SBCT. xxxvn.] ORBITS AND PERIODIC TIMES. 417 



of these stellar systems have been determined by various 

 astronomers, together with the elliptical elements of .their 

 orbits, and the periods of their revolutions. M. Savary has 

 the merit of having first determined the elements of the 

 orbit of a double star from observation. The difficulty of 

 doing so is great, because the nearest fixed star is 200,000 

 times farther from the sun than the earth is, and the orbit 

 itself is only visilfle with the best telescopes ; consequently 

 a very small error in observation occasions an enormous 

 error in the determination of quantities at that distance. 



In observing the relative position of the stars of a binary 

 system, the distance between them, and also the angle of 

 position, that is, the angle which the meridian, or a parallel 

 to the equator, makes with the line joining the two stars, 

 are measured. The different values of the angle of position 

 show whether the revolving star moves from east to west, or 

 the contrary ; whether the motion be uniform or variable, 

 and at what points it is greatest or least. The measures of 

 the distances show whether the two stars approach or re- 

 cede from one another. From these the form and nature 

 of the orbit are determined. Were observations 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 accuracy of each result depends upon taking the mean 

 of a great number of the best observations, and eliminat- 

 ing 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 con- 

 sequently that one of the two stars revolves in an ellipse 

 about the other, supposed to be at rest, though not neces- 

 sarily in the focus. A curve is thus constructed graphi- 



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