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!