This little island _l2_ is of a triangular shape, and each side of it is a mile long; it is surrounded by a coral reef which, as usual, presented a beautiful piece of marine scenery. The stone which forms the basis of the island, and is scattered loosely over the surface, is a kind of porphyry; a small piece of it, applied to the theodolite, did not affect the needle, although, on moving the instrument a few yards southward, the east variation was increased 2° 23'. Not much vegetable earth was contained amongst the stones on the surface, yet the island was thickly covered with trees and brush wood, whose foliage was not devoid of luxuriance. Pines grow here, but they were more abundant, and seemingly larger, upon some other of the islands, particularly on _l3_, to the westward. There did not appear to be any fixed inhabitants; but proofs of the island having been visited some months before, were numerous; and upon the larger island _l_, there was a smoke. The time of high water coincided with the swinging of the ship, and took place one hour before the moon's passage, as it had done amongst the barrier reefs; from ten to fifteen feet seemed to be the rise by the shore, and the flood came from the northward. We returned on board the ship at noon; but I deferred getting under way till next morning, on account of the wind blowing fresh, and some business to be executed which could not be attended to whilst among the reefs. This gave an opportunity of making further observations by the time keepers, from which it appeared that they gave only 8' 36.3" of longitude west from Upper Head, with the rates there found; whereas by the survey, we had made 12' 37". The time keeper No. 520, taken alone, gave 11' 35.8"; and when the correction, afterwards found necessary in the Gulph of Carpentaria, is applied, the difference becomes 12' 41", almost exactly as by survey. The previous positions of the ship amongst the reefs, and wherever I had not any bearings of fixed points, have therefore been deduced from this time keeper. The _latitude_ of the anchorage, from observations to the north and south., was 20° 45' 28' S. _Longitude_ from a chain of bearings, connected with the fixed station in Broad Sound, 149° 34' 12" E. _Variation_ of the theodolite, observed on the north-west beach of _l2_, 7° 39' east; but it differed on the north head of the island, from 7° to 9° 23' east, in the space of a few yards. The variation amongst the Barrier Reefs has not been mentioned; but five azimuths and amplitudes were taken between the 6th, p.m. and the 15th a.m. When corrected to the meridian, the extremes were 7° 53' and 7° 11'; and the mean, in latitude 20° 44', longitude 150° 32', will be 7° 30' east. SUNDAY 17 OCTOBER 1802