206 DR. J. BOTTOMLEY ON THE INTENSITY OF LIGHT AFTER 



If t be small compared with R, we may write 



Let the attracting body be the earth; then for m we 

 may substitute gK l ', and we obtain 



- ff -r 



d=De a (6) 



In this case the expression for the intensity becomes 



I = Ce?" DS 



To determine C make I = I Q and r=o. Then 

 and the expression for the intensity becomes 



I=I /v- -> (7) 



This is the expression for the intensity of light which has 

 passed through a length r of the atmosphere,, supposed to 

 be of uniform temperature, neglecting the differences in 

 the force of gravity at different heights. If the law of 

 decrease of temperature with altitude be given, then a in 

 (6) must be multiplied by some function of t. When t 

 becomes large the expression (7) tends towards a limiting 

 value 



T T --*D 



I=I e 3 • 



The atmosphere, especially in the lower layers, is never 

 free from dust; of the whole atmospheric absorption a 

 considerable portion would probably be due to this. 



