Six years after his great discovery, Herschel, with the 40-foot telescope of 4 feet in aperture which he had now built, discovered two satellites, and believed himself to have discovered four more. Later observations have shown that, in the case of the four, small stars near the planet had been mistaken for satellites. Subsequently two more were discovered, one by Lassell, and one by Otto Struve, making the number of the Uranian retinue up to four, so far as our present knowledge goes. These four satellites, known as Ariel, Umbriel, Oberon, and Titania, are distinguished by the fact that their orbits are almost perpendicular to the plane of the orbit of Uranus, and that the motions of all of them are retrograde. Titania and Oberon, the two discovered by Herschel, are the easiest objects; but although they are said to have been seen with a 4·3-inch refractor, this is a feat which no ordinary observer need hope to emulate. An 8-inch is a more likely instrument for such a task, and a 12-inch more likely still; the average observer will probably find the latter none too big. Accordingly, they are quite beyond the range of such observation as we are contemplating. The rotation period of Uranus is not known. In a few years after the discovery of Uranus, it became apparent that by no possible ingenuity could his places as determined by present observation be satisfactorily combined with those determined by the twenty observations available, as already mentioned, from the period before he was recognised as a planet. Either the old observations were bad, or else the new planet was wandering from the track which it had formerly followed. It appeared to Bouvard, who was constructing the tables for the motions of Uranus, the simplest course to reject the old observations as probably erroneous, and to confine himself to the modern ones. Accordingly this course was pursued, and his tables were published in 1821, but only for it to be found that in a few years they also began to prove unsatisfactory; discrepancies began to appear and to increase, and it quickly became apparent that an attempt must be made to discover the cause of them.