THEORY 6- METHODS OF SPECTRO PHOTO ME TRY. 215 



the intensity of the light remaining unabsorbed is reduced precisely to 

 one-tenth, would be extremely great. Fortunately, the coefficient of 

 extinction can be determined in a manner presenting far smaller practical 

 difficulties and admitting of great accuracy. 



If, instead of varying the thickness of the stratum of the coloured 

 solution until the initial intensity of the light entering it is reduced to 

 one-tenth its value, we invariably examine in our photometric investi- 

 gations a stratum of unit width (say 1 cm.), or a stratum of known 

 width, and possess the means of estimating the proportion of light which 

 remains unabsorbed, we possess data enabling us to calculate the ex- 

 tinction-coefficient. 



It was previously shown that /' == and that g = -3, and when x = d, 

 T yV Then log I' = x log n , and d log n = l .\s = log n = - ; 



so that, if the thickness of the stratum traversed by the light be known, 

 and the intensity of the unabsorbed light /' ascertained, the coefficient 

 e can be calculated. But if x be of the constant value 1 (say 1 cm.), 

 then B = log /'; that is to say, the extinction-coefficient is equal to the 

 negative logarithm of the unabsorbed light. Let us suppose that by pass- 

 ing through a stratum of coloured solution 1 cm. wide, the intensity of 

 light has been reduced to two-thirds its original value, then 



2 

 6 = log 9 = log 3 log 2 



J = 0176091 



3. Definition of the term " absorption relation!' It has already been 

 stated (see previous page) that the more concentrated a coloured liquid, 

 the greater its absorbing power, the smaller, therefore, is the width of 

 the stratum required to reduce the intensity of the light passed through 

 it to one-tenth of its initial value. As the extinction-coefficient is, by 

 definition, the reciprocal of the thickness of the stratum required to 

 bring about this result, it follows that the greater the concentration of 

 the solution, the greater will be the extinction-coefficient ; in other words, 

 the extinction-coefficient g and the concentration c are proportional. 

 Let c and c f represent the concentration of two coloured solutions, of 

 which the extinction-coefficients are g and g' respectively, then 



c c 

 and - = = A 



z z 



i.e. the relation of the concentration of a coloured solution to its extinction- 

 coefficient is a constant, represented ly A, and termed the "Absorption- 

 relation " (Absorptionsverhciltniss, Vierordt). Upon the determination of 

 this constant rests Vierordt's method of quantitative spectrophotometric 

 analysis. If we have, in the case of a solution of a particular body, 

 determined by analysis its concentration c, and then with the spectro- 

 photometer determined its extinction-coefficient for a particular spectral 

 region, and thus obtained the value of A, we can find out how much 

 of the same substance is contained in a solution of unknown strength 

 (c') by merely determining g', according to the equation ; 



c' = As, 



