8 
medium. In the present paper the author treats of the 
intensity of light which has passed through a medium of 
variable density. Such cases occur in nature, for instance, 
the atmosphere increases in density as we approach the 
earth, also we might have coloured glass in which the 
colouring matter is not uniformly distributed, or the case of 
a coloured soluble salt on which water is poured, the 
colour in the immediate vicinity of the salt is most intense 
and gradually fades as the distance increases. Also the 
same reasoning would apply very approximately to the case 
of fluids containing in suspension layers of different density 
of finely divided matter, or to the case of an atmosphere 
containing fine dust in suspension. For simplicity it is 
supposed that we are dealing with homogeneous light, or 
with white light which has passed through a grey solution. 
Suppose a ray of light has penetrated a length t of a medium 
which is not homogeneous and that its intensity is I when 
it falls on a surface for which the coefficient of transmission 
is e~ m , consider a plate of thickness At and let e ~ [m+Am ) be 
the coefficient of transmission at the upper surface. Let I' be 
the intensity of the light emergent from this surface. Then 
^>1 e -C*H-A»»)A< 
If we expand the exponentials and write A I for I' - I there 
results 
Al 
I 
i_ m 2 A ft . 
-mAt-v — ~ b &c. 
. X + A m) 2 0 . 
- (m + Am) At + ^ L A t 2 + &c. 
Proceeding to the limit, there results 
dlogl = -mdt (1) 
Now suppose light to penetrate a unit length of an absorbing 
medium containing q units of colouring matter, there results 
the following relationship 
£ — m = e -M<Z 
