Herschel did not merely prove the revolution of the binary stars; he assigned periods to those which he had particularly studied. He believed the period of Castor to be 342 years; γ Leonis 1200 years; δ Serpentis 375 years; and ε Böotis 1681 years. Herschel did not compute the orbits mathematically. This was not done for nearly thirty years, when the calculation of binary star-orbits was commenced by Savary, Sir John Herschel, and Encke.

In 1782 the French astronomer, Charles Messier (1730-1817), published a list of 103 nebulæ. In the following year Herschel commenced his famous sweeps of the heavens with his large reflectors, and during these he made many remarkable discoveries. In 1786 he published in the ‘Philosophical Transactions’ of the Royal Society a catalogue of a thousand new nebulæ and star-clusters, in which he gave the position of each object with a short description of its appearance, written by Caroline Herschel while her brother actually had the object before his eyes. In 1786 Herschel published a catalogue of another thousand clusters and nebulæ, followed in 1802 by a list of 500; making a total of 2500 clusters and nebulæ discovered by the great astronomer. This alone would have gained a great name for William Herschel in this branch of astronomy. In the space of only twenty years 2500 nebulæ and clusters had been discovered. The various nebulæ and clusters were divided into eight classes, as follows: the first class being “bright nebulæ,” the second “faint nebulæ,” the third “very faint nebulæ,” the fourth “planetary nebulæ,” so named by Herschel from their resemblance to planetary discs, the fifth class contained “very large nebulæ,” the sixth “very compressed and rich clusters of stars,” the seventh “pretty much compressed clusters of large or small stars,” and the eighth “coarsely scattered clusters of stars.”

At first Herschel believed all nebulæ to be clusters of stars, the irresolvable nebulæ being supposed to be farther from our system than the resolvable nebulæ. As many of the nebulæ which Messier could not resolve had yielded to Herschel’s instruments, Herschel believed that increase of telescopic power would resolve the hazy spots of light which remained nebulous. In the paper of 1785, in which Herschel dealt with the construction of the heavens, he stated his belief that many of the nebulæ were external galaxies—universes beyond the Milky Way; and in 1786 he remarked that he had discovered fifteen hundred universes!

Arago, Mitchel, Nichol, Chambers, and other writers quite misinterpreted Herschel’s views on the nebulæ when they said that he believed them to be all external galaxies. In 1785 Herschel believed many to be connected with the sidereal system; considering that in some parts of the Galaxy “the stars are now drawing towards various secondary centres, and will in time separate into different clusters.” He was coming to the view that the star-clusters were secondary aggregations within the Galaxy, probably the true theory. He pointed out that in Scorpio, the cluster Messier 80 is bounded by a black chasm, four degrees wide, from which he believed the stars had been drawn in the course of time to form the cluster. His sister records that one night, after a “long, awful silence,” he exclaimed on coming on this chasm—“Hier ist wahrhaftig ein Loch im Himmel!” (Here, truly, is a hole in the heavens.)

Herschel was now gradually giving up his theory of external galaxies and his “disc-theory” of the Universe; but he still believed even the nebulous objects to be irresolvable only through immensity of distance. In 1791, however, he drew attention to a remarkable star in Taurus, surrounded by a nebulous atmosphere, regarding which he wrote, “View, for instance, the nineteenth cluster of my sixth class, and afterwards cast your eye on this cloudy star. Our judgment, I will venture to say, will be that the nebulosity about the star is not of a starry nature. We therefore either have a central body which is not a star, or have a star which is involved in a shining fluid, of a nature totally unknown to us.” And with caution he added that “the envelope of a cloudy star is more fit to produce a star by its condensation than to depend upon the star for its existence.”

