Daylight on the 5th found us standing to the eastward--East-North-East--with a light northerly wind, in soundings ranging from 14 to 40 fathoms, and over a bottom of white and brown sand in the deep, and coral rock in the shoal water. In the afternoon we had the good fortune to discover one of the reefs, which render the navigation of this part of the coast rather hazardous. The position of this danger, is however well marked by a bank of very white sand and dead coral, from which the reef extends two miles and a half, in a North-North-West and one mile in a South-South-East direction; and which rising some 15 feet above the mean level of the blue surrounding water, became a conspicuous object from our deck, even at the distance of six miles. We gave our discovery the name of Beagle Bank, as another memorial of the useful services in which our little vessel had been so frequently engaged, and our observations enabled us to fix the centre of it in latitude 15 degrees 20 minutes South, longitude 123 degrees 36 minutes East. SHOAL SOUNDINGS. We anchored in the evening in 16 fathoms, the bank distant 3 1/2 miles in a South by East direction: half a mile nearer to it, we found only 4 fathoms. The tide rose at this anchorage 12 feet. The flood stream began by setting to the South-South-West, and ended at South-east by East. The ebb set West by North, and the utmost strength of stream never exceeded one mile per hour. It was high-water at 10 o'clock P.M., and the stream changed at the same time. The tide was therefore two hours later here than in the entrance to King's Sound, from which it would appear that the tidal wave approaches this coast from the West-South-West. April 6. We made slight progress towards Port George the Fourth, during the forenoon; the water deepening to 20 and 30 fathoms, soon after we had weighed. We espied a ridge extending to the South-east from Beagle Bank, which supplies another fact in support of the opinion I have before advanced, and which gives a north-westerly trend to these ledges. The wind failing, and the ebb-tide drifting us again to the westward, in sight of Beagle Bank, the anchor was dropped 4 1/2 miles East by North of it, and in a depth of 12 fathoms, to which we had suddenly shoaled from 29, this position marked the limit of shoal soundings in an East by North direction from Beagle Bank. Between sunset and midnight we were able to make 17 miles, in an East by North direction, when a contrary tide, and an accompanying calm, compelled us to anchor in 31 fathoms: the soundings during the run had varied from 35 to 39 fathoms: the bottom, latterly a soft mud, of a dirty grey colour. A twilight star placed our position 17 miles west of Red Island, which corresponded with the bearings at daylight. April 7.