The Intensity of Transmitted Light. 155 



In this investigation it is supposed that the matter in any 

 section of the cylinder remains in that section after chemical 

 change ; it is easy to see that this condition may not always 

 be fulfilled, for the new matter may be of different density 

 from the old, and may rise or sink, so as to pass into a 

 different section ; such cases would require a different in- 

 vestigation. I have spoken previously of the bodies being 

 in solution, though this condition is not absolutely necessary ; 

 for in a previous paper published in these memoirs, on the 

 absorption of light by turbid media, I have pointed out 

 that in media containing finely divided matter in suspension^ 

 the extinction of light by absorption follows the same law 

 as in the clear solutions. Also we might have the body A 

 initially distributed through the cylinder not uniformly, 

 but so that the density in any section shall be some function 

 of the distance of that section from the base of the cylinder ; 

 the arbitrar^^ functions of the integral of the differential 

 equation must be adapted to each particular case. 



It is supposed that the light absorded by A is spent in 

 converting it into B ; from what is known of physical 

 laws it would seem reasonable to infer that the quantity of 

 B produced would be proportional to the quantity of light 

 absorbed. It will therefore be necessary to have some 

 expression for quantity of light ; let this be denoted by Q. 

 If light of constant intensity fall for a given time on a 

 given area, it seems reasonable to consider the quantity 

 proportional to the product of the intensity and the time ; 

 hence, k being some constant, we shall have the equation 



Q = HT, (8) 



T denoting the time that the area has been exposed to 

 the light ; if the intensity vary during the time T, then if 

 I be the intensity at any instant, for the above equation we 

 must substitute 



