The Intensity of Transmitted Light. 173 



at time /, would be 

 and at time ^+^/, 



lience the loss due to the presence of A will be at time /, 

 and at time t-\-'^t 



hence the quantity of light absorbed by A during the short 

 interval ^t will lie between 



H,£-^^(l-e-^^)a^, and /(:I,£-^(? + ^^)(l - .-'"^^ + ^-^^)a^- 



hence, since ^q the quantity of B formed is supposed to be 

 proportional to the quantity of light absorbed by A during 

 the short interval ^/, we shall have 



The lower of these expressions may be written in the form 



where R denotes a sum of products and powers of small 

 quantities of the second and higher orders ; hence ultimately 

 we obtain 



^ = mor'^'^(l-e-^^); (57) 



in this equation the letter h denotes some constant ; we 

 may now substitute 



^ for ^^ 

 dt dt 



by differentiating the equation q = n(P — /) ; hence we obtain 

 by eliminating ^, an equation of the following form 



S=-«(^"'-n (58) 



wherein, for brevity, a has been written for 



n 



