460 J. W. Gibbs—Double Refraction amd Circular 
Art. LIV.—WNotes on the Electromagnetic Theory of Light; by 
J. Wi~uarp Gisss. No. Il.—On Double Refraction in per- 
fectly transparent Media which exhibit the Phenomena of Circular 
Polarization. 
1. In the April number of this Journal,* the velocity of 
he i of a system of plane waves of light, regarded as 
scillating electrical fluxes, was discussed with such a degree 
i approximation as would account for the di ee Y colors 
and give Fresnel’s laws of double refraction. It is the object 
of this paper to supplement that discussion by aie rhe ap- 
proximation so much further as is necessary in order to 
embrace the phenomena of circularly polarizing media. 
2. If we imagine all the velocities in any progressive system 
of plane waves to be reversed at a given instant without 
affecting the displacements, and the system of wave-motion 
thus obtained to be superposed upon the original system, we 
obtain a system of stationary waves having the same wave- 
length and period of oscillation as the original progressive sys- 
tem. we then reduce the magnitude of the hel Sool ae in 
the uniform ratio of two to one, they will be identical, at an i 
stant of maximum displacement, with those of the original x 
tem at the same instant. 
Following the same method as in the paper cited, let us 
especially consider the system of stationary waves, and divide 
the whole displacement an the regular part, represented b 
4, C, and the irregular part, represented by &’, 7’, 2’, in accord- 
ance with the detnidous of R 2 of that paper. 
3. The regular part of the displacement is subject to the 
equations of wave-motion, which may be written (in the most 
general case of plane stationary waves 
> 
u ; Uu t 
&=( a, cos 27—+ a, sin 2m) cos 2 
: Z l Pp 
n=(B, cos oni + Bi sin 2m) eos ae (1) 
2=(y, COS ono + ys sin 2m) cos on J 
where / denotes the wave-length, p the period of clei u 
the distance of the point considered from the wave-plane pas 
ing through the origin, a,, 8, 7, the amplitudes of the dais 
ments §, 7, € in the wave-plane passing through the origin, and 
@, By 7, their amplitudes in a wave-plane one-quarter of a 
, * See page 262 of this volume. 
