Page:Scientific Papers of Josiah Willard Gibbs - Volume 2.djvu/237

Rh period; that is, would give no dispersion of colors. The case is essentially the same in transparent bodies which are not isotropic. The case is worse with metals, which are characterized electrically by great conductivity, and optically by great opacity. In their papers cited above, Lorentz and Rayleigh have observed that the experiments of Jamin on the reflection of light from metallic surfaces would often require, as ordinarily interpreted on the electromagnetic theory, a negative value for the inductive capacity of the metal. This would imply that the electrical equilibrium in the metal is unstable. The objection, therefore, is essentially the same as that which Lord Rayleigh had previously made to Cauchy's theory of metallic reflection, viz., that the apparent mechanical explanation of the phenomena is illusory, since the numerical values given by experiment as interpreted on Cauchy's theory would involve an unstable equilibrium of the ether in the metal. 13. All this points to the same conclusion—that the ordinary view of the phenomena is inadequate. The object of this paper will be accomplished, if it has been made dear how a point of view more in accordance with what we know of the molecular constitution of bodies will give that part of the ordinary theory which is verified by experiment, without including that part which is in opposition to observed facts. The consideration of the processes which we may suppose to take place in the smallest parts of a body through which light is transmitted, farther than is necessary to establish the general equation given above, is foreign to the design of this paper. Yet a word may be added with respect to the difficulties signalized in the ordinary form of the theory. The comparatively simple case of a perfectly transparent body has been examined more in detail in one of the papers already cited, where there is given an explanation of the dispersion of colors from the point of view of this paper. It is there shown that the effect of the non-homogeneity of the body in its smallest parts is to add a term to the expression for the kinetic energy of electrical waves, which for an isotropic body may be roughly described as similar to that which would be required if the electricity had a certain mass or inertia. (See especially §§ 7, 9 and 12, [this volume pages 185 ff.]) The same must be true of media of any degree of opacity. Now the difficulty with the optical properties of the metals is that the real part of $$\Theta$$ (or $$\Theta^{-1}$$) is in some cases negative. This implies that at a moment of greatest displacement the electromotive force is in the direction opposite to the displacement, instead of having the same direction, as in transparent isotropic bodies. Now a certain part of the electromotive force must be required to oppose the apparent inertia, and another part to oppose the electrical elasticity of the medium. These parts of the force must have opposite directions. In transparent bodies the latter part is by far the greater. But it need not surprise us that the former should be the greater in some metals. It has been remarked by Lorents that the difficulty with respect to metals would be in a measure relieved if we should suppose electricity to have the property of inertia. (See § 11 of his third paper, Schlömilch's Zeitschrift, vol. xxiii, p. 206.) But a supposition of this kind, taken literally, would involve a dispersion of colors in vacuo, and still be inadequate, as Lorentz remarks, to explain the phenomena observed in metals.