THE VISUAL PIGMENTS 



From the definition of quantum efficiency, the rate of decrease in the 

 number of visual purple chromophores, — dnjdt, is equal to the 

 product of the quantum efficiency and the intensity of Ught absorbed 

 by the visual purple. This latter quantity is related to the total light 

 absorbed, (/ — 7^), by the ratio of olcI to the total density. We have, 

 therefore, 



dn _ Vdc _ CLcl 



~dt^~~dt~~'^' oLcl + za'(co - c)l + d, '^ ~ '^ ^ ^ 



whence, by eliminating dcjdt between (9) and (10) and rearranging 

 the result, 



dit (xcl — zoi'cl I — h' ^yJ 



Itdt oLcl + zol\cq — c)l + di' I A 

 Now the density of the completely bleached solution is 



(11) 



log,^=zaVo + ^,. (12) 



and, subtracting equation (12) from equation (8), 



log, -^ = ac/ - za'c/ . (13) 



(14) 



whence, by substituting equations (8) and (13) in (11), 



dl, ^ \og,m I-h ^ 

 l,dt log,///, • / 'A' 



On multiplying both sides of this equation by - — ^— we have, 



V ~ A 

 ^^ ^^^ = <^ ^^. (15) 



/,-/, l,dt ^ A 



Since, as we have seen, the function (j) can be treated as a constant in 

 any one experiment, equation (15) can be integrated to give, 



loge *-— = cf)^ .t + constant (16) 



which is identical with the equation (7) obtained in the case where 

 the products of bleaching were assumed to be non-absorbing. The 

 same equation thus describes all possible conditions. The correcting 



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