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a velocity sufficient to alter its colour sensibly to the eye, still no change of colour would be perceived, for the reason that beyond the visible spectrum, at both extremities, there exists a store of invisible waves which would be at the same time exalted or degraded into visibility, to take the place of the waves which had been raised or lowered in refrangibility by the star’s motion. No change of colour, therefore, could take place until the whole of those invisible waves of force had been expended, which would only be the case when the relative motion of the source of light and the observer was several times greater than that of light.
In 1845, Ballot published a series of acoustic experiments which support Doppler’s theory in the case of sound. In the same paper Ballot advances several objections to Doppler’s application of his theory to the colours of the stars*.
This paper was followed by several papers by Doppler in reply to the objections which were brought against his conclusions f.
In 1847 two memoirs were published by Sestinj on the colours of the stars in connexion with Doppler’s theory J.
More recently, in 1866, Klinkerfues § published a memoir on the influence of the motion of a source of light upon the refrangibility of its rays, and described therein a series of observations from which he deduces certain amounts of motion, in the case of some of the objects observed by him.
The method employed by Klinkerfues has been critically discussed by Dr. Sohncke ||.
It may be sufficient to state that as Klinkerfues employs an achromatic prism, it does not seem possible, by his method of observing, to obtain any information of the motion of the stars; for in such a prism the difference of period of the luminous waves would be as far as possible, annulled. It is, however, conceivable that his observations of the light when travelling from E. to W., and from W. to E., might show a difference in the two cases, arising from the earth’s motion through the ether.
Father Secchi has quite recently called attention to this subject^]". In his paper he states that he has not been able to detect any change of refrangibility in the case of certain stars, of an amount equal to the difference between the components of the double line D. These results are in accordance with those obtained by myself and Dr. Miller in 1863, so far as they refer to the stars which had been examined by us.
Father Secchi’s method of using an unrefracted image as a fiducial mark with diverging rays passing through the prisms might, it is conceivable, be open to objection.
* “ Akustische Yersuche auf der Niederlandischen Eisenbahn nebst gelegentlichen Bemerkungen zur Theorie des Hrn. Prof. Doppler,” Pogg. Ann. B. lxvi, s. 321.
f See Pogg. Ann. B. lxxxi. s. 270, and Pogg. Ann. B. lxxxvi. s. 371.
X Memoria sopra i colori delle stelle del catalogo de Baily osservati dal P. Band Sestini. Boma, 1847.
§ “ Fernere Mittheilungen liber den Einfluss der Bewegung der Lichtquelle auf die Brechbarkeit eines Strahls, von W. KLnrcERFTTES,” Nachr. K. G. der W. zu Gottingen, No. 4, s. 33.
|| “ Ueber den Einfluss der Bewegung der Lichtquelle auf die Brechung, kritische Bemerkungen zu der Ent-deckung des Hrn. Prof. Klustzerfues. Yon Hrn. Dr. Sohjstcke, Astron.” Nadir. No. 1646.
IT Comptes Bendus, 2 Mars 1868, p. 398.
He appears to consider that, to produce a certain alteration of refrangibility, half the velocity would be required in the case of the approach of a star to that which would be necessary if the star were receding. This is not the case, for equal velocities of separation or approach give equal changes of wave-length. It is true that a difference of an octave is produced by a relative velocity of separation equal to that of light, and by a velocity of approach equal to half that of light; but the difference in length of a wave and its octave below (which is twice as long) is in the same proportion greater than the difference between it and the octave above (which is half as long).
The experiments of M. Fizeau in connexion with this subject are referred to by Mr. Maxwell in the following statement of his views and experiments, which was received by me on June 12, 1867.
On the Influence of the Motions of the Heavenly Bodies on the Index of Refraction of
Let a source of light be such that it produces n disturbances or vibrations per second, and let it be at such a distance from the earth that the light requires a time T to reach the earth. Let the distance of the source of light from the earth be altered, either by the motion of the source of light, or by that of the earth, so that the light which emanates from the source t seconds afterwards reaches the earth in a time T'.
During the t seconds nt vibrations of the source of light took place, and these reached the earth between the time T and the time tf+T', that is, during tf+T'—T seconds. The number of vibrations which reached the earth per second was therefore no longer n,
but n ; + T*,_T-
If v is the velocity of separation of the source of light from the earth, and V the velocity of light between the bodies relative to the earth, then ^=Y(T'—T), and the
number of vibrations per second at the earth will be n ^r— ■
X V + w
If Y0 is the velocity of propagation of light in the .luminiferous medium, and if v0 is
the velocity of the earth, V—v
V - V0 W0,
and the wave-length will be increased by a fraction of itself equal to
Since v„ only introduces a correction which is small compared even with the alteration of wave-length, it cannot be determined by spectroscopic observations with our present instruments, and it need not be considered in the discussion of our observations.
If, therefore, the light of the star is due to the combustion of sodium, or any other element which gives rise to vibrations of definite period, or if the light of the star is absorbed by sodium vapour, so as to be deficient in vibrations of a definite period, then the light, when it reaches the earth, will have an excess or defect of rays whose period of vibration is to that of the sodium period as V -\-v is to V.