Fig. 1—VANIKORO, situated in the western part of the South Pacific; taken from the survey by Captain D’Urville in the _Astrolabe_; the soundings on the southern side of the island, namely, from thirty to forty fathoms, are given from the voyage of the Chev. Dillon; the other soundings are laid down from the survey by D’Urville; height of the summit of the island is 3,032 feet. The principal small detached reefs within the lagoon-channel have in this instance been represented. The southern shore of the island is narrowly fringed by a reef: if the engraver had carried this reef entirely round both islands, this figure would have served (by leaving out in imagination the barrier-reef) as a good specimen of an abruptly-sided island, surrounded by a reef of the fringing class. Fig. 2—HOGOLEU, or ROUG, in the Caroline Archipelago; taken from the “Atlas of the Voyage of the _Astrolabe,_” compiled from the surveys of Captains Duperrey and D’Urville; the depth of the immense lagoon-like space within the reef is not known. Fig. 3—RAIATEA, in the Society Archipelago; from the map given in the quarto edition of “Cook’s First Voyage;” it is probably not accurate. Fig. 4—BOW, or HEYOU ATOLL (or lagoon-island), in the Low Archipelago, from the survey by Captain Beechey, R.N.; the lagoon is choked up with reefs, but the average greatest depth of about twenty fathoms, is given from the published account of the voyage. Fig. 5—BOLABOLA, in the Society Archipelago, from the survey of Captain Duperrey in the _ Coquille_: the soundings in this and the following figures have been altered from French feet to English fathoms; height of highest point of the island 4,026 feet. [Illustration: Map showing the resemblance in form.] Fig. 6.—MAURUA, in the Society Archipelago; from the survey by Captain Duperrey in the _ Coquille_: height of land about eight hundred feet. Fig. 7—POUYNIPÈTE, or SENIAVINE, in the Caroline Archipelago; from the survey by Admiral Lutké. Fig. 8—GAMBIER ISLANDS, in the southern part of the Low Archipelago; from the survey by Captain Beechey; height of highest island, 1,246 feet; the islands are surrounded by extensive and irregular reefs; the reef on the southern side is submerged. Fig. 9—PEROS BANHOS ATOLL (or lagoon-island), in the Chagos group in the Indian Ocean; from the survey by Captain Moresby and Lieutenant Powell; not nearly all the small submerged reefs in the lagoon are represented; the annular reef on the southern side is submerged. Fig. 10—KEELING, or COCOS ATOLL (or lagoon-island), in the Indian Ocean; from the survey by Captain Fitzroy; the lagoon south of the dotted line is very shallow, and is left almost bare at low water; the part north of the line is choked up with irregular reefs. The annular reef on the north-west side is broken, and blends into a shoal sandbank, on which the sea breaks. Chapter I ATOLLS OR LAGOON-ISLANDS _Section I_—KEELING ATOLL