Remarks on the Formulce for the Intensity of Light that 
has passed through Absorbing Media, and on a Method 
of Experimental Verification. 
In my last paper on colorimetry I pointed out that the 
function which expresses the connection of the intensity of 
light with the quantity of colouring matter is of the same 
form as the function expressing the relationship of the 
intensity and the length of the absorbing column, and if we 
accept Herschel’s formula ^a¥ for the latter relationship^ 
then an expression of the form must be taken to ex- 
press the former relationship. The connection of these two 
may be shown more directly than I indicated in my last 
paper. If we grant one of the laws, the other may be 
deduced from it as a corollary. Take for instance the law 
as given by Herschel, 
T = (i-Jc-i -f- "H &c. 
Now it is manifest that if q be the quantity of colouring 
matter per unit of length, we may write the above formula 
i. L 
T = adcP 4 + + &c. 
1 1 L 
For , kf, h , &c., substitute new constants ki, fca, Kg, &c. 
Then we way write 
T = Sa/c«' 
Since q denotes the quantity of colouring matter per unit of 
length and t the total length, we shall have (^—qt, when 
Q denotes the whole quantity of colouring matter, so that 
we finally deduce 
T - 
As the basis of a method of colorimetry, I took the rela- 
tionship, that the length of the column was inversely as 
the quantity of colouring matter present when the colour 
was made constant. It may be readily shown to be a 
consequence of the laws stated above. Suppose C to be the 
constant colour, then 
C = 
The form of the equation shows that C is the sum of a 
number of constants Ci, C 2 , Cg, &c., such that 
Cl = 
