54 PROBLEMS IN PHOTOSYNTHESIS 



intensity dU/dE, i.e., tan a, becomes larger and approaches a limit which 

 can be mathematically expressed as 



?7o ~ lim -r^ — constant (22) 



Warburg set out to determine the highest value of rj at low intensities. 

 Figure 27 shows that U is generally not proportional to E, but is actually 

 dependent upon £■ in a complicated manner. Mathematically, the relation 

 may be expressed as 



U = a -\- bE -\- cE' 

 a, b and c being constants. Differentiation gives 



and for E = 



dU 



% = b -j- 2cE 



dE 



ryo = lim ^j^ = b (23) 



The constant /; is therefore the limiting value sought. It is shown graphi- 

 cally in Figure 27 by the tangent of the angle ofo at which the curve rises 

 from the zero point of the system of coordinates. 



If jE" = 0, then U = 0, so that a = 0. Both h and c may be determined by 

 two measurements made at two different intensities such as 



By eliminating c we find 



Ui = bEx + cEi^ 

 U2 = bEo + cE-^ 



E-zEi" - E1E2' ^^ ' 



The production of 1 mole O2 corresponds to an increase of total energy of 

 1 12000 cal. Therefore, when .to, /xl O2 develops, then 



TT 1 12000 _„„, ._. 



^ = "«^ 2240(00000 = ^-^^^ "«^ ^'^^ 



one mole being 22400 X 1000 /xl. The value of Aq, is determined mano- 

 metrically. Warburg and Negelein used a differential manometer in their 

 fundamental studies. 



It is possible to calculate -q and r?,, from the values of .Vq, and i obtained ex- 

 perimentally. If i is the intensity absorbed per cm^ per sec, the radiation 

 energy E absorbed in the time / of illumination is iFt. Since Xq^_ is determined 

 manometrically, the chemical energy U may be calculated from equation 25 

 and 77 determined. By two measurements of U and E at different intensities 

 b and consequently 770 may be calculated from equations 23 and 24. 



