Page:Scientific Papers of Josiah Willard Gibbs - Volume 2.djvu/265

vacuo, $n$ for the index of refraction of the medium considered, and $k$ for the velocity of light in vacuo, which we shall regard as constant, in accordance with general usage. By substitution of these letters we easily obtain

${\frac {k}{\text{V}}}=n,$⁠${\frac {k}{\text{U}}}={\frac {d(n\lambda ^{-1})}{d(\lambda ^{-1})}}\cdot$

The data for the calculation of these quantities for carbon disulphide are given by Verdet (Annales de Chimie et de Physique, (3), vol. lxix, p. 470). They give

${\text{for the line D, }}k/{\text{V}}=1.624,\,k/{\text{U}}=1.722,$ ${\text{for the line E, }}k/{\text{V}}=1.637,\,k/{\text{U}}=1.767.$

The quotient of the velocity in vacuo divided by the velocity in carbon disulphide, according to Professor Michelson's experiments with the light of an arc lamp, is 1.76 ± .02, which agrees very well with $k/{\text{U}}.$ Another theory, which would make the velocity observed in such experiments ${\text{V}}^{2}/{\text{U}}$ (Nature, vol. xxv, p. 52), receives no countenance from these experiments. The value of $k{\text{U}}/{\text{V}}^{2}$ would be about 1.53. Some may think that the experiments on water point in a different direction. Taking our data from Beer's Einleitung in die höhere Optik, 1853, p. 411, we get

${\text{for D}},\,k/{\text{V}}=1.334,\,k/{\text{U}}=1.352,\,k{\text{U}}/{\text{V}}^{2}=1.316,$ ${\text{for E}},\,k/{\text{V}}=1.336,\,k/{\text{U}}=1.359,\,k{\text{U}}/{\text{V}}^{2}=1.313.$

The number obtained by experiment was 1.330, which agrees better with $k/{\text{V}},$ or even with $k{\text{U}}/{\text{V}}^{2},$ than with $k/{\text{U}},$ but the differences are here too small to have much significance.

Theoretische Optik, gegründet auf das Bessel-Sellmeier'sche Princip, zugleich mit den experimentellen Belegen.

Von Dr. E. Ketteler, Professor an der Universität in Bonn. Viewig und Sohn. Braunschweig, 1885.

The principle of Sellmeier, here referred to, relates to vibrations of ponderable particles excited by the etherial vibrations of light, and to the reaction of the former upon the latter. The name of Bessel is added on account of his previous solution of a somewhat analogous problem relating to the pendulum. The object of this work is "to treat theoretical optics in a complete and uniform manner on the new foundation of the simultaneous vibration of etherial and ponderable particles, and to substitute a consistent and systematic new structure for the present conglomerate of more or less disconnected principles." Such a work demands a critical examination, which should not be