The Intensity of Transmitted Light. 175 



dt ^' 

 whence we have / = constant ; a result which is in agreement 

 with the hypothesis that B is formed from A by the absorption 

 of hght, for if no Hght is absorbed no change will take place 

 in the contents of the cylinder. 



If the conversion from A to B is attended with no 

 visible change, then ^=0, and (58) may be put in the form 



of which the integral is 



if the value of the constant c be determined by the condi- 

 tions /=0,/ = P, we may put the last equation in the form 



Throughout this investigation it has been considered 

 sufficient to proceed only so far as to determine / ; for the 

 value of g may then be deduced by (2) or by (7) ; then these 

 values of/ and q substituted in the equation 



T = T -f^P-'^<l 



will give the intensity of the light transmitted at any instant 

 through any section of the cylinder. 



If the light be not homogeneous, or if the absorption 

 be not the same for every species, in place of the last 

 equation we must use the equation 



In this case the letters fi and m will have different values 

 for rays of different wave length. Objection may be raised 

 to those results in this paper which postulate the existence 

 of perfectly transparent media, on the ground that no such 

 medium has yet been discovered ; in reply, it may be stated 

 that in this, as in other branches of science, a limitation of 



