that leaves or leaf-scars, with tufts of thorns in their axils, may be observed on the ovary just as on the stem.--The flattened shoots of the Cactaceæ are formed in various ways, either by the compression of cylindrical axes (_Opuntia_) or, as in _Melocactus_, etc., from winged stems in which all the wings are suppressed except two. The thorns are produced directly from the growing points of the axillary buds, and are modified leaves. The axillary bud is united at its base with its subtending leaf, which as a rule is extremely rudimentary; and these together form a kind of leaf-cushion, larger in some genera than in others. This leaf-cushion attains its highest development in _Mammillaria_, in which it is a large, conical wart (see Fig. 368 _A_), bearing on its apex the tuft of thorns and rudimentary lamina.--The _seedlings_ have normal cotyledons and a fleshy hypocotyl. All the species (1,000?) are American (one epiphytic species of _Rhipsalis_ is indigenous in S. Africa, Mauritius and Ceylon), especially from the tropical table-lands (Mexico, etc.). Some species, especially those without thorns, as _Rhipsalis_, are epiphytes. _Opuntia vulgaris_, the fruits of which are edible, is naturalized in the Mediterranean. The cochineal insect (_Coccus cacti_) lives on this and some closely allied species (_O. coccinellifera_, etc.), particularly in Mexico and the Canary Islands. Several are ornamental plants. Family 9. =Polycarpicæ.= The flowers _as a rule are_ ☿, _regular_ and _hypogynous_; however in some orders they are unisexual, _e.g._ in the Myristicaceæ, or zygomorphic (in Monkshood and Larkspur in the Ranunculaceæ); in the Lauraceæ, (Fig. 386) for example, perigynous, and in _Nymphæa_ (Fig. 383) even partially epigynous flowers are typical.--The flowers are acyclic in very many of the genera of the two first orders, if not completely so, at any rate in the numerous stamens and carpels, thus denoting an old type. It is a remarkable characteristic that in the majority of the orders the number 3 prevails in the calyx and corolla; the number 5 also occurs, but the number 2 is seldom met with. Most orders have a double perianth; chorisis does not occur, suppression is rare, and the parts of the flower are developed in acropetal succession. The most characteristic feature in the order is the _free, one-leaved_, as a rule _numerous carpels_ (apocarpous gynœceum). The number of carpels in some of the last mentioned orders dwindles down to 1 (_e.g._ the _Berberideæ_ and _Myristicaceæ_). The carpels in _Nymphæaceæ_ become united into _one pistil_ (syncarpous), a condition which we also find distributed among the other orders. _Endosperm occurs in almost all_ the orders (except _e.g. Lauraceæ_). The nutritive tissue in _Cabombeæ_ and _Nymphæeæ_ is chiefly _perisperm_. [Illustration: FIG. 370.--Diagram of _Aquilegia vulgaris_: _sp_ spur. A cyclic flower.]