XL 



ON DOUBLE REFRACTION AND THE DISPERSION OF 

 COLORS IN PERFECTLY TRANSPARENT MEDIA. 



[American Journal of Science, ser. 3, vol. xxm, pp. 262-275, April, 1882.] 



1. IN calculating the velocity of a system of plane waves of homo- 

 geneous light, regarded as oscillating electrical fluxes, in transparent 

 and sensibly homogeneous bodies, whether singly or doubly refracting, 

 we may assume that such a body is a very fine-grained structure, so 

 that it can be divided into parts having their dimensions very small 

 in comparison with the wave-length, each of which may be regarded 

 as entirely similar to every other, while in the interior of each there 

 are wide differences in electrical as in other physical properties. 

 Hence, the average electrical displacement in such parts of the body 

 may be expressed as a function of the time and the coordinates of 

 position by the ordinary equations of wave-motion, while the real 

 displacement at any point will in general differ greatly from that 

 represented by such equations. 



It is the object of this paper to investigate the velocity of light in 

 perfectly transparent media which have not the property of circular 

 polarization in a manner which shall take account of this difference 

 between the real displacements and those represented by the ordinary 

 equations of wave-motion. We shall find that this difference will 

 account for the dispersion of colors, without affecting the validity 

 of the laws of Huyghens and Fresnel for double refraction with 

 respect to light of any one color. 



In this investigation, it is assumed that the electrical displacements 

 are solenoidal, or, in other words, that they are such as not to produce 

 any change in electrical density. The disturbance in the medium is 

 treated as consisting entirely of such electrical displacements and 

 fluxes, and not complicated by any distinctively magnetic phenomena. 

 It might therefore be more accurate to call the theory (as here 

 developed) electrical rather than electromagnetic. The latter term is 

 nevertheless retained in accordance with general usage, and with that 

 of the author of the theory. 



Since the velocity which we are seeking is equal to the wave-length 

 divided by the period of oscillation, the problem reduces to finding 

 the ratio of these quantities, and may be simplified in some respects 



