Globose or at length ovate, 2.5 to 7.5 cm. high, simple or branched from the base and even cespitose: tubercles ovate, 6 mm. long, dilated at base (corky and persistent when old), with naked axils: radial spines 15 to 30 in a single series, white, often dusky-tipped, slender but rigid, naked or puberulent, 6 to 12 mm. long, the shorter ones uppermost, the longer ones lateral; central spines 1 to 3, blackish from a paler base, the lower (often the only) one stouter and longer (6 to 18 mm.), hooked upward, the one or two upper ones (when present) shorter and slenderer, divergent: flowers 2 to 2.5 cm. long, rose-colored: fruit 2 to 2.5 cm. long: seeds 0.8 to 1 mm. long, black and pitted. (Ill. Cact. Mex. Bound. t. 6. figs. 1-8) Type, Wright of 1852 and Bigelow of 1852 in Herb. Mo. Bot. Gard. In rocky places, from the mountains of extreme southwestern Texas (west of the Pecos) to southern Utah, southern California (common along the Colorado), and Sonora. Fl. June-August. Specimens examined: Texas (Wright of 1852; Newberry of 1858; G. R. Vasey of 1881; Miller of 1881; Briggs of 1892): New Mexico (Evans of 1891): Arizona (Bigelow of 1852; Schott of 1858; Cous of 1865; Palmer of 1869, 1870; Engelmann of 1880; Pringle of 1884): Utah (Parry of 1874): Sonora (Schott of 1853): also specimens cultivated in the Mo. Bot. Gard. in 1881. In all references to the fruit of this species it is described as "oval and green," except in Ives Report, where Dr. Engelmann describes its real character as the ordinary fruit of Eumamillaria. The immature fruit is "oval and green," but with maturity it becomes clavate and scarlet. The Utah specimens of Parry show an exceptional character in their 30 to 33 scabrous radial spines, but otherwise they are quite normal. M. microcarpa Engelm., Emory's Rep. 156. f. 3, should be dropped as a synonym of this species, at least as to figure and description. In all probability C.grahami is one of the forms of the Mexican C. schelhasii (Pfeiff.). Except that in C. grahami the radial spines are apt to be more numerous and longer, and the centrals much darker; and in C. schelhasii the 3 centrals seem to be always present and sometimes all hooked, the descriptions suggest no difference. In the absence of authentic specimens of the latter species, however, and with its fruit and seed entirely unknown, such a reference of C. grahami must be deferred. 20. Cactus bocasanus (Poselger). Mamillaria bocasana Poselger, Gart. Zeit. 94 (1853).