above sea-level. In the case of many volcanic islands it is not unreasonable to conclude that a barrier reef a mile from the island-shore has a vertical thickness of 1,000 ft. This conclusion evidently rejects the idea that a barrier reef is built upon a shallow platform of non-reef origin, which appears to me as improbable as that a volcanic island rests upon a shallow foundation of non-volcanic origin. Mature Reef Plains.—Although coasts of recent submergence usually present favourable conditions for the growth of fringing or of barrier reefs, these conditions may not persist indefinitely on coasts that long remain stationary after a less recent submergence; for, if the land drained by the coastal rivers is of large-enough area, deltas, E (fig. 3), will in time not Fig. 3. only fill the drowned-valley embayments of a still-standing island, but will unite around the spur-ends and form a confluent alluvial lagoon plain, F, with a shore-line of comparatively simple pattern. As the advance or the progradation of such a plain continues, the fringing reefs on the spur-ends will be smothered with detritus. Such appears to have been the fate of many fringing reefs on the island of Tahiti, where an alluvial plain extends along much of the island-border. As the plain is still farther prograded, and as overwash of debris from the outer face to the inner slope of the outgrowing reef continues, the lagoon will be filled and converted into a mature reef plain, MP. If the outwash of alluvium still goes on, the barrier reef, R, in spite of the width it may have then attained by outward growth, will be smothered, and its corals will be killed. Thereupon the sea will attack the reef and cut it away; and if this process be once begun there appears to be no reason for it to stop. The alluvial reef plain must in time be consumed, and then the central island will be attacked and cliffed; for as long as the island stands still, and as long as outwashed alluvium supplies material for a beach, coral growth cannot be re-established (Davis, 1917A). This sequence of events is evidently hypothetical in a high degree; nevertheless, the successive stages of such a sequence, and of all other reasonable sequences, should be carefully conceived by an observer of coral reefs while he is still on his voyage of investigation, in order that he may be able to confront the successive stages of the various sequences with the reefs that he sees, and thus discover which sequence gives the best history of their origin. The danger of being buried and smothered in alluvium appears to threaten the barrier reef along the south coast of Viti Levu, Fiji, where the delta of the Rewa River has almost filled the lagoon; and a long stretch of the barrier reef on the south side of New Guinea appears to be