Then, the angle N P C is called the position-angle of the pair. It is counted round the circle from 0° to 360°. The angle drawn in the figure is nearly 120°. Were the companion C in the direction S the position angle would be 180°; to the right of P it would he 270°; to the right of N it would be between 270° and 360°.
The distance is the angle P C, which is expressed in seconds of arc.
We cannot set any well-defined limits to the range of distance. The general rule is that the greater the distance beyond a few seconds the less the interest that attaches to a double star, partly because the observation of distant pairs offers no difficulty, partly because of the increasing possibility that the components have no physical connection and so form only an optically double star. With every increase of telescopic power so many closer and closer pairs are found that we cannot set any limit to the number of stars that may have companions. It is therefore to the closer pairs that the attention of astronomers is more especially directed.
The difficulty of seeing a star as double, or, in the familiar language of observers, of 'separating' the components, arises from two sources, the proximity of the companion to the principal star and the difference in magnitude between the two. It was only in rare cases that Struve could separate a pair of distance half a second. Now Burnham finds pairs whose distance is one-quarter of a second or less; possibly the limit of a tenth of a second is being approached. It goes without saying that a very minute companion to a bright star may, when the distance is small, be lost in the rays of its brighter neighbor. For all these reasons no estimate can be made of the actual number of double stars in the heavens. With every increase of telescopic power and observing skill more difficult pairs are being found without a sign of a limit.
The great interest which attaches to double stars arises from the proof which they afford that the law of gravitation extends to the stars. Struve, by comparing his own observations with each other, or with those of Herschel, found that many of the pairs which he measured were in relative motion; the position angle progressively changing from year to year, and sometimes the distance also. The lesser star was therefore revolving round the greater, or, to speak with more precision, both were revolving round their common center of gravity. To such a pair the name binary system is now applied.
There can be no reasonable doubt that the two components of all physically connected double stars revolve round each other. If they did not their mutual gravitation would bring them together and fuse them into a single mass. We are therefore justified in considering all double stars as binary systems, except those which are merely optically double. For reasons already set forth, the pairs of the latter
