URANUS, SATELLITES OF. In the beginning of the year 1787 Sir William Herschel discovered two satellites around Uranus. Having made a series of careful observations of their position with respect to the primary, he next proceeded to determine the elements of their orbits. The results of this investigation are contained in a paper which he communicated to the Royal Society in the following year. He obtained for the times of revolution of the two satellites these values :— He also determined the apparent distance of the second satellite from the centre of the planet to be 44".23. The first satellite, that is, the satellite next to the planet, was an object of such faintness that he was unable to arrive at a definite conclusion with respect to the appa• rent distance. He however deduced the value of this element from the periodic times of the two satellites, and the apparent distance of the second, by the aid of Kepler's third law. In this way he found the apparent distance of the satellite to be 33'49. In a paper which he communicated to the Royal Society in the year 1797, he announced two interesting facts with respect to the movements of those minute bodies. The first was that their motions are retrograde, or, in other words, that their revolutions are effected in a direction contrary to the order of the signs ; the second consisted in this, that the orbits of the satellites are nearly perpendicular to the plane of the ecliptic.
In the same paper Herschel announced his discovery of four addi tional satellites around the planet. This made the aggregate number of satellites revolving around the planet to amount to six. The follow ing values of the periodic time and distance of each satellite were given by him. The distances are expressed in terms of the semi diameter of the planet :— It will be seen from this table that the two satellites originally dis covered by the second and fourth, counting in the order of distance from the primary. The periodic times and distances of these satellites were satisfactorily determined by an investigation founded on their observed positions. The case, however, was different with respect to the other satellites. The distance of the first satellite was indeed the result of micrometrical measures, but the distances of the other satellites were mere estimations. The orbit of the third satellite was supposed to bisect the linear interval between the second and fourth satellites ; the fifth satellite was supposed to be twice as distant from the planet as the fourth ; and the sixth 'satellite to be twice the distance of the fifth. The periodic times of the four satel lites were deduced from these data, and the elements of the second and fourth satellites by the aid of Kepler's third law.
A paper which Herschel communicated to the Royal Society in the year 1815, contains his final researches on the motions of the satellites of Uranus. It appeared from his observations that the planet passed through the common ascending node of the satellites on the 12th of March, 1798. lie hence determined the longitude of the node to be 165' 30'. He also obtained 78' 59' for the inclination of the orbits of the satellites to the ecliptic. On the same occasion he determined anew the synodic revolution. of the second and fourth satellites, which he found to be 16" 56' 5•2*, and 11" 8" 59. respectively. lie still retained his belief with respect to the existence of four additional satellites, and, although he was unable to assign any further proof of a positive nature In support of his opinion, he communicated a series of rough notes of their observed position. which might aid the labours of future inquirers.
In 1S28, Sir John Herschel, having directed one of his 20-foot reflectors towards Uranus, succeeded in obtaining a view of the two satellites originally discovered by his father. Having subsequently executed a series of micrometric measures of their observed positions, he instituted a comparison between them and the corresponding results of his father's observations, and in this way he was enabled to deduce new values of the periodic times of the two satellites. He found the period of the second satellite to be S. 113b 56' 31.3., and that of the fourth to be 13. 11' 7" 12 6'. It. will be neon that these results do not differ materially from the corresponding numbers which the elder Henschel derived from his researches. M. Lamont, Director of the Munich Observatory, having In the year 1837 made a series of observa Rona of the same satellites with a refractor of II inches aperture, obtained, by a comparison of his own measures with those of the two Herschel'', values of the periodic times agreeing very closely with those deduced by Sir John Herschel.
Recently, Mr. Lassell has discovered two satellites revolving within the orbit of Herschel's second satellite, but neither of which appears to coincide with Herschel's first satellite. He has applied to them the names Ariel and Umbriel, designating at the same time the second and fourth satellites of Herschel by the names Titania and Oberon. He does not recognise the existence of any other satellites around tho planet except the four to which he has applied these names. The following synopsis may be useful :—