This section is from "Scientific American Supplement Volumes 275, 286, 288, 299, 303, 312, 315, 324, 344 and 358". Also available from Amazon: Scientific American Reference Book.
The discovery soon attracted the notice of royalty, and the reigning sovereign, George III., anxious to practically express his appreciation of the valuable labors of Herschel, awarded him a pension of £200 a year and furnished him with a residence at Slough, near Windsor, and the means to erect a gigantic telescope with which he might be enabled to continue his important researches. This instrument consisted of a reflector on the "Front-view" construction, with a speculum 4 feet in diameter and of 40 feet focal length. Upon its completion, Herschel immediately began to observe the region of the new planet with the idea of discovering any satellites which might belong to it, for analogy suggested that it was surrounded by a numerous retinue of such bodies. He was soon successful, for, on the night of January 11, 1787. he saw two minute objects near the planet, which renewed observations revealed to be satellites; and he detected two additional ones in 1790, and two others in 1794, making six in all. But the observations were of extreme difficulty. The path of the planet frequently passed near minute stars, and it became hard to distinguish between them and the suspected satellites. Herschel, however, considered he had obtained conclusive evidence of the existence of six satellites with sidereal periods ranging from 5d. 21h. 25m. to 107d. 16h. 39m., and his means of observation being much superior to those possessed by any of his contemporaries it was impossible to have corroborative testimony.
The matter was thus allowed to rest until the middle of the present century, when Lassell, in the pure sky at Malta, endeavored to reobserve the satellites with a two-foot reflector. This instrument was considered superior to Herschel's telescope; and the atmosphere at this station being decidedly more suitable for such delicate observations than in England, it was removed there for the express purpose of dealing successfully with objects of extreme difficulty. The results were very important. Mr. Lassell became convinced that Uranus had only four satellites, and that if any others existed they remained to be discovered. Two of these were found to be identical with those seen by Herschel in 1787, and now called Titania and Oberon. The other two, Ariel and Umbriel, could not be identified with any of those alleged to have been previously detected by Herschel, so that the inference was that they were new bodies, and that the priority of discovery was due to Mr. Lassell; whence it also followed that the older observations were erroneous, and that in fact Herschel had been entirely mistaken with regard to the four satellites he believed he had detected subsequently to 1787.
In November, 1873, a fine twenty-six-inch object glass, by Alvan Clark, was mounted at the U. S. Naval Observatory at Washington, and it was soon employed upon the difficult task of solving the problem as to the exact periods of the Uranian satellites. This was very satisfactorily effected, and with distinct and conclusive favor to Mr. Lassell, whose observations were fully corroborated. Only four satellites could be distinguished by the American observers, and their periods, as computed from a valuable series of measures, agreed with those previously derived at Malta. In Appendix I. to the "Washington Observations" for 1873, Prof. Newcomb gave a valuable summary of results--the first obtained, be it noted, with that splendid instrument which soon afterward, in 1877, revealed the satellites of Mars--which included the elements of the satellites of Uranus as follows:
Satellite. Epoch 1871. Radius of Period of Dec. 31, W.M.T. Orbit. Revolution in days. I. Ariel........ 21.83° 13.78" 2.52038 II. Umbriel..... 13.52 19.20 4.14418 III. Titania..... 229.93 31.48 7.70590 IV. Oberon...... 154.83 42.10 13.43327
Speaking of the comparative brightness of the satellites, Prof. Newcomb says:
"The greater proximity of the inner satellites to the planet makes it difficult to compare them photometrically with the outer ones, as actual feebleness of light cannot be distinguished from difficulty of seeing arising from the proximity of the planet. However, that Umbriel is intrinsically fainter than Titania is evinced by the fact that, although the least distance of the latter is somewhat less than the greatest distance of the former, there is never any difficulty in seeing it in that position. From their relative aspects in these respective positions I judge Umbriel to be about half as bright as Titania. Ariel must be brighter than Umbriel, because I have never seen the latter unless it was farther from the planet than the former at its maximum distance.... I think I may say with considerable certainty that there is no satellite within 2' of the planet, and outside of Oberon, having one-third the brilliancy of the latter, and therefore that none of Sir William Herschel's supposed outer satellites can have any real existence. The distances of the four known satellites increase in so regular a way that it can hardly be supposed that any others exist between them. Of what may be inside of Ariel it is impossible to speak with certainty, since in the state of atmosphere which prevails during our winter all the satellites named disappear at 10" from the planet."
Prof. Newcomb mentions that no systematic search for new satellites was undertaken because it must have interfered with the fullness and accuracy of the micrometer measures of the old satellites, which constituted the main purpose of the observations. Some faint objects were occasionally glimpsed near the planet, and their relative places determined, but they were never found to accompany Uranus. The fact, therefore, that no additional satellites were discovered is not to be regarded as a strong point in favor of the theory of their non-existence, because the great power and excellence of the telescope was expressly directed to the attainment of other ends; and moreover the season in which the planet came to opposition was distinctly unfavorable for the prosecution of a rigorous search for new satellites. There can, however, be no doubt that the analogies of the planetary systems interior to Uranus plainly suggest that this planet is attended by several satellites which the power of our greatest telescopes has hitherto failed to reveal; and that it is in this direction and that of Neptune we may anticipate further discoveries in future years when the conditions are more auspicious and the work is entered upon with special energy, aided by instruments of even greater capacity than those which have already so far conduced to our knowledge of the heavenly bodies.