M. Grahami (Graham’s).—­A pretty little species, with globose stems, scarcely 3 in. high, and nearly the same in diameter, branching sometimes when old; tubercles 1/4 in. long, egg-shaped, corky when old, and persistent.  Spines in tufts of about twenty, all radiating except one in the centre, which is hooked; they are about 1/2 in. long.  Flowers 1 in. long, usually produced in a circle round the stem.  Fruit a small, oval berry, 1/2 in. long.  This is a native of Colorado, in mountainous regions.  It is very rare in cultivation.  The flowers are developed in June and July.

M. Haageana (Haage’s); Fig. 62.—­The habit of this is shown in the Figure, which is reduced to about one-fourth the natural size.  As the stem gets older, it becomes more elongated.  Tubercles small, four-sided at the base, pointed at the top, where the spines are arranged in a star, about twenty of them on each tubercle, with two central ones, which are longer, stiffer, and much darker in colour than those on the outside; flowers small, almost hidden beneath the spines, bright carmine-rose; they are produced on the sides of the upper portion of the stem in June.  There is a close resemblance between this and M. cirrhifera, and the treatment for both should be the same.  Mexico, 1835.

[Illustration:  Fig. 62.  Mamillaria haageana.]

M. longimamma (long-tubercled); Fig. 63.—­A well-marked species in the size of its mammae, or tubercles, which are at least 1 in. long by 1/3 in. in diameter, terete, slightly curved, and narrowed to a pointed apex, the texture being very soft and watery.  Each tubercle bears a radiating tuft of about twelve spines, one central and projecting outwards; they are pale brown when old, and white when young; their length is about 1/2 in.  A tuft of short, white wool is developed at the base of the spines on the young mammae.  The stem is seldom more than 4 in. in height, and it branches at the base when old.  Flowers large and handsome, citron-yellow; the tube short, and hidden in the mammae; the petals 11/2 in. long, narrow, pointed, and all directed upwards; stamens numerous, short.  Flowering season, early summer.  Native country, Mexico.  It requires greenhouse treatment, or it may be placed in a sunny frame out of doors during summer.  It is not easily multiplied from seeds, but is free in the production of offsets from the base of the stem.

[Illustration:  Fig. 63.  Mamillaria longimamma.]

M. macromeris (large-flowered); Fig. 64.—­Stem about 4 in. high, naked at the base, woody and wrinkled when old.  Tubercles as in M. longimamma, but with curving radial spines, like needles, often 2 in. in length, white or rose-tinted when young, almost black when old.  Flowers from the centre of the stem, 3 in. long, and about the same in width; the petals regular and spreading, as in the Ox-eye daisy; stamens numerous, short, forming a disk; colour carmine,