OF THE REFLECTION AND REFRACTION OF LIGHT. 
703 
I shall not consider the general equations of wave propagation in the Cartesian form 
as they are the same as those given by Maxwell in a more general form, for he 
assumes that the static energy of the medium is expressed more generally than I have 
assumed, but as the Quaternion investigation is not long I shall give it. 
The equation of motion is 
/x9t+87rCV v~+^VvYv 91 = 0 
CLU Iv 
. d 
and if z be the normal to a wave-plane, we may evidently assume V =k—, and as 91 is 
in the wave-plane we have 
9x = ai sin ~^(vt — z) + bj cos 
X 
and as our equation becomes 
/rOl + 8 77-Cy. V k 
dm , 1 TT7 rf T7J (19t 
Substituting for 91, and equating the coefficients of i and j separately to zero, we get 
o 167r 2 Cy 7 a ? „ 167r 2 C7 b 
afjiv* - -— L .bv—— = 0, bfjiV 2 --— .av——=0 
from which it is easy to see that «=dz b and that v is determined by the equation 
0 16?r 2 C 7 1 
which gives of course two different values of v, one for each circularly polarised ray, 
or disregarding the solutions for waves going in the negative direction, we have 
approximately 
1 87r 2 C7 1 87r 2 C7 
1 \/[xK. ’ ~ fxK \ 2 fx 
and of course C can easily be determined from these by observing the rotation 
produced, but there is nothing except experiment to prove that C may not be a 
function of X, as we know K to be, to some extent at least; so that using these formulae 
in order to obtain the laws of dispersion of rotatory polarisation seems to approach 
towards deducing the known from the unknown. All we can be sure of is that C is 
in general extremely minute. 
4x2 
