266 Froceedings 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 
(^;2 - A) {v"" - {VP + G m'^ + HV^) } 
= F(A.T2 + B'm'2 + CV2) 
Now, if w^e suppose that the velocity of propagation of 
the wave through the material molecules is such that 
v"^ = k'^v^, the above becomes a quadratic in v^, viz. : — 
^2^* - {A^2 ^ FT2 + GW2 + HV2} v'' 
+ A(F7'2 + GW2 + HV2) 
- F(Ar2 + + = 0 . . . (27) 
Hence, in this case, there are two values of for given 
values of I'mn. 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 ^ dw _ Q 
dx dy dz ~ 
la + mjS + ?^y — 0 
or lu + mv + mv = 0 
Now from equation (24) 
u _ V 
But 
Therefore the vibrations of the material molecules are 
also transversal and parallel to the plane 
Ix + yny + nz = 0 
V — I m! — m n = n 
Let and Vc^ be the roots of the equation (27), and let 
w x2 /A7'2 + BV2 + CV2\ 
_ hi + mv + nw 
lu' + mv' + nw 
lu 4- mv + nw = 0 
lu' + mv' + nw' = 0 
