[Illustration: FIG. 86.--Types of _Spadicifloræ_. _A_, inflorescence of Jack-in-the-pulpit (_Arisæma_, _Aroideæ_). The flowers (_fl._) are at the base of a spike (spadix), surrounded by a sheath (spathe), which has been cut away on one side in order to show the flowers, × ½. _B_, leaf of the same plant, × ¼. _C_, vertical section of a female flower, × 2. _D_, three male flowers, each consisting of four stamens, × 2. _E_, two plants of a duck-weed (_Lemna_), the one at the left is in flower, × 4. _F_, another common species. _L_, _Trisulea_, × 1. _G_, male flower of _E_, × 25. _H_, optical section of the female flower, showing the single ovule (_ov._), × 25. _I_, part of the inflorescence of the bur-reed (_Sparganium_), with female flowers, × ½ (_Typhaceæ_). _J_, a single, female flower, × 2. _K_, a ripe fruit, × 1. _L_, longitudinal section of the same. _M_, two male flowers, × 1. _N_, a pond-weed (_Potomogeton_), × 1 (_Naiadaceæ_). _O_, a single flower, × 2. _P_, the same, with the perianth removed, × 2. _Q_, fruit of the same, × 2.] Probably to be regarded as reduced aroids are the duck-weeds (_Lemnaceæ_) (Fig. 86, _F_, _H_), minute floating plants without any differentiation of the plant body into stem and leaves. They are globular or discoid masses of cells, most of them having roots; but one genus (_Wolffia_) has no roots nor any trace of fibro-vascular bundles. The flowers are reduced to a single stamen or carpel (Figs. _E_, _G_, _H_). The cat-tail (_Typha_) and bur-reed (_Sparganium_) (Fig. 86, _I_, _L_) are common representatives of the family _Typhaceæ_, and the pond-weeds (_Naias_ and _Potomogeton_) are common examples of the family _Naiadeæ_. These are aquatic plants, completely submerged (_Naias_), or sometimes partially floating (_Potomogeton_). The latter genus includes a number of species with leaves varying from linear (very narrow and pointed) to broadly oval, and are everywhere common in slow streams. The largest members of the group are the screw-pines (_Pandaneæ_) and the palms (_Palmæ_). These are represented in the United States by only a few species of the latter family, confined to the southern and southwestern portions. The palmettoes (_Sabal_ and _Chamærops_) are the best known. Both the palms and screw-pines are often cultivated for ornament, and as is well known, in the warmer parts of the world the palms are among the most valuable of all plants. The date palm (_Phœnix dactylifera_) and the cocoanut (_Cocos nucifera_) are the best known. The apparently compound ("pinnate" or feather-shaped) leaves of many palms are not strictly compound; that is, they do not arise from the branching of an originally single leaf, but are really broad, undivided leaves, which are closely folded like a fan in the bud, and tear apart along the folds as the leaf opens.