172 Dr. James Bottomley on 



condition ^ = implies the condition mn = ju, and therefore 

 j-w^j-mn. consequently, if we have a cylinder containing in 

 solution a body A of which the coefficient of transmission 

 is s-f* and this body is converted into a body B, so that 

 each unit of A furnishes n units of B of which the 

 coefficient of transmission is c ~'^, then if mn = fx there will 

 be no visible evidence of any structural change, the intensity 

 of the transmitted light depending on the length of the 

 absorbing column, but being independent of the time. 

 This may be merely a mathematical refinement, but in 

 the present state of our knowledge respecting the intimate 

 constitution of material combinations, I do not think that 

 we should be justified in saying that no internal change 

 has taken place, because none is visible. 



Another variety of the problem which is the subject 

 of this paper arises from the following consideration ; 

 suppose the change from A to B to be so slow, and the 

 contents of the cylinder kept in such a state of brisk 

 agitation, that the absorbing medium may be considered 

 homogeneous, what will be the intensity of light at any 

 time. In this case,/ and q being at any time the quantities 

 of A and B coexistent in in the entire length of the 

 cylinder, the intensity of the emergent light at the same 

 time will be given by the equation 



T_T -f^p-mq . 

 therefore the loss of intensity will be 



1,(1 -e-^^-*^^); 



at the end of the short interval ^t the intensity of the 

 emergent light will be 



T ^^ - f^^v + ^^) - ^'M + h)\ 



and the loss of intensity at that time, 



J /I _ g - f^^p + ¥) - ^^Aq + h)\ . 



If the body B only were in solution, the loss of intensity 



