REFLEXION AND REFRACTION OF POLARIZED LIGHT. 173 



m and m' denoting the corresponding masses of the ether in 

 motion in the two media. Eliminating between these equa- 

 tions we have 



m + m' 1 m + m' 



expressions which are remarkable as being identical with those 

 of the velocities of two elastic balls after impact. 



In order to determine m and m' 9 let BA, AC represent 

 the velocities and directions of the incident and refracted 

 rays ; AA X the separating surface of the two media ; and 

 BB X , CC', lines parallel to that surface. Then the corres- 

 ponding volumes of the ether in motion in the two media are 

 as the parallelograms A X B, A X C ; 

 that is, as AB sin A X AB to 

 AC sin A X AC, or in the ratio of 



sin i cos i : sin r cos r, 



A \ 

 i and r being the angles of inci- V 



dence and refraction. But by the V 



third of the foregoing principles, c 



the densities of the ether in the two media are in the ratio 



of 1 to ju 2 , or as 



sinV : sin 2 ^. 



Combining these ratios, the ratio of the masses is 



m / _ tan i 

 m tan r 



Substituting this value of in the second of the two equa- 

 tions of condition, and dividing by the square of the first, w is 

 eliminated, and we find 



1 tan i 



1 + v~ tan r 

 Wherefore 



sin (i -r) - 2 cos i sin r 



V= : -r-. (> t?.l40 : 7: r-' 



sin ( i + r) sin (i + r) 



