S hortly after Mr. Jukes-Browne's return from Barbados in 1889, he asked me to identify a collection of fossil corals which he had made on that island. A very cursory examination showed that the synonymy of the coral fauna of the West Indies was in such confusion that it would be impossible properly to execute this task, and work out the relations of these Barbadian fossils, with the material then available to me. The causes of the difficulty were as follows:—In the West Indies there are two coral faunas, one recent and the other fossil. The former has been described by the neontologists, the latter by the palæontologists; and neither school has devoted adequate attention to the work of the other. If the two faunas had been wholly distinct, this would not have mattered so much; but unfortunately they overlap, and thus the same species have been twice described. The extent to which this has been carried has been greatly increased by the fact that many late Pleistocene species have been mixed in collections with those of the older Kainozoic deposits. The synonymy has been still further complicated by the imperfection of the original figures and descriptions upon which most of the species are based. The West Indian corals were favourite objects in the collections of the early naturalists, and thus the great majority of the species date back to the works of the museographers of the last century. The illustrations given by these authors show the mode of growth and