136 J. W. Gibbs — Comparison of the Electric Theory of 



cient of t is negative, indicate media in which light is ab- 

 sorbed. Values in which the coefficient of t is positive would 

 represent media in which the opposite phenomenon took place.* 



It is no part of the object of this paper to go into the de- 

 tails by which we may derive, so far as observable phenomena 

 are concerned, Fresnel's law of double refraction for transpar- 

 ent bodies, as well as the more general law of the same char- 

 acter which relates to aeolotropic bodies of more or less opac- 

 ity, and which differs from Fresnel's only in that certain 

 quantities become complex, or Fresnel's laws for the intensi- 

 ties of reflected and refracted light at the boundary of trans- 

 parent isotropic media, with the more general laws for the 

 case of bodies aeolotropic or opaque or both. The principal 

 cases have already been discussed on the new elastic theory in the 

 Philosophical Magazine^ and a farther discussion is promised. 

 For the electrical theory, the case of double refraction in per- 

 fectly transparent media has been discussed quite in detail in 

 this Journal,;]: and the intensities of reflected and refracted 

 light have been abundantly deduced from the above conditions 

 by various authors.§ So far as all these laws are concerned, 

 the object of this paper will be attained, if it has been made 

 clear, that the two theories, in their extreme cases, give iden- 

 tical results. The greater or less degree of elegance, or com- 

 pleteness, or perspicuity, with which these laws may be devel- 

 oped by different authors, should weigh nothing in favor of 

 either theory. 



The non-magnetic rotation of the plane of polarization, 

 with the allied phenomena in aeolotropic bodies, lie in a cer- 

 tain sense outside of the above laws, as depending on minute 

 quantities which have been neglected in this discussion. The 

 manner in which these minute quantities affect the equations 

 of motion on the electrical theory has been shown in a former 

 paper,| where these phenomena in transparent bodies are 

 treated quite at length. For the new theory, a discussion of 

 this subject is promised by Mr. Glazebrook. . 



But the magnetic rotation of the plane of polarization, with 

 the allied phenomena when an aeolotropic body is subjected to 

 magnetic influence, fall entirely within the scope of the above 

 equations and surface- conditions. The characteristic of this 



* But t might have been introduced into the equatious in such a way that a 

 positive coefficient in the value of n? would indicate absorption, and a negative 

 coefficient the impossible case. 



f Sir William Thomson, loc. citat. R. T. Glazebrook, loc. citat. 



% Vol. xxiii, p. 262. 



§ Lorentz, Schlomilch's Zeitschrift, vol. xxii, pp. 1-30 and 205-219; vol. xxiii, 

 pp. 197-210; Fitzgerald, Phil. Trans., vol. clxxi, p. 691 ; J. J. Thomson, Phil. 

 Mag. (V), vol. ix, p. 284; Rayleigh, Phil. Mag. (V), vol. xii, p. 81. Glazebrook, 

 Proc. Cambr. Phil. Soc, vol. iv, p. 155. 



|| This Journal, vol. xxiii, p. 460. 



