In 1699, that celebrated astronomer Dr. Edmund Halley was appointed to the command of his Majesty’s ship the Paramour Pink, on an expedition for improving the knowledge of the longitude, and of the variation of the compass; and for discovering the unknown lands supposed to lie in the southern part of the Atlantic Ocean. In this voyage he determined the longitude of several places; and after his return, constructed his Variation Chart, and proposed a method of observing the longitude at sea, by means of the appulses, and occultations of the fixed stars. But, though he so successfully attended to the two first articles of his instructions, he did not find any unknown southern land. The Dutch, in 1721, fitted out three ships to make discoveries in the South Pacific Ocean, under the command of Admiral Roggewein. He left the Texel on the 21st of August, and arriving in that ocean, by going round Cape Horn, discovered Easter island; probably seen before, though not visited by Davis[1];—then, between 14° 41ʹ and 15° 47ʹ South latitude, and between the longitude of 142° and 150° West, fell in with several other islands, which I take to be some of those seen by the late English navigators.—He next discovered two islands in latitude 15° South, longitude 170° West, which he called Baumen’s islands;—and, lastly, Single island, in latitude 13° 41ʹ South, longitude 171° 30ʹ West.—These three islands are, undoubtedly, the same that Bougainville calls the Isles of Navigators. In 1738, the French East India Company sent Lozier Bouvet with two ships, the Eagle and Mary, to make discoveries in the South Atlantic Ocean. He sailed from Port L’Orient on the 19th of July, in that year; touched at the island of St. Catharine; and from thence shaped his course towards the S. E. On the 1st of January, 1739, he discovered land, or what he judged to be land, in the latitude 54° South, longitude 11° East. It will appear in the course of the following narrative, that we made several attempts to find this land without success. It is, therefore, very probable, that what Bouvet saw was nothing more than a large ice-island. From hence he stood to the East, in 51° of latitude, to 35° of East longitude: after which the two ships separated; one going to the island of Mauritius, and the other returning to France. After this voyage of Bouvet, the spirit of discovery ceased, till his present Majesty formed a design of making discoveries, and exploring the Southern Hemisphere; and, in the year 1764, directed it to be put in execution. Accordingly, Commodore Byron, having under his command the Dolphin and Tamer, sailed from the Downs on the 21st of June the same year; and having visited the Falkland islands, passed through the Straits of Magalhaens into the Pacific Ocean, where he discovered the islands of Disappointment;—George’s;—Prince of Wales’s;—the isles of Danger;—York island;—and Byron island.