198 DR. J. BOTTOMLEY ON THE INTENSITY OF LIGHT 



XVIII. On the Formula for the Intensity of Light trans- 

 mitted through an Absorbing Medium as deduced from 

 Experiment. By James Bottomley, B.A., D.Sc, 

 F.C.S. 



Eead October 17th, 1882. 



In a former communication an experimental method was 

 suggested for testing the validity of an assumed law of 

 intensity of light that has passed through an absorbing 

 medium. The method was this : take two surfaces of 

 different degrees of brightness, survey them through some 

 absorbing medium, adjust the lengths of the columns so 

 that the intensities shall be the same ; then, if the law of 

 absorption be true, the intensities will again be equal if 

 both columns are increased by the same length. Some 

 experiments which I made gave results in agreement with 

 the theory. In these experiments surfaces of different 

 degrees of whiteness were observed through a grey solu- 

 tion. The error arising from the finite extent of the 

 surface is small, and the mean intensity which we observe 

 may be taken as the intensity of the central ray. 



But suppose we had started with no hypothesis as to 

 the form of the function expressing the intensity of trans- 

 mitted light, but had found, as an experimental result, 

 that when the intensities are equal, they remain equal, 

 when the columns receive equal increments; what form 

 for the function might be deduced from such a result ? 



Suppose there are two lights of initial brightness, I 

 and I' Q respectively, then if x and y be the lengths of the 



