of these angles have been determined experimentally by Quincke1 for silver, and by Sir John Conroy for gold and silver, when certain other media are substituted for air. The following table shows the results obtained by the latter, when the incident light was red. In a second series of experiments, Sir J. Conroy3 found the The following table shows the percentage of light reflected at different angles of incidence from the following mirrors. 1 Pogg. Ann. Vol. cxxvII. p. 541. 2 Proc. Roy. Soc. Vol. xxvIII. p. 242; Ibid. pp. 248 and 250. 3 Proc. Roy. Soc. Vol. xxxi. pp. 490, 496. 4 Proc. Roy. Soc. Vol. xxxv. pp. 31, 32; and Vol. xxxvi. p. 187. KUNDT'S EXPERIMENTS. 341 381. The ratio of the velocity of light in air to that in metals, has been investigated experimentally by Quincke, Wernicke, Voigt1 and Kundt2. The values which Kundt has obtained for this ratio are given in the following table for red, white and blue light. From this table it appears, that the velocity of light in silver is nearly four times as great as in vacuo; but the dispersion was so small, that it could not be measured. Also in gold and copper, the velocity is greater than in vacuo, and the dispersion is normal; but in the other four metals it is anomalous. Beer has calculated the above ratio according to Cauchy's theory, from Jamin's observations on reflection. He found, that silver exhibited no marked dispersion, and that the mean ratio of the velocities was 0.25. Copper showed strong normal dispersion, and for the red rays the ratio was less than unity; iron, on the contrary, showed anomalous dispersion, giving red = 2.54, violet 147, where μ is the ratio of the velocity of light in air to that in the metal. 382. Kundt also found, that there is a close relation between the velocity of light in metals, and their electrical conductivities. In the accompanying table, the velocity of light and the electrical conductivity of silver are both taken to be 100, and the conductivities are taken from Everett's Units and Physical Constants, p. 159. 1 Wied. Ann. Vol. xxi. pp. 104-147; Vol. xxv. pp. 95–114. 2 Sitz. der Kön. Preuss. Akad. der Wissen., 1888; translated Phil. Mag. July 1888. 3 Pogg. Ann. Vol. xcă, p. 417. With the exception of copper and bismuth, it appears that there is a fair agreement between the two sets of numbers. 383. Eisenlohr in the paper referred to in § 371, has applied Jamin's experimental results to calculate the quantities R and a by means of Cauchy's formulæ, and some of the values found by him are given in the following table. from which we see that for silver and speculum metal, μ must be a complex quantity, whose real part is negative. For steel, the real part of μ is positive; for copper it is negative for red light, and positive for yellow and blue; whilst for zinc it is positive for red, yellow and blue, but is negative for the remainder of the spectrum, since Eisenlohr found that for indigo a = 46° 23', and for the extreme violet a = 49° 08'. 384. The circumstance that Cauchy's formulæ lead to the conclusion, that for certain metals the real part of μ must be negative, has led to an important criticism by Lord Rayleigh', which we shall now consider. If we suppose that the opacity of metals can be represented mathematically by a term proportional to the velocity, the equa1 Hon. J. W. Strutt, Phil. Mag. May, 1872. LORD RAYLEIGH'S CRITICISM. 343 tion of motion within the metal, upon the elastic solid theory, may where h is necessarily a positive constant. The equation of motion outside the metal, will be (29), Under these circumstances, it follows that μ is a complex quantity, whose real part is positive; hence a must lie between 0 and T. Lord Rayleigh's investigation accordingly shows, that for silver and all metals for which a>, reflection cannot be accounted for on the elastic solid theory, by the introduction of a viscous term. 385. When we consider the electromagnetic theory of light, it will be shown, that if we attempt to explain metallic reflection by taking into account the conductivity of the metal, we shall be led to equations of the same form. Hence metallic reflection cannot be completely explained, upon the electromagnetic theory, by means of this hypothesis. 386. We shall now show, that the circumstance of the square of the pseudo-refractive index being a complex quantity, whose real part is negative, may be explained by Von Helmholtz' theory. Measuring the axis of z in the direction of propagation, and the axis of x in the direction of vibration, the equations of motion (11) and (10) of § 357 and 356, are Since we require a solution in which μ is a complex quantity, we must not neglect the viscous term, and we shall find it convenient to conduct the integration of these equations, in a manner somewhat different from that of § 357. = If Po be the density of the ether, and U the velocity of light in free space, n/p, U2; also since the pseudo-index of refraction of a metal is defined to be the ratio of U/V, we obtain from (30) με 1+ Το προ 4π2ρ1 (x2 — т2) — (h2/p1 + a2) «272 +41πhK2T) hx2+} (31). Rationalizing the denominator, we see that the imaginary part of μ2 is positive, whilst the real part is equal to a2т2x2 {4π2ρı (x2 — T2) — (h2/p1 + a2) K2t2} (32). 387. In order to apply this result to metallic reflection, we shall suppose that h is a small quantity, whose square may be neglected, under which circumstances, the real part of μ2 which we shall denote by v2, becomes equal to This expression is the same as the square of the refractive index of a substance, which produces anomalous dispersion, and has a single absorption band; and it follows from § 359, that it may be negative in two distinct ways. In the first place, if 7, is the least value of 7 for which v2 = 0, and 7 is the value of 7, which makes the denominator of the third term zero, the real part of μ will be negative for values of T lying between 7, and 72. In the second place, there is another value 73 of 7, which is greater than 72, for which 2 = 0; and for all values of T> T3, v2 is negative. We may therefore explain T3 |