ARE THE LIGHT CURVES HYPERBOLIC? 1045 



(28.48J) P = n/a = n/(l - 10-«icw]i) 



(mole CO2 reduced per second per cm.^ of illuminated area). 



If the illuminating light is nonmonochromatic, the first part of this rela- 

 tion remains valid, but 7a is now expressed by an integral: 



(28.48K) /a = / - r 



Xi 



'\^'hen the incident light intensity increases so that light saturation sets 

 in, in the most exposed pigment laj^er, the light curve of the integral 

 yield bends, and does not become horizontal until saturation has become 

 complete in the deepest laj^er. Consequently (as discussed before, cf. p. 

 1007 and fig. 28.20), the qualitative effect of inhomogeneous light absorp- 

 tion must be to broaden the transitional region connecting the linearly 

 ascending and the horizontal part of the light curves. AVhat we want to 

 know is how the shape of the light curves is changed by this integration. 

 Let us assume for the sake of simplicity that the "differential" light cuives 

 are rectangular hyperbolae: 



p. 



= k*Ii 



pmax. _ p^ 



jL*r)inax. riQ-Q:(Chl]( 



(28.48L) Pt = I _|_ ^*j jQ-a[chi]i 



The integrated rate (per unit area) is then : 



(28.48M) P = J^ ^'^^ = U [Chi] In 10 ^" 



U[Chll In 10 1 + ^•*n0^lChlJ^ 



or: 



m dSV'^ — ^ = In [( 1 + A-*/)/(l + fc*/10-'^[ch']'.) 



^zs.is.n; p^^^ _ p ^^^[(^yj jj^ jQ _ jj^ j^ ^ A;*7)/(l + fc*/10-«Ichi](o) ] 



an ctiuation which does not represent a rectangular hyperbola. It can he 

 developed into a series: 



P 



(28.480) 



pmax. p 



]l 



2! "^ 3!2! (1 + k*I) 



^^^ (^ _ «[Chl]/oln 10 («[Chl]lo In 10) = (2 + k*I) 



(«[Chl]Zoln 10)3 (3 + k*I){2 + k*I) 



4!3! (1 + k*IY "*" 



..,) 



This series shows that the integral light curve remains practically a 

 rectangular hyperbola until the third term in the development ceases to be 

 small compared to 1; then, it looses the hyperbolic shape (because of a 

 third degree term, containing the product PP). Since the second factor 

 in the third term decreases from 2 to 1 with increasing light intensity, the 



