126 
**** Central spines more than one and none of them hooked. 
Centrals 2: radials 6 to 20. 
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), scolyimoides (48), echinus (50), conoideus (54), tuberculosus (56), vivi- 
parus (57), radiosus (58), neo-mexicanus (59), arizonicus (60), macromeris (64). 
Centrals 6 or 7: radials 12 to 40. 
potsit (55), tuberculosus (56), viviparus (57), neo-mexicanus (59), arizonicus (60), 
chloranthus (62). 
Centrals 8 to 14: radials 12 to 40 or more. 
potsit (55), tuberculosis (56), vwviparus (57), neo-mexicanus (59), deserti (61), chlor- 
anthus (62), alversoni (63). 
GEOGRAPHICAL DISTRIBUTION, 
It is only possible to deal with the forms that occur within the bor- 
ders of the United States, as even individual stations of common Mex- 
ican forms are little if at all known. These United States forms repre- 
sent a northern extension of an abundant Mexican display. The group 
EUMAMILLARIA, containing twelve of the thirty-one forms defined as 
occurring north of the Rio Grande, makes the feeblest extension north- 
ward, at no place being found far from the boundary, and all the twelve 
are Mexican forms which extend but slightly into the United States. 
Only five of the forms are found east of the Pecos: heyderi, the most 
widely distributed KUMAMILLARIA, extending from the southeastern 
border of Texas westward along the whole Mexican boundary except 
in California; hemisphericus, extending through southern Texas and 
southern New Mexico; meiacanthus, also along the Mexican border of 
Texas and New Mexico; teranus, a low ground form of the Rio Grande 
Valley, extending from the mouth of the river to El Paso, and suggest- 
ing a connection with the West Indian stellatus; and sphaericus, another 
low ground valley form of similar range, but apparently only extending 
up the Kio Grande to the region of Eagle Pass. 
The Pecos forms the eastern boundary of five other EUMAMILLARIA 
forms: micromeris, extending northward from Coahuila and Chihuahua, 
apparently only in the mountains between the Pecos and El Paso; 
wrighttt, of similar narrow northward extension, but ranging further 
northward on the high plains of the Upper Pecos in New Mexico; 
denudatus, also with a narrow northward extension west of the Pecos: 
lasiacanthus, extending from Chihuahua with a northern limit between 
the Pecos and Arizona; and grahami, a Sonoran type which has spread 
between the Pecos and southeastern California. 
The ten preceding forms have evidently entered our borders from the 
highlands of Sonora and Chihuahua, with the exception of the Rio 
Grande Valley forms, teranus and sphericus. Another species, tetran- 
eistrus, is also a Sonoran type which has reached the eastern slopes of 
