extension in the mountains between the Pecos and the Upper Rio Grande （above。 El Paso）； viz。： dasyacanthus； tuberculosus； scheerii （which has also spread somewhat east of the Pecos）； and the three pectinate and closely related forms radians； echinus； and scolymoides。 Of the four remaining Mexican forms； macromeris is a low ground Rio Grande Valley form； extending from above El Paso well towards the Lower Rio Grande； potsii just crosses the border in the neighborhood of Laredo； and radiosus and neo…mexicanus have by far the greatest northern extension； stretching from Sonora and Chihuahua to southern Utah and central Colorado； and eastward to the Guadalupe River of Texas。
The nine remaining coryphanths are distinctly forms of the United States； occupying two well…marked regions； viz。： the northern plains； and the desert region of western Arizona and adjacent California； Nevada； and Utah。 In the former region is found the widespread viviparus； which extends from the southern borders of British America to the plains of eastern Colorado and western Kansas； and even crosses the Rocky Mountain divide into northern Idaho and northeastern Washington； and missouriensis； which also ranges from the high prairies of the Upper Missouri to the same southern limit； and is continued southward into Texas in its varieties similis and robustior。
In the Arizona desert region； four distinct but closely allied forms have become differentiated from the strong radiosus stock； viz。： arizonicus； deserti； alversoni； and chloranthus； all of which might be regarded as distinct species。 In southeastern Texas is found an isolated form； sulcatus； occurring between the Brazos and Nueces rivers。 That viviparus must be regarded as a strong northern extension of the radiosus stock can not be doubted； as the low depressed cespitose northern form seems to merge southward so gradually into the simple more robust ovate to cylindrical forms of radiosus as to suggest the propriety of regarding them all as specifically identical。
The result of a closer inspection of the distribution of these nearly related forms is worthy of note。 C。 viviparus extends from British America and the Upper Missouri to eastern Colorado and western Kansas； neo…mexicanus （the form most nearly related to viviparus） extends from central Colorado and southern Utah into Mexico； at the southeastern edge of this range begins radiosus and extends eastward through southern Texas； from the western edge of neo…mexicanus the form arizonicus extends westward into southern California； touching chloranthus at its Utah limit； and at its California extension reaching alversoni and deserti； the latter of which extends northward into the desert region of southeastern California and adjacent Nevada。 Taking this type as of Mexican origin； it seems to have entered the United States from Sonora and Chihuahua； and to have spread in three directions； viz。： eastward through southern Texas； westward and northwestward into southern California and southern； Utah； and northward to the head waters of the Missouri and British America； though we would limit the northern extension of the present specific type to central Colorado； and would regard the still more northern forms as of the same origin but entitled to specific rank。
2。 ANHALONIUM Lem。 Cact。 Gen。 Nov。 （1839）。
Depressed or flattened； simple； unarmed plants； covered with peculiar imbricated tubercles above and their scale…like remains below： tubercle with lower and upper parts very different； lower part comparatively thin and flat； upper exposed part triangular in outline and divergent； very thick and hard； the lower surface smooth and keeled； the upper surface plane or convex； smooth or tuberculate or variously fissured； with a broad wool…bearing groove or simply a more or less evident tomentulose apical areola： spine…bearing areola obsolete： flower…bearing areola at the summit of the lower peduncle…like portion of the very young tubercle （thus appearing axillary with reference to the exposed part of the tubercle） and bearing a dense penicellate tuft of long soft hairs which conceals the lower part of the flower and the entire fruit and persists about the apical region of the plant as matted and apparently axillary wool： ovary naked： seeds large； black； and tuberculate： embryo obovate； straight。
According to the present views concerning generic limitations in Cactaceae； Anhalonium must certainly be kept distinct from Mamillaria； and to such a view Dr。 Engelmann had finally come。 The generic distinction is based upon such characters as （1） the complete suppression of the spine…bearing areolae； （2） the strong differentiation of the tubercles into two very distinct regions； （3） the production of the flower at the apex of the basal or penduncle…like portion （which becomes flattened and expanded at maturity） of a very young tubercle； and （4） the large tuberculate seeds。
