"The length, tension, and weight of a musical string being given, it is required to find how many vibrations it will make in a given time, when a small given weight is fastened to its middle and vibrates with it."
In the Philosophical Transactions of the Royal Society for 1780, are two papers of his. The title of the first is, Astronomical Observations on the Periodical Star in Collo Ceti, by Mr. William Herschel, of Bath. This was communicated to the Society by Dr. William Watson, Jr., and was read May 11, 1780, at the same time as the other paper on the mountains of the moon. It is to be noted that Herschel was at this time plain "Mr. William Herschel, of Bath." It was only in 1786 that he became "Dr. Herschel," through the Oxford degree of LL.D.
Neither of these two papers is specially remarkable on its purely astronomical side. The problems examined were such as lay open before all, and the treatment of them was such as would naturally be suggested.
The second of these two contained, however, a short description of his Newtonian telescope, and he speaks of it with a just pride: "I believe that for distinctness of vision this instrument is perhaps equal to any that was ever made." He was, at least, certain of having obtained excellence in the making of his instruments.
In his next paper, however, read January 11, 1781, a subject is approached which shows a different kind of thought. It is the first obvious proof of the truth of the statement which he made long afterwards (1811), when he said: "A knowledge of the construction of the heavens has always been the ultimate object of my observations."
The title of this paper was Astronomical Observations on the Rotation of the Planets round their Axes, made with a view to determine whether the Earth's diurnal motion is perfectly equable. Here the question is a difficult and a remote one, and the method adopted for its solution is perfectly suitable in principle. It marks a step onward from mere observations to philosophizing upon their results. In practical astronomy, too, we note an advance. Not only are his results given, but also careful estimates of the errors to be feared in them, and a discussion of the sources of such errors. The same volume of the Philosophical Transactions which contains this paper, also contains another, Account of a Comet, read April 26, 1781. This comet was the major planet Uranus, or, as Herschel named it, Georgium Sidus. He had found it on the night of Tuesday, March 13, 1781. "In examining the small stars in the neighborhood of H Geminorum, I perceived one that appeared visibly larger than the rest; being struck with its uncommon appearance, I compared it to H Geminorum and the small star in the quartile between Auriga and Gemini, and finding it so much larger than either of them, I suspected it to be a comet." The "comet" was observed over all Europe. Its orbit was computed by various astronomers, and its distance from the sun was found to be nineteen times that of our earth. This was no comet, but a new major planet. The discovery of the amateur astronomer of Bath was the most striking since the invention of the telescope. It had absolutely no parallel, for every other major planet had been known from time immemorial.[13]
The effect of the discoveries of Galileo was felt almost more in the moral than in the scientific world. The mystic number of the planets was broken up by the introduction of four satellites to Jupiter. That Venus emulated the phases of our moon, overthrew superstition and seated the Copernican theory firmly. The discovery of "an innumerable multitude of fixed stars" in the Milky Way confounded the received ideas. This was the great mission of the telescope in Galileo's hands.
The epoch of mere astronomical discovery began with the detection of the large satellite of Saturn by Huyghens, in 1655. Even then superstition was not dead. Huyghens did not search for more moons, because by that discovery he had raised the number of known satellites to six,[14] and because these, with the six planets, made "the perfect number twelve."
From 1671 to 1684 Cassini discovered four more moons revolving about Saturn. Since 1684 no new body had been added to the solar system. It was thought complete for nearly a century.
In England, the remarkable discoveries of Bradley (1727-62) had been in the field of practical astronomy, and his example had set the key-note for further researches. France was just about beginning the brilliant period of her discoveries in mathematical astronomy, and had no observatory devoted to investigations like Herschel's, with the possible exception of Darquier's and Flaugergues'. The observatories of Schroeter and Von Hahn, in Germany, were not yet active. The field which Herschel was created to fill was vacant, the whole world over. It was especially so in England. The Royal Observatory at Greenwich, under Maskelyne, a skilful observer, whose work was mostly confined to meridian observations, was no rival to a private observatory like Herschel's. The private observatories themselves were but small affairs; those of the king, at Kew, of Dr. Wilson, at Glasgow, of Mr. Aubert, at Loampit Hill, of the Count von Bruhl, in London, being perhaps the most important. The whole field was open. What was perhaps more remarkable, there was in England, during Herschel's lifetime, no astronomer, public or private, whose talents, even as an observer, lay in the same direction.