Under these circumstances was it possible for them to retain even the shadow of a hope? No! What was their sole remaining chance? That a vessel should appear in sight off the rock? But they knew only too well from experience that no ships ever visited this part of the Pacific. Could they calculate that, by a truly providential coincidence, the Scotch yacht would arrive precisely at this time in search of Ayrton at Tabor Island? It was scarcely probable; and, besides, supposing she should come there, as the colonists had not been able to deposit a notice pointing out Ayrton's change of abode, the commander of the yacht, after having explored Tabor Island without result, would again set sail and return to lower latitudes. No! no hope of being saved could be retained, and a horrible death, death from hunger and thirst, awaited them upon this rock. Already they were stretched on the rock, inanimate, and no longer conscious of what passed around them. Ayrton alone, by a supreme effort, from time to time raised his head, and cast a despairing glance over the desert ocean. But on the morning of the 24th of March Ayrton's arms were extended towards a point in the horizon; he raised himself, at first on his knees, then upright, and his hand seemed to make a signal. A sail was in sight off the rock. She was evidently not without an object. The reef was the mark for which she was making in a direct line, under all steam, and the unfortunate colonists might have made her out some hours before if they had had the strength to watch the horizon. "The _Duncan_!" murmured Ayrton--and fell back without sign of life. When Cyrus Harding and his companions recovered consciousness, thanks to the attention lavished upon them, they found themselves in the cabin of a steamer, without being able to comprehend how they had escaped death. A word from Ayrton explained everything. "The _Duncan_!" he murmured. "The _Duncan_!" exclaimed Cyrus Harding. And raising his hand to Heaven, he said, "Oh! Almighty God! mercifully hast Thou preserved us!" It was, in fact, the _Duncan_, Lord Glenarvan's yacht, now commanded by Robert, son of Captain Grant, who had been despatched to Tabor Island to find Ayrton, and bring him back to his native land after twelve years of expiation. The colonists were not only saved, but already on the way to their native country. "Captain Grant," asked Cyrus Harding, "who can have suggested to you the idea, after having left Tabor Island, where you did not find Ayrton, of coming a hundred miles farther north-east?" "Captain Harding," replied Robert Grant, "it was in order to find, not only Ayrton, but yourself and your companions." "My companions and myself?" "Doubtless, at Lincoln Island." "At Lincoln Island!" exclaimed in a breath Gideon Spilett, Herbert, Neb, and Pencroft, in the highest degree astonished.