1.  Melocactus.  Stem globose; flowers in a dense cap-like head, composed of layers of bristly wool and slender spines, amongst which the small flowers are developed.  The cap is persistent, and increases annually with the stem.

2.  Mamillaria.  Stems short, usually globose, and covered with tubercles or mammae, rarely ridged, the apex bearing spiny cushions; flowers mostly in rings round the stem.

3.  Pelecyphora.  Stem small, club-shaped; tubercles in spiral rows, and flattened on the top, where are two rows of short scale-like spines.

4.  Leuchtenbergia.  Stem naked at the base; tubercles on the upper part large, fleshy, elongated, three-angled, bearing at the apex a tuft of long, thin, gristle-like spines.

5.  Echinocactus.  Stem short, ridged, spiny; calyx tube of the flower large, bell-shaped; ovary and fruit scaly.

6.  DISCOCACTUS.  Stem short; calyx tube thin, the throat filled by the stamens; ovary and fruit smooth.

7.  Cereus.  Stem often long and erect, sometimes scandent, branching, ridged or angular; flowers from the sides of the stem; calyx tube elongated and regular; stamens free.

8.  Phyllocactus.  Stem flattened, jointed, and notched; flowers from the sides, large, having long, thin tubes and a regular arrangement of the petals.

9.  Epiphyllum.  Stem flattened, jointed; joints short; flowers from the apices of the joints; calyx tube short; petals irregular, almost bilabiate.

Tribe II.—­Calyx-tube not produced beyond the Ovary.  Stem branching, jointed.

10.  Rhipsalis.  Stem thin and rounded, angular, or flattened, bearing tufts of hair when young; flowers small; petals spreading; ovary smooth; fruit a small pea-like berry.

11.  Opuntia.  Stem jointed, joints broad and fleshy, or rounded; spines barbed; flowers large; fruit spinous, large, pear-like.

12.  Pereskia.  Stem woody, spiny, branching freely; leaves fleshy, large, persistent; flowers medium in size, in panicles on the ends of the branches.

The above is a key to the genera on the plan of the most recent botanical arrangement, but for horticultural purposes it is necessary that the two genera Echinopsis and Pilocereus should be kept up.  They come next to Cereus, and are distinguished as follows: 

Echinopsis.  Stem as in Echinocactus, but the flowers are produced low down from the side of the stem, and the flower tube is long and curved.

Pilocereus.  Stem tall, columnar, bearing long silky hairs as well as spines; flowers in a head on the top of the stem, rarely produced.

With the aid of this key anyone ought to be able to make out to what genus a particular Cactus belongs, and by referring to the descriptions of the species, he may succeed in making out what the plant is.

For the classification of Cactuses, botanists rely mainly on their floral organs and fruit.  We may, therefore, take a plant of Phyllocactus, with which most of us are familiar, and, by observing the structure of its flowers, obtain some idea of the botanical characters of the whole order.