The estimated uncertainty was only 0·02, or 1⁄6 of the difference between observation and theory.
The comparison of red and blue light was made differentially. The colours selected were of wave-length about 0.62 for red and 0.49 for blue. Putting Vr and Vb for the speeds of red and blue light respectively in bisulphide of carbon, the mean result compares with theory as follows:—
| Observed value of the ratio Vr, Vb | 1.0245 |
| Theoretical value (Verdet) | 1.025 |
This agreement may be regarded as perfect. It shows that the divergence of the speed of yellow light in the medium from theory, as found above, holds through the entire spectrum.
The excess of the retardation above that resulting from theory is probably due to a difference between “wave-speed” and “group-speed” pointed out by Rayleigh. Let fig. 5 represent a short series of progressive undulations of constant period and wave-length. The wave-speed is that required to carry a wave crest A to the position of the crest B in the wave time. But when a flash of light like that measured passes through a refracting medium, the front waves of the flash are continually dying away, as shown at the end of the figure, and the place of each is taken by the wave following. A familiar case of this sort is seen when a stone is thrown into a pond. The front waves die out one at a time, to be followed by others, each of which goes further than its predecessor, while new waves are formed in the rear. Hence the group, as represented in the figure by the larger waves in the middle, moves as a whole more slowly than do the individual waves. When the speed of light is measured the result is not the wave-speed as above defined, but something less, because the result depends on the time of the group passing through the medium. This lower speed is called the group-velocity of light. In a vacuum there is no dying out of the waves, so that the group-speed and the wave-speed are identical. From Michelson’s experiments it would follow that the retardation was about 1⁄14 of the whole speed. This would indicate that in carbon bisulphide each individual light wave forming the front of a moving ray dies out in a space of about 15 wave-lengths.
| Fig. 5. |
Authorities.—For Foucault’s descriptions of his experiments see Comptes Rendus (September 22 and November 24, 1862), and Recueil de Travaux Scientifiques de Léon Foucault (2 vols., 4to, Paris, 1878). Cornu’s determination is found in Annales de l’Observatoire de Paris, Mémoires, vol. xiii. The works of Michelson and Newcomb are published in extenso in the Astronomical Papers of the American Ephemeris, vols. i. and ii.
(S. N.)
[1] The invention of “aethers” is to be carried back, at least, to the Greek philosophers, and with the growth of knowledge they were empirically postulated to explain many diverse phenomena. Only one “aether” has survived in modern science—that associated with light and electricity, and of which Lord Salisbury, in his presidential address to the British Association in 1894, said, “For more than two generations the main, if not the only, function of the word ‘aether’ has been to furnish a nominative case to the verb ‘to undulate.’” (See [Aether].)