the column of fluid remains constant, the intensity of light 
will be a function of the quantity of colouring matter only, 
say, (p(q). Suppose, now, in the cylinders which we may 
distinguish as A and B we pour a unit length of the standard 
fluid, then the light transmitted will be the same in both ; 
hence we shall have Dissolve in A another 
unit of the colouring matter and make the column of the 
standard solution two units long in B, the colour will 
remain the same; hence we have ^(2) = ^(2). If we 
dissolved three units in A and made B three units long, 
we should again And ;//(3)=^(3), and generally 
If then we know \p(n) we shall obtain ^(n). For the 
intensity of light transmitted through a column n units 
long, Sir John Herschel has given an expression (to which 
I have referred in a previous paper) of the form 
h being the intensity of light passing through a unit thick- 
ness, a the intensity of the incident light, and the summa- 
tion having reference to the composite nature of light. 
This formula is given by Herschel in the “Encyclopsedia 
Metropolitana,” also in an article on the absorption of light 
by coloured media in the “ Transactions of the Royal Society 
of Edinburgh.” In neither of these works do I And the ex- 
perimental confirmation of the formula. It appears to have 
been obtained a ^priori. If we assume its accuracy we 
shall obtain for the expression ak'^, if we suppose we 
are dealing with homogeneous light ; if we substitute q for 
n we shall obtain ak"^ for the intensity of light which has 
passed through a unit length containing q units of colour- 
ing matter. We may now suppose the length to vary — for 
two units of length the expression will be for three 
