112 The Maximum Efficiency of Photosynthesis 



cause inequalities of CO-2 pressures, which have yet to be shown to have effects over wide ranges 

 of Variation, can easily be readjusted by regassing. Thus, the greater part of our efficiency deter- 

 minations have been carried out with equal liquid and different gas volumes. 



Another source of error is the differential time factor which may occur if the pressure changes 

 produced by light in the two vessels are not observed simultaneously (an exaggerated instance of 

 this was previously discussed in Early Experiments with respect to Ref.5). The ideal would be to 

 illuminate the two vessels simultaneously* by two light beams, identical not only in total intensity, 

 but also in geometrical design. We did not have such a pair of beams at our disposal and so we 

 illuminated the two vessels one after another closely together in point of time. We illuminated 

 in periods of usually 10 min., by moving one light beam from one vessel to the other and vice 

 versa and taking the readings for both vessels simultaneously. When this alternation was repeated 

 many times we obtained for every vessel a series of dark values and of light values, or of light 

 values of the intensities z'o and i - \i; and when for each vessel all the dark values were summed 

 up and likewise all the light values, the time factor was virtually eliminated and the pressure 

 changes in the two vessels were obtained essentially simultaneously. 



7. The Equations of the Two-Vessel Method 



These equations, derived in 1924 7 , are adapted here to the special purposes of 

 photosynthesis. Because the experiments with compensated respiration play so 

 important a role in this work, the equations are presented not for a sequence of 

 darkness and illumination, but for a sequence of two illuminations with two diffe- 

 rent light intensities, one of which may approach zero as a limit. When the lower 

 light intensity is zero, then the equations hold true for the ordinary sequence of 

 darkness and illumination. The light intensities are denoted as J and J + AJ. They 

 have the units of quanta/min. and are related to i by the equation 



J = i X cm. 2 (quanta/min.). 



Let both vessels be illuminated first with an intensity J and then with an intensity J - AJ; 



and let the pressure changes be hj and Äj+^j for vessel I, and h'j and h'j^ \j for vessel II. Then 



when the pressure changes are observed for equal time periods, and when the two vessels contain 



the same amount of cells, the gas exchanges xo 2 and .rcu 2 , which are equal in the two vessels, can 



be calculated by the equations : 



hj x &co 2 — h'j X &'co 2 rfil 



(*o 2 )j = ~T 77 r, TT, L J 



&CO2/KO2 — « COo/ß O2 



hj x kp 2 — h'j x k'p 2 f71 



(*C0 2 )j = T ,, U , ,7/ L J 



K02/&CO2 — k 02/« co 2 



flJ+AJ > &C0 2 /z'j+JJ •' &'c'0 2 r fi -i 



(X0v)j+JJ = 7 TT TT rT, L dJ 



&C0 2 /*02 — k CO0/& o 2 



hj+jj x kp 2 — h'j+Aj x k'p 2 r „ , 



(^C0 2 )j-JJ = U IU U> IW ' 



ko 2 lkc02 k O2/« CO2 



where ko 2 and ^co 2 are the simple vessel constants, no prime mark for vessel I and a prime mark 

 for vessel II. All h values are positive when the light intensity J overcompensates respiration. All 

 h values are usually negative when J = 0, except at high \J values. 



From Eqs. [6], [7], [6a], and [7a] we can calculate the action of the light increment AJ, if 

 we assume that the gas exchange measured at the intensity J continues during the illumination 

 with the intensity J -f AJ. Then we may subtract [6] from [6 a] and [7] from [7a] and obtain: 



( hj+AJ — hj) x £co 2 — (fr'j+JJ ~- h'j) x ^'002 rgl 



(*o 2 )j+jj — (*o 2 )j = , ,, , , ,, , l J 



«C02/«02 « C0 2 /« 02 



* Zusatz 1961. Vergleiche Arbeit 11 dieses Buchs, wo die gleichzeitige Belich- 

 tung der beiden Gefäße durch einen geteilten Lichtstrahl beschrieben ist. 