In the case of engelmanni the broad woolly groove of the upper portion of the tubercle expands below into the flower…bearing areola； but terminates blindly above just behind the sharp apex。 In prismaticum and furfuraceum the groove is obliterated； but there usually remains a small （more or less tufted） areola and depression just behind the apex to mark its upper extremity。 This apical areola therefore； does not represent a spine…bearing areola； but the closed upper extremity of a tubercle groove。
It seems evident that Anhalonium is a much modified Cactus； and that its affinity is with the coryphanths； through such a species as C。 macromeris； in which the flower becomes extra…axillary。 If in macromeris； with the flower standing well up on the tubercle； the portions of the tubercle above and below the flower should become very different from each other； the upper portion being so much modified as to cause the spine…bearing areola to be obliterated； the condition of things in Anhalonium would be obtained。
* Upper surface of tubercle with a broad and deep wool…bearing longitudinal groove which widens below。
1。 Anhalonium engelmanni Lem。 Cact 42 （1839）。
Mamillaria fissurata Engelm。 Syn。 Cact。 270 （1856）。 Anhalonium fissuratum Engelm。 Bot。 Mex。 Bound。 75 （1859）。
Depressed globose or flat； top…shaped below and tapering into a thick root； 5 to 12 cm。 in diameter： tubercles （upper portion） appressed…imbricate； 12 to 18 mm。 long and about as wide at base； the upper surface convex and variously fissured （presenting an irregular warty appearance） even to the edges： flowers apparently central； about 2。5 cm。 long and broad； shading from whitish to rose： fruit oval； pale green； about 10 mm。 long： seeds 1。6 mm。 long。 （Ill。 Bot。 Mex。 Bound。 t。 16） Type unknown； but specimens of Wright； Bigelow； and Parry in Herb。 Mo。 Bot。 Gard。 are the basis of Engelmann's Mamillaria fissurata。
On limestone hills； in the 〃Great Bend〃 region of the Rio Grande in Texas； and southward into Coahuila。 Fl。 September…October。
Specimens examined： Texas （Wright of 1850； Bigelow of 1852； Parry； with no number or date； Lloyd of 1890； Evans of 1891； Briggs of 1892）： also growing in Mo。 Bot。 Gard。 1893。
This species is very closely related to the Mexican A。 kotchubeyi Lem。 （A。 sulcatum Salm…Dyck）； but unfortunately no type of that species seems to be in existence； and Dr。 Engelmann notes （Mex。 Bound。 Rep。 75） that 〃it seems no living or dead specimen is at present extant in Europe。〃 Judging from the description； the upper surface of the tubercles in A。 kotchubeyi； aside from the central furrow； is smooth； at least the margin is 〃very entire。〃
** Upper surface of tubercle not grooved； but usually with a tomentose pulvillus at the tip。
2。 Anhalonium prismaticum Lem。 Cact。 1 （1839）。
Mamillaria prismatica Lem。 Hort。 Univ。 i。 231 （1839）。 Cactus prismaticus Kuntze； Rev。 Gen。 Pl。 261 （1891）。
Flat above； top…shaped below； 7。5 to 12。5 cm。 in diameter： tubercles （upper portion） close＇y imbricate but squarrose… spreading； sharply triangular…pyramidal and very acute （with a sharp cartilaginous tip； which usually disappears with age and leaves the older tubercles blunt or retuse）； 18 to 25 mm。 long and about as wide at base； the upper surface almost plane and smooth； except that it is more or less pulverulent and usually bears a small tomentose pulvillus （often evanescent later） just behind the claw…like tip： flowers rose…color： fruit elongated… oval and reddish。 （Ill。 Lem。 Cact。 t。 1。） Type unknown。
Referred to Mexico in general； but reported definitely only from San Luis Potosi。 Undoubtedly found in Coahuila； and possibly crosses the Rio Grande in the region of the 〃Great Bend。〃
Specimens examined： San Luis Potosi （Eschanzier of 1891）： Mexico in general （specimens from Coll。 Salm…Dyck in 1858； Schott of 1858）： also specimens cultivated in Mo。 Bot。 Gard。 in 1881； also growing in same garden in 1893。
3。 Anhalonium furfuraceum （Watson）。
Mamillaria furfuracea Watson； Proc。 Amer。 Acad。 xxv。 150 （1890）。
Very closely related to prismaticum； but triangular portion of tubercle acuminate and shorter； having an irregularly mamillate upper surface； and the acumination ending abruptly in a cartilaginous depression containing a tomentose pulvillus： flowers 2。5 to 3 cm。 long； white or pinkish； the sepals brownish。 Type； Pringle 2580 in Gray Herb。
At Carneros Pass； Coahuila。
Specimens examined： Coahuila （Pringle 2580 of 1889）。
The type of this species was not among the collections received from Cambridge； but a specimen of the same distribution from the National Herbarium shows tubercle dimensions different from those recorded in Dr。 Watson's description。 In that description the triangular terminal surface is said to be 〃about an inch broad by one…half inch；〃 which is decidedly different from the equilateral surface of the tubercle of prismaticum。 In the National Herbarium specimen of furfuraceum； however； of the same distribution； the surface is almost equilateral； measuring 15 mm。 long by 18 mm。 wide at base。 Without the acuminate upper portion the breadth of the triangular portion would be about double its length。 The lower rim of the cup…like depression which terminates the tubercle and contains the pulvillus is sometimes slightly prolonge