154 Dr. James Bottomley on 



absorbed light has long been an interesting question ta 

 physicists ; from our present knowledge of the transmuta- 

 tion of energy it seems likely that in many cases it is 

 converted into heat, but there are cases in which the 

 transmission of light seems to be attended with structural 

 change of the medium, and this I suppose not to be effected 

 without expenditure of energy. It seems not unlikely that 

 in the case of light we have here something analogous to the 

 disgregation of Clausius in the theory of heat. This action 

 of light on the absorptive power of a medium has suggested 

 the investigation of the following problem : A cylinder 

 contains in solution a body A unalterable in the dark, but con- 

 verted by exposure to light into another body B, of differcjtt 

 absorptive power ; what zvill be the intensity of the light at any 

 instant transmitted through any section, supposing the light 

 absorbed by A to be spent in converting it into B ? As we 

 shall have to deal with partial differential equations, it will 

 facilitate the investigation to suppose the change taking 

 place in a cylinder having opaque sides, and that light of 

 constant intensity is incident on one extremity of the 

 cylinder ; by this limitation we shall have to deal with only 

 one dimension of space. Let I^ be the intensity of the 

 incident light, L the whole length of the cylinder, let the 

 body A be initially uniformly distributed through the 

 cylinder ; then if P' denote the quantity existing initially in 

 a column of length ;i; measured from the extremity admitting 

 light, we shall have 



V = ^x. (5) 



Li 



Let / and ^ be quantities of A and B co-existent at any 

 instant in the column x] now the quantity of B formed 

 must be proportional to the quantity of A which has dis- 

 appeared in the column ; therefore we must have the equation 



q = n(r-p), (6) 



or by substitution from (5) 



