We judged the extreme point of the shoal to bear from us about N.W. and the point from which it seemed to run out bore S. 3/4 W., distant twenty miles.  This point I named Sandy Cape, from two very large patches of white sand which lay upon it.  It is sufficiently high to be seen at the distance of twelve leagues, in clear weather, and lies in latitude 24 deg.45’, longitude 206 deg. 51’:  The land trends from it S.W. as far as can be seen.  We kept along the east side of the shoal till two in the afternoon, when, judging that there was a sufficient depth of water upon it to allow passage for the ship, I sent the boat a-head to sound, and upon her making the signal for more than five fathom, we hauled our wind, and stood over the tail of it in six fathom.  At this time we were in latitude 24 deg.22’, and Sandy Cape bore S. 1/2 E., distant eight leagues; but the direction of the shoal is nearest N.N.W. and S.S.E.  It is remarkable that when on board the ship we had six fathom, the boat, which was scarcely a quarter of a mile to the southward, had little more than five, and that immediately after six fathom we had thirteen, and then twenty, as fast as the man could cast the lead:  From these circumstances, I conjectured that the west side of the shoal was steep.  This shoal I called the Break Sea Spit, because we had now smooth water, and to the southward of it we had always a high sea from the S.E.  At six in the evening, the land of Sandy Cape extended from S. 17 E. to S. 27 E., at the distance of eight leagues; our depth of water was twenty-three fathom:  With the same soundings we stood to the westward all night.  At seven in the morning, we saw, from the mast-head, the land of Sandy Cape bearing S.E. 1/2 E., distant about thirteen leagues:  At nine, we discovered land to the westward, and soon after saw smoke in several places.  Our depth of water was now decreased to seventeen fathom, and by noon we had no more than thirteen, though we were seven leagues from the land, which extended from S. by W. to W.N.W.  Our latitude at this time was 24 deg. 28’ S. For a few days past we had seen several of the sea-birds called boobies, not having met with any of them before; last night a small flock of them passed the ship, and went away to the N.W.; and in the morning, from about half an hour before sun-rise, to half an hour after, flights of them were continually coming from the N.N.W. and flying to the S.S.E. nor was one of them seen to fly in any other direction; we therefore conjectured that there was a lagoon, river, or inlet of shallow water, in the bottom of the deep bay, to the southward of us, whither these birds resorted to feed in the day, and that not far to the northward there were some islands to which they repaired in the night.  To this bay I gave the name of Hervey’s Bay, in honour of Captain Hervey.  In the afternoon we stood in for the land, steering S.W. with a gentle breeze at S.E. till four o’clock, when, being in latitude 24 deg. 36’, about two leagues from