156 Dr. James Bottomley on 



If we have a series of coloured plates, and allow light to 

 pass through them, the result will be the same in whatever 

 order the plates are arranged ; this we may apply to 

 determine the intensity of the light passing through the 

 cylinder at any instant ; for in each section at any Jme t 

 after the commencement of the experiment, we shall have 

 the absorbing bodies A and B in different proportions ; 

 if we supposed no further change to take place, then at this 

 instant, the intensity of light transmitted through a column 

 of length X would be the same if there were to be a redis- 

 tribution of A and B, so that all A were collected in one 

 portion of the cylinder, and all B in the other portion ; 

 lo being the initial intensity of the light, after traversing A, 

 the intensity will become t~/^^, p being the quantity of A 

 existing at that instant in the length x, then this light after 

 traversing B will have]^the intensity \jE~f^^~^'^y q being the 

 quantity of B existing at that instant in the column x ; 

 therefore for the transmitted light we shall have the equation 



l^l^^-f^P-m (10) 



On account of the variability of / and g with the time, 

 I will vary and at the end of a short time 8/ will become 

 I + SI. Now consider a section if the cylinder distant x 

 from the extremity admitting light, and of thickness dx^ also 

 let S^ and ^ be the quantities of B and A simultaneously 

 present in the thin section ; since these quantities are 

 variations due to the variation of ;ir,we may, when convenient, 

 substitute for them 



^^x and , ^a:. 

 ax ax 



After the expiration of a short time 8/, the quantities §^ 

 and ^g will be subject to small variations due to the lapse 

 of time ; let these variations be denoted by dSp and ddg ; 



