It seems impossible to make a simple artificial key that will serve as a useful guide to each individual species and variety.Our knowledge of so many of the species is imperfect, that no set of characters can be applied throughout.However, as no plants are collected in such fragmentary condition, it will be useful to construct a key based upon such characters as are always likely to be present, even if specific distinctions are not always reached.In many cases, species are so closely and differently related to each other that the complete descriptions will have to be consulted to determine the differences, and in such cases the artificial key can only indicate the group.Even the full descriptions are very compact, all characters not necessary for discrimination having been eliminated.No attempt need be made to determine any species by means of the flowers alone.In most cases more or less of the plant body will be available, presenting spine and tubercle characters, and these are used in the following key.The distinction between Eumamillaria and Coryphantha, on the basis of grooveless and grooved tubercles should always be made outeasily.It may be useful to suggest as a caution, however, that often tubercles in drying develop folds which simulate grooves, and especially is this true in quadrangular tubercles.In such cases it is necessary to restore the original plumpness of the tubercle by boiling, before the presence or absence of the groove can be definitely determined.The species and varieties are indicated only by their specific or varietal names in the following key, and the numbers refer to the serial numbers of the synoptical presentation.Forms occurring within the United States are marked with an "":
I.Tubercles never grooved.
Central spines none.
Radials 5 to 9, stout.meiacanthus(7).
Radials 20 to 40.micromeris(12), greggii (13).
Radials 40 to 80.lasiacanthus(10), denudatus(11).
Central spine solitary and not hooked.
Central spine longer than the radials.
Radials 7 or 8: tubercles very long (40 to 50 mm.).longimamma (36).
Radials 15 to 20: tubercles 6 to 8 mm. long.eschanzieri (21).
Central spine shorter than the radials. Radials 5 to 9, stout. meiacanthus(7).
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 atbase: 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 themhooked.
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).
Central spine solitary and hooked. brunneus (53).
Central spines more than one and none of them hooked. Centrals 2: radials6 to20. scheerii(40), robustispinus(41),recurvatus (42), scolymoides(48).
Centrals 3: radials 6 to 40. scheerii(40), scolymoides(48), echinus(50), conoideus (54), neo-mexicanus(59), arizonicus(60).
Centrals 4 or 5: radials 6 to 40. scheerii(40), scolymoides(48),echinus(50), conoideus (54), tuberculosus(56), viviparus(57),radiosus(58), neo-mexicanus(59). arizonicus(60), macromeris(64).
Centrals 6 or 7: radials 12 to 40. potsii(55), tuberculosus(56),viviparus(57), neo-mexicanus(59), arizonicus(60), chloranthus (62).
Centrals 8 to 14: radials 12 to 40 or more. potsii(55), tuberculosus(56), viviparus(57), neo-mexicanus(59), deserti(61), chloranthus(62), alversoni(63).
