December the 27th, we came within the vicinity of another new discovery of a whaler, and at meridian, had it bearing, by our calculation, S.E. ten miles. We ran for it until six, P.M., December 28th, when no appearance of land being in sight, we hove about, and stood to the northward, for a newly discovered reef, which, at meridian, bore from us, by calculation N. by E., distant one hundred miles. Latitude observed, twenty-six degrees ten minutes N.; longitude, by chronometer, one hundred and seventy-six degrees fifty-one minutes, W. The reef for which we were now steering was called, by the discoverer, Clark's Reef. It was said to extend sixty miles, in a south-west and north-easterly direction, and we thought it impossible that it should escape our observation, if laid down any where near the given latitude and longitude. At nine, P.M., December the 30th, we were within twenty-five miles of the centre of the reef, by our calculation, and as it was blowing a gale, and we were scudding before it with an unusually high sea, we hove to for the night. At three, A.M., we again made sail, and ran for the centre of the reef. At meridian, December the 31st, the centre of it was still twenty miles from us, bearing N. E. by N. From meridian to one, P.M., we steered N. by E., and then bore up, and steered east all the rest of the twenty-four hours, without seeing the reef or any indications of it. At meridian, observed, in latitude twenty-six degrees forty-seven minutes, N.; longitude, by chronometer, one hundred and seventy-two degrees eleven minutes, W. We continued on to the eastward, with the hope of falling in with two islands and a reef, of another whaler's discovery. Our confidence in their given latitude and longitude, however, was quite destroyed by frequent disappointments, and we now looked for their discoveries, as we would have sought for lands, known only in the tradition of the natives of some unfrequented island, with the hope of finding them, but with little expectation of success. It happened with these, as with all the rest of the new discoveries we had looked for. We passed within a few miles of the latitude, and ran down from one to two degrees of longitude, without observing any thing that indicated the vicinity of land. On the second of January, 1826, we ran off to the southward of east for Ballard's Island. During the middle of the day, the sea, from being very heavy, became comparatively smooth, and continued so for sixty miles, when the heavy swell again set in from the westward, as before.