At each corner four mirrors were placed, by reflection from which the length of path traversed by the light was increased to ten times its former value. The width of the fringes of interference, which were the subject of observation, measured from forty to sixty divisions of the observing micrometer. The light came from an Argand burner sent through a lens. To prevent jars from stopping and starting, the float was kept constantly in slow circulation, revolving once in six minutes. Sixteen equidistant marks were made on the stationary frame-work within which the float moved. Observations were taken on the fringes, whenever any one of these marks came in the range of the micrometer. The observations were made near noon and at 6 p. m. The noon and evening observations were plotted on separate curves. One division of the micrometer measured one-fiftieth of a wave-length. Mr. Michelson was confident that there was no displacement of the fringes exceeding one-hundredth of a wave length. It should have been from twenty to forty times greater than this. Mr. Michelson concludes that this result is in opposition to Fresnel's theory of aberration.
As late as 1872, Le Verrier thought that a new measurement of the velocity of light by Fizeau very important in the interest of astronomy; and in 1871, Cornu wrote that the parallax of the sun, and hence the size of the earth’s orbit, were not yet known with the desirable precision. In 1875, Villarceau made a communication to the Paris Academy on the theory of aberration. He says that the parallax of the sun by astronomical measurement is 8″.86. Foucault’s velocity of light combined with Struve’s aberration makes the sun’s parallax 8″.86. Cornu’s velocity of light gives the same result only when it is combined with Bradley’s aberration, which differs from that of Struve by 0″.20. Villarcean thinks that there is an uncertainty about the value of aberration on account of the motion of the solar system. In 1883, M. O. Struve discussed seven series of observations made by his father, Nyrén, and others, with various instruments and by different methods, at the Observatory of Pulkowa. He was certain that the mean result for the value of abeiration was 20″.492, with a probable error of less than 1/100 of a second. This aberration, combined with the velocity of light as deduced from the experiments of Cornu and Michelson, made the parallax of the sun 8″.784; differing from the most exact results of the geometric method by only a few hundredths of a second. Villarceau proposed to get the solar motion by aberration; selecting two places on the earth in latitude 35° 16' north and south, and after the example of Struve, observing the zenith distances of stars near the zenith. The
tangents of these latitudes are ± 1/sqrt(2) so that they contain the best sta
tions for obtaining the constant of aberration, and the three components of the motion of translation of the solar system. In 1887, Ubaghs, a Belgian astronomer, published his results on the determination of the
direction and velocity of the movement of the solar system through space. For finding the direction he used the method of Folie. For calculating the velocity he combined the observations on three groups of stars, the brightest belonging probably to the solar nebula. The resulting velocity was only about 10,000,000 miles a year. Homann, working on the spectroscopic observations at Greenwich, had obtained a velocity of 527,000,000 of miles. As late as 1887, Fizeau studied the nature of the phenomena when light was reflected from a mirror moving with a great velocity, and inferred that aberration was the same in this case as when the light was taken directly from a star.
Glaseuapp calculated the time taken by the light in travelling the mean distance of the earth's orbit as equal to 500″.85 ± 1.02. This time combined with Michelson's velocity of light makes the solar parallax 8″.76. Struve's constant of aberration with Michelson's velocity gives a parallax of 8″.81. From Gill's mean of the nine best modern determinations of aberration (=20″.496) the parallax comes out equal to 8″.78. If we regard the solar parallax as known, the eclipses give nearly the same velocity as aberration, though the former is a group-velocity and the latter a wave velocity. Gill’s parallax from observations of Mars (8″.78) agrees with Michelson’s velocity of light and the mean constant of aberration.
In 1877–’78, Lord Rayleigh, in his profound treatise on the Theory of Sound, discussed the distinction between wave-velocity and group-velocity. In 1881, he recognized the same difference in the case of luminous waves. In the experiments of Young and Forbes, the wavevelocity might be nearly three per cent, less than the group-velocity. With toothed wheels and the revolving mirror, group-velocity was the subject of observation. Aberration gave wave-velocity; Jupiter’s satellites, group-velocity; experiment however showed but little difference. Lord Rayleigh found formulae for the relation between these two kinds of velocity, which involved the wave-length and the index of refraction, and J. Willard Gibbs has compared them, and other formulae proposed by Schuster and Gouy, with the experimental velocities of light. Michelson’s experiment on the index of refraction of carbon disulphide agrees with the assumption that he was dealing with the group-velocity.
Although there is not a complete accordance between the results of