SPECTRA OF PHOTOSYNTHETIC PIGMENTS 363 



spectra could be used to compute the absorption curves of active pig- 

 ments in vivo. Few such curves are available at the present time, but 

 by suitable selection of organisms this method could yield badly needed 

 data. Several investigators (Button and Manning, 1941 ; Emerson and 

 Lewis, 1943) have used extracted pigments for the determination of the 

 partition of light among various components. This is not entirely satis- 

 factory, however, since shifts of position and of the shape of the absorp- 

 tion curves are known to occur in the living organism as compared with 

 extracts. 



An equation^ can be derived for calculating the optical densities of the 

 active pigments from the absorption and action spectra. Data so treated 

 give absorption spectra of the active pigments corrected for the distortion 

 introduced by the inactive pigments. 



As an illustration, the equation has been used on the Coilodesme and 

 Ulva curves (see Fig. 6-7). The absorption curve for chlorophyll a in 

 vivo is not known in the blue part of the spectrum; however, a close 



2 Derivation of the equation for calculating the optical density of the active pig- 

 ment from an action spectrum and an absorption spectrum : Let 



F = fraction of incident monochromatic light absorbed by whole system. 

 Fa = fraction of F absorbed by active pigments. 



K = proportionality constant which cancels out. 



D = optical density of whole system. 

 Da = optical density of active pigments. 



P = rate of photosynthesis or other action under such conditions that it is pro- 

 portional to quantum intensity of light absorbed by active pigment. 



/ = incident light intensity. 



Primes designate the quantities at a particular wave length where all absorption is 

 due to the active pigment, as, for instance, at the red absorption maximum of chloro- 

 phyll. The fraction of absorbed light absorbed by the active pigment is given 

 (Kistiakowsky, 1928, p. 39) by 



Fa = Da/D, (6-1) 



P' = KIF', (6-2) 



P = KIF Fa. (6-3) 



The ratio of Eq. (6-2) to (6-3) is 



P'/P = KIF'/KIFFa = F'/FFa, (6-4j 



or 



Fa = F'P/P'F. (6-5) 



Substitution of Eq. (6-1) in Eq. (6-5) gives 



D.,/D = F'P/P'F, (6-6) 



or 



Da = F'PD/P'F. (6-7) 



Since, bj Bter's law, 



D = log [1/(1 - F)], (6-8) 



Da = F'P/P'F log [1/(1 - F)J. (6-9j 



