pericenter and corresponds to the aphelion of a planetary orhit. The law of motion is here the same as in the case of a body of the solar system; the radius vector, joining the two bodies, sweeps over equal areas in equal times. The apparent orbit is the orbit as it appears to us. It differs from the actual orbit because we see it from a more or less oblique direction. In some cases the plane of the orbit passes near our system. Then to us the orbit will appear as a straight line and the small star will seem to swing from one side of the large one to the other like a pendulum, though the actual orbit may differ little from a circle. In some cases there may be two pericenters and two apocenters to the apparent orbit. This will be the case when a nearly circular orbit is seen at a considerable obliquity.
It is a remarkable and interesting fact that the law of areas holds good in the apparent as in the actual orbit. This is because all parts of the plane of the orbit are seen at the same angle, so that the obliquity of vision diminishes all the equal areas in the same proportion and thus leaves them equal.
The two most interesting binary systems are those of Sirius and Procyon. In the case of each the existence and orbit of the companion were inferred from the motions of the principal star before the companion had been seen. Before the middle of the century it was found that Sirius did not move with the uniform proper motion which characterizes the stars in general; and the inequality of its motion was attributed to the attraction of an unseen satellite. Later Auwers, from an exhaustive investigation of all the observations of the star, placed the inequality beyond doubt and determined the elements of the orbit of the otherwise unknown satellite. Before his final work was published the satellite was discovered by Alvan G. Clark, of Cambridgeport, Mass., son and successor of the first and greatest American maker of telescopes. Additional interest was imparted to the discovery by the fact that it was made in testing a newly constructed telescope, the largest refractor that had been made up to that time. The discoverer was, at the time, unaware of the work of Peters and Auwers demonstrating the existence of the satellite. The latter was, however, in the direction predicted by Auwers, and a few years of observation showed that it was moving in fairly close accordance with the prediction.
The orbit as seen from the earth is very eccentric, the greatest distance of the satellite from the star being about ten seconds, the least less than three seconds. Owing to the brilliant light of Sirius the satellite is quite invisible, even in the most powerful telescopes, when nearest its primary. This was the case in the years 1890-92 and will again be the case about 1940, when another revolution will be completed.
The history of Procyon is remarkably similar. An inequality of its motion was suspected, but not proved, by Peters. Auwers showed from
