The Scarborough transport, Captain Marshall, left Port Jackson on the 6th of May 1788, and proceeded towards China, being engaged to take in a cargo of teas at Canton for the East India Company.  For several days they had very unsettled weather, with frequent squalls and heavy rain.  In the afternoon of the 16th, they saw Lord Howe’s Island, bearing east by south seven leagues distant; and the next day at noon, they found the Supply brig, the Lady Penrhyn, and the Charlotte, standing off and on under the island.  By two o’clock the Scarborough was close in with the land, but the weather not permitting them to go on shore, the night was spent in standing off and on.  Early the next morning, Captain Marshall sent his boat with the chief mate and six men on shore at Lord Howe’s Island, in expectation of procuring some turtle, as the Supply, Lieutenant Ball, had caught a large quantity at this island in February:  however, they were not able, after the most diligent search, to meet with any turtle; but this excursion was not altogether a fruitless one, for they brought off a quantity of fine birds, sufficient to serve the ship’s crew three days; many of them were very fat, somewhat resembling a Guinea hen, and proved excellent food.  Having procured such refreshments as the island afforded, they made sail at four o’clock, with the Charlotte in company, and stood to the eastward, with a moderate breeze at south-west.  At eight o’clock in the morning of the 22d, they saw Norfolk Island, bearing east by south twelve leagues distant.  At two o’clock, they were within one mile of the land, and had soundings in sixteen fathoms water over a hard bottom:  the Charlotte being a considerable distance a-stern, Captain Marshall lay to for her to come up, and when she joined the Scarborough he stood under an easy sail to the distance of six leagues westward of the island, and carried soundings from sixteen to twenty-five fathoms, the ground various; in some places being soft, in other parts a corally bottom, and sometimes coarse white sand, intermixed with broken shells.

26 May 1788

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 deg. 22’ south latitude, and 170 deg. 41’ longitude, east of Greenwich.