[Illustration: New Caledonia, Menchikoff Atoll, etc.] Fig. 3.—Menchikoff Atoll (or lagoon-island), in the Marshall Archipelago, Northern Pacific Ocean; from Krusenstern’s “Atlas of the Pacific;” originally surveyed by Captain Hagemeister; the depth within the lagoons is unknown. Fig. 4.—MAHLOS MAHDOO ATOLL, together with Horsburgh atoll, in the Maldiva Archipelago; from the survey by Captain Moresby and Lieutenant Powell; the white spaces in the middle of the separate small reefs, both on the margin and in the middle part, are meant to represent little lagoons; but it was found not possible to distinguish them clearly from the small islets, which have been formed on these same small reefs; many of the smaller reefs could not be introduced; the nautical mark (dot over a dash) over the figures 250 and 200, between Mahlos Mahdoo and Horsburgh atoll and Powell’s island, signifies that soundings were not obtained at these depths. Fig. 5.—NEW CALEDONIA, in the western part of the Pacific; from Krusenstern’s “Atlas,” compiled from several surveys; I have slightly altered the northern point of the reef, in accordance with the “Atlas of the Voyage of the _Astrolabe_.” In Krusenstern’s “Atlas,” the reef is represented by a single line with crosses; I have for the sake of uniformity added an interior line. Fig. 6.—MALDIVA ARCHIPELAGO, in the Indian Ocean; from the survey by Captain Moresby and Lieutenant Powell. The Great Chagos bank alone remains to be described. In the Chagos group there are some ordinary atolls, some annular reefs rising to the surface but without any islets on them, and some atoll-formed banks, either quite submerged, or nearly so. Of the latter, the Great Chagos Bank is much the largest, and differs in its structure from the others: a plan of it is given in Plate II, Fig. 1, in which, for the sake of clearness, I have had the parts under ten fathoms deep finely shaded: an east and west vertical section is given in Fig. 2, in which the vertical scale has been necessarily exaggerated. Its longest axis is ninety nautical miles, and another line drawn at right angles to the first, across the broadest part, is seventy. The central part consists of a level muddy flat, between forty and fifty fathoms deep, which is surrounded on all sides, with the exception of some breaches, by the steep edges of a set of banks, rudely arranged in a circle. These banks consist of sand, with a very little live coral; they vary in breadth from five to twelve miles, and on an average lie about sixteen fathoms beneath the surface; they are bordered by the steep edges of a third narrow and upper bank, which forms the rim to the whole. This rim is about a mile in width, and with the exception of two or three spots where islets have been formed, is submerged between five and ten fathoms. It consists of smooth hard rock, covered with a thin layer of sand, but with scarcely any live coral; it is steep on both sides, and outwards slopes abruptly