Radials 9 to 22. heyderi* (5), hemisphaericus* (6), gummiferus (8), gabbii (34), sphaericus (35). *** Central spine solitary and hooked. + Stems slender cylindric: Lower Californian. Centrals 1, 20 to 30 mm. long. roseanus (23). Centrals 1 to 4, 20 to 50 mm. long. setispinus (24). ++ Stems depressed-globose to ovate. Radials 4 to 6, rigid. uncinatus (9). Radials 8 to 12. wrightii* (15). Radials 15 to 30. grahami* (19), eschanzieri (21). Radials 50 to 60. barbatus (18). **** Central spines more than one, and none of them hooked. + Slender or sometimes stout cylindrical plants, branching at base: Lower Californian. brandegei (3), setispinus (24), halei (25). ++ Depressed-globose to ovate and stout cylindrical. ++ Radials few (3 to 12) and rigid: Mexican. Radials 3: centrals 3. alternatus (1) Radials 7 or 8: tubercles 40 to 50 mm. long. longimamma (36). Radials 10 to 12: tubercles 12 to 15 mm. long. gummiferus (8). ++++ Radials numerous (16 to 60), capillary or bristle-like. Radials 15 to 30, slender but rigid (bristly). acanthophlegmus(2), densispinus (4), bispinus (14), rhodanthus (26), sulphureospinus (27), palmeri (29), pringlei (32). Radials 30 to 60 or more, mostly capillary. tetrancistrus* (22), capillaris (28), texanus* (31), spaerotrichus (33). ***** Central spines more than one and but one of them hooked. Radials 10 to 15. goodrichii* (16), setispinus (24). Radials 15 to 30. pondii (17), grahami* (19), bocasanus (20). Radials 30 to 60. tetrancistrus (22). ****** Central spines more than one, and more then one of them hooked. Radials 8 to 12. wrightii* (15). Radials 30 to 60. tetrancistrus (22). II. Tubercles with a more or less prominent groove. * Central spines none. + Radials whitish and rigid, oppressed (pectinate) and interwoven with adjacent clusters. Depressed-globose and simple. compactus (44). Globose and simple. radians* (45), corniferus (47). Cespitose. pectenoides (46), sulcatus* (49). ++ Radials more slender and spreading. Radials 10 to 17. missouriensis* (37), similis* (38), macromeris* (64). Radials 30 to 50, capillary. dasyacanthus* (51). ** Central spine solitary, not hooked. + Central spine porrect. Radials 6 to 17. missouriensis* (37), robustior* (39), scheerii* (40). Radials 30 to 50, white and capillary. dasyacanthus* (51). ++ Central spine curved downwards. Radials 8 to 12. sulcatus* (49). Radials 12 to 26. robustispinus (41), recurvatus (42), corniferus (47), scolymoides* (48). +++ Central spine erect: Mexican. Radials 7 or 8: central 50 mm. long. salm-dyckianus (43). Radials 10 or 11: central 25 to 35 mm. long. maculatus (52). Radials 13 to 16. compactus (44).