Page:Scientific Papers of Josiah Willard Gibbs - Volume 2.djvu/254

absorbed. Values in which the coefficient of i is positive would represent media in which the opposite phenomenon took place.^[1]

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 concerned, 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 boundary 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^[2] and a further discussion is promised. For the electrical theory, the case of double refraction in perfectly transparent media has been discussed quite in detail in this Journal,^[3] and the intensities of reflected and refracted light have been abundantly deduced from the above conditions by various authors.^[4] 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,^[5] 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 case is that $\Psi$ and $\Phi$ are not self-conjugate.^[6] This is what we might expect on the electric

1. But $\iota$ 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.
2. Sir William Thomson, loc. citat. R. T. Glazebrook, loc. citat.
3. This vol. p. 182.
4. Lorentz, Schlömilch's Zeitschrift, vol. xxii, pp. 1–30 and 205–219; vol. xziii, pp. 197–210; Fitzgerald, Phil. Trans., vol. clxxxi, 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., vol. iv, p. 155.
5. This vol. p. 195.
6. See this vol. p. 217.