On quitting Thirsty Sound we steered north-westward, to pass round a chain of rocks extending six miles out from Pier Head, and behind which there was a bight in Long Island, with some appearance of an opening. It was my intention to examine Broad Sound up to the furthest navigable part, and we hauled up between the north point of Long Island and a cluster of small isles lying three miles to the north-west; but finding the water too shallow, and that it would be more advantageous to begin the examination on the west side, I desired Mr. Murray to lead round the _North-point Isles_ and across the sound. A small reef lies between four and five miles N. E. by E. from the largest and easternmost of these isles; it is covered at half tide, and therefore dangerous, but we had 7 to 8 fathoms at less than a mile distance, on the inside. At noon, the depth was 8 fathoms, the largest North-point Isle, which is nearly separated into two, was distant four miles, and our situation was as under: Latitude observed to the north, 21° 56' 17" Pier Head top, bore S. 38 E. Northumberland Island, peak marked 'h', N. 15 W. North-point I., westernmost, highest part, S. 56 W. North-point I., largest, S. 37 to 16 W. In steering W. by N., rippling water was seen ahead at one o'clock. and the depth diminishing to 4 fathoms, we hauled a little to the southward and then resumed our course. This rippling seems to have been on a part of the same shoal near which captain Cook anchored in 3 fathoms; for it lies five miles from the North-point Isles, and as he says, "half way between them and three small islands which lie directly without them." [EAST COAST. BROAD SOUND.] Our course for the west side of Broad Sound passed close to some low, flat isles, lying to the south-east of the peaked West Hill set from Pier Head. At dusk I sought to anchor behind the hill, for it had the appearance of being separated from the main land; but the water being too shallow, we hauled off upon a wind. At ten o'clock, however, the breeze having become light and the sea gone down, an anchor was dropped in 5 fathoms, sandy bottom; whence the top of West Hill bore N. 68° W. three miles. A flood tide was found running from the N. N. E., one mile and a quarter per hour. THURSDAY 9 SEPTEMBER 1802