386 
Journal of Agricultural Research 
Vol. XXVI, No. 9 
An example will serve to illustrate how results are obtained from the 
spectrophotometric data. Using mercury light of wave length 435.8 and 
a carotin solution of 0.336 cgm. 7 per liter in a 2 cm. cell, the angles 74.23° 
and 9.33 0 were read on the instrument. The angles were designated as 
0j and 0 2 respectively. The cotangent of 0 i times the tangent of 0 2 gives 
the value for the transmittancy, which is 0.0464. The log of 0.0464 is 
8.6665 — 10 or — 1.3335 which is given on the right hand side of the graph. 
These numbers have already been plotted in reference to the transmit- 
tancies. Hence, in plotting, or in obtaining the concentration of certain 
unknown solutions from the lines plotted, it is necessary to know only 
the value for the transmittancy. 
The specific transmissive index of carotin for the above wave length is 
at once found by dividing 1.3335 by 2, the thickness, and by 0.336, the 
concentration in centigrams. The specific transmissive index will be 
illustrated by an example later on in this paper. 
Data obtained by using the spectrophotometer are usually presented 
in the form of spectral transmittancy curves. Typical curves are shown 
in the Bureau of Standards Scientific Paper No. 440 (j). The curves of 
a theoretical pigment have been illustrated in Figure 1. These are drawn 
for convenience in explaining the method. They represent transmit- 
tancies between wave lengths 380 and 670 ra/i. Each curve represents a 
different concentration of the colored solution. The curves differ from 
each other only by virtue of their concentrations. In order to use such 
curves for quantitative work it would be necessary to obtain a large 
number of them, each of which would then represent a definite concentra¬ 
tion of pigment solution. Such a series of curves would serve as a stand¬ 
ard, with which the curve for an unknown concentration of the same 
pigment could be compared. This method would be slow and very 
laborious, for the standard curves would have to be prepared and then 
several points would need to be determined on the curve of the unknown. 
For these reasons a better method was sought whereby an accurate 
determination could be made by reading only one point on the spectro¬ 
photometer. 
From each of the three curves at any given wave length (440 for 
instance) let us obtain the numerical values for the transmittancies. 
For this wave length they are approximately 0.308 for the 5 cgm. concen¬ 
tration curve, 0.10 for the 10 cgm. and 0.01 for the 20 cgm. curve. 
These transmittancy values are, however, plotted in another manner 
in this chart. At the top of the page, on the X-axis, concentrations 
(5, 10, 20, cgm. per liter) are represented; at the left-hand side Y-axis 
of the chart, transmittancies are represented. Now, plotting the trans¬ 
mittancies 0.308, 0.10 and 0.01 at their respective concentrations and 
drawing a line through these three points and through 1.00 transmittancy, 
which represents complete transmittancy at zero concentration, the line 
will be found to be a straight line (marked 440 in fig. 1), extending 
diagonally across the chart. If wave length 560 is used, then the line 
marked 560 will be obtained; similarly line marked 380 and 500 for wave 
lengths 380 and 500; line marked 610 for wave length 610, and so on. 
Therefore, in the diagram the transmittancies for any wave length which 
cuts the curve may be used to obtain a straight line, from which quanti¬ 
tative data regarding the concentration of solutions may be obtained. 
7 The carotin used in this test was not pure. 
