238 COMPARISON OF THE ELECTRIC THEORY OF LIGHT 



absorbed. 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 details 

 by which we may derive, so far as observable phenomena are con- 

 cerned, Fresnel's law of double refraction for transparent bodies, 

 as well as the more general law of the same character which relates to 

 aeolotropic bodies of more or less opacity, and which differs from 

 Fresnel's only in that certain quantities become complex, or Fresnel's 

 laws for the intensities of reflected and refracted light at the boun- 

 dary of transparent 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 t and a further discussion is promised. For 

 the electrical theory, the case of double refraction in perfectly trans- 

 parent media has been discussed quite in detail in this Journal, J 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 

 if it has been made clear that the two theories, in their extreme cases, 

 give identical results. The greater or less degree of elegance, or 

 completeness, or perspicuity, with which these laws may be developed 

 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 certain 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 trans- 

 parent 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 case is that ^ and <1> 

 are not self-conjugate.1F This is what we might expect on the electric 



* But L might have been introduced into the equations in such a way that a positive 

 coefficient in the value of n 2 would indicate absorption, and a negative coefficient the 

 impossible case. 



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



J This vol. p. 182. 



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. (5), vol. ix, p. 284 ; Rayleigh, Phil. Mag. (5), vol. xii, p. 81. Glazebrook, Proc. 

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



|| This vol. p. 195. 



IT See this vol. p. 217. 



