About one o’clock we made sail to the westward, and about half an hour after three we saw land again to the N. W. We got up with it at sunset, and it proved to be a low woody island, of a circular form, and not much above a mile in compass. We discovered no inhabitants, nor could we distinguish any cocoa-nut trees, though we were within half a mile of the shore. The land, however, was covered with verdure of many hues. It lies in latitude 18° 35ʹ S., and longitude 139° 48ʹ W., and is distant from Lagoon Island, in the direction of N. 62 W., about seven leagues. We called it THRUMB-CAP. I discovered by the appearance of the shore, that at this place it was low water; and I had observed at Lagoon Island, that it was either high water, or that the sea neither ebbed nor flowed. I infer, therefore, that a S. by E. or S. moon makes high water. We went on with a fine trade-wind and pleasant weather, and on the 5th, about three in the afternoon, we discovered land to the westward. It proved to be a low island of much greater extent than either of those that we had seen before, being about ten or twelve leagues in compass. Several of us remained at the mast-head the whole evening, admiring its extraordinary figure: it was shaped exactly like a bow, the arch and cord of which were land, and the space between them water: the cord was a flat beach, without any signs of vegetation, having nothing upon it but heaps of sea-weed, which lay in different ridges, as higher or lower tides had left them. It appeared to be about three or four leagues long, and not more than two hundred yards wide; but as a horizontal plane is always seen in perspective, and greatly foreshortened, it is certainly much wider than it appeared: the horns, or extremities of the bow, were two large tufts of cocoa-nut trees; and much the greater part of the arch was covered with trees of different height, figure, and hue; in some parts, however, it was naked and low, like the cord. Some of us thought they discovered openings through the cord, into the pool or lake, that was included between that and the bow; but whether there were or were not such openings is uncertain. We sailed abreast of the low beach or bow-string, within less than a league of the shore, till sunset, and we then judged ourselves to be about half-way between the two horns. Here we brought to, and sounded, but found no bottom with one hundred and thirty fathom; and, as it is dark almost instantly after sunset in these latitudes, we suddenly lost sight of the land, and making sail again, before the line was well hauled in, we steered by the sound of the breakers, which were distinctly heard till we got clear of the coast.