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Dispersion of Colors in perfectly transparent Media. 263 
tem of stationary waves may be formed by two systems of pro- 
gressive waves having opposite directions. 
. Let x, y, 2 be the rectangular codrdinates of any point in 
the medium, which with the system of waves we may regard 
as indefinitely extended, and let €+€’, 7+7', €+€' be the compo- 
nents of electrical displace:nent at that point at the time 7; 
&, 7, € being the average values of the components of electrical 
displacement at that time in a wave-plane passing through the 
point. en €, 7, €, €’, 7’, ¢’ are perfectly defined quantities, 
of which &, 7, € are connected with «, y, z, and ¢ by the ordinary 
equations of wave-motion, while each of the quantities &, 7’, € 
has always zero for its average value in any wave-plane. We may 
eall §, 7, € the components of the regular part of the displace- 
ment, and &', 7’, ¢’ the components of the wreguiar part of the 
displacement. In like manner, the differential coefficients of these 
components of displacement in that element. The same will 
be true of the quantities &’, 7’, ¢’ and &, 7, €. 
3. Since we have excluded the case of media which have the 
property of circular polarization, we shall not impair the gener- 
ality of our results if we suppose that we have to do wit 
linearly polarized light, 7. e., that the regular part of the dis- 
placement is everywhere parallel to the same fixed line, all 
cases not already excluded being reducible to this, Then, with 
_ the origin of codrdinates and the zero of time suitably chosen, 
