At eleven o'clock, the south head of Broken Bay bore W. by N. three leagues; and Mr. Westall then made a sketch of the entrance, with that of the Hawkesbury River, which falls into it (Atlas, Plate XVIII, View 2). The colonists have called this place Broken Bay, but it is not what was so named by captain Cook; for he says it lies in latitude 33° 42' (Hawkesworth III. 103), whereas the southernmost point of entrance is not further than 33° 34' south. There is, in captain Cook's latitude, a very small opening, and the hills behind it answer to his description of "some broken land that seemed to form a bay," when seen at four leagues, the distance he was off; but in reality, there is nothing more than a shallow lagoon in that place. In consequence of this difference in position, Cape Three-points has been sought three or four leagues to the north of Broken Bay; whereas it is the north head of the entrance into the bay itself which was so named, and it corresponds both in situation and appearance. At noon, the south-eastern bluff of Cape Three-points bore S. 64° W., seven or eight miles, and was found to lie in 33° 32½' south and 151° 23½' east. In steering northward along the coast, at from six to two miles distance, we passed two rocky islets lying under the high shore; and at sunset, Coal Island, in the entrance of Port Hunter, bore N. 9° W., five or six miles. This port was discovered in 1797 by the late captain John Shortland, and lies in 32° 56' south, longitude 151° 43' east. We passed Port Stephens a little before midnight; and the breeze being fresh at W. by S., the Lady Nelson was left astern, and we lay to for an hour next morning [FRIDAY 23 JULY 1802], to wait her coming up. The land was then scarcely visible, but a north course brought us in with the Three Brothers (Atlas Plate IX.); and at four in the afternoon, they bore from S. 56° to 65° W., the nearest land being a low, but steep point, distant four or five miles in the first direction. The Three Brothers lie from one to five miles behind the shore, at the eastern extremity of a range of high land, coming out of the interior country. The northernmost hill is the broadest, most elevated, and nearest to the water side; and being visible fifty miles from a ship's deck, is an excellent landmark for vessels passing along the coast: its latitude is 31° 43' south, and longitude 152° 45' east.