The Monosphærida comprise all those Sphæroidea in which the carapace is represented only by one single lattice-shell. Originally this shell is probably everywhere an extracapsular or "cortical shell," which is developed on the outside of the jelly-veil enveloping the central capsule, and serves as a protective carapace for these soft enclosed parts. But with the progress of growth the central capsule becomes larger than the including shell, and sends out through its pores club-shaped prolongations or cæcal-sacs (Pl. 11, figs. 1, 5; Pl. 19, figs. 2, 3, 5; Pl. 20, fig. 1a; Pl. 27, fig. 3). These protruded sacs may fuse together again outside the shell and form a spherical bladder, now enveloping the smaller shell; the latter now becomes an intracapsular or "medullary shell."

As Pliosphærida (or Sphæroidea concentrica) we can oppose to the simple Monosphærida all other Sphæroidea, the lattice-shell of which is composed of two or more concentric shells, connected by radial beams. Probably all Pliosphærida (or at least the greater part of them) arise from the Monosphærida by centrifugal growth; two or more radial spines are developed from the surface of the simple lattice-sphere, and are united together by communicating lateral branches, developed at equal distances from the centre; and this same process may be repeated, two, three, four, or more times. In this way originate the characteristic systems of concentric spheres, all united by piercing radial beams which arise from the surface of the innermost sphere (not from its centre). Regarding this mode of growth, we can distinguish the innermost as "original" or "primary" shell, and all subsequent ones as "apposed" or "secondary" shells; if the number of concentric shells amount to three or more, commonly both innermost shells lie within the central capsule and are medullary shells, whilst all others lie outside it and are therefore cortical shells. This difference can be commonly recognised also in the isolated shell, without its central capsule; the distance between the cortical and the medullary shells being commonly much larger than the distance between the two medullary shells.

The Dyosphærida, or the Sphæroidea with two concentric shells, are the most numerous among the Pliosphærida. Commonly in this group the inner or primary shell lies within the central capsule as a true "medullary shell," whilst the outer lies outside it as a "cortical shell"; therefore the radial beams, connecting both, pierce the wall of the capsule. But in several forms, mainly in the peculiar group of Diplosphærida, both concentric shells remain outside the central capsule, and both are therefore "cortical shells."

The Triosphærida, or the Sphæroidea with three concentric shells, are also very rich in different forms, though not so numerous by far as the Dyosphærida. Commonly in the Triosphærida both inner shells lie within the central capsule as "medullary shells," whilst the third lies outside it as a "cortical shell"; therefore the central capsule remains intermediate in size between the outer and the middle shell. But in some genera (e.g., Rhodosphæra) both outer shells are cortical and only the innermost is a medullary shell. In this case the size of the capsule remains intermediate between the inner and the middle shell.

The Tetrasphærida, or the Sphæroidea with four concentric shells, are in general not frequent, and not rich in different forms. In most of the observed species two inner shells are medullary, two outer cortical shells, the former within, the latter without, the central capsule; and the wall of the capsule, pierced by the connecting radial beams, lies between the two middle shells. But there are some Tetrasphærida in which all four shells seem to be external or cortical shells.

The Polysphærida, or the Sphæroidea with five or more concentric shells, seem of course to offer the greatest possibility for the development of very different forms; but in reality this group is the poorest and smallest of all; and only one part of it, the Arachnosphærida, is rather common. In this peculiar division the shell is composed of five to ten or more, very delicate, cobweb-like concentric shells, which are connected by radial beams; all are cortical shells, and lie outside the central capsule. Much more rare are those Polysphærida, in which both innermost shells, as true medullary shells, lie within the central capsule, all others being outside it. The total number of concentric shells in this group is commonly between five and ten, rarely more.

