showing displacement, apparently due to the motions of the bright components of a close binary. These displacements were explained in 1891 by Pickering as the result of the revolution of the unlike components of a binary system, having a relative velocity of 300 miles per second, and a radius of 50,000,000 miles. Belopolsky has also investigated this object, obtaining results which differ somewhat from those given above. Professor G. W. Myers has made a mathematical discussion of the problem, reaching the conclusion that the phenomena can be explained on the theory of a binary system, composed of two gaseous, scarcely separated, components of different masses, mutually eclipsing each other during their revolutions. Indeed the two components may not have separated, but exist still as a single body of unusual form, such as Poincaré's, or Darwin's figures of equilibrium. The problem is extremely complicated, and well illustrates the almost infinite diversity which is met with in the various problems about variable stars. The binary character of this type of variables seems sure in many cases, while in others even three bodies appear to be present; but the details involved are still in doubt.
The variable stars found in clusters have periods ranging for the most part from ten to fourteen hours. The elements of about 300 of them have been determined by the writer. The uniformity of the periods found in the same cluster is remarkable, pointing unmistakably to a common cause. What that cause is has not yet been found. The form of light-curve is shown in Figs. 3 and 4. Owing to the faintness of these stars, which generally vary between the twelfth and fifteenth magnitudes, it has not yet been possible to determine either the nature of the spectrum or the radial motion. The light-curve shows no indication of eclipsing phenomena. The uniformity in the period, traced in many cases through more than 5,000 returns of maximum, points to axial rotation or orbital revolution. Variability might result, undoubtedly, from the rotation of an elliptical, or unevenly luminous body; but the light-curves of cluster variables are difficult of explanation on this theory. They may be binaries with small, elliptical orbits, but even this is hardly consistent with the form of light-curve. The rejection of these hypotheses, nevertheless, seems to leave the phenomena without plausible explanation. A few cluster variables have been found where the maxima succeed each other at intervals of about six hours, one half the usual period. This indicates pretty clearly a double variable with alternating maxima, both components having the same period. These apparently accidental cases of duplicity may throw some light on the physical condition of all these stars.
V. Of the Algol variables Algol itself is a good example. Its light usually remains at a uniform brightness of the second magnitude, but once in a little less than three days it falls to the third magnitude, where it remains for some twenty minutes before beginning to regain
