36 H. TAMIYA d al. VOL. 12 (lOSS^I 



where ^p is the hght-saturated value of A'p and a is a constant which corresponds to tlie 

 value of dA-p d/ at / -^ o. Substituting (7) in (6), we have 



akpkj^I (8) 



or 



akol (q) 



k 



Ag — a/ 



where ^g is the light-saturated rate of growth, namely 



^ _ Ap^D (10) 



kp — kjy 



The rate constant (A^) of the dark process is given by 



_ Mg (II) 



"D 



Ap— A-G 



Eqs. (8) and (9), which are the counterpart of Eq. (7) for photos3'nthesis, show that 



fdk,\ (12) 



= a 



\ d/ / 7 _> 



indicating, in agreement ^^^th our observation, that the light-limited rate of gro\\i:h is the 

 same as that of photosj^nthesis. If the half-saturating light intensities for photosynthesis 

 and gro\\i:h are denoted by /Hp and /Hg, respectively, we have from (7), (8) and (9), 



^p . ^p^D ^G (13) 



Ht, = — and /^g = ., , I, X = — 



From Eqs. (3) and (4) we can derive the relation 



Therefore, 



and 



^ .V dt 



_ Ap — Ag _ aAp/" -f ApAp (15) 



Ap kpkj) + a(^p + Ap)/ 



This equation shows that, in conformity with our observations, the dark cell ratio 

 is unity when 1 = 0, and decreases with the increase of / till it attains, at sufficiently 

 high light intensity, a final value (zlg) which is given b}- 



. ^D ^G (16) 



^p + Ap kp 



* This equation shows that, at a given temperature, we can estimate kg from J and vice versa, 

 if the value of ^p at that temperature is known. Provided that the cellular characteristics of dark and 

 light cells are known, the value J also allows us to gauge the properties of the whole algal population 

 in a given culture. 



References p. 40. 



