After leaving Norfolk Island, they stretched to the northward and eastward, and at one o'clock on the twenty-sixth they saw a small island bearing north north-east eight or nine leagues distant; when about four miles from the island, they sounded with fifty fathoms of line, but got no bottom. Towards evening, Captain Marshall was close in with the island, and being desirous to examine it, he plied occasionally during the night. At day light the next morning, he was close to the land, and found it to be a barren rock, not more than half a mile over in the broadest part; it is very high, and was entirely covered with birds of various kinds, but there was no possibility of landing on account of a frightful surf that entirely surrounded it. This rock was seen first by Captain Gilbert, of the Charlotte, in the forenoon of the 26th, and named by him, Matthew's Island; it is situated in 22° 22' south latitude, and 170° 41' longitude, east of Greenwich.
On the 30th, in 17° 13' south latitude, and 172° 43' east longitude, they passed several large trees, and a number of cocoa-nuts floating in the water, but no land was to be seen. Nothing occurred worthy of note till the 4th of June, when the water appearing coloured, they sounded and struck the ground in fifteen fathoms water, although no land was to be seen: a man was then sent to the mast-head, who could plainly discern that the shoal run to the westward, on which Captain Marshall altered his course and stretched to the eastward, carrying soundings from fifteen to thirty fathoms water, over a rocky bottom, and in many places they could see the ground very distinctly. After running to the eastward, about eight miles, they found no bottom with seventy fathoms of line, which occasioned the Captain to tack and stand to the southward. Vast numbers of birds of different kinds were flying to the westward of the shoal, so that there probably is an island near that situation. The east part of this shoal is situated in 173° 12' east longitude, and the south part of it in 15° 50' south latitude, but how far it extends to the westward and northward is very uncertain, though doubtless to a considerable distance, as the water had a white appearance from the mast head as far as the eye could reach. Being now entirely free from the shoal, they stood to the northward, with a light easterly breeze, and moderate weather. On the 9th, in 7° 59' south latitude, the wind shifted to the westward and continued in the western board till the 13th when it again changed to the eastward.