THE VISUAL PIGMENTS 



In any experiment / and A are constants, and so are a and y if the 

 assumptions are justified. Thus by plotting log^ IJ(I — I^ against r, 

 a straight hne of slope = aLyljA should be obtained. In general, 

 however, this is not the case. While it is possible (by carrying out the 

 bleaching with Ught of suitably long wavelength) to meet the require- 

 ment that the photoproduct does not absorb the bleaching light, it is 

 less easy to ensure that the solutions are free from impurities which 

 do. In the experiment just described (Fig. 3.3), for example, the 

 solution had an optical density of 0-07 after complete bleaching. 

 This solution, moreover, was one of the purest in dartnall, 

 GOODBYE and lythgoe's investigation, the final density in one 

 instance being as high as 0-45 — nearly all due to impurity. Conse- 

 quently when logg I^|{I — 7^) was plotted against t, the results did not 

 fall on a straight Hne but on a curve. In all cases, however, it was 

 found that, if instead of log^ /J(/ — 7^), log^ 7^/(7, — 7^) were plotted 

 against time, a straight hne was obtained (see Fig. 3.4). 



Second case — impurities absorbing, photoproducts non-absorbing. 

 From the experimental result that 



logg - — ^— = mt + constant (5) 



ff ~ ^t 



an expression for the bleaching of visual purple solutions which 

 contain stable light-absorbing impurities can be deduced. As before 

 it is assumed that the photoproducts do not absorb the bleaching 

 light. In equation (5), the slope m of the line is not equal to 

 (x.yI/A but it can be shown (dartnall, 1936) to be related to this 

 quantity by the equation. 



;„ = -^ . ^-^ . ^l£^' . ^. (6) 



Substitution of this value of m in equation (5) gives the required 

 equation, 



log, -— ^ = </> ^ . / + constant (7) 



where <^ has been written for the quantity in brackets in equation (6). 



At first sight it may seem that equations (5) and (7) are mutually 



exclusive — for m, the coefficient of t in equation (5), is constant (as 



shown by the fact that a straight Une is obtained when the L.H.S. is 



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