9. Cornigerus, Dc

Globose or depressed-globose, 10-16 in. diam.: ribs about 21, very acute and wavy (not tuberculately interrupted): radial spines 6-10, white and comparatively slender, or wanting; centrals red and very robust, angular-compressed, with long, sharp, horny tips, the upper 3 erect-spreading, 1-1 1/2 in. long, the lower 2 weaker and declined, the central one longer, more rigid and keeled, very broad (1/5-1/3 in ) and hooked downward: flowers purple, 1-1 1/2 in. long. Mex.

10. Polyancistrus, Engelm. & Bigel

Ovate or at length subcylindric, becoming 4-10 in. high and 3-4 in. diam.: ribs 13-17, obtuse, tuberculately interrupted: radial spines 20 or more, compressed and white, the uppermost wanting, the 4 upper ones broader and longer (1-2 in.) and dusky-tipped, the laterals shorter (4/5-l in.), the lowest very short (1/2in.) and subsetaceous; central spines of several forms, the uppermost one (rarely a second similar but smaller one above or beside it) compressed-quadrangular, elongated (3-5 in.), white with dusky tip, curved upward, the other 5-10 teretish or subangled, bright purple-brown; upper ones long (2-4 in.) and mostly straight, the others gradually shortening (to about 1 in.) downward and sharply hooked: flowers red or yellow, 2-2% in. long and wide. Nev. and S. E. Calif.

aa. Spines not hooked (Nos. 11-48). b. Central spines none or indistinct.

11. Monvillii, Lem

Stout, globose and bright green: ribs 13-17, tuberculate, broadest toward the base, undulate; tubercles somewhat hexagonal, strongly dilated below: radial spines 9-12, the lower ones somewhat longer, very stout, spreading, yellowish translucent, reddish at base; central wanting: flowers varying from white to yellow and red. Paraguay.

12. Pfeififeri, Zucc

Oblong-globose, becoming 1-2 ft. high and 1 ft. diam.: ribs 11-13, compressed and somewhat acute: spines 6, about equal, rigid, straight, divergent or erect, pale transparent yellow with a brownish base; very rarely a solitary central spine. Mex.

13. Coptonogdnus, Lem., variety Major, Salm-Dyck

Depressed, from a large indurated naked napiform base, 2-4 in. across the top: ribs 10-15, acute from a broad base, more or less transversely interrupted and sinuous: spines 3, annulate, very stout and erect from deeply sunken areoles, reddish when young, becoming ashy gray; upper spine stoutest, erect and straight, or slightly curved upward, flattened and keeled, and occasionally twisted, l 1/2-2 1/4 in. long; the 2 laterals erect-divergent, straight or slightly curved, terete above and somewhat quadrangular below, 1-1 1/2 in. long; all from an abruptly enlarged base: flowers said to be small and white, with purplish median lines. Mex.

14. Multicostatus, Hildmann

Depressed-globose: ribs very numerous, 90-120, compressed into thin plates which run vertically or are twisted in every direction: spines exceedingly variable, in some cases wanting entirely, in others 3 or 4, short, rigid, and translucent yellow; in others more numerous, larger, and often flattish; in still other cases very long and flat, interlacing all over the plant; no centrals: flowers white, with a broad purple stripe. Mex.

15. Capricornis, A. Dietr

Globose: ribs about 11, broad, spotted all over with white dots: clusters of spines distant, usually seen only near the apex; spines 5-10, long and flexuous; centrals not distinct: flowers large, yellow. Mex.

16. Rinconensis, Poselg

Cylindrical, covered with ivory-white spines which are tipped with crimson: spines 3, with no centrals: flowers large, purple-crimson, darker at base. N. Mex.

17. Phyllacanthus, Mart

From globose to cylindrical, with depressed vertex, simple or proliferous, 2 1/3-3 3/5 in. broad: ribs 40-55 (sometimes as few as 30), very much crowded and compressed, thin, acute, very wavy, continuous or somewhat interrupted: radial spines 5 (sometimes 6 or 7), straight and spreading, the 2 lowest ones white, rigid, 1/6- 1/4in. long, half as long as the 2 darker, angled, larger laterals, the uppermost spine thin and broad, channeled above, faintly annulate, flexible, grayish pink, 3/5-l in. long; central spines none: flowers small, dirty white. Mex.

bb. Central spine solitary (sometimes 2-4 in E. cris-patus, E. helophorus, and E. setispinus, or wanting in E. lophothele).

c. stems with less than 13 ribs.

18. Leucacanthus, Zucc

Somewhat clavate-cylindri-cal, pale: ribs 8-10, thick, obtuse, strongly tuberculate, the areoles with strong wool: radial spines 7 or 8, similar, straight, finely pubescent, at first yellowish, at length white; central spine solitary, more or less erect, rarely wanting: flowers light yellow. Mex.

19. Ornatus, Dc. (E. Mirbellii, Lem.)

Subglobose: ribs 8, broad, compressed, vertical, thickly covered with close-set white woolly spots, making the whole plant almost white: radial spines 7, straight, stout, yellowish or becoming gray; central spine solitary. Mex.

20. Ingens, Zucc. (E. Visnaga, Hook.)

Very large (sometimes as much as 10 ft. high and as much in circumference), globose or oblong, purplish toward the top: ribs 8, obtuse, tuberculate: areoles large, distant, with very copious yellowish wool: radial spines 8 or more; central spine solitary; all the spines shaded yellow and red or brownish, straight, rigid, and interwoven: flowers bright yellow, about 3 in. broad. Mex.

21. Horizonthalonius, Lem

Glaucous, depressed-globose or at length ovate or even cylindric with age, 2-8 in. high, 2 1/2- 4 in. diam.: ribs 8-10 (fewer in very young specimens), often spirally arranged, the tubercles scarcely distinct by inconspicuous transverse grooves: spines 6-9, stout, compressed, reddish (at length ashy), recurved or sometimes almost straight, nearly equal, 4/5-1 1/2 in. long (sometimes long and slender and almost terete, sometimes short, stout and broad); radials 5-8, upper ones weaker, lowest wanting; a single stouter decurved central (sometimes wanting): flowers pale rose-purple, 2 1/2 in. long or more. New Mex. and N. Mex.

cc. stems with 13-27 ribs.