It has been stated that the observed light curves are satisfied better by the unequal-albedo explanation, but the observations are so delicate that this can scarcely be considered decisive. On the albedo hypothesis the variation of light would have the same period as the rotation, on the other hypothesis half the period. The periods of light-change are a few hours—three hours for Eunomia, five and a quarter for Eros, eight and three-quarters for Tercidina. It may be possible to examine the shape of Eros at the near approach, in Jan. 1931, as it should show a disc with large instruments.
The explosion hypothesis, after having been generally aban doned, has been revived in recent years by some astronomers. Dr.
H. J. Jeffreys ("The Earth," p. 6o) suggests that a primitive satellite of Jupiter may have escaped from the control of that planet and subsequently exploded, possibly through the raising of its internal temperature by radioactive matter; some of the fragments might again explode, which would explain the wide distribution of the orbits. Again Prof. K. Hirayama, after an exhaustive study of the orbits, and an attempt to find their primitive or undisturbed forms, found five families of planets, each family having orbits so closely related as to suggest a com mon origin. The families are named from their brightest member ; the Flora family, distance 2.2, has 57 members ; the Maria family, distance 2.5, 13 members; the Coronis family, distance 2.9, 15 members ; the Eos family, distance 3.o, 23 members ; the Themis family, distance 3.1, 25 members. Prof. Hirayama conjectured that each family was produced by the explosion of a single planet, but it appears that the facts might also be explained on the "planetesimal" hypothesis, by postulating that several knots or condensations were present in the streams of particles, each knot subdividing before final concentration so as to form a group of tiny planets instead of a single larger one. The well-defined "Hilda" group may perhaps be added to the five families. Another interesting group is named after "Albert," the first member to be discovered; it has two other members, Alinda and Ganymede (not to be confused with Jupiter's third satellite). These are extremely small bodies (the first two are about three miles in diameter, the third about 2o). They have periods of about four years ; and they approach at perihelion within some twenty million miles of the earth's orbit, but recede at aphelion to within a unit of Jupiter's orbit. When in opposition at perihelion they have direct
motion in longitude, whereas retrograde motion is the usual rule in that position ; the reason is that their linear velocity then exceeds that of the earth. Owing to their small size they cannot be observed at all except when fairly near perihelion. Albert was unfortunately insufficiently observed at its first apparition, and is now lost ; but the other two have been very well observed. A still more remarkable asteroid is No. 944 Hidalgo, discovered by Dr. Baade at Bergedorf observatory in 1920. Its perihelion dis tance is two units from the sun, its aphelion distance nine and a half units (near the orbit of Saturn), its period 13.84 years, and the inclination of its orbit to the ecliptic 431 degrees. The orbit is distinctly of a cometary character, but the object was care fully examined, and failed to show the faintest sign of nebulosity, so it is difficult to classify it as a comet. It approaches Jupiter's orbit closely one and three-quarter years after perihelion, so its present orbit may be due to perturbations by that planet. A similar but still more remarkable asteroid, discovered at Tokyo in January 1927, and temporarily designated Tokyo 1, has peri helion distance one and a quarter units, but aphelion near the orbit of Uranus, its period being 34.8 years. Its inclination is only six degrees, so it passes near Jupiter's orbit. It seems possible that both this object and Hidalgo are the remains of comets which have lost their supply of gas, and whose nuclei resemble asteroids in appearance.
The task of keeping the thousand members of the asteroid family from being lost is a heavy one, and needs international co operation both in computation and observation. The chief centres for computation are the Recheninstitut at Berlin, the Nice and Marseilles observatories, and Berkeley observatory, California; while observations (mainly photographic) are made at Konigstuhl, Bergedorf, Simeis (Crimea), Uccle, Marseilles, Nice, Algiers, Barcelona, Johannesburg, Yerkes observatory, etc. The late Dr. J. Palisa made many discoveries and observations at Vienna.
The following work by Dr. G. Stracke gives full details about the discovery and the elements of all the asteroids found up to the year 1925, together with other particulars. "Identifizier ungsnachweis and Elemente der Kleinen Planeten" (Veroffent lichungen des Astronomischen Rechen-Instituts zu Berlin-Dahlem, No. 45). (A. C. D. C.)