At one o'clock, on the 11th, we saw an island in the W.S.W. and stood, for it. At four in the afternoon, we were within a quarter of a mile of the shore, and ran along it, sounding continually, but could get no ground. It is surrounded on every side by rocks, on which the sea breaks very high. It is full of trees, but not one cocoa-nut, and has much the same appearance with Egmont Island, but is much narrower. Among the rocks, at the west end, we saw about sixteen of the natives, but no canoes: They carried long pikes or poles in their hands, and seemed to be, in every respect, the same kind of people that we had seen before. As nothing was to be had here, and it blew very hard, I made sail till eight in the evening, and then brought to. To this island, which is about six miles long, and from one mile to one quarter of a mile broad, I gave the name of _Gloucester Island_, in honour of his royal highness the Duke. It lies in latitude 19°11'S., and longitude, by observation, 140°4'W. At five o'clock in the morning, we made sail, and soon after saw another island. At ten o'clock, the weather being tempestuous, with much rain, we saw a long reef, with breakers on each side of the island, and therefore brought the ship to, with her head off the shore. To this island, which lies in latitude 19°18'S., longitude, by observation, 140°36'W., I gave the name of _Cumberland Island_, in honour of his royal highness the Duke. It lies low, and is about the same size as Queen Charlotte's Island. We found the variation, of the needle here to be 7°10'E. As I had no hope of finding any refreshment here, I stood on to the westward. At day-break, on Saturday the 13th, we saw another small low island, in the N.N.W. right to windward. It had the appearance of small flat keys. This place I called _Prince William Henry's Island_, in honour of his majesty's third son. It lies in latitude 19°S., longitude, by observation, 141°6' W. I made no stay here, hoping that to the westward I should find higher land, where the ship might come to an anchor, and such refreshments as we wanted be procured. Soon after day-light, on the 17th, we saw land bearing W. by N. and making in a small round hummock. At noon, when it bore N. 64° W. distant about five leagues, its appearance greatly resembled the Mewstone in Plymouth Sound, but it seemed to be much larger. We found the ship this day twenty miles to the northward of her reckoning, which I imputed to a great S.W. swell. At five in the evening, this island bore N.W. distant about eight miles. I then hauled the wind, and stood on and off all night. At ten, we saw a light upon the shore, which, though the island was small, proved that it was inhabited, and gave us hopes that we should find anchorage near it. We observed with great pleasure, that the land was very high, and covered with cocoa-trees; a sure sign that there was water.