366 BINARY SYSTEMS. SECT. XXXVII. 



since their first discovery, already accomplished nearly 

 a whole revolution ; and one, rj Coronae, is actually con- 

 siderably advanced in its second period. These inte- 

 resting systems thus present a species of sidereal chro- 

 nometer, by which the chronology of the heavens will 

 be marked out to future ages by epochs of their own, 

 liable to no fluctuations from such planetary disturbances 

 as take place in our system. 



In observing the relative position of the stars of a bi- 

 nary 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 recede 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 corre- 

 sponding 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 observa- 

 tions, and eliminating error by mutual comparison. The 

 distances between the stars are so minute that they can- 

 not be measured with the same accuracy as the angles 

 of position ; therefore, 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 sub- 

 ject 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 fo- 

 cus. A curve is thus constructed graphically by means 

 of the angles of position and the corresponding times of 

 observation. The angular velocities of the tars are 

 obtained by drawing tangents to this curve at stated in- 

 tervals, whence the apparent distances, or radii vectores, 

 of the revolving star become known for each angle of 

 position ; because, by the laws of elliptical motion, they 



