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ASTRONOMY

the motion of the whole system nearly in the same plane, as if it were a rigid body. Especially is this the case with the ring, in the form of which not the slightest deviation from a plane can be detected, whereas, if each of its particles moved independently, the whole would form a mass so broad as to quite conceal the planet from our view. The most remarkable features of this system are the cases of libration among the motions of the satellites, most of which are quite unique in form. We note for comparison the well - known relation among three of the satellites of Jupiter: if L, L', and L" are the respective mean longitudes of the first, second, and third of these bodies, we find that they always move so as to satisfy the equation— L - 31/ + 2L" = 180°. Let us, for brevity, call W the combination L - 3L' + 2L". It was shown by Laplace that, if W differed slightly from 180°, there would be small residual forces arising from the mutual action of the three bodies, tending always to bring it towards 180°. That is, if W were less than 180°, the force would tend to increase it; if greater, to diminish it, and thus W might swing back and forth on each side of 180° as a pendulum swings on each side of the vertical. This swing would be a libration. As a matter of fact, the swing is too slight to be observed; W stays at 180° as a pendulum might constantly hang in the vertical position. The similar librations in the Saturnian system have the remarkable feature that not only the mean longitude, but also the longitudes of the pericentres come into ten equations. The first case of this sort noticed was between the sixth and seventh satellites, Titan and Hyperion—the latter being the outer one of the two, and the faintest of the eight known satellites. Its orbit has long been known to be the most eccentric of the system, the eccentricity being 0T0. Professor Hall, by comparing his own observations with those of his predecessors, showed that the pericentre of the orbit performs a complete revolution in about eighteen years in a retrograde direction, this being the reverse of the secular motion due to the action of a disturbing body. It was found that this seeming anomaly arises from a peculiar action of Titan, having its origin in a near approach to commensurability between the mean motions of the two bodies, three times that of Titan being nearly equal to four times that of Hyperion. The motions are so adjusted that if we put L, L' = the mean longitude of Titan and Hyperion, it' the longitude of the pericentre of Hyperion, and Y = 4L' — 3L - tt', then the angle Y will never differ much from 180°, but will continually oscillate on each side of this value, as just explained in the case of the angle W for Jupiter. The annual retrograde motion of tt is, from the observations of Hermann Struve, 18’663°, so that the period of its revolution is 19‘3 years. The eccentricity of Titan has the effect of making all the elements of Hyperion go through a change in nearly this period, which is determined by the angular distance of the pericentres of the two satellites. The expression for the inequalities thus arising in the eccentricity and pericentre of Hyperion are— A tt' = 14'0° sin (tt - tt') A e' = 0'0230 cos (tt — tt'). The motion in question has also been theoretically investigated by G. W. Hill and Ormond Stone. They have established it to determine the mass of Titan, which is shown to be about 1/4300 that of Saturn itself. This is remarkable, because it seems certain that the angular diameter of the satellite is much less than one second, while that of Saturn when nearest the earth is about twenty seconds. The satellite would therefore seem to be

less than 1/10000 the size of Saturn, so that the mass found by Hill and Stone shows its density to be at least twice that of the planet. The masses of the other satellites have been found by Struve to be very minute, varying from 1/250000, in the case of Rhea, to 1/13610000 in that of Mimas. The determinations of the mass of Saturn have been singularly discordant. They are made by measures of the major axes of the orbits of the satellites and by the action of Saturn on Jupiter. From measures with the heliometer on the brightest satellite, Titan, Bessel found /x = 3501-6. A subsequent correction increases the number by one or two units. Leverrier, from the action of Jupiter, found 3529,6 (Annales de VObservatoire de Paris, xii. p. 9). Asaph Hall, from measures of Japetus with the 26-inch Washington telescope, 3481‘3 ± 0’54 (Washington Observations for 1882, app., p. 70). The small probable error of this last value, the great power of the instrument, and the considerable mean distance of the satellite, more than 500", would seem to inspire confidence in it. It was strengthened by the use of two quite distinct methods of observing—one with the micrometer, the other by transits giving differences of R. A. between the planet and the satellite. But Hill, from the action on Jupiter, found a result in substantial agreement with Bessel’s. To decide the question Asaph Hall, jun., observed Titan with the heliometer of the Yale Observatory, and obtained a result confirming Bessel’s. Yet H. Struve, from measures of Japetus and Titan with the Pulkowa 14-inch equatorial, found 3498 ; and from Titan and the nearer satellites, with the great 30-inch instrument, 3495'3. In Hill’s tables of Jupiter, and the other tables of the American Ephemeris, the value 3501’6 is adopted. Still, the preponderance of evidence at the present time seems to favour a number rather below than above 3500. For the angular diameters of Uranus and Hep tune Barnard found, with the filar micrometer:— Uranus and Uranus, 4’040" at dist. 19T83 Neptune. Neptune, 2-433" „ 30'0551. The masses adopted in the new tables are :— Uranus, /x = 22869 Neptune,/x= 19314. III. The Fixed Stars. Our knowledge of the fixed stars has in recent years been widened to an extent which would not have been deemed possible two generations ago. The revelations of the spectroscope have given rise to a branch of astronomy so wide in its scope that it is sometimes regarded as a new science, that of astrophysics—a term now applied to the results of studies on the physical constitution of the heavenly bodies generally, whether the planets or the stars. It is impossible to draw a sharp line between the results of this branch of study and those of the older methods of investigation, sometimes called astrometry, which includes all forms of celestial measurement, whether of distance, motions, or magnitudes; as astrophysics progresses, it necessarily enters this field. Its most remarkable discoveries have resulted from the measurements of motions in the line of sight, the results of which belong strictly to astrometry. Our summary of the advances in stellar astronomy may be introduced by a brief general view of activity in the field at large. One prominent feature of recent progress has been the study of the southern heavens. A natural result of the great preponderance of observatories and means of recent research in the northern hemisphere progress was that, before the present generation, our knowledge of the southern heavens lagged far behind that