252 P A R A L L A X near the planet) from the other satellites may likewise yield a reliable value of k. On the relations between the constant of aberration, the solar parallax, and the velocity of light, see LIGHT, vol. xiv. pp. 584, 585. The mean of the nine best modern determinations of the constant of aberration (i.e., from 1830 to 1855) gives 20" 496. 1 The most recent and valuable paper on this constant is that of Nyren (Mi m. de I Acad. de St Petersboury, 7th ser., vol. xxxi. No. 9), in which the constant is derived from independent researches extending over many years, with each of the three great fixed instruments of the Pulkowa observatory. The independent mean results are From observations with the prime vertical transit 20 490 ,, ,, vertical circle 20 495 transit instrument. . . 20 491 Mean 20"492 This result, combined with the above quoted values of the velocity of light, gives the following values of the solar parallax : Combined with Cornu s velocity . . 8778 ,, Michelson s velocity 8791 ,, Newcomb s velocity 8798 Mean 8789 There still remain some little theoretical difficulties with regard to the theory of aberration. That theory is perfectly obvious on the emission theory of light, but is priori by no means so obvious on the undulatory theory. Is it certain that the velocity of light in the celestial spaces is identical with (or bears an exactly known relation to) the velocity of light which, having travelled a certain space in air, undergoes reflexion and returns 1 This is a question for the physicist, and a question that probably demands a practical as well as a theoretical answer. 2 Also Yillarceau (Comptes Rendus, 1872, October 14) points out that in the ordinary theory of aberration no account is taken of the sun s motion of translation through space, and shows that, if the normal constant of aberration is A, the constant for any particular star is A + A x a, where a depends on the angle which the star s direction makes with the direction of the sun s translation in space. In the observations of Nyren, above referred to, there is a well-marked periodic variation in the values of the con stant of aberration derived for twenty-seven stars, which seems to be a function of the right ascension of the stars. This variation may be due to some cause (such as lateral refraction in the north-and-south direction) depending on the seasons, or it may have a real physical significance on the theory of Villarceau. If further observation (especi ally in the southern hemisphere, where the seasons are reversed) should confirm the latter hypothesis, two im portant conclusions result : (ft) We obtain some idea of the direction and amount of motion of the milky way, combined with that of the solar system in space ; and (b) We may conclude that our theory of light is correct, which supposes that a ray of light is transmitted through space with uniform velocity, independently of the velocity of the source of light, and that ether is fixed and infinite that is, nowhere limited in extent. On the other hand a negative result would go far to show that our conception of ether is not correct, at least would force us to adopt one of two conclusions, either that the milky way is stationary in space (within limits of our power of measurement), or that the ether accom- 1 See Mem. R. A. S., vol. xlvi. p. 166. 2 See also letter by Lord Hnyleigli in Nature 1881, August 25. panics the milky way and is not fixed in space and not infinite. It is, however, a priori improbable that from any of these causes the deduced value of the solar parallax will be affected by y^tr f its deduced amount. The tendency of the best modern determinations is to fix the solar parallax at 8"-78 or 8"-79, and hence the mean distance of the earth from the sun at 93 millions of miles, a result which is almost certainly exact within 200,000 miles. LUNAR PARALLAX. The constant of the lunar parallax may be determined by a method precisely similar to that followed in the meridian declination observations of Mars. Our knowledge of the parallax of the moon de pends at present entirely on such observations made nearly simultaneously at the Royal Observatories of Greenwich and the Cape of Good Hope. The resulting values of the parallax, found directly from these observations, are then multiplied by a factor which expresses the relation between the constant of the lunar parallax (ASTRONOMY, vol. ii. p. 798) to the moon s tabular parallax at the time; thus each nearly simultaneous observation at the two observatories gives an independent determination of the constant of the lunar parallax. A better method, however, will be found when the results of numerous occultations of stars have been employed to determine the constants of a new and more accurate lunar theory a work about to be undertaken by Prof. Simon Newcomb. The best determination of the constant of the lunar parallax is that of Mr Stone, viz., 3422" 71 (Mem. R.A.S., vol. xxxiv. pp. 11-16), derived from meridian observa tions at Greenwich and the Cape of Good Hope. STELLAR PARALLAX. The constant of parallax of a fixed star is the maximum angle which a line equal to the earth s mean distance from the sun would subtend if viewed at the star. The distances of the fixed stars are so remote that till very recent times their parallaxes have been found to be insensible ; that is to say, the earth s orbit viewed from the nearest fixed star presents a disk (or ellipse) too small for measurement. The limits of this article do not permit a detailed history of the early attempts of astronomers to determine the parallaxes of the fixed stars. The reader is referred on this point to Peters s Precis historique des travaux sur la parallaxe des etoiles fixes, forming the first section of his celebrated work .Recherches sur la Parallaxe des / toil es fixes (Mem. de I Acad. Imp. de St Petersbourg, sec. Math, et Physiques, vol. v.). The most notable incident in that history was the discovery of aberration by Bradley, in 1728, when engaged in an unsuccessful attempt to determine the parallax of the star y Draconis. The first determination of the parallax of a fixed star is, due to Henderson, His Majesty s astronomer at the Cape of Good Hope in 1832 and 1833. 3 It was followed by the nearly simultaneous discoveries of the parallax of 61 Cygni by Bessel 4 and that of a Lyrae by Struvc r> from observations made in the years preceding 1840. Since that time similar researches have been prosecuted with gradually increasing success. The methods of observation may be divided into two classes, the absolute and the differential. The absolute met/tod depends on observation of the zenith distance of a star about the epochs of maximum 3 Mem. R. A. .ST., vol. xii. p. 329. 4 Astron. Nachrichlen, Nos. 365, 366, and 401. 5 Astrm. Xachrichtcn, No. 396.
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