9 
l u being a constant, therefore 
m — fjiq 
and equation (1) becomes 
dlogI = - fiqdt (2) 
For q we may substitute d where d denotes the density of 
the colouring matter, the unit of density being that due to 
the distribution of the unit mass through the unit volume. 
Now suppose d to vary and to be some function of t , so that 
d = (f>(t) 
Let be the integral of this, so that 
x (t)=Mt)dt. 
Substituting in equation (2) and integrating, we get 
logI=- FX (0 + c 
or as it may be written 
i = Ce"^ ( ‘ ) (3) 
To determine the constant we must know simultaneous 
values of I and t. The above equation (3) is the general 
equation for determining the intensity of transmitted light 
when the density is an assigned function of the distance 
traversed. The remainder of the paper is taken up with 
special cases of this general fromula. Firstly, when the 
density varies as the distance from the plane of incidence. 
Secondly, when the absorbing medium is an elastic fluid 
surrounding an attracting sphere, the law of attraction being 
that of the inverse square. Thirdly, when the colouring 
matter is so distributed as to give recurring values of the 
density, taking as a particular case the relation 
d = m- %sin£ 
m and n being constants and m greater than n, as t varies 
we obtain periodic values of d. In this case the curve of 
intensity is represented by a sinuous curve always situated 
between two logarithmic curves and touching them alter- 
nately. Finally, it is shown that the general equation may 
