2 1 4 H^EMO GL OB IN. 
1. Relation between the concentration of a solution and the percentage 
of light absorbed by it. — Before investigating the theory of the methods 
of spectrophotometry, to be subsequently described, it is essential to 
examine (1) the relation which exists between the power of light 
absorption exerted by a coloured liquid of constant composition and the 
thickness of the layer traversed ; (2) to study the influence of concen- 
tration on the absorption of light by a stratum of a liquid holding a 
colouring matter in solution. 
It was shown by Lambert that if light of intensity 7, by transmission 
through one layer of an absorbing medium of thickness 1, has its in- 
tensity reduced to I — - by transmission through <l such layers, the 
final intensity of the light, which we shall represent by /', will be re- 
duced to — , i.e. T = — . Beer showed that Lambert's law holds good, 
not only for transparent solid media, but also for liquids, i.e. that the 
amount of light absorbed by a solution of a given colouring matter of con- 
stant concentration is dependent upon flic thickness of the strut inn} This 
law is mih/ true, however, in respect to monochromatic light. 
We must now examine the influence of the concentration of a liquid 
containing a colouring matter in solution upon the percentage of light 
which it absorbs and transmits, when the stratum examined remains of a 
constant width, 1. It has been experimentally proved that the absorp- 
tion exerted by a stratum of a coloured solution of known width is 
equal to that exerted by a stratum twice as thick of a solution of half 
the concentration; i.e. the absorption which light undergoes in passing 
through a stratum of coloured liquid of unit thickness increases propor- 
tionally to f/ie concentration. 
2. Definition of the " extinction-coefficient." — In their photo-chemical 
researches, studying the comparative al 'sorption of light by different 
gases, Bunsen and Boscoe 2 introduced the conception of, and defined, 
the so-called extinction-coefficient. They ascertained the relative thick- 
nesses of the strata of various media required to reduce the intensity 
of light passed through them to one-tenth of its initial value, and defined 
the extinction-coefficient as the reciprocal of the number expressing the 
width of the stratum of a given medium, required in reduce the intensity of 
light passed ///rough if fa one-tenth its initial value. 
For any given coloured medium, e.g. a solution of a colouring matter 
of a definite strength, there must be a definite thickness of layer which 
we shall call d, capable of reducing the intensity of light to one-tenth 
its original value. The reciprocal of el is -j, and if by g we represent 
the extinction-coefficient, 
1 
6 = d 
As will be shown in the sequel, the method of spectrophotometry 
discovered by Vierordt rests upon the determination of this constant g, 
for particular, very limited, regions of the spectrum. The practical diffi- 
culties of varying the thickness of the stratum of a coloured liquid, until 
1 When the thicknesses of various strata increase in arithmetical, the intensities of 
the light decrease in geometrical, ratio. 
- Ann. d. Cfhem., Leipzig, 1857, Bel. ci. S. 238. 