The Spongosphærida are distinguished from all other Sphæroidea by the spongy structure of the spherical shell, which is composed wholly or partially of an irregular spongy framework. The relation of this group to the other groups of Sphæroidea is probably rather complicated, for in some Spongosphærida the whole shell is composed of massive spongy reticulation, whilst in others it contains a spherical central cavity, and in a third group this cavity is filled up by one or two concentric lattice-shells, connected by radial beams. Many of these Spongosphærida are very common, and of considerable size.

The Collosphærida form a peculiar separate group of Sphæroidea, distinguished from all others by their social life or aggregation in colonies (cœnobia). They represent the only group of Sphærellaria in which this association of numerous individual capsules or cells is realised. The shell is almost constantly simple, without regularly disposed radial spines; therefore they may be called "social Monosphærida," or better "polyzoic Ethmosphærida." Only in one small group (Clathrosphærida) the shell, enveloping every central capsule, is double or surrounded by an external mantle; these may be compared to the Diplosphærida (or better to a part of the Carposphærida, Liosphæra, p. 76). In most of the Collosphærida the lattice-shell is more or less irregular in form and structure.

The Lattice Work of the fenestrated shells is in the Sphæroidea of the greatest variability, and its innumerable modifications serve mainly for the distinction of species. In general we can distinguish as the most important modifications a regular network (with equal size, form, and distance of the pores or meshes) and an irregular network (with differences in the size, form, or distance of the meshes or pores). In both groups the pores may be either angular or round; so that there may exist together four different main forms of network—(A) regular lattice with equal hexagonal pores; (B) regular lattice with equal circular pores; (C) irregular lattice with unequal polygonal pores; (D) irregular lattice with unequal roundish pores. Besides these modifications, the pores may be prolonged into tubules which are directed radially towards the outside (rarely towards the inside) of the sphere. In other cases they are surrounded by elevated or honeycomb-like frames.

The Radial Spines exhibit in the Sphæroidea the greatest variety in form, size, disposition, &c., and their numerous modifications serve mainly for the distinction of genera, their peculiar formation and size also for the distinction of species. In general we may distinguish as the most important modifications primary and secondary spines. The primary spines or "main spines" are commonly direct outward prolongations of the internal radial beams, connecting the concentric shells. The secondary or "by-spines" arise only from the surface of the lattice-shell, without reference to the internal beams. The by-spines are commonly smaller, and much more numerous than the main spines. Regarding the form, the radial spines are either roundish (cylindrical or conical, often also club-shaped, rarely spindle-shaped) or angular (commonly three-sided, prismatic or pyramidal). The spines are constantly solid, never hollow; the "internal canals," described by some authors, are only microscopic views of the transparent edges. In many cases the spines are branched or forked. The most important difference in the variable shape of the spines is their regular or irregular number and disposition, which afford characters for the distinction of our five families.

The Three Dimensive Axes—or the three diameters of the sphere, perpendicular one to another—are in the great majority of the Sphæroidea significant in the promorphological consideration of the body, and are indicated either by the position of the external radial spines, or at least of the internal radial beams, connecting the concentric spheres. Commonly two radial spines are placed opposite in each axis. The most perfect group in this respect seems to be that of the Cubosphærida, in which the three axes are represented by three pairs of spines. Next come the Staurosphærida, in which two axes in cross-form are exhibited by two pairs of spines. The most simple group are the Stylosphærida, in which only one pair of spines is developed, indicating one single axis. These three families form together a continuous natural series,—the Sphæroidea with real dimensive axes,—and exhibit at the same time relations to the three other suborders of Sphærellaria, the Larcoidea, Discoidea, and Prunoidea respectively. At both ends of this series stand two other families, on one side the Liosphærida, without any radial spines on the surface of the sphere, on the other side the Astrosphærida, in which the radial spines are developed in great and variable numbers, at least eight to twelve, commonly twenty to forty, often more than a hundred or even a thousand.

