266 Proceedings of the Royal Physical Society. 



necessarily very small compared with the other terms, and 

 are only important when considering the dispersion of light. 

 Then the equation (26) becomes 



O 2 - A) {v 2 - (FT 2 + W + HV 2 ) } 

 = F(AT 2 + B'm' 2 + CV 2 ) 



Now, if we suppose that the velocity of propagation of 

 the wave through the material molecules is such that 

 v' 2 = k 2 v 2 , the above becomes a quadratic in v 2 , viz. :■ — 



W - {Ak 2 + FT 2 + G'm' 2 + HV 2 } v 2 

 + A(F'l' 2 + G'm 2 + HV 2 ) 

 - F(AT 2 + B'm' 2 + CV 2 ) = 0 . . . (27) 



Hence, in this case, there are two values of v 2 for given 

 values of I'm'n. Hence, in general, there would be two 

 refracted rays for a given incident ray, and thus we have a 

 general explanation of the double refraction of light. 



Also, since the vibrations are transversal, 



du dv ^ div _ q 

 dx dy dz ~~ 



.'.la + mfi + ny — 0 



or hi + mv + nw = 0 



Now from equation (24) 



u _ v_ w _ X 2 { A! I' 2 + BW 2 + CV 2 \ 

 v! ~ v' ~ vf ~ X' 2 V v 2 - A ) ' ' 



lu + mv + nw 

 ~ lu' + mv + nw 



But lu + mv + nw — 0 



. • . In' + mv' + nw = 0 



Therefore the vibrations of the material molecules are 

 also transversal and parallel to the plane 



Ix + my + nz — 0 

 . • . V — I m' — m n = ri 



Let v 2 and v 2 2 be the roots of the equation (27), and let 



