Depressed or flattened, simple, unarmed plants, covered with peculiar imbricated tubercles above and their scale-like remains below: tubercle with lower and upper parts very different; lower part comparatively thin and flat; upper exposed part triangular in outline and divergent, very thick and hard, the lower surface smooth and keeled, the upper surface plane or convex, smooth or tuberculate or variously fissured, with a broad wool-bearing groove or simply a more or less evident tomentulose apical areola: spine-bearing areola obsolete: flower-bearing areola at the summit of the lower peduncle-like portion of the very young tubercle (thus appearing axillary with reference to the exposed part of the tubercle) and bearing a dense penicellate tuft of long soft hairs which conceals the lower part of the flower and the entire fruit and persists about the apical region of the plant as matted and apparently axillary wool: ovary naked: seeds large, black, and tuberculate: embryo obovate, straight. According to the present views concerning generic limitations in Cactaceae, Anhalonium must certainly be kept distinct from Mamillaria, and to such a view Dr. Engelmann had finally come. The generic distinction is based upon such characters as (1) the complete suppression of the spine-bearing areolae; (2) the strong differentiation of the tubercles into two very distinct regions; (3) the production of the flower at the apex of the basal or penduncle-like portion (which becomes flattened and expanded at maturity) of a very young tubercle; and (4) the large tuberculate seeds. In the case of engelmanni the broad woolly groove of the upper portion of the tubercle expands below into the flower-bearing areola, but terminates blindly above just behind the sharp apex. In prismaticum and furfuraceum the groove is obliterated, but there usually remains a small (more or less tufted) areola and depression just behind the apex to mark its upper extremity. This apical areola therefore, does not represent a spine-bearing areola, but the closed upper extremity of a tubercle groove. It seems evident that Anhalonium is a much modified Cactus, and that its affinity is with the coryphanths, through such a species as C. macromeris, in which the flower becomes extra-axillary. If in macromeris, with the flower standing well up on the tubercle, the portions of the tubercle above and below the flower should become very different from each other, the upper portion being so much modified as to cause the spine-bearing areola to be obliterated, the condition of things in Anhalonium would be obtained. * Upper surface of tubercle with a broad and deep wool-bearing longitudinal groove which widens below. 1. Anhalonium engelmanni Lem. Cact 42 (1839). Mamillaria fissurata Engelm. Syn. Cact. 270 (1856). Anhalonium fissuratum Engelm. Bot. Mex. Bound. 75 (1859).