equal poles, whilst no transverse axes are differentiated. All horizontal planes which cut the axis at right angles are circles, and increase in size from the poles towards the equator. The most important ground-forms of this group are the phacoid (the lens or oblate spheroid) and the ellipsoid (or prolate spheroid). Phacoids (or geometrical lenses with blunt margins) are very often presented by the central capsules of the Discoidea and of many Acantharia (Quadrilonchida and Hexalaspida), but the lattice-shells of many Spumellaria and Acantharia exhibit the same form, as also do a few Phæodaria (e.g., Aulophacus). True geometrical ellipsoids are seen in the central capsules of many Prunoidea among the Spumellaria, and of many Amphilonchida and Belonaspida among the Acantharia. Furthermore, the lattice shells of many species of these groups retain the same essential form, e.g., many Ellipsida, Druppulida, and Spongurida (Pls. 13-17, and 39), as well as most Belonaspida. (See Gener. Morphol., Bd. i. p. 422.)
32. Allopolar-Monaxon or Conotypic Ground-Form.—The allopolar uniaxial or conotypic ground-form is characterised by the possession of a vertical main axis whose two poles are unlike, while no transverse axes are differentiated. All horizontal planes cutting the main axis at right angles are circles, and decrease more rapidly from the largest plane towards the basal than towards the apical pole. The most important ground-forms of this group are the ovoid, the cone, and the hemisphere. They often occur (and in geometrical perfection) in the egg-shaped central capsule and podoconus of the Nassellaria, as well as in the shells of several groups of this legion, particularly in the Cyrtocalpida or Monocyrtida eradiata (Pl. 51, figs. 10-13), and in many Stichocyrtida eradiata; furthermore, they are also seen among the Phæodaria, e.g., certain Challengerida (Pl. 99, figs. 19-22). (See Gener. Morphol., Bd. i. p. 426.)
33. The Regular Dipyramidal or Quadrilonchial Ground-Form.—The ground-forms whose geometrical type is the regular double pyramid are characterised by a vertical main axis which possesses equal poles, and which is crossed at its centre by several equal transverse axes. The horizontal equatorial plane is therefore a regular polygon, and divides the body into two equal regular pyramids. The simplest and commonest form of this group is the quadratic octahedron, the ground-form of the quadratic crystallographic system; its equatorial plane is a square. This regular dipyramidal ground-form occurs among the Spumellaria in the shells of the Staurosphærida as well as of many Discoidea, in which several equidistant radial spines or arms lie in the quadratic equatorial plane of the body, and project from the margin of the lenticular disc (e.g., Sethostaurus, Pl. 31; Histiastrum, Pl. 46, &c.). It is, however, among the Acantharia that the most important part is played by this ground-form (and especially by the quadratic octahedron); it forms the basis of all those Acanthometra and Acanthophracta in which twenty radial spines are disposed according to the Müllerian Law, and in which
