1134 THE LIGHT FACTOR. II. QUANTUM YIELD CHAP. 29 



A more ambitious and significant undertaking would be to represent 

 by a single equation the whole light curve, including the saturation region, 

 and to calculate 70 from the yields observed in high light, using parameters 

 such as the maximum yield {P"'"-), and the half-saturating light intensity, 



i/J. 



We have seen in chapters 27 and 28 that theoretical kinetic curves 

 representing photosynthesis as a function of the supply of "reactants" 

 (carbon dioxide, reductants, light quanta), are hyperbolae, even when rather 

 complicated mechanisms are postulated, as long as no "third-order" reac- 

 tions [such as 2 COo + A -> A(C02)2, or Chi + 2 hv -^ Chi**] are consid- 

 ered, and not more than two successive reaction steps are postulated be- 

 tween the external supply of the reactant and the "rate-determining" step. 

 (For example, in the case of the carbon dioxide factor, simultaneous con- 

 sideration of diffusion and carboxylation leads to a hyperbolic carbon dioxide 

 curve; but if one more supply step is interpolated, the resulting equation 

 is of the third order.) 



The known light curves are much too unreliable to permit a useful in- 

 quiry into the question whether they actually are hyperbolae {cf. section 

 7/, chapter 28). If it were possible to demonstrate, by new and more pre- 

 cise measurements, that the light curves are hyperbolic, then each curve 

 could be determined completely by three points, i. e., values of P at three 

 known values of /. 



Parameters such as 70 (i- e., the initial slope), .// or P'"''^ could replace 

 one measurement each. The general equation of a hyperbolic light curve 

 in terms of 70, i/J and P'^^^- is : 



P / 270 1/2/ 2_\ P^ ^ jn^ J 



(2*J-5) pmax. _ p "I Wpmax.)2 pm&x.J pmax. _ p pmax 



(This equation is obtained from the general equation of a hyperbola by 

 transformation to a set of coordinates with origin in a point on the hyperbola 

 and the abscissa parallel to the asymptote at a distance — p™'^''- from the 

 latter.) 



In treating several particularly simple mechanisms in chapters 27 and 

 28, we obtained light curves (or carbon dioxide curves) that obeyed an even 

 simpler relation: 



(2i).(i) p/(^pmu.. _ p) = const. X / 



or: P/(Pu.ax. - P) = const. X [CO.] 



Comparison shows that this simplification means the disappearance of 

 the P- term in (29.5), i. e., the validity of the relation: 

 (29.6a) 70 = P^^^/^/^I 



The relationship provides a simple way to check whether the kinetic 

 mechanism is of corresponding simplicity. 



