440 HAROLD F. BLUM 



to the molecular extinction coefficient as ordinarily expressed in 

 equation (8), and C and I are, respectively, the concentration of the 

 light absorber and the thickness of the sj^stem. 



Now, if Na is the number of quanta absorbed by the light 

 absorber : 



Na = No- N • (16) 



We may substitute in (15) and rearrange: 



Na = No(l - e-^'^') (17) 



Expanding the exponential: 



If the absorption is less than, say, 10%, no important error is intro- 

 duced by neglecting powers higher than unity, and: 



Na = A^o^C^ (19) 



Now, if C and I are constant, as may be assumed to be the case in 

 many photobiological processes, and if their values are such that ab- 

 sorption is small: 



A^. ^ N,g (20) 



Since g is proportional to the absorption coefficient, k, the extinction 

 coefficient. A-', and to the molecular extinction coefficient, e, any of 

 these quantities can be substituted in the proportionality (20). 



Assuming that the mmiber of quanta required is the same for all 

 wavelengths, the relative effectiveness for a given wavelength may be 

 represented as the 7eciprocal of the relative number of quanta ab- 

 sorbed, so l/(QoX) or l/(/oX) may be plotted as the measurement of 

 effectiveness (equations 13 and 14), as has been done in Figures 5, 

 8, and 9. This permits a direct comparison with the aosorption spec- 

 trum of a substance suspected of being the light absorber; the choice 

 of expression of the absorption being immaterial, since: 



l/((?0 X) cc (7 cc A^ oc // oc e oc Z) ■ (21) 



We note that the analysis above is based on several assumptions, 

 and that close agreement between absorption spectrum and action 

 spectrum is to be regarded only as the ideal case. Actually the agree- 

 ment is sometimes very good as is illustrated by the action spectrum 



