, Science. 46, 197 (1917). Crocker, Bot. Gaz., 65, 287 (1918). 



"Benecke, Zeit. f. Bot, 13, 424 (1921). 



"Jost, Bot. Zeitg., 64, 72 (1906). 



