In 1898 De Witt discovered the small planet Eros which at its nearest approach comes to within 15 million miles or one-sixth of the sun's distance. The opposition of 190o was extensively ob served visually and photographically at many observatories. The collection and discussion of the extensive series of observations was made by Mr. Hinks who obtained the value for the solar paral lax A still nearer approach of this planet to the earth will occur in 1931.
The velocities of stars towards or from the earth are determined from spectroscopic observations. By choosing times when the orbital motion of the earth is carrying it towards or from a star the velocity of the earth in its orbit may be obtained. In this way the solar parallax was found from observations at the Cape of Good Hope to be Gravitational Methods.—( ) In the theory of the moon there is a term of period one month known as the parallactic in equality. The coefficient of the term contains the ratio of the parallaxes of the sun and moon as a factor. The large size of this coefficient makes it of value. From the discussion of occulta tions of stars at the Cape observatory, Jones finds the value I for this term giving for the solar parallax 8".8o5 ±".004.
(2) The ratio of the mass of the earth+moon to that of the sun may be determined from the disturbing action of the earth+ moon on the elliptic motion of the planets. The ratio of the moon's mass to that of the earth is 1/81.53, and thus the ratio of the earth's mass to that of the sun is found. In a manner simi lar to that described above for the moon's parallax the solar paral lax is then derived. From an exhaustive discussion of the pertur bations of the planet Eros Noteboom has made a very accurate determination of the solar parallax as There is thus a general agreement of different methods that the solar parallax is not far from 8".8o4. This corresponds to a mean distance of the sun of 149,500,000 kilometres or 92,900,000 miles.
Stellar Parallax.—The stars are too distant for any difference of position to be perceptible from two places on the earth's sur face; but as the earth is 93 million miles from the sun, stars are seen from widely different view points in the course of the year. The effect on their positions is called annual parallax, defined as the difference in position of a star as seen from the earth and sun. Its amount and direction varies with the time of year, and its maximum is a/r where a is the radius of the earth's orbit and r the distance of the star. The quantity is very small and never reaches 1/206,265 in radian or r" in sexagesimal measure. Unsuc cessful attempts to measure the parallax of a star were made con tinuously after the acceptance of the Copernican system, including one by Bradley which led to the discovery of aberration (see ABERRATION OF LIGHT) and by Herschel which led to the dis covery of binary stars. The first successful results were obtained
in 1838 when the parallax of a Centauri was announced by Hen derson, a Lyrae by Struve and 61 Cygni by Bessel. For his ob servations Bessel used the heliometer, an instrument constructed by Fraunhofer, in which the object glass is cut in two, and so mounted that the whole can be rotated, and the separate halves made to slide relatively to one another and their movement meas ured with great precision. In this way the distance between two stars is measured by the separation of the two halves required to make the images of the two stars coincident. Bessel found small movements of 61 Cygni relative to two neighbouring stars which from their magnitude and want of proper motion were judged to be so distant that no parallactic effect could be perceived. With instruments of this kind having small object glasses of not more than 4 or 6in. and focal lengths of a few feet, research on stellar parallax was carried on to the end of the 19th century and the parallaxes determined of approximately 100 of the brightest stars and those showing the largest proper motion. The intro duction of photography simplified the problem, and after the re searches of Hinks and Russell at Cambridge, and still more of Schlesinger at Yerkes, a number of observatories have engaged in the work and have determined the parallaxes of many stars with great accuracy. Two observational conditions have to be fulfilled (1) The telescope must be in the same position for observations at different times of the year. (2) By some means, e.g., a rotating shutter with a suitable slit—the photographic image of the star observed must be made equal to that of the stars with whose posi tion it is compared. In practice, a few photographs are taken when the star is on the meridian shortly after sunset at one period of the year and shortly before sunrise at another period. As the stars' positions change owing to their proper motion, a minimum of three epochs is required but the possibility of systematic errors make it desirable to extend the observations over a larger number of epochs. With 25 photographs spread over five epochs, the parallax of a star is obtained with a probable error of less than although the diameter of the photographic disk of the star is seldom less than 2".0. The concerted action of the observa tories of Allegheny, McCormick, Swarthmore, Dearborn, Yerkes, Mount Wilson and Greenwich has resulted in the determination of the parallaxes of 1,800 stars, 1,600 north and 200 south of the Equator. The determination of parallaxes of stars in the Southern hemisphere has been commenced at the Yale Observatory at Johannesburg and the Royal Observatory at the Cape, and will in a few years correct this large disparity. In the Northern hemi sphere the parallaxes have been measured of 191 of the 207 stars brighter than 47'0,381 of 1,041 stars between 4`70 and 57'5 and of many stars whose comparative nearness is suggested by their large proper motions. Rather more than one half of the stars have parallaxes greater than 0".02 or are within 5o parsecs of us, a parsec being defined as the distance of a star whose parallax is I" and equal to 206,265 times the earth's distance from the sun or approximately 19 million million miles.