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； and all the species studied have been arranged in a lineal series of uniform prominence。 So far as known the subject of geographical distribution is considered； but it will be seen how meager is our knowledge of this subject。 It is to be hoped that this preliminary presentation will provoke exploration and study； and that species will not only be collected； but all the facts of their distribution noted。 It is more than probable that our present notion of species in this group must be much modified； and doubtless many forms are at present kept specifically distinct which will prove to be but different phases of a single species。
In the matter of generic delimitation we are in still greater uncertainty； and several generic lines at present recognized must be regarded as purely arbitrary； a fact which must become still more evident with additional material。 The whole group is to be regarded as made up of poorly differentiated forms and only long observation under cultivation can determine the possibilities of specific variation under the influence of environment； of age； of inherent tendencies。 For instance； that these plants change in form and in spine characters with increasing age and after they have begun to flower can not be doubted； but what described forms have thus been separated in descriptions can only be guessed at。
John M。 Coulter。 Lake Forest University； Lake Forest； Ill。； January； 1891。
CACTUS； ANHALONIUM； AND LOPHOPHORA。
1。 CACTUS Linn。 Sp。 Pl。 466 （1753）； restricted。
MAMILLARIA Haw。 Synop。 177 （1812）； not Stackh。 （1809）。
Usually globose to oblong plants （simple； branching or cespitose）； but sometimes slender…cylindrical； covered with spine…bearing tubercles： flower…bearing areola axillary （with reference to tubercles）； entirely separate from the terminal spine…bearing areola； although sometimes （Coryphantha） connected with it by a woolly groove along the upper face of the tubercle： ovary naked： seeds smooth or pitted： embryo usually straight； with short cotyledons。 Originally defined by Linnaeus in his Systema； ed。 l （1735）。
The Linnaean genus Cactus of 1753 included 22 species and was coextensive with the present order。 In 1812 the species were separated by Haworth into five genera； the original generic name Cactus being discarded。 Among these species C。 mamillaris seems to have stood as the type； not only of the Linnaean genus Cactus； but also of Haworth's Mamillaria； and as such should retain the original generic name。 Besides； Mamillaria was used as the generic name of an alga in 1809。 Cactus mamillaris L。 is the West Indian Mamillaria simplex Haw。
From one point of view the two sections of the genus （Eumamillaria and Coryphantha） deserve generic separation； for the character of grooveless and grooved tubercles seems to hold without exception； and the sections are separated with more certainty than are certain species of Coryphantha and Echinocactus。 If genera are simply groups of convenience the separation should be made。
I。 EUMAMILLARIA。 Flowers from the axils of the older or full…grown tubercles （hence usually appearing lateral）； mostly small； and generally from whitish to pink or red： tubercles never grooved： fruit almost always clavate and scarlet。
A。 Tubercles more or less quadrangular。
* Central spines not hooked。 ＋ More than one central spine。
1。 Cactus alternatus； sp。 nov。
Subglobose； 10 cm。 in diameter； simple： tubercles long （15 to 20 mm。） and spreading； with woolly axils： radial spines 3； rigid and recurved； 5 mm。 long； central spines 3； very stout and much recurved； 20 to 30 mm。 long； alternating with the radials； all ashy colored and often twisted： flower and fruit unknown。Type in Herb。 Coulter。
The few spines； with the very short radials alternating with the very long and stout centrals； furnish a striking character。 Occasionally one of the centrals is wanting。
2。Cactus acanthophlegmus （Lehm。） Kuntze； Rev。 Gen。 Pl。 260 （1891）。
Mamillaria acanthophlegma Lehm。 Delect。 Sem。 Hamb。 （1833）
Subglobose with a deeply depressed vertex； or becoming cylindrical； 3 to 8。5 cm。 in diameter： tubercles sharply quadrangular…conical； with densely woolly axils： radial spines 15 to 30； white； very slender （bristly） and radiant； sometimes coarse capillary； 4 to 7 mm。 long； interwoven with those of neighboring tubercles and so covering the whole plant； central spines 2 to 4； robust and straight； erect or divergent； whitish or reddish； black…tipped； 5 to 6。5 mm。 long： flowers reddish； 1 to 2 cm。 broad： fruit unknown。 Type unknown。
From Coahuila and San Luis Potosi to Oaxaca。 Fl。 May。
Specimens examined： Coahuila （Poselger of 1856； Pringle 3116 of 1890）： San Luis Potosi （Eschanzier of 1891）。
The central spines are quite variable in number and arrangement。 In case there are two they are vertically placed and are either erect and parallel or widely divergent。 Even three centrals may occur in the same vertical plane； but more usually the three or four centrals are arranged about a center and are widely divergent。 The tubercles are apt to persist and to become naked and corky with age。 The axillary wool and the capillary radials are also apt to be more or less persistent； thus giving the whole plant a woolly appearance。
3。Cactus brandegei； sp。 nov。
Cylindrical： tubercles sharply quadrangular…conical； 6 to 8 mm。 long； with densely woolly axils： radial spines about 10； slender and rigid； whitish with dusky tips； spreading but not radiant； 7 to 10 mm。 long； central spines 3 or 4； stouter and slightly longer； erect…spreading （sometimes slightly curved）； reddish…brown below； becoming blackish above： flowers small （scarcely longer than the tubercle？）： fruit unknown。 Type in Herb。 Calif。 Acad。
San Jorge； Lower California。 Fl。 April。
Specimens examined： Lower California （Brandegee of 1889； at San Jorge）。
The species has somewhat the spine characters of C。 palmeri； but the sharply quadrangular and longer tubercles with axillary wool free from bristles suggest a very different affinity。
4。Cactus densispinus； sp。 nov。
Globose； 7。5 cm。 in diameter； simple： tubercles short； with woolly axils： radial spines about 25； erect…spreading； slender but rigid； yellow （brownish to black with age）； unequal； 8 to 10 mm。 long； central spines 6； a little longer （10 to 12 mm。） and straight； more rigid and darker； black…tipped： seeds obovate； reddish…brown； 1 mm。 long。 Type in Herb。 Coulter。
Very easily distinguished by its dense； erect spines； which so completely cover the plant as to give it the appearance of a large chestnut bur。 Another much smaller form； which seems to be a variety； has stouter and longer ashy…white spines； the centrals darker…tipped； and the lower centrals slightly curved。
＋＋ One short central spine （rarely two or none）： ovaries immersed： seeds small； yellow and rugulose： simple。
5。Cactus heyderi （Muhlenpf。） Kuntze； Rev。 Gen。 Pl。 260 （1891）。
Mamillaria heyderi Muhlenpf。 Allg。 Gart。 Zeit。 xvi。 20（1848）。 Mamillaria declivis Dietr。 Allg。 Gart。 Zeit。 xviii。 235 （1850）。 Mamillaria applanata Engelm。 Pl。 Lindh 198 （1850）。 Mamillaria texensis Labouret； Monogr。 Cact。 89 （1858）。
Depressed； globose； us