An Introduction to Polynesian Anthropology
At the end of Cook's last voyage, nearly all the important islands in Polynesia had been discovered. Between the years 1780 and 1800, Vavau was discovered by Maurelle (1781), Aitutaki in the Cook group by Captain Bligh in the Bounty (1789), the northwest group of the Marquesas by Joseph Ingraham on the American ship Hope (April 1791), and the Mangareva (Gambier) Islands by James Wilson on the London Missionary Society's ship Duff (1797).
In the early part of the nineteenth century, the Russian voyagers Kotzebue and Bellingshausen added a number of atolls in the Tuamotu Archipelago to the list of discoveries. Captain Beechey in H.M.S. Blossom checked up on the position of a number of islands in the Tuamotus and found three others not previously discovered. Rarotonga was officially credited to the missionary John Williams (1823), and though other navigators, Goodenough for one, had evidently called there before Williams, they had not made any claim. In the course of time, the remaining islands in the Tuamotus were discovered and some were rediscovered. Isolated islands of little importance at the time, such as uninhabited islands near the equator and in the Phoenix group, were added to the chart of the Pacific. Even the United States Exploring Expedition under the command of Commodore Wilkes discovered, as late as 1838 to 1842, islands in the Ellice, Tokelau, and Phoenix groups.