DELAMBRE ISLAND has very extensive reefs stretching to the northward, and also to the eastward, but on its western side did not appear to extend for more than half a mile: the hill at the north end of the island is in latitude 20 degrees 23 minutes 35 seconds, and longitude 117 degrees 1 minute 25 seconds; the passage between it and the reef off HAUY ISLAND, is about two miles and a half wide, and from nine to ten fathoms deep. The edge of the reef off the latter island is not well defined, for we passed several straggling rocks. LEGENDRE ISLAND is the northernmost of Dampier's Archipelago: it is nine miles long, and from half to one and a half mile broad: near its south-east end, which is connected to HAUY ISLAND, there are several rocky islets, and near its extremity it has three remarkable hillocks; its North-West point is in latitude 20 degrees 18 minutes 45 seconds, and longitude 116 degrees 46 minutes; its north-east coast and north-west extremity are of bold approach: the latter has a reef that fronts its shores, extending for about a quarter of a mile into the sea; the ground under its lee is rocky, and not safe to anchor near. Our cable hooked a rock, fortunately however it was rotten, and broke away, so that the cable, being a chain was not damaged. The islands of DAMPIER'S ARCHIPELAGO, are of high rocky character, and very different from either the coast or the islands in their vicinity. It consists of about twenty islands, besides smaller ones, scattered over a space of forty miles in extent: Delambre is the easternmost island, and a small sandy island to the South-West of Enderby Island is the westernmost. GIDLEY ISLAND, and two others to the eastward, extend in a north and south direction; they are high and rocky. The west shore of Gidley Island appeared to be fronted by a continuous reef, on which some patches of dry rocks were observed. Gidley Island is separated from Legendre Island by a very shoal and rocky strait, apparently impassable for anything larger than boats. It has several small sandy islets scattered about it, and at low water the greater part is dry. There is doubtless a deep passage through, but it must be intricate and dangerous, and only to be attempted in a case of the most pressing emergency. On the island to the southward, are two sandy bays. The land to the southward is doubtless a part of the main: and is, like the other islands, high and rocky. It forms the eastern shore of MERMAID's STRAIT, which is an excellent port, affording safe and secure anchorage at all seasons.