Nature, however, knows no such arithmetical doctrines as those which Huyghens attributed to her. Had he been less influenced by such prejudices, he might, perhaps, have anticipated the labours of Cassini, who, by discovering other satellites of Saturn, demonstrated the absurdity of the doctrine of numerical equality between planets and satellites. As further discoveries were made, the number of satellites was at first raised above the number of planets; but in recent times, when the swarm of minor planets came to be discovered, the number of planets speedily reached and speedily passed the number of their attendant satellites. It was in 1671, about sixteen years after the discovery of the first satellite of Saturn, that a second was discovered by Cassini. This is the outermost of the older satellites; it takes 79 days to travel round Saturn. In the following year he discovered another; and twelve years later, in 1684, still two more; thus making a total of five satellites to this planet. [Illustration: Fig. 68.--Transit of Titan and its Shadow, by F. Terby Louvain, 12th April, 1892.] The complexity of the Saturnian system had now no rival in the heavens. Saturn had five satellites, and Jupiter had but four, while at least one of the satellites of Saturn, named Titan, was larger than any satellite of Jupiter.[28] Some of the discoveries of Cassini had been made with telescopes of quite monstrous dimensions. The length of the instrument, or rather the distance at which the object-glass was placed, was one hundred feet or more from the eye of the observer. It seemed hardly possible to push telescopic research farther with instruments of this cumbrous type. At length, however, the great reformation in the construction of astronomical instruments began to dawn. In the hands of Herschel, it was found possible to construct reflecting telescopes of manageable dimensions, which were both more powerful and more accurate than the long-focussed lenses of Cassini. A great instrument of this kind, forty feet long, just completed by Herschel, was directed to Saturn on the 28th of August, 1789. Never before had the wondrous planet been submitted to a scrutiny so minute. Herschel was familiar with the labours of his predecessors. He had often looked at Saturn and his five moons in inferior telescopes; now again he saw the five moons and a star-like object so near the plane of the ring that he conjectured this to be a sixth satellite. A speedy method of testing this conjecture was at hand. Saturn was then moving rapidly over the heavens. If this new object were in truth a satellite, then it must be carried on by Saturn. Herschel watched with anxiety to see whether this would be the case. A short time sufficed to answer the question; in two hours and a half the planet had moved to a distance quite appreciable, and had carried with him not only the five satellites already known, but also this sixth object.