The type of the genus _Thrinax_ is the Jamaican _T. parviflora_, a tree 3 to 6 metres high with the trunk swollen at base. The leaves are said to be 30–60 cm. long with rigid lanceolate divisions; the stipes longer than the leaves, terete-compressed. The spadix is said to be terminal, nearly erect and 60–90 cm. long. The tree grows in dry maritime situations in Jamaica and Santo Domingo. It does not appear that the original specimens of this species have been examined by Sargent or other recent writers, but it seems reasonable to use the name for the group of short species with uniform albumen and a basal cavity instead of a complete perforation. Swartz’s statement regarding the seed “_intus albus, medio ruber_,” in connection with its context “_nauco osseo fragile tectus_” might possibly be rendered “white inside, red between” and might refer to the red coat of the seed rather than to a red center as commonly inferred. Of course Swartz might have cut his seed transversely, but if so he would doubtless have discovered and noted the perforation had one existed. Patrick Brown’s account of the Jamaica species, cited by Swartz, evidently refers to a palm with the habits of _T. Ponceana_. On the other hand the “very slender” palm referred to under this name in the Jamaica Bulletin (=I=: 196. 1894) shows greater similarity with _Thrincoma_. =Thrinax praeceps= sp. nov. Trunk 8–12 cm. in diameter at base, columnar or slightly enlarged upward, seldom attaining over 3 or 4 meters in height. The leaf-bases split in the middle of the midrib and long remain adherent to the trunk. When they finally fall away on older trees a rather rough grayish and longitudinally chinked rimose surface is exposed. The stalks of large leaves measure 75–80 cm. in length and 1.2–1.5 cm. in width. The middle divisions of the leaf are 55 cm. and under in length and attain a width of 4.8 cm., and in the middle of large leaves are united for more than half their length. Cross-veinules numerous, distinct in both surfaces but especially the upper. The white pubescence or tomentum which clothes the young leaves and is especially abundant on the ligule soon disappears, leaving the under side glaucous or slightly pruinose. This species is described at some length a little later in a comparison of generic characters under _Thrincoma alta_. The type specimen (no. 850) was collected on the precipitous mountain-side which overhangs the road between Utuado and Arecibo, a short distance to the northward from the station where _Thrincoma alta_ was obtained. What is believed to be the same species was collected in a similar situation on the side of a mountain overlooking the town and valley of Lares. =Thrinax Ponceana= sp. nov. Plate 43