SECT. XXXVI. BINARY SYSTEMS. 397 



perfectly accurate, four values of the angle of position, and of 

 the corresponding distances at given epochs, would be sufficient 

 to assign the form and position of the curve described by the 

 revolving star ; this, however, scarcely ever happens. The accu- 

 racy of each result depends upon taking the mean of a great 

 number of the best observations, and eliminating error by mutual 

 comparison. The distances between the stars are so minute that 

 they cannot be measured with the same accuracy as the angles 

 of position ; therefore, in order to determine the orbit of a star 

 independently of the distance, it is necessary to assume, as the 

 most probable hypothesis, that the stars are subject to the law of 

 gravitation, and consequently that one of the two stars revolves 

 in an ellipse about the other, supposed to be at rest, though not 

 necessarily in the focus. A curve is thus constructed graphically 

 by means of the angles of position and the corresponding times of 

 observation. The angular velocities of the stars are obtained by 

 drawing tangents to this curve at stated intervals, whence the 

 apparent distances, or radii vectores of the revolving star, become 

 known for each angle of position, because, by the laws of ellipti- 

 cal motion, they are equal to the square roots of the apparent an- 

 gular velocities. Now that the angles of position estimated from 

 a given line, and the corresponding distances of the two stars, are 

 known, another curve may be drawn, which will represent on 

 paper the actual orbit of the star projected on the visible surface 

 of the heavens ; so that the elliptical elements of the true orbit, 

 and its position in space, may be determined by a combined 

 system of measurements and computation. But, as this orbit has 

 been obtained on the hypothesis that gravitation prevails in these 

 distant regions, which could not be known a priori, it must be 

 compared with as many observations as can be obtained, to ascer- 

 tain how far the computed ellipse agrees with the curve actually 

 described by the star. 



y Virginis consists of two stars of nearly the same magnitude ; 

 they were so far apart in the beginning and middle of last century, 

 that they were mentioned by Bradley, and marked in Mayer's 

 catalogue, as two distinct stars. Since that time they have been 

 continually approaching each other, till in January, 1836, one 

 star was seen to eclipse the other, by Admiral Smyth at his Ob- 

 servatory at Bedford, and by Sir John Herschel at the Cape of 

 Good Hope. A series of observations since the beginning of the 



