TRANSMISSION THROUGH AN ABSORBING MEDIUM. 205 



II. As another example, suppose the absorbing medium 

 to be an elastic fluid arranged in concentric layers about 

 an attracting sphere of radius R, the law of attraction 

 being that of the inverse square. Let t be the distance 

 of any point from the centre, then if / be the attractive 

 force, 



m being a constant. It may be shown that the density at 

 any point will be given by the equation 



d=A(F { , (4) 



where a is a constant denoting the relationship of the 

 density to the pressure, and A another constant which 

 may be determined as follows : — 



Let D be the density at the surface of the sphere ; then 

 making /=R, we get 



A = I ) e -aR. 



Hence we have 



m m 



and for the intensity of the transmitted light we have 



m m 



I =C «-^" a )^* (5) 



The value of C may be obtained by substituting for I its 

 value at the surface of the sphere, and after integrating 

 the quantity under the integral sign, substituting R for t. 

 Equation (4) may be written in the form 



rf=De «R € «( r +t). 



