ROUTE FROM NEW ZEALAND TO OTAHEITE, WITH AN ACCOUNT OF SOME LOW ISLANDS, SUPPOSED TO BE THE SAME THAT WERE SEEN BY M. DE BOUGAINVILLE. On the 7th of June, at four in the morning, the wind being more favourable, we unmoored, and at seven weighed and put to sea, with the Adventure in company. We had no sooner got out of the sound, than we found the wind at south; so that we had to ply through the Straits. About noon the tide of ebb setting out in our favour, made our boards advantageous; so that, at five o’clock in the evening, Cape Palliser, on the Island of Eahei-nomauwe, bore S. S. E. 1/2 S. and Cape Koamaroo, or the S. E. point of the sound, N. by W. 3/4 W. presently after it fell calm, and the tide of flood now making against us, carried us, at a great rate, back to the north. A little before high-water, the calm was succeeded by a breeze from the north, which soon increased to a brisk gale. This, together with the ebb, carried us, by eight o’clock the next morning, quite through the Strait. Cape Palliser, at this time, bore E. N. E. and at noon N. by W. distant seven leagues. This day at noon, when we attended the winding up of the watches, the fusee of Mr. Arnold’s would not turn round; so that, after several unsuccessful trials, we were obliged to let it go down. After getting clear of the Straits, I directed my course S. E. by E. having a gentle gale, but variable, between the north and west. The late S. E. winds having caused a swell from the same quarter, which did not go down for some days, we had little hopes of meeting with land in that direction. We, however, continued to steer to the S. E. and on the 11th, crossed the meridian of 180°, and got into the west longitude, according to my way of reckoning. On the 16th, at seven in the morning, the wind having veered round to S. E. we tacked and stretched to N. E. being, at this time, in the latitude of 47° 7ʹ longitude 173° west. In this situation we had a great swell from N. E. The wind continued at S. E., and S. S. E. blew fresh at intervals; and was attended with sometimes fair, and at other times rainy weather, till the 20th; on which day, being in the latitude of 44° 30ʹ, longitude 165° 45ʹ west, the wind shifted to the west, blew a gentle gale, and was attended with fair weather. With this we steered E. by N., E. by S., and E. till the 23d at noon, when, being in the latitude of 44° 38ʹ south, longitude 161° 27ʹ west, we had a few hours’ calm. The calm was succeeded by a wind at east, with which we stood to the north. The wind increased and blew in squalls, attended with rain, which at last brought us under our courses; and at two o’clock in the afternoon of the next day, we were obliged to lie to, under the foresail; having a very hard gale from E. N. E. and a great sea from the same direction.