XII. 



ON DOUBLE REFRACTION IN PERFECTLY TRANSPARENT 

 MEDIA WHICH EXHIBIT THE PHENOMENA OF CIR- 

 CULAR POLARIZATION. 



[American Journal of Science, ser. 3, vol. XXIII, pp. 460-476, June, 1882.] 



1. IN the April number of this Journal,* the velocity of propagation 

 of a system of plane waves of light, regarded as oscillating electrical 

 fluxes, was discussed with such a degree of approximation as would 

 account for the dispersion of colors and give Fresnel's laws of double 

 refraction. It is the object of this paper to supplement that discussion 

 by carrying the approximation 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 system. If we then reduce the magnitude of 

 the displacements in the uniform ratio of two to one, they will be 

 identical, at an instant of maximum displacement, with those of the 

 original system 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 dis- 

 placement into the regular part, represented by rj, f, and the 

 irregular part, represented by ', rf, f, in accordance with the 

 definitions of 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 u\ t 



= ( a, cos 27r-7--f-a 9 sm 2?r -r ) COSZTT , 

 = \i / j // CM > 



\ (/ v / U 



( It . U\ t 



p 1 cos27ry + /3 2 sin27r-T- ) cos2x- , 



(ni 1t/\ 



y x cos 2-7T y + y 2 sin 2?r j J cos 



- , 



*See page 182 of this volume. 



