1044 THE LIGHT FACTOR. I. INTENSITY CHAr. 2S 



curves, cf. chapter 29, p. 1132 ff.), another parameter may be chosen 

 instead, such as ■//, the Hght intensity at which photosynthesis reaches 

 one-quarter of its saturation vahie. This choice leads to a very simple 

 relation : 



pmax. 



(28.48D) 70 



and gives, as equation of the light curve: 



p r 4P "I 



(28.48E) / = p^,,. _ p |_6./, I - ,// + p^. (,// - 3,//)J 



For the hyperbola (28.48E) to be i-ectangular, it must satisfy the very 

 simple condition: 



(28.48F) ,/./ = 3,// 



Its equation is then: 



(28.48G) / = p^i^^^zrp (6 v/ - v/)' "^ 



]\Iore generally, a hyperbola could be represented in our chosen co- 

 ordinates, using any three of its points (Pi,/i; PiJ-i; and P3,h) as param- 

 eters; for a rectangular hyperbola, two points suffice. 



These derivations should be kept in mind in evaluating papers, in 

 which failure to represent empirical data by equations of type (28.48B) 

 has been taken to mean that the light curves were ''not hyperbolic" {cf 

 Smith 1936, 1937, 1938). 



It was stated on page 1020 that all our derivations of light curve equa- 

 tions were based on the assumption of uniform light absorption, and are 

 therefore strictly applicable only to optically thin layers. 



The question arises to what extent the considerable optical density of 

 most actually studied plant objects distorts the shape of light curves — for 

 example, whether the observed "integral" light curves will be nonhyper- 

 bolic if the "differential" light curves for each thin layer, with practically 

 uniform light absorption, are hyperbolae. For monochromatic light, for 

 which the absorption coefficient is a, the total light flux absorbed in a layer 

 I (for the sake of simplicity, we assume uniform pigment distribution and 

 absence of scattering) is : 

 (28.481) /a = /(I - lO-«tci>'io 



(assuming chlorophyll to be the absorbing pigment). 



If the quantum yield of the over-all process is n, and if /a is expressed 

 in einsteins per cm.^ per sec, the total rate of photosynthesis is: 



