On Thursday the 7th of December, at noon, Cape Bret bore S.S.E. 1/2 E. distant ten miles, and our latitude, by observation, was 34° 59' S.; soon after we made several observations of the sun and moon, the result of which made our longitude 185° 36' W. The wind being against us, we had made but little way. In the afternoon, we stood in shore, and fetched close under the Cavalles, from which islands the main trends W. by N.: Several canoes put off and followed us, but a light breeze springing up, I did not chuse to wait for them. I kept standing to the W.N.W. and N.W. till the next morning at ten o'clock, when I tacked and stood in for the shore, from which we were about five leagues distant. At noon, the westernmost land in sight bore W. by S. and was about four leagues distant. In the afternoon, we had a gentle breeze to the west, which in the evening came to the south, and continuing so all night, by day-light brought us pretty well in with the land, seven leagues to the westward of the Cavalles, where we found a deep bay running in S.W. by W. and W.S.W. the bottom of which we could but just see, and there the land appeared to be low and level. To this bay, which I called _Doubtless Bay_, the entrance is formed by two points, which lie W.N.W. and E.S.E. and are five miles distant from each other. The wind not permitting us to look in here, we steered for the westermost land in sight, which bore from us W.N.W. about three leagues, but before we got the length of it it fell calm.