The Stylosphærida (Pls. [13]-[17]) can be derived from the Cubosphærida by reduction of two dimensive axes and loss of two pairs of spines. Therefore, here one pair of spines only is developed, opposite in one single axis. This "monaxonial" form brings the Stylosphærida very near to the ellipsoidal Prunoidea (mainly to many two-spined forms of Ellipsida and Druppulida); but they differ from these by the spherical (not ellipsoidal) form of the central capsule and of the enclosing lattice-shell. In the greater part of the Stylosphærida both spines are of equal size and form, accurately opposite in the "main axis." But in many forms both spines become unequal in size or form, often very different. More rarely they are not accurately opposed, but placed in two different axes, intersecting at a small variable angle. The small group of Saturnalida presents a very remarkable and peculiar structure, in which both spines (at equal distances from the centre) are united by a circular or elliptical ring (Pl. [13], figs. 15, 16; Pl. [16], figs. 16, 17).
The Astrosphærida are distinguished from the other Sphæroidea by the great and variable number of their external radial spines (Pls. [11], [18]-[20], [26]-[30]). Commonly this number amounts to from twelve to twenty, rarely to only eight to ten, very often to thirty-two to forty or more; in many species more than one hundred are present. As already mentioned above, it would be important to distinguish between primary spines (as outer prolongations of the inner radial beams) and secondary spines (developed from the surface of the shell), but in many cases this distinction is difficult or impossible. More practical is the distinction between larger "main spines" and smaller "by-spines." The size and form of the radial spines is extremely variable. Much more important is their number and disposition. In general we can here distinguish the following different cases:—(A) radial spines are developed from all the nodal points of the network on the shell surface; (B) the number of the spines is smaller than that of the nodal points, but they are irregularly scattered; (C) the radial spines exhibit a limited number and a certain regular disposition. In this latter case the following modes of distribution seem to be the most important:—(a) eight spines placed in the four diagonal axes of the regular cube (Pl. [18], figs. 1-3); (b) twelve spines (placed in the corner axes of the regular icosahedron); (c) fourteen spines (six placed in the three dimensive axes of the regular octahedron, eight in the centres of its eight faces); (d) twenty spines (placed either in the same order as in many Larcoidea and Acantharia [?], or in the twenty corners of the regular dodecahedron); (e) thirty-two spines (twelve placed in the twelve corners of the regular icosahedron, twenty in the centre of its triangular faces). Besides these most important and quite geometrical modes of disposition there also seem to occur in the Astrosphærida the following subregular (or symmetrical?) modes: 9, 10, 16, 18, 24, 40, 60, 80. But it is very difficult to give a correct account of these modes. In every case this manifold and regular disposition of the radial spines is of the highest interest for the study of general "Promorphology."
The Central Capsule is in all Sphæroidea (without any exception) a perfect sphere in the geometrical sense, even in those forms in which the enclosing lattice-shell is more or less irregular (i.e., many Collosphærida). This is the most important character, which separates the Sphæroidea from all other Sphærellaria. For in the Prunoidea the capsule is ellipsoidal, with one prolonged axis; in the Discoidea lenticular, with one shortened axis; in the Larcoidea lentelliptical, with three different dimensive axes. The central capsule is originally always enclosed by the lattice-shell; but in many cases with increasing growth this relation becomes inverted; the capsule sending out many club-shaped blind sacs through the meshes of the lattice-shell, and these melting together outside the latter, a new membrane is formed, enclosing a "medullary shell."
The Nucleus of the cell exhibits a very different shape in the solitary and the social Sphæroidea. In the solitary or monozoic Sphæroidea the centre of the central capsule is occupied by a large spherical concentric nucleus, with or without nucleoli; also this nucleus is originally always within the innermost lattice-shell, but with increasing size may overgrow and enclose it. A short time before the formation of the vibratile spores the central nucleus becomes resolved into many small nuclei. In the social or polyzoic Sphæroidea—the Collosphærida—commonly the simple central nucleus very early (a long time before the formation of the spores) is divided into a great number of small nuclei, whilst the centre of the capsule becomes filled with a large oil-globule. Therefore we find the same difference between the solitary and social forms in the Sphæroidea as in the Colloidea. Here also the calymma, or the jelly-mantle, enveloping the central capsule, is in the social forms very large and voluminous, differentiated into alveoles, whilst in the solitary forms it is much smaller, without alveoles.
Synopsis of the Families of Sphæroidea.
| Surface of the spherical shell smooth, rough, or thorny, but not armed with radial spines. |  | A. Liosphærida monozoa. Single cells (each with shell) living solitary. |  | Spherical shell commonly quite regular, simple, or composed of two or more concentric spheres, | 05. Liosphærida. |
| B. Liosphærida polyzoa. Aggregated cells (each with shell) living in colonies. |  | Spherical shell commonly more or less irregular, simple (rarely composed of two concentric spheres), | 06. Collosphærida. | ||
| Surface of the spherical shell armed with two, four, or six radial main spines, opposite in pairs in one, two, or three dimensive axes (always solitary). |  | Two radial main-spines, opposite in one axis of the shell | 07. Stylosphærida. | ||
| Four radial main-spines, opposite in pairs in two dimensive axes, perpendicular one to another, | 08. Staurosphærida. | ||||
| Six radial main-spines, opposite in pairs in three dimensive axes (perpendicular one to another), | 09. Cubosphærida. | ||||
| Surface of the spherical shell covered with numerous (commonly irregularly disposed) radial spines, often also twelve to twenty, more or less regularly disposed, | 10. Astrosphærida. | ||||
| Surface of the spherical shell smooth, rough, or thorny, but not armed with radial spines. | ||||||
| A. Liosphærida monozoa. Single cells (each with shell) living solitary. | ||||||
| Spherical shell commonly quite regular, simple, or composed of two or more concentric spheres, | ||||||
| 5. Liosphærida. | ||||||
| B. Liosphærida polyzoa. Aggregated cells (each with shell) living in colonies. | ||||||
| Spherical shell commonly more or less irregular, simple (rarely composed of two concentric spheres), | ||||||
| 6. Collosphærida. | ||||||
| Surface of the spherical shell armed with two, four, or six radial main spines, opposite in pairs in one, two, or three dimensive axes (always solitary). | ||||||
| Two radial main-spines, opposite in one axis of the shell | ||||||
| 7. Stylosphærida. | ||||||
| Four radial main-spines, opposite in pairs in two dimensive axes, perpendicular one to another, | ||||||
| 8. Staurosphærida. | ||||||
| Six radial main-spines, opposite in pairs in three dimensive axes (perpendicular one to another), | ||||||
| 9. Cubosphærida. | ||||||
| Surface of the spherical shell covered with numerous (commonly irregularly disposed) radial spines, often also twelve to twenty, more or less regularly disposed, | ||||||
| 10. Astrosphærida. | ||||||
Family V. Liosphærida, Haeckel, 1881.
Liosphærida, Haeckel, 1881, Prodromus, p. 449.
Definition.—Sphæroidea without radial spines on the surface of the spherical shell; living solitary (not associated in colonies).