1046 



THE LIGHT FACTOR. I. INTENSITY 



CHAP. 28 



maximum value of this term is a[Chll/o In 10/6. This means that for the 

 maximum deviation of the integral light curve from hyperbolical shape to 

 exceed 5%, the integral absorption must exceed 50%: 



(7o// = 2; log/o// = a[Chl]ioln 10 = 0.30; a[Chl]/oln 10/6 = 0.05) 



At 75% absorption, the maximum deviation will reach 10%. This indi- 

 cates that to obtain experimental light curves which will permit one to 

 judge the true shape of the function P = f{I), objects with an optical den- 

 sity of up to log h/I = 0.5 can be used. 



A corresponding derivation for a general hyperbola is much more in- 

 volved, but conclusions are likely to be not too different from those obtained 

 here for a rectangular hyperbola. 



In the literature one can find many attempts to derive analytical ex- 

 pressions for the light curves of photosynthesis, partly by using very simple 

 kinetic models, and partly by empirical approximation. 



Among the simplified kinetic equations, reference may be made to those 

 of Ghosh (1928), Emerson and Green (1934), Baly (1935) and Burk and 

 Lineweaver (1935); while among the empirical approximations, we may 

 mention those of Brackett (1935) and Smith (1936, 1937, 1938). 



-4 



O 

 O 



o 

 o 



-5 



•P CD 



o 2 



16 



-8— 



12 



3 4 5 



LOG I, meter candles 



Fig. 28.23. Are photosynthesis curves hyperbolae? (after Smith 

 1938). SoHd Hnes are derived from nonhyperbolic functions (27.77) 

 and (28.48P); dashed line from rectangular hyperbolic function. 

 See text page 1047. 



Brackett sought to expres.s the sudden approach of the light curves to 

 saturation by an exponential curve, while Smith suggested an algebraic 

 function of a higher order: 



