Soon after sun-rise on the 7th, I took several azimuths, with four needles belonging to the azimuth compass, the mean result of which gave the variation 7° 56' E. At noon, our latitude, by observation, was 33° 22' S.: We were about three leagues from the shore; the northermost land in sight bore N. 19 E. and some lands which projected in three bluff points, and which, for that reason; I called _Cape Three Points_, bore S.W. distant five leagues. Our longitude from Botany Bay was 19' E. In the afternoon, we saw smoke in several places upon the shore, and in the evening, found the variation to be 8° 25' E. At this time we were between two and three miles from the shore, in twenty-eight fathom; and at noon the next day, we had not advanced one step to the northward. We stood off shore, with the winds northerly, till twelve at night, and at the distance of about five leagues, had seventy fathom; at the distance of six leagues we had eighty fathom, which is the extent of the soundings; for at the distance of ten leagues, we had no ground with 150 fathom. The wind continuing northerly, till the morning of the 10th, we continued to stand in and off the shore, with very little change of situation in other respects; but a gale then springing up at S.W. we made the best of our way along the shore to the northward. At sun-rise, our latitude was 33° 2' S. and the variation 8° E. At nine in the forenoon, we passed a remarkable hill, which stood a little way inland, and somewhat resembled the crown of a hat: And at noon, our latitude, by observation, was 32° 53' S., and our longitude 208° W. We were about two leagues distant from the land, which extended from N. 41 E. to S. 41 W., and a small round rock, or island, which lay close under the land, bore S. 82 W. distant between three and four leagues. At four in the afternoon, we passed, at the distance of about a mile, a low rocky point, which I called _Point Stephens_, on the north side of which is an inlet, which I called _Port Stephens_: This inlet appeared to me, from the mast-head, to be sheltered from all winds. It lies in latitude 32° 40', longitude 207° 51', and at the entrance are three small islands, two of which are high; and on the main near the shore are some high round hills, which at a distance appear like islands. In passing this bay, at the distance of two or three miles from the shore, our soundings were from thirty-three to twenty-seven fathom, from which I conjectured that there must be a sufficient depth of water within it. At a little distance within land, we saw smoke in several places; and at half an hour past five, the northermost land in sight bore N. 36 E. and Point Stephens S.W. distant four leagues. Our soundings in the night, were from forty-eight to sixty-two fathom, at the distance of between three and four leagues from the shore, which made in two hillocks. This Point I called _Cape Hawke_: It lies in the latitude of 32° 14' S., longitude