The Liosphærida comprise all those Sphæroidea in which the surface of the shell is smooth, without radial spines (Pls. 12, 20). The simplest of these are the Ethmosphærida, with one single lattice-shell, enveloping the spherical central capsule. Cenosphæra, the most simple form of the Ethmosphærida, may be regarded as the common ancestral form of all Sphæroidea, in an ontogenetical as well as in a phylogenetical and morphological sense. From this simple lattice sphere all other Sphæroidea can be derived either by radial or by tangential growth. If the radial beams, arising from the surface of the simple fenestrated sphere, become connected (at equal distances from the centre) by tangential beams, we get the compound shells of the "Liosphærida concentrica" (with two, three, four, or more concentric spheres). The radial beams connecting these exhibit in many Liosphærida the same regular disposition and number as the external radial spines in the Astrosphærida. Perhaps these forms in a "natural system" would be better united (e.g., Liosphærida with twelve or twenty internal radial beams, and Astrosphærida with twelve or twenty external radial spines); but in many cases (mainly for higher numbers) the certain determination of their number and disposition is very difficult or quite impossible.

The Cubosphærida (Pls. 21-25) represent the large and very important family of Sphæroidea, in which all three dimensive axes are equally distinguished by pairs of spines, corresponding to three axes of a cube or of a regular octahedron, agreeing therefore also with the three axes of the cubic or regular crystalline system. In the majority of the Cubosphærida the six radial spines are accurately opposite each other in pairs in three axes, perpendicular one to another, and commonly they are of equal size and form; but in some genera the three pairs of spines become differentiated, whilst both spines of each pair remain equal. Either one pair is larger than the two others (which are equal), corresponding to the axes of the quadratic crystalline system; or all three pairs are different (corresponding to the three unequal axes of the rhombic crystalline system); the former nearer to the Discoidea, the latter to the Larcoidea. We may suppose with some probability, that the Cubosphærida are for the most part the common ancestral group of those Sphæroidea, in which a certain number of radial spines or beams is disposed in a regular order; the Staurosphærida may be derived from them by loss of one pair of spines, the Stylosphærida by loss of two pairs of spines, and most Astrosphærida by multiplying the radial spines, six to fourteen or more secondary spines being added to the six primary "dimensive spines." However, in many Astrosphærida (e.g., in those with eight spines, Centrocubus, Octodendron, &c.) the regular geometrical disposition of the radial spines seems to follow another mathematical order, quite independent of the Cubosphærida.

The Staurosphærida (Pl. 15) are distinguished by the possession of four radial spines, opposite in pairs in two axes, perpendicular one to another. This rectangular cross determines a certain plane, the "equatorial plane," and this brings the Staurosphærida near to the Discoidea, mainly to those which also bear on the periphery of the circular equatorial plane four crossed spines (such as Staurodisculus, Stethostaurus, Staurodictya, &c.). But in these cruciform Discoidea the shell and the enclosed central capsule are discoidal or lenticular, whilst in the Staurosphærida they remain spherical. Commonly the cross is quite regular, with four right angles and four equal beams; but often also it becomes more or less irregular. In some genera one pair of equal opposite spines is larger than the other pair. These forms represent the three different axes of the rhombic crystal system, whilst the common regular Staurosphærida represent those of the quadratic crystal system. The latter can be derived from the Cubosphærida (representing the regular crystal system) by reduction of one axis and loss of its pair of spines. In general the number of species (and particularly of the individuals) is much smaller in the Staurosphærida than in all other families of Sphæroidea.

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.

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).

The family Liosphærida comprises all those solitary Sphæroidea in which the surface of the spherical shell is not armed with radial spines. Nearly the half of this large group is formed by the Ethmosphærida, in which the carapace is a quite simple, spherical lattice-shell; this subfamily is probably the common ancestral group from which all other Sphæroidea, or even all Sphærellaria, can be derived in a phylogenetical as well as in a morphological sense. The central capsule in this first subfamily is constantly enclosed by the fenestrated shell, and separated from it by the jelly-veil. The shell is therefore an extracapsular or medullary shell.

