On the 2d of January, at day-break, we weighed anchor, and resumed our course to the N., having fine weather, and a gentle breeze at E., and E.S.E., till we got into the latitude of 7 deg. 45' N., and the longitude of 205 deg. E., where we had one calm day. This was succeeded by a N.E. by E., and E.N.E. wind. At first it blew faint, but freshened as we advanced to the N. We continued to see birds every day of the sorts last mentioned, sometimes in greater numbers than others, and between the latitude of 10 deg. and 11 deg., we saw several turtles. All these are looked upon as signs of the vicinity of land. However, we discovered none till day-break, in the morning of the 18th, when an island made its appearance, bearing N.E. by E.; and soon after, we saw more land bearing N., and entirely detached from the former. Both had the appearance of being high land. At noon, the first bore N.E. by E. 1/2 E., by estimation about eight or nine leagues distant; and an elevated hill, near the east end of the other, bore N. 1/2 W. Our latitude, at this time, was 21 deg. 12' N., and longitude 200 deg. 41' E. We had now light airs and calms by turns, so that, at sunset, we were not less than nine or ten leagues from the nearest land. On the 19th, at sun-rise, the island first seen, bore E., several leagues distant. This being directly to windward, which prevented our getting near it, I stood for the other, which we could reach; and, not long after, discovered a third island in the direction of W.N.W., as far distant as land could be seen. We had now a fine breeze at E. by N., and I steered for the east end of the second island, which, at noon, extended from N. 1/2 E. to W.N.W. 1/4 W., the nearest part being about two leagues distant. At this time, we were in some doubt whether or no the land before us was inhabited; but this doubt was soon cleared up, by seeing some canoes coming off from the shore toward the ships. I immediately brought-to, to give them time to join us. They had from three to six men each; and, on their approach, we were agreeably surprised to find that they spoke the language of Otaheite, and of the other islands we had lately visited. It required but very little address to get them to come along-side; but no entreaties could prevail upon any of them to come on board. I tied some brass medals to a rope, and gave them to those in one of the canoes, who, in return, tied some small mackerel to the rope as an equivalent. This was repeated; and some small nails, or bits of iron, which they valued more than any other article, were given them. For these they exchanged more fish and a sweet potatoe, a sure sign that they had some notion of bartering, or, at least, of returning one present for another. They had nothing else in their canoes, except some large gourd shells, and a kind of fishing-net; but one of them offered for sale the piece of stuff that he wore round his waist, after the manner of the other islands.