29.2 DR. J. B0TT0MLEY ON THE INTENSITY OF LIGHT AFTER 



XIX. On the Intensity of Light that has been transmitted 

 through an Absorbing Medium, in which the Density 

 of the Colouring -matter is a Function of the Distance 

 traversed. By James Bottomley, B.A., D.Sc, F.C.S. 



Read October 17th, 1882. 



In previous papers it has been supposed that the absorbing 

 matter was uniformly distributed throughout the medium. 

 For such a case the laws I=2«e -W and I=^a6~ ttq are 

 applicable, t denoting the length of the absorbing column, 

 and q the mass of colouring-matter contained in it. In 

 the present paper these laws are applied to the case of 

 light passing through media of variable density. Such 

 cases occur in nature ; for instance, the atmosphere is of 

 variable density, increasing 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. The same 

 reasoning will also apply very approximately to fluids 

 containing in suspension very finely divided matter in 

 layers of variable density, or to an atmosphere charged 

 with very fine dust. 



For simplicity I shall suppose that we are dealing with 

 homogeneous light, or with white light that has passed 

 through a grey solution. 



Suppose that a ray has penetrated a length t of a 

 variable medium, and that the intensity is I when it falls 



