PARALLAX of the Fixed Stars

PARALLAX of the Fixed Stars, see ASTRONOMY, art. 268. which contains an account of the method used by Dr Herschel, to ascertain the parallax of a star which appears to be double, from observations made at opposite points of the orbit of the earth. M. Piazzi, the discoverer of the planet Ceres, has made many observations of the zenith distances of $\backslash alpha$ Lyrae, Arcturus, Procyon, and Aquile, &c. at those times when the effects of parallax ought to be the greatest. His observations are published in the 10th volume of the Italian Society. Let $p$ be the absolute parallax, consequently, fine $p\; =\; \backslash frac\{1\}\{\backslash text\{distance\; of\; the\; star\; from\; the\; earth\}\}$; then the parallax of Arcturus in declination will be $0.395\; p$, and that in right ascension, $1.025\; p$; hence, he observes, that observations of the right ascension of this star are preferable to those of the declination, for determining the parallax of this star.

M. Calendrelli, in a work printed at Rome in 1806, has given the result of his observations of the zenith distances of $\backslash alpha$ Lyrae, made with the sector of Mess. Maire and Boscovich. By comparing five observations in June, with four in December 1805, and five in March with the same number in June, he deduced the parallax of $\backslash alpha$ Lyrae in declination to be $4\text{'}\text{'}.7$, and that in right ascension $6\text{'}\text{'}.85$.—According to M. Piazzi, the parallax is less than half of these quantities; and, hence, the required quantity not exceeding the unavoidable differences attending observations, it appears difficult to determine it, so as to be free from doubt.

Mess. Delambre and Mechain have made many observations of the pole star, and $\backslash beta$ Ursae minoris, being those stars which ought to have the greatest parallax in declination, at the times most proper to discover their parallax; but from the comparison, which M. Delambre made, of the zenith distances of these stars, he discovered nothing that could give the least suspicion of a parallax; and the small anomalies which he observed are often in a contrary direction. M. Delambre adds,

that these stars being of the second magnitude, may be too far distant from us to have a parallax; however, although this may be the case, yet it appears to him that the fixed stars have no parallax.

The parallax of Venus affords the most correct method, hitherto proposed, of finding the distance of the earth from the sun; and, hence the distances of the other planets, and also their magnitudes. For this discovery we are indebted to the celebrated Dr Halley. From observations of the transits of this planet, in 1761 and 1769, the parallax of the sun has been more accurately determined than previous thereto. The parallax of Mars has also been employed for the same purpose.