Friday, 8th. Forepart of P.M. had a Gentle breeze at North-North-West, with which we stood in shore and fetched close under the Cavalle Islands. They are a Group of Small Islands lying close under the Main land, and 7 Leagues North 60 West from Cape Brett, and 3 1/2 Leagues from Point Rodney. From these Islands the Main land trends West by North. We were here Visited by several Canoes, and the People in them seem'd desirous of Trafficking with us, but at this time a breeze of wind sprung up at South, they could not keep up with the Ship, and I would not wait for them. The wind did not continue long at South before it veer'd to South-West and West, a light breeze. Found the Variation in the Evening to be 12 degrees 42 minutes East, and in the Morning 13 degrees East. Keept standing to the West-North-West and North-West until 10 A.M., at which time we tacked and stood in for the Shore, being about 5 Leagues off, and in this situation had 118 fathoms Water. At Noon Cape Brett bore South-East, distant 13 Leagues, and the Westermost land in sight bore West by South, being at this time about 4 Leagues from Land. Latitude in per Observation, 34 degrees 42 minutes South. Saturday, 9th. P.M., had a Gentle Breeze at West, which in the Evening came to South and continued so all night; this by daylight brought us pretty well in with the land, 7 Leagues to the Westward of the Cavalle Isles, and where lies a deep Bay running in South-West by West and West-South-West, the bottom of which we could but just see, and there the land appear'd to be low and level, the 2 points which form the Entrance lie West-North-West and East-South-East 5 Miles from each other. This Bay I have named Doubtless Bay;* (* There is a small settlement called Mangonui in Doubtless Bay.) the wind not permitting us to look into this Bay we steer'd for the Westermost land we had in sight, which bore from us West-North-West, distant 3 Leagues, but before we got the length of it it fell calm, and continued so until 10 o'Clock, when a breeze sprung up at West-North-West, and with it we stood off North. While we lay becalm'd, several of the Natives came off to the Ship in 5 Canoes, but were fearful of venturing alongside. After these were gone, 6 more came off; these last came boldly alongside, and sold us fish of different sorts sufficient to give all hands a little. At noon, the Cavalle Islands bore South-East by East, distant 8 Leagues, and the Entrance of Doubtless Bay South by West distant 3 Leagues, and the North-West Extremity of the Land in sight, which we judge to be the Main, bore North-West by West. Our Latitude by observation was 34 degrees 44 minutes South. [Off Rangaunu Bay, North Island, New Zealand.]