THE "cardinal POINTS" AND THE "LIMITING FACTORS" 861 



Blackman and his pupils made attempts to fit the experimental data into 

 this oversimplified theoretical picture. Others objected to this, and a con- 

 troversy arose, with the result that articles "for" or "against" Blackman's 

 theory have been appearing in botanical journals for now over forty j'^ears. 

 This protracted and largely unnecessary controversy has hampered rather 

 than helped the penetration into plant physiology of the general principles 

 of i-eaction kinetics a.nd photochemistry (such as the law of mass action, 

 Boltzman's and Arrhenius' activation equations and the quantum principle 

 of photochemistry), which alone can provide adequate basis for the kinetic 

 treatment of any chemical reaction, whether in vitro or in vivo. It will ))e 

 shown below that, from the point of view of these principles, Blackman's 

 "law" is only an idealization, which can be more or less closely approxi- 

 mated under certain special conditions. 



Brown and Heise (1917) and Brown (1918) were among the first to 

 criticize the way in which Blackman supported the law of limiting factors 

 by reinterpretation of the observations of earlier investigators, and to point 

 out that even Blackman's own measurements did not conform strictly to 

 the type of figure 26.2. Some subsequent investigations, e. g., that of 

 van der Honert (1930), produced curves that so closely approached the 

 "Blackman type" (c/., for example, fig. 27.2) that the authors believed the 

 law of limiting factors to be strictly valid under ideal experimental condi- 

 tions {e.g., uniform illumination of all cells; cf. page 864). Other, equally 

 reliable measurements gave, however, an entirely different picture — 

 families of P = /(Fi) curves that diverged from the very origin {cf., for 

 example, fig. 27.1). On the basis of measurements of this type, Bose (1924) 

 went to another extreme and suggested, as an alternative to Blackman's 

 postulate, that the effect of a certain change in a factor, Fi, on the yield of 

 photosynthesis, is independent of the prevailing values of all the other fac- 

 tors, F-2, Fs . . . (while according to Blackman this effect should depend en- 

 tirely on whether Fi is the "Hmiting factor" or not). Bose's postulate 

 requires that the curves representing the yield of photosynthesis in relation 

 to a factor Fi at different values of F2 have shapes of the type shown in 

 figure 26.3. Bose's "law" was derived from a very small number of meas- 

 urements, and is merely another approximation, applicable to certain con- 

 ditions opposite to those that favor the "Blackman behavior." 



"Blackman type" curve systems have widely separated saturation 

 plateaus, but coincident initial slopes; "Bose type" cun^e systems also 

 have separated saturation plateaus, but distinct initial slopes. We will 

 often refer to Blackman type curve systems as the "first type," and to Bose 

 type curve systems as the "second type." A third type of kinetic curves, 

 also encountered in photosynthesis, is characterized by initial divergence, 

 but final convergence in a common saturation plateau (as in fig. 26.4). 



