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As an example, let us suppose the star to be fixed and the earth to be moving directly away from the star with the velocity due to its motion round the sun. The coefficient of aberration indicates that the velocity of light is about 10,000 times that of the earth
in its orbit, and it appears from the observations of Angstrom and Ditscheiner that the wave-length of the less refrangible of the lines forming D exceeds that of the other by about one-thousandth part of itself. Hence, if the lines corresponding to D in the light of the star are due to sodium in the star, these lines in the starlight will be less refrangible than the corresponding lines in a terrestrial sodium-flame by about a tenth part of the difference between D, and D2.
When the earth is moving towards the star, the lines will be more refrangible than the corresponding terrestrial lines by about the same quantity.
The effect of the proper motion of stars would of course have to be compounded with the effect of the earth’s own motion, in order to determine the velocity of approach or separation.
To observe these differences of the light from stars, a spectroscope is necessary, that is, an instrument for separating the rays of different periods; and it is immaterial in what direction the refraction of the light through the prisms takes place, because the period of the light is the thing to be observed by comparison with that of a terrestrial flame.
If, instead of a spectroscope, an achromatic prism were used, which produces an equal deviation on rays of different periods, no difference between the light of different stars could be detected, as the only difference which could exist is that of their period.
If the motion of a luminiferous medium in the place where the experiment is made is different from that of the earth, a difference in the deviation might be expected according to the direction of the ray within the prisms, and this difference would be nearly the same whatever the source of the light.
There are therefore two different and independent subjects of experiment. The one is the alteration in the period of vibration of light due to the relative motion of the stars and the earth. The fact of such an alteration is independent of the form under which we accept the theory of undulations, and the possibility of establishing its existence depends on the discovery of lines in the stellar spectra, indicating by their arrangement that their origin is due to the existence of substances in the star having the same properties as substances found on the earth. Any method of observing small differences in the period of vibration of rays, if sufficiently exact, will enable us to verify the theory, and to determine the actual rate of approach or separation between the earth and any star.
The other subject of experiment is the relation between the index of refraction of a ray and the direction in which it traverses the prism. The essentials of this experiment are entirely terrestrial, and independent of the source of light, and depend only on the relative motion of the prism and the luminiferous medium, and on the direction in which the ray passes through the prism.
The theory of this experiment, however, depends on the form in which we accept the theory of undulations. In every form of the theory, the index of refraction depends on
the retardation which a ray experiences on account of having to traverse a dense medium instead of a vacuum. Let us calculate this retardation.
Let there be a transparent medium whose thickness is a, and let it be supposed fixed. Let the luminiferous ether be supposed to move with velocity v in air, and with velocity v' within the medium. Let light be propagated through the ether with velocity Y in air and with velocity V' within the medium. Then the absolute velocity of the light will be v-f-V in air and t/+V' within the medium, and the retardation, or difference of time in traversing a thickness a of the medium, and an equal thickness of air, will be
and the retardation in distance reckoned as at the velocity, V will be JV v\ «ra/V3 v2\ ]
VIJ "t"V2\\ls t>,2y j’
Now, according to every form of the theory, y,=/a, the index of refraction, and according to Fresnel’s form of the theory, in which the density of the medium varies
as /K/2, the equation of continuity requires that In this case the second term dis-
appears and the retardation is a((t—1)+terms in which may be neglected, as Y is
more than 10000 times v.
Hence, on Fresnel’s theory, the retardation due to the prism is not sensibly affected by the motion of the earth. The same would be true on the hypothesis that the luminiferous ether near the earth’s surface moves along with the earth, whatever the form of the theory of the medium.
Since the deviation of light by the prism depends entirely on the retardation of the rays within the glass, no effect of the earth’s motion on the refrangibility of light is to be expected. Professor Stokes (Phil. Mag. 1846, p. 63) has also given a direct proof of this statement, and the experiment of Arago confirms it to a certain degree of exactness.
In order to test the equality of the index of refraction for light moving in opposite directions through a prism, I employed in 1864 the following arrangement.
I made use of a spectroscope constructed by Mr. Becker, and provided with a tube at right angles to the axis of the observing-telescope, carrying a transparent plate of parallel glass placed between the object-glass and its focus, so as to reflect the light which enters the tube along the axis of the telescope towards the object-glass. In this tube is placed a screen with a vertical slit, in the middle of which is a vertical spider-line so arranged that its virtual image formed by the first surface of the glass plate coincides with the crossing of the spider-lines of the telescope at the principal focus of the object-glass. This coincidence is tested by observing the cross lines through the other telescope, with the two telescopes facing each other. The eyepiece of the second telescope is then removed, and a plane mirror is placed at the focus of the object-glass, perpendicular to the axis, and the telescopes are so adjusted that light entering by the side tube is