The most remarkable of them, to a common reader, is the conjecture of the return of a comet. Some earlier astronomers, as Kepler, had imagined the motion of these bodies to be rectilinear. Newton, in explaining the principle of universal gravitation, showed how a comet might describe a parabola, and also how to calculate its motion, and compare it with observation. Hevelius had already indicated the curvature of a comet’s path, and Dörfel, a Saxon clergyman, had calculated the path of the comet of 1680 upon this supposition. Halley, in computing the parabolic elements of all the comets which had been well observed up to his time, suspected, from the general likeness of the three, that the comets of 1531, 1607, and 1682, were the same. He was the more confirmed in this, by knowing that comets had been seen, though no good observations were recorded, in the years 1305, 1380, and 1456, giving, with the former dates, a chain of differences of 75 and 76 years alternately. Halley supposed, therefore, that the orbit of this comet was, not a parabola, but a very elongated ellipse, and that it would return about the year 1758. The truth of his conjecture was fully confirmed in January, 1759, by Messier. The first person, however, who saw Halley’s comet, as it is now called, was George Palitzch, a farmer in the neighbourhood of Dresden, who had studied astronomy by himself, and fitted up a small observatory. But a much more useful exertion of Halley’s genius and power of calculation is to be found in his researches on the lunar theory. It is to him that we are indebted for first starting the idea of finding the longitude at sea by means of the moon’s place, which is now universally adopted. The principle of this problem is as follows. An observer at sea can readily find the time of day by means of the sun or a star, and can thereby correct a watch. If he could at the same moment in which he finds his own time, also discover that at Greenwich, the difference between the two, turned into degrees, minutes, and seconds, would be his longitude east or west of Greenwich. If, therefore, he carries with him a Nautical Almanac, in which the times of various astronomical phenomena are registered, as they will take place at Greenwich, or rather as they will be seen by an observer placed at the centre of the earth with a Greenwich clock, he can observe any one of these phenomena, and reduce it also to the centre. He will then know the corresponding moments of time, for his own position and that of Greenwich. The moon traverses the whole of its orbit in little more than 27 days, and therefore moves rapidly with respect to the fixed stars, its motion being nearly a whole sign of the zodiac in 48 hours. If we observe the distance between the moon and a star, and find it to be ten degrees, the longitude of the place in which the observation is made can be known as aforesaid, if the almanac will tell what time it was at Greenwich when the moon was at