To these simple Ethmosphærida all other subfamilies can be opposed as "Liosphærida concentrica," as their carapace is composed of two or more concentric lattice-shells; two in the Carposphærida, three in the Thecosphærida, four in the Cromyosphærida, five or more in the Caryosphærida. In all these four subfamilies the concentric shells are simple (not spongy) fenestrated shells. In a sixth subfamily, in the Plegmosphærida, the shell is wholly or partially composed of spongy wicker-work, with or without a latticed medullary shell in the centre.

The internal radial beams, in the "Liosphærida composita" connecting the concentric spheres, exhibit in their number and disposition similar important differences, such as the external radial spines in the Astrosphærida. The following eight different cases of regular disposition were observed:—(A) two opposite beams in one axis; (B) four beams, opposite in pairs in two axes perpendicular one to another; (C) six beams, opposite in pairs in the three dimensive axes; (D) eight beams, opposite in pairs in the four diagonals of the regular cube; (E) twelve beams corresponding to the twelve axes of the regular icosahedron; (F) fourteen beams quite regularly disposed (six corresponding to the three axes of the regular octahedron, eight to the central points of its faces); (G) twenty beams (probably corresponding to the twenty corners of a regular dodecahedron); (H) thirty-two beams, regularly disposed. Rarely the number of the radial beams is intermediate between these eight cases, and rarely it is higher; then commonly the disposition is irregular. The regularity of their disposition in the great majority of cases is very remarkable and evident.

Synopsis of the Genera of Liosphærida.

Subfamily Ethmosphærida,^[25] Haeckel, 1862, Monogr. d. Radiol., p. 348 (sensu restricto).

Definition.—Liosphærida with one single spherical lattice-shell; living solitary, not aggregated in colonies.

Genus 15. Cenosphæra,^[26] Ehrenberg, 1854, Monatsber. d. k. preuss. Akad. d. Wiss. Berlin, p. 237.

Definition.—Liosphærida with one single latticed sphere, with simple shell-pores (not prolonged into free tubuli) and with simple shell-cavity (without internal radial beams).

The genus Cenosphæra is the most simple form of all Sphæroidea, and may be regarded as the common ancestral form of this order. The siliceous latticed shell, in which the central capsule is enclosed, represents a simple regular sphere, with simple cavity. The pores of the shell-wall are simple, not prolonged into radial tubuli (as in Ethmosphæra and Sethosphæra). According to the different form of the pores, the numerous species of this genus can be disposed in four different subgenera. Some species may be easily confounded with isolated shells of the corresponding social Collosphæra; but in this latter the spherical shell-form is commonly more or less irregular, in Cenosphæra quite regular.

Subgenus 1. Phormosphæra, Haeckel, 1881, Prodromus, p. 448.

Definition.—Pores of the shell regular or subregular, hexagonal or circular, with hexagonal frames or lobes; all nearly of equal size and form.

1. Cenosphæra primordialis, n. sp.

Shell very thin walled, smooth. Pores hexagonal, regular, or subregular; twelve to fifteen on the half meridian of the shell; bars between them extremely delicate (only visible when three hundred or four hundred times enlarged). Diameter of the shell nine to ten times that of the meshes. This species is remarkable for the extreme delicacy of the arachnoidal network of the simple spherical shell; it may be regarded as the common ancestral form of all Sphæroidea. The shell equals that of Heliosphæra tenuissima (figured in my Monograph, 1862, pl. ix. fig. 2), but differs from it by the smooth surface and the absence of all spines or thorns. I observed this species living in the Indian Ocean, near Ceylon, in 1882; the spherical diameter of the central capsule is about one-third of that of the shell; the contents of the central capsule are colourless and transparent, except the central dark globular nucleus. The same shells also occur in some mounted preparations of surface organisms from the Challenger.

Dimensions.—Diameter of the shell 0.12, of the pores 0.012.

Habitat.—Indian Ocean, Ceylon, Haeckel; Central Pacific, Stations 266, 271, surface.

2. Cenosphæra inermis, Haeckel.