As no answer came this morning from the Great Man, Captain Maxwell took the ships into a more secure anchorage at the north-east corner of the bay; our first anchorage being too close to a reef, and moreover open to the south-west winds. The place we had now shifted to, though apparently exposed, is, in fact, sheltered by a chain of reefs under water outside of us to the westward. By this change, we have been brought close to the bridge spoken of before, and are now abreast the east end of the town: the Lyra not being more than a quarter of a mile from the shore. A strict watch is kept on shore, so that no boat leaves the ships without being observed. Orders have been given for the whole anchorage to be carefully sounded; in doing this, the boats often approach the shore, and whenever this happens, a crowd of the natives, headed by one or other of the chiefs, repair to the spot, and wave them to keep farther off. 21st of September.--There appears to be some embargo upon the canoes, for there has not been one near us this morning, and only one on board the Alceste. It was found necessary to-day to move the frigate still farther in, and four or five hawsers were laid out for the purpose of warping her a-head. While this was going on, the beach, and all the heights near us, were crowded with people, wondering, no doubt, how the ship was made to move without sails, for the hawsers were low down, and might have escaped their observation. In the canoe which visited the Alceste, there came two men, who had not been seen before; they remained but a short time, which was spent in examining the hawsers and the mode of warping the ship. As soon as they had made themselves master of this subject, they went on shore, as if to make a report. During their visit they said little, being intent upon what was going on; but the interpreter learnt from one of them, that a Great Man had actually come, or was expected in the town to-day. A report prevails, that the King of the island has lately been on board in disguise. We cannot trace the report to any good foundation, and it is probably false. At the same time, if his Majesty has any curiosity, it is not unlikely that he may have come near enough to see such a strange sight as we must be. It is possible that our moving up so close to the town has alarmed the people, and may have prevented their visiting us as heretofore; at all events, it is very unfair in our friends, the Chiefs, neither to let the people come on board, nor to allow us to go on shore to look at them.