There being no island marked in the Dutch chart so near to the head of the Gulph as this hill, made me conclude that it was upon the main land; and to hope that the space of four leagues, between it and the southern coast, was an opening of some importance.  In the morning [WEDNESDAY 17 NOVEMBER 1802], a fresh land wind at south-east favoured our course, the water deepened to 10 fathoms, and at eight o’clock to no ground with 13, near the south end of a reef extending out from the hill.  On coming into 5 fathoms behind the reef, the anchor was dropped on a muddy bottom, with the hill bearing N. 15 deg.  E., one mile and a quarter, and the dry extremity of the reef S. E. 1/2 E. The coast to the southward was scarcely visible from the mast head, but land was seen to extend westward from the hill, as far as nine or ten miles; and in order to gain a better knowledge of what this land might be, I went on shore, taking instruments with me to observe for the rates of the time keepers.

The hill proved to be a mass of calcareous rock, whose surface was cut and honeycombed as if it had been exposed to the washing of a surf.  It was the highest land we had seen in Carpentaria, after having followed one hundred and seventy-five leagues of coast; nor was any land to be distinguished from the top of the hill which had an equal degree of elevation; yet it did not much exceed the height of the ship’s mast head!  The land round it proved to be an island of five miles long; separated from other land to the west by a channel of nearly two miles in width.  The wide opening between this land and the low coast to the southward, I take to have been what is called Maatsuyker’s River in the old chart; and that the island, which Tasman, or whoever made the examination, did not distinguish well from being too far off, is the projecting point marked on the west side of that river.  Maatsuyker was one of the counsellors at Batavia, who signed Tasman’s instructions in 1644; but as there is no river here, his name, as it stands applied in the old chart, cannot remain.  I would have followed in the intention of doing him honour, by transferring his name to the island, but Maatsuyker’s Isles already exist on the south coast of Van Diemen’s Land; I therefore adopt the name of Sweers, another member of the same Batavia council; and call the island at the entrance of the supposed river, Sweers’ Island.  The hill obtained the name of Inspection Hill; and after taking bearings from it, I rowed into the channel which separates Sweers’ Island from the western land; and finding the shelter to be good, the bottom soft, and soundings regular between 3 and 6 fathoms, the shores on each side were searched for fresh water, with a view to filling up the holds there and caulking the ship, before proceeding further in the examination of the Gulph:  the search, however, was unsuccessful.