class which are near together must be very few in number; indeed, there are probably none among the close double stars whose brightest component can be seen by the naked eye.
The time of revolution of the binary systems is so long that there are only about fifty cases in which it has yet been determined with any certainty. Leaving out the 'spectroscopic binaries,' to be hereafter described, the shortest period yet found is eleven years. In only a small minority of cases is the period less than a century. In the large majority either no motion at all has yet been detected, or it is so slow as to indicate that the period must be several centuries, perhaps several thousand years.
There is a great difficulty in determining the period with precision until the stars have been observed through nearly a revolution, owing to the number of elements, seven in all, that fix the orbit, and the difficulty of making the measures of position angle and distance with precision. It thus happens that many of the orbits of binary systems which have been computed and published have no sound basis. Two cases in point may be mentioned.
The first magnitude star Castor, or α Geminorum, can be seen to be double with quite a small telescope. The components are in relative motion. Owing to the interesting character of the pair it has been well observed, and a number of orbits have been computed. The periodic times found by the components have a wide range. The fact is, nothing is known of the period except that it is to be measured by centuries, perhaps by thousands of years.
The history of 61 Cygni, a star ever memorable from being the first of which the parallax was determined, is quite similar. Although, since accurate observations have been made on it the components have moved through an apparent angle of 30°, the observations barely suffice to show a very slight curvature in the path which the two bodies are describing round each other. Whether the period is to be measured by centuries or by thousands of years cannot be determined for many years to come.
In his work on the 'Evolution of the Stellar Systems,' Prof. T. J. J. See has investigated the orbits of forty double stars having the shortest periods. There are twenty-eight periods of less than one hundred years
In considering the orbits of binary systems we must distinguish between the actual and the apparent orbit. The former is the orbit as it would appear to an observer looking at it from a direction perpendicular to its plane. This orbit, like that of a planet or comet moving round the sun, is an ellipse, having the principal star in its focus. The point nearest the latter is called the periastron, or pericenter, and corresponds to the perihelion of a planetary orbit. The point most distant from the principal star is the apocenter. It is opposite the
