200 DR. J. BOTTOMLEY ON THE INTENSITY OF LIGHT 



Dividing both sides by k and diminishing k without limit, 

 the resulting equation will be 



eliminating I and F by (5), 



The integral of this is 



log0(^)=(/)'(o)<r+c > 



or 



When x=o } 

 Therefore 



<£(#) = 1. 

 C=i. 



Also as x increases, the intensity diminishes, therefore 

 (£'(o) must be some negative constant ; let it be denoted 

 by —m. Then the equation becomes 



and equation (1) may be written 



IT —mx 



Hence experiment leads to the same form for the function 

 as the hypothetical form with which we started. 



If, in the above investigation, we had made the length 

 of the column invariable, and x denoted a mass of some 

 colouring-matter which undergoes no decomposition on 

 dilution, we might have obtained experimentally the form 

 of the function expressing the intensity of the light trans- 

 mitted through a column of fluid of invariable length, 

 containing a variable quantity of colouring-matter. 



