THEOR \ ' 6h METHODS OF SPECTROPHO TOME TR Y. 215 
the intensity of the Lighl 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-tentli its value, we invariably examine in our photometric investi- 
gations a Btratum of unit width (say 1 cm.), or a stratum of known 
width, .Hid possess the means of estimating the proportion of light which 
remains unabsorbed, we possess data enabling us to calculate tl. 
tinction-coefficient. 
It was previously shown that /' = — and that = = ,. and when x = d, 
\o<y J' 
T= T V Then li ig T = - x log n , and d log ft = 1 .'. s = log n = — ; 
so that, if the thickness of the stratum traversed by the light be known, 
and the intensity of the unabsdrbed light /' ascertained, the coefficient 
: can be calculated. But if x be of the constant value 1 (say 1 cm.), 
then z = — log /': that is to say, the extinction-coefficient is equal to the 
negative logarithm of tht unabsorbed light. Let us suppose that bypass- 
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 
z — - log o = 1°K 3 — loo; 2 
= 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 
lution, the greater will be the extinction-coefficient; in other words, 
the extinction-coefficient z and the concentration c are proportional. 
Let c and c represent the concentration of two coloured solutions, of 
which the extinction-coefficients are z and i respectively, then 
c : z = c' : z 
and - = — = A 
z z 
i.e. the relation of the concentration of a coloured solution to its extinction- 
coefficient is a constant, represented by A, and termed the "Absorption- 
relation" (Absorptionsverhaltniss, Vierordt). Upon the determination of 
this constant rests Vierordt's method of quantitative spectrophotometry 
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 <> 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 z', according to the equation : 
c' = Az 
