On going to the Alceste we found that the Loo-choo surgeon had placed Captain Maxwell's broken finger in a thick paste made of eggs, flour, and some other substance which he brought along with him. He then wrapped the whole in the skin of a newly-killed fowl. This skin dried in a short time and held the paste firm, by which the broken finger was kept steady. The doctor went through a number of ceremonies, such as feeling the pulse, looking at the tongue, and so on. He had a box along with him, containing upwards of a hundred medicines. Captain Maxwell mentioned, that while he was sitting in a shed after the accident, he was surprised to see a person enter the door crawling on all fours, and half dead with terror. This it appeared was the surgeon, who had been sent for by the chiefs. He was horror-struck at the accident, but soon recovered himself on observing Captain Maxwell's perfect tranquillity. Captain Maxwell's gentleness and forbearance, and his uniform attention to the wishes of the natives, and the great personal kindness which he had shewn to so many of them, had very early won their confidence and esteem. As our intercourse became more intimate, these feelings naturally became stronger, and the concern which the natives felt upon this occasion was very general, and was expressed, not only by Madera and the chiefs, but by the lower orders, in a manner highly flattering to Captain Maxwell. 23d of October.--A deputation of the chiefs went on board the Alceste early this morning to say, that the Prince of the island, who was the next person in rank to the King, and heir to the throne, meant to come on board the frigate this afternoon, as well for the purpose of paying a visit of ceremony, as of enquiring into the state of Captain Maxwell's health after the accident.