Ovate or cylindrical, 5 to 12.5 cm. high and about 5 cm. in diameter, simple or sparingly proliferous: tubercles terete, more or less grooved above, 8 to 12 mm. long: radial spines 20 to 30, straight, slender, with with dusky apex, very unequal, 6 to 8 mm long; central spines 4 or 5, stouter, yellowish or tawny, 8 to 12 mm. long, the upper ones the longer and more robust, the lowest one shorter and porrect: flowers 3.5 to 5.5 cm. long, about the same diameter when fully open, violet to dark purple: stigmas 7 to 9, obtuse: fruit oval and green: seeds yellowish or brown, obovate, pitted, fully 2 mm, long. (Ill. Cact. Mex. Bound. t. 74, fig.5, seeds) Type, Lindheimer of 1846 in Herb. Mo. Bot. Gard. Extending across southern Texas, from the Guadalupe to El Paso. thence into contiguous New Mexico and across the Rio Grande near Juarez (northern Chihuahua). Fl. May-June. Specimens examined: Texas (Lindheimer of 1846): New Mexico (Bigelow of 1855): Chihuahua, near Juarez (Evans of 1891): also specimens cultivated from the type in St. Louis in 1846. Attention has been called under C. viviparus to the characters that distinguish from C. radiosus The characters there given for the latter species apply to to the whole group of included forms. The type of the species is the var. Texana of Engelmann's Syn. Cact. and Mex. Bound., which is characterized in the above. description. 59. Cactus radiosus neo-mexicanus (Engelm.). Mamillaria vivipara radiosa neo-mexicana Engelm. Syn. Cact. 269 (1856). Generally lower (3.5 to 10 cm.) and subglobose to ovate or even sub-cylindrical, branching at base or simple, with more numerous (12 to 40) radial spines, more numerous (3 to 12) and purplish centrals, and smaller seeds. (Ill. Cact. Mex. Bound. t. 74. fig. 4, seeds) Type, presumably the Wright, Bigelow, and Schott specimens from western Texas, New Mexico, and Sonora, all in Herb. Mo. Bot. Gard. From southern Utah, central Colorado, and western Kansas, southward through western Texas, New Mexico and Arizona into Chihuahua and Sonora. Specimens examined: Kansas (Carleton 530 of 1891, in Meade County): Oklahoma (Carleton 233 of 1891): Colorado (Hall and Harbour of 1862; Brandegee 645 of 1873; Hicks of 1890): Utah (Siler of 1870): New Mexico (Wislizenus of 1846; Fendler 244, 271, of 1847: Wright 298; Bigelow of 1853; G. R. Vasey of 1881): Texas (Wright of 1849, 1851, 1852; Bigelow of 1853): Arizona (Rothrock, with no number or date): Sonora (Schott of 1855): Chihuahua (Evans of 1891, near Juarez). It is through this variety that C. radiosus approaches most nearly to C. viviparus, in the forms with few radials and centrals, but the specific characters seem to hold. This is the Mamillaria vivipara of the Syn Fl. Colorado (Porter and Coulter). 60. Cactus radiosus arizonicus (Engelm.). Mamillaria arizonica Engelm Bot. Calif. i. 244 (1876).