428 PLANT PHOTOPERIODISM 



by the far-red-absorbing form of the pigment. As they are returned in 

 darkness after various numbers of hours to 20°C, germination de- 

 creases but can again be promoted by exposure to red radiation. 



In lettuce seed germination the half-time for pigment conversion at 

 30°C would be the order of 18 hr and not more than 10 hr at 35 °C. 

 Estimates of the half-time can also be made for photoperiodic control 

 in flowering, as was suggested by Dr. Borthwick. These are of the order 

 of magnitudes of 1 hr at 20° to 30 "C. Such rates of pigment conver- 

 sion are compatible with the conversion being an important factor, or 

 the essential factor, measuring the duration of the dark period in 

 photoperiodic systems. 



ABSORPTION COEFFICIENT AND QUANTUM EFFICIENCY 



The major features of the photoreaction can be found in an elegant 

 way without assumption. A reversible first-order reaction allows calcu- 

 lation of F, the fraction of pigment conversion corresponding to a 

 particular physiological response for a given irradiance, E. The method 

 is equivalent to that used by Warburg and Negelein (1929) to find 

 the absorption coefficient and quantum efficiencies for photodissocia- 

 tion of cytochrome oxidase-carbon monoxide. Its development in de- 

 tail is given by Hendricks et al. (1956) and empirically illustrated by 

 Downs et al (1957). 



After irradiation with energy E in the region A ± AA, the pigment 

 conversion is given by the first order differential equation dF/dE = 

 A(l — F). The solution of the equation is kE = log [1/(1 — F)]. If 

 the energies, Ei and E2, required for two physiological responses 1 and 

 2 have the ratio a = E1E2 then 



a log [1/(1 - Fi)] = log [1/(1 - F.)] 



The same response in the reverse direction will be obtained with 

 energies having a different ratio, (S, and 



13 log (1/F,) = (1/FO 



if a and 13 are measured for any two arbitrary degrees of response, 

 values of Fi and F- can be calculated. 



The dependence of the second internode length of pinto beans on 



