Tuesday, 4th. A Steady fresh Trade and clear weather. At 1/2 past 10 a.m. saw land bearing south, distance 3 or 4 Leagues. Haul'd up for it, and soon found it to be an Island of about 2 Leagues in Circuit and of an Oval form, with a Lagoon in the Middle, for which I named it Lagoon Island. The Border of land Circumscribing this Lagoon is in many places very low and narrow, particularly on the south side, where it is mostly a Beach or Reef of rocks; it is the same on the North side in 3 places, and these disjoins the firm land and make it appear like so many Islands covered with wood. On the West end of the Island is a large Tree which looks like a large Tower, and about the Middle of the Island are two Cocoa Nutt Trees that appears above all the other wood, which as we approached the Island looked very much like a flag. We approached the north side of this Island within a Mile, and found no Bottom with 130 fathoms of line, nor did there appear to be Anchorage about it. We saw several of the Inhabitants, the most of them men, and these Marched along the shore abreast of the Ships with long Clubs in their hands as tho' they meant to oppose our landing. They were all naked except their Privy parts, and were of a Dark Copper Colour with long black Hair, but upon our leaving the Island some of them were seen to put on a Covering, and one or two we saw in the Skirts of the Wood was Cloathed in White; these we supposed to be Women. This Island lies in the Latitude of 18 degrees 47 minutes and Longitude 139 degrees 28 minutes West from the Meridian of Greenwich;* (* This island is Vahitahi, one of the Paumotu or Low Archipelago.) variation 2 degrees 54 minutes East. Wind East, East by South; course North 88 degrees West; distance 114 miles; latitude 18 degrees 42 minutes South, longitude 139 degrees 29 minutes West. Wednesday, 5th. A fresh steady gale and fine weather. At 1 p.m. made Sail to the Westward, and at 1/2 past 3 saw land to the North-West, which we got up with at Sun sett and proved to be a low woody Island of a Circular form, and not much above a Mile in Compass. This Island I called Thrum Cap* (* Akiaki. It is inhabited.); it lies in the Latitude of 18 degrees 35 minutes South and in the Longitude of 139 degrees 48 minutes West from Greenwich, and North 62 degrees West, 7 Leagues from Lagoon Island. We saw no inhabitants, nor the appearance of any, and yet we were within 1/2 a Mile of the Shore. I observed by the Shore that it was near low Water, and at Lagoon Island I observed that it was either high Water or else there was no Ebbing and flowing of the Sea. From these Circumstances I infer that a South by East or South Moon makes high Water. Here we caught a King Fish, being the first fish we have got in these Seas. Wind East; course North 77 degrees 30 minutes West; distance 79 miles; latitude 18 degrees 25 minutes South, longitude 140 degrees 51 minutes West.