The Intensity of Transmitted Light, 157 



then during the short interval S/, the intensity of the light 

 transmitted through the thin plate will lie between 



-and the loss of intensity will lie between 



m_^ -/^Sp-mSg^ and (I + ^T)(1- e-M5i>+%)-w(^5'+%)\ 



If none of the body A were present in the section the loss 

 of intensity would lie between 



1(1 - e -^^^), and (I + ai)(l - e-^(^^+%)); 



hence the loss of intensity due to the presence of A in the 

 section will lie between 



j^-mSg^l _ e"^^) and (I + ai)e"'^^^^+^^^)(l - e'^^^ + ^^-P^) ; 



now the formation of B is by hypothesis due to the absorp- 

 tion of light by A, the quantity of B present in the thin plate 

 at time t was S^ and at time /+^A S^+^^^, hence the 

 increment due to time ^t is 8S^, which we may also write 

 in the form 



■Sq as before remarked may be written in the form 



ax 

 so that for SS^ we may substitute the expression 



^? . ^ 



this will denote the quantity of B formed in the section 

 during the short interval St. Since quantity of light is 

 proportional to the product of the intensity and the time, 

 from equation (9) it will follow that if we multiply the 

 •expressions obtained for the loss of intensity by kdtwe shall 

 obtain the limits between which the quantity of light 

 -absorbed by the body A in the thin plate during the time 

 ^/ falls ; hence h being some constant, we have 



