14 
c. in 500 cubic c. of water, length of column 21*2 cm. — obser- 
vations made with right eye. 
ABC 
40 5*35 39-6 
Thus the result is very near. 
The solutions of caramel ought not to be kept many days. 
After the lapse of twelve days some of the solutions were 
turbid and unfit for comparison, owing to the development 
of vegetable organisms. It seems very probable that even 
with large differences between the lengths of the columns 
0 
and with larger quantities of colouring matter the relation 
g^zrconstant, is valid when the colour is constant. But 
suppose the colour to vary, what wiU be the connection 
between the quantity of colouring matter, the length of the 
column, and the intensity of colour ? If q denote the quan- 
tity of colouring matter per unit of length, and t the total 
length, we have the relation qt=c if the colour be constant; 
but if the colour vary, c will be a function of the trans- 
mitted light. Hence 
if T denote the transmitted light, therefore qt=f(T) or as 
we may write it Tz= (j)(qt), the probable form of this func- 
tion may be obtained as follows: suppose we have two 
perfectly transparent cylinders of unit area and a fluid of 
such a nature, that if in any portion of it we dissolve some 
colouring matter, on further addition of the fluid no decom- 
position takes place. Suppose we have a standard solution 
containing one unit of colouring matter per unit of volume. 
If the colouring matter remain constant in quantity, then 
the intensity of the light will be a function of the length 
of the column of fluid only, say and if the length of 
