152 Dr. James Bottomley on 



On the Intensity of Transmitted Light when the co- 

 efficient of transmission of the medium is a functioa 

 of time. By James Bottomley, B.A., D.Sc, F.CS. 



\Received December i6, iSpo.} 



In this investigation I suppose that we have a cylinder 

 containing in solution some colouring matter which is 

 undergoing chemical change, and that in consequence its. 

 absorptive power varies. Let the side of the cylinder be 

 opaque so that light is admitted by the base and is trans- 

 mitted parallel to the axis ; to simplify the formulae let 

 this light be homogeneous (or white light if the absorption 

 be the same for every species). Let P be the mass of the 

 colouring matter, c"/^ the coefficient of transmission of its 

 solution, and L the intensity of the incident light, then if I 

 denote the intensity of the transmitted light, we shall have 

 initially 



I = I,e-^^ (1) 



Now suppose the original body, which we may denote by 



A, to be gradually changed into another body which we 

 may denote by B, and that e""* is the coefficient of trans- 

 mission of its solution ; let / and q be the masses of A and 

 B existing at any time. Now A must be changed into B 

 in one of three ways, (i) by simple molecular change ; in 

 which case the mass of A will be the same as the mass of 



B, (2) or by the addition of matter (3) or by the sub- 

 traction of matter ; all these three cases are however 

 included in the formula 



q = n(P-p), (2) 



n being some constant, which in the first case is equal to 

 unity, in the second case greater, and in the third case less 