This was written in 1791, five years before Laplace propounded his nebular theory. Meanwhile Herschel, believing that “these nebulous stars may serve as a clue to unravel other mysterious phenomena,” found that the theory of a “shining fluid” would suit the appearance of the irresolvable planetary nebulæ and the great nebula in Orion much better than the extravagant idea of “external universes.” Herschel now considered the Orion nebula to be much nearer to the Solar System than he formerly did, and ceased to regard it as external to the Galaxy. For twenty years Herschel patiently observed the nebulæ, and it was not until 1811 that he propounded his nebular hypothesis of the evolution of the Sun and stars. He found the gaseous matter in all stages of condensation, from the diffused cloudy nebulæ like that in Orion, through the planetary nebula and the regular nebula, to the perfect stars, like Sirius and the Sun. Herschel’s nebular theory was a grand conception, and a magnificent attack on the secrets of nature.

Sir Robert Ball says: “Not from abstract speculation like Kant, nor from mathematical suggestion like Laplace, but from accurate and laborious study of the heavens, was the great William Herschel led to the conception of the nebular theory of evolution.” Herschel’s nebular theory was wider and less rigorous than that of Laplace. Laplace reached his theory by reasoning backwards; Herschel by observing the nebulæ in process of condensation. Consequently, while Laplace’s theory has required modification, Herschel’s, from its width, is universally accepted, because there is nothing mathematically rigorous in it. The great German did not go into details like his French contemporary. He sketched the evolution of the stars in a wider sense.

The astronomer’s “1500 universes,” Miss Clerke remarks, “had now logically ceased to exist.” Herschel had gathered much evidence about nebular distribution which shattered his belief in external universes, although he still thought in 1818 that some galaxies were included among the non-gaseous nebulæ. In 1784 Herschel pointed out that the clusters and nebulæ “are arranged to run in strata”; and some time later he found that the nebulæ were aggregated near the galactic poles; in other words, where nebulæ are numerous, stars are scarce, and vice versa. So rigorously did this rule hold, that when dictating his observations to his sister Caroline, he would, on noting a paucity of stars, warn her to “prepare for nebulæ.”

“A knowledge of the construction of the heavens has always been the ultimate object of my observations.” So Herschel wrote in 1811. All his investigations were secondary to the problem which was constantly before his mind—the extent and structure of the Universe. He aspired to be the Copernicus of the Sidereal System. Although Bruno, Kepler, Wright, Kant, and Lambert had speculated regarding the construction of the heavens, they had not the slightest evidence on which to base their ideas. There was no science of sidereal astronomy. The stars were observed only to assist navigation, and the primary object of star-catalogues was to further knowledge of the motions of the planets. In Herschel’s day, also, the distances of the stars had not been measured, and he had to base his views on the distribution of the stars. In 1784, therefore, he commenced a survey of the heavens, in order to ascertain the number of stars in various parts of the sky. This method, which he named “star-gauging,” consisted in counting the number of stars in the telescopic field. Totally he secured 3400 gauges. His studies showed that in the region of the Galaxy the stars were much more numerous than near the galactic poles. Sometimes he saw as many as 588 stars in a telescopic field, at other times only 2. He remarked that he had “often known more than 50,000 pass before his sight within an hour.” Assuming that the stars were, on the average, of about the same size, and scattered through space with some approach to uniformity, Herschel was able to compute the extent to which his telescope penetrated into space; and, assuming that the Universe was finite and that his “gauging-telescope” was sufficiently powerful to completely resolve the Milky Way, he was enabled to sketch the shape and extent of the Universe.

Thus Herschel concluded that the Universe extended in the direction of the Galaxy to 850 times the mean distance of stars of the first magnitude. In the direction of the galactic poles the thickness was only 155 times the distance of stars of the same magnitude. Herschel was thus enabled to sketch the probable form of the Universe, which he regarded as cloven at one of its extremities, the cleft being represented by the famous gap in the Milky Way. The Universe was, in fact, supposed to be a cloven disc, and the Milky Way was merely a vastly extended portion of it and not a region of actual clustering. On this theory the clusters and nebulæ were supposed to be galaxies external to the Universe. Even in 1785, however, Herschel believed that there were regions in the Milky Way where the stars were more closely clustered than others. “It would not be difficult,” he wrote in 1785, “to point out two or three hundred gathering clusters in our system.”