Dec. i, 1923 
Quantitative Determination of Carotin 385 
In all of the spectrophotometric work presented in this paper, the 
transmission of a cell containing the solution is always compared with that 
of a duplicate cell containing the solvent, hence, the quantity obtained 
from actual observations on a solution of given thickness and concentra¬ 
tion is the transmittancy. 
— Log 10 transmittancy, designated as ( — log 10 T) is identical with the 
product of thickness b , concentration c, and the specific transmissive 
index, k, and is represented by the term bck. For unit concentration and 
thickness, — log 10 transmittancy becomes identical with specific trans¬ 
missive index, which is the characteristic quantity, determined for any 
solution at a definite wave length or frequency. 
In Figure 1 the concentration of pigment in centigrams per liter (at 
top) can be read on the X-axis. On the right hand side of the graph 
Concentration cg/liter 
Fig. I.— Spectral transmittancy of a theoretical pigment in solution. 
(0.00 to 2.00) the ordinates chosen are the logarithms (to base 10) of the 
numbers 0.01 to 1.00. The scale on the left is chosen to represent the 
values of the transmittancies. In this way for a given value of T on the 
left — log 10 T can be read at once on the right-hand scale. 
The numbers on the right- and left-hand sides of the graph have been 
plotted so as to make their use convenient, for if one knows the trans¬ 
mittancy (obtained from the instrument) it is only necessary to look on 
the right-hand side of the chart where the corresponding — log 10 T will be 
found. 
Now, if Beer’s law 6 holds for dilute carotin solutions (0.00-4.20 mgm. 
per liter) then transmittancies of different concentrations when plotted 
on this logarithmic paper should give a straight line, that is, if bck=. 
— log 10 T, and b and k are kept constant, then c is proportional to - log 10 T. 
6 Briefly, Beer’s law states that the specific transmissive index k is constant regardless of thickness or 
concentration 
