THE VARIABLE VELOCITIES OF B CAPRICORNI AND v SAGITTARII IN THE LINE OF SIGHT. W. W. Campbell SUGGESTIONS FOR THE DETERMINATION OF STELLAR PARALLAX BY MEANS OF PHOTOGRAPHY. Frank Schlesinger THE PERIODS OF THE VARIABLE STARS IN THE CLUSTER Messier NOTE ON THE RELATION BETWEEN THE VISUAL AND PHOTO- GRAPHIC LIGHT CURVES OF VARIABLE STARS OF SHORT THE ANNULAR NEBULA H IV. 13 IN CYGNUS. James E. Keeler - ON THE EFFECT OF PRESSURE UPON THE WAVE-LENGTHS OF THE LINES OF THE HYDROGEN SPECTRUM. J. Wilsing ON THE PRESENCE OF OXYGEN IN THE ATMOSPHERES OF CER- MINOR CONTRIBUTIONS AND NOTES: Corrections to Determinations of Absolute Wave-length, Edwin B. Frost, 283; Position of Nova Sagittarii, Edward C. Pickering, 285; The Yerkes Observatory of the University of Chicago, Bulletin No. 12, George E. Hale, 287; Results of an Examination of Spectro- grams of a Orionis Obtained during the Recent Irregular Mini- THE ARC-SPECTRUM OF VANADIUM. B. Hasselberg REVIEWS: Untersuchungen über die Spectra von 528 Sternen, H. C. Vogel und J. Wilsing (E. B. F.), 362; Comparative Photo- graphic Spectra of Stars to the 31⁄2 magnitude, Frank McClean; Spectra of Southern Stars, Frank McClean (E. B. F.), 367; Annales de l'Observatoire d'Astronomie Physique de THE following formulae and tables are intended to facilitate the elimination of the Earth's orbital velocity from observations for motion in the line of sight. Let A, B, be the mean longitude and latitude of the observed star. T, the Sun's longitude at perigee (281° 20′). a, the semi-axis major of the Earth's orbit (149,480,000 kilometers). e, the eccentricity of the Earth's orbit (0.0167). 90°-i, the angle between the Earth's direction of motion and the radius vector of the orbit. T, the Earth's sidereal period (31,558,000 mean solar seconds). v, the mean velocity of the Earth in its orbit, defined more precisely below. ,, the Earth's velocity at the moment of observation. x, the desired correction to the observed velocity of a star, or the projection of v, upon the line of sight. From the theory of elliptical motion1 we have Eliminating i and simplifying we obtain x = v cos ẞ sin (。 − λ) + ve cos ß sin (Ã — λ). Or, if we put we have finally The quantities b and c do not involve the longitude of the Sun and are, therefore, practically constant for any particular star. Neglecting proper motion, ẞ cannot change more than 49" in a century while T-λ is increased about 20' in the same period. The maximum value of b is about 30 kilometers per second, and c never exceeds 0.50 kilometers per second. It follows that if we tabulate the values of b and c for the present epoch they will hold during the coming century without ever introducing so large an error in x as 0.01 kilometers per second. It is interesting to note that the first term in the above expression for x is what would have resulted from the assumption of a circular orbit for the Earth. That is, although the Earth's velocity varies in both amount and direction from that of a circular orbit, yet the combined effect is constant for any particular star. The analogue to this proposition is found in the theory of aberration." In the accompanying table the constants log b and c have been computed for all the brighter stars visible from northern observatories. Some variables and a few stars with large proper motions are also given. The unit of velocity is the kilometer per second, and the tables and formulae conform to the usual convention of denoting approach by the negative, and recession by the positive sign. The stars are arranged in the order of increasing right ascensions. To enable a star to be readily BESSEL, Tabulae Regiomontanae, XIX. found the approximate right ascension is given at frequent intervals. The longitude for 1900 and the latitude have also been tabulated, though only the former is needed in the reductions. The longitude must be brought up to the year of observation, 1900 + t, by adding to the tabular longitude, dλ= 0.838' Xt. A short table giving the values of dλ for every year up to 1930 will be found at the end of the paper. For a few stars with very large proper motions, such as 1830 Groombridge, 61 Cygni, o Eridani, μ Cassiopeiae, etc., the above expression for dλ will not suffice when t becomes large. The value adopted for a, the semi-axis major of the Earth's orbit, is based upon 8.80" as the solar parallax; an error of 0.01" in this constant corresponds to a maximum error of 0.034 kilometers per second in the correction to an observed velocity. Had a different parallax been employed the only effect upon these tables would have been the addition of a constant to each log b. For F, the Sun's longitude at perigee, the round value 281° 20′ has been employed; this is about its value for 1950, referred however to the equinox of 1900. Much assistance in checking the computations was obtained. from a table of the longitudes and latitudes of six hundred stars, published by C. Chabrol in the Connaissance des Temps for the year XII (1804), and referred to the equinox of 1800. This table contains nearly all the stars in the present paper, and very little labor was required to bring the data up to 1900 with sufficient accuracy. However, these results were used merely as a check, all the computations being based directly upon the right ascensions and declinations of the stars referred to the equinox and epoch of 1900. The following formulae were employed : For a graphical check was constructed, with log b and λ as the arguments. |