The family Tympanida (or Parastephida) differs from the other Stephoidea in the development of two horizontal rings, which lie in horizontal planes and arise from the upper and the lower poles of the primary sagittal ring. Therefore the same formation, which we found in the Semantida on the basal pole only of the main axis, here takes place also on its apical pole. On both poles arise at each side from the sagittal ring two corresponding pairs of curved branches: the lateral ends of the opposite branches (dorsal and ventral branch) become united in the frontal plane and so form two complete horizontal rings. The upper ring, composed of the superior or mitral branches, may be called the mitral ring, the lower ring, formed by the inferior or basal branches, the basal ring. Both rings are commonly of nearly equal size, more rarely of different sizes. Their connection is effected either by the primary (sagittal) ring only, or also by secondary vertical rings, a frontal ring in the lateral plane, or some diagonal meridian rings between the latter and the former. These vertical rings, which connect both horizontal rings in the form of "columellæ," may be either complete or incomplete; in the latter case their apical and basal parts are lost, the dorsal and ventral parts only being preserved.

The Tympanida develop a great variety of different forms, greater than in the three other families of Stephoidea, so that we may distinguish here not less than sixteen genera and seventy-two species. Hitherto only three species were known: Prismatium tripleurum, figured in 1862 in my Monograph, Tympanidium barbadense, figured by Bury in the "fossil Polycystins of Barbados," and Tympaniscus fibula, described in 1875 by Ehrenberg as a Ceratospyris fibula. The number of species in this large and richly developed group will be considerably augmented by further researches. A great many of them exhibit remarkable relations to different Nassellaria. For better survey of the whole family we distinguish here four subfamilies, the first of which (Protympanida) is probably the common ancestral group of the other three. They may have been derived originally either from the Semantida or directly from the Stephanida.

The first subfamily, Protympanida, exhibits a complete primary or vertical sagittal ring, bearing on the upper part a horizontal mitral ring, on the lower part a horizontal basal ring. Therefore the gates of these two parallel rings become bisected by the sagittal ring, each divided into a right and a left half. The sagittal ring itself becomes divided by the two horizontal rings into four parts or rods; two opposite of these are more or less vertical; the dorsal (posterior) and the ventral (anterior) rod; the two other rods are more or less horizontal; the mitral (upper) and the basal (lower) rod.

In Protympanium (Pl. 93, fig. 14), the simplest and most primitive form of Tympanida, the connection of the two horizontal rings is effected only by the dorsal and ventral rods of the sagittal ring forming two parallel more or less vertical "columellæ." In all other Protympanida accessory columellæ are developed between the latter. In the greater number we find two secondary columellæ in the lateral plane, being the lateral segments of an incomplete frontal ring (Acrocubus, Pl. 93, figs. 15-17). Between the latter and the former there are sometimes developed four tertiary columellæ, as segments of two crossed incomplete diagonal rings (Tympanidium, Pl. 94, figs. 1, 18). At other times we find six columellæ; here probably the frontal ring is cleft into halves on each side (Tympaniscus, Pl. 94, figs. 4-7). Some genera are distinguished by the development of an equatorial ring, or a third horizontal ring (between the upper mitral and the lower basal ring); this equatorial ring is either complete (Microcubus Pl. 94, figs. 8-10) or incomplete, developed only laterally (Octotympanum, Pl. 94, figs. 2, 3). The genus Toxarium (Pl. 93, figs. 18-20) is distinguished by the development of accessory pairs of bows in the frontal plane, upper or galear bows and lower or thoracal bows, remarkable as beginnings of the accessory joints, which we distinguish in many Spyroidea and Cyrtoidea as "galea and thorax."

The second subfamily of Tympanida are the Paratympanida, in which the two horizontal rings become closed by lattice-work. The numerous columellæ connecting the two rings are here either divergent (Paratympanum, with two unequal rings, Pl. 94, fig. 14) or parallel and vertical (Lithotympanum, with two equal rings, Pl. 83, fig. 1). The shell of the latter assumes the form of a drum.

A third small subfamily, Dystympanida, is represented by a single genus only, Dystympanium (Pl. 94, figs. 15, 16). Here only the upper or mitral ring is closed by lattice-work, whilst the lower or basal ring exhibits quite a simple opening, a large "basal gate" which has probably arisen by loss of the basilar rod of the sagittal ring. These curious forms exhibit a remarkable resemblance to some Monocyrtida, and also to the Dictyocha (Phæodaria).

The fourth subfamily, the Eutympanida, are distinguished by the simple wide aperture of the two horizontal rings; the upper enclosing a simple "mitral gate," the lower a simple "basal gate." Here probably the two horizontal parts of the sagittal ring (the upper mitral rod and the lower basilar rod) are lost by reduction; its two vertical parts (the dorsal and ventral rods) only remaining and forming the two parallel columellæ, which connect the two horizontal rings (Parastephanus, Pl. 93, fig. 21). In this group also secondary columellæ are commonly developed between the two rings, alternating with the two primary columellæ. Pseudocubus (Pl. 94, figs. 11, 12), resembling an obelisk, exhibits four divergent columellæ; the two sagittal of these are probably the vertical parts of the primary ring, whilst the two lateral are the halves of an incomplete frontal ring. In Lithocubus (Pl. 82, fig. 12) the four columellæ are parallel and vertical, the two rings being equal; the shell here assumes the form of a geometrical cube. Prismatium is distinguished by three parallel columellæ; two of these are probably parts of a frontal ring, whilst the third is the remains of a reduced sagittal ring. In Circotympanum (Pl. 94, fig. 17) and in Lithotympanum (Pl. 82, fig. 11) the number of the columellæ is augmented, there being six to eight or more; in the former they are divergent (the two rings being of different sizes), in the latter parallel (the two rings being equal); the fundamental form of the former is a truncated pyramid, of the latter a prism.

Comparing these differences between the four subfamilies of Tympanida, we may suppose that the common ancestral group are the Protympanida, derived from the Semantida by the formation of a mitral ring. If the two horizontal rings become closed by lattice-work, the Paratympanida arise. When the mitral ring only becomes latticed, the basal ring being simple, the Dystympanida originate. Finally, the fourth subfamily, the Eutympanida, may be derived from the Protympanida by the loss of the two horizontal parts of the sagittal ring.

The two horizontal rings (upper mitral and lower basal) and the two vertical rings (primary sagittal and secondary frontal), which thus compose the loose framework of the Tympanida, are rarely smooth, commonly armed with spines or branches, similar to those of the Coronida. The rods or bars are either roundish (with circular transverse section) or angular (commonly with triangular transverse section). The paired branches of the two vertical rings often preserve the characteristic arrangement inherited from the Semantida and Stephanida. The two horizontal rings sometimes exhibit typical apophyses, which recur in the Spyroidea and Cyrtoidea. The mitral ring may possess one odd apical horn and two paired frontal horns (Pl. 93, figs. 16, 17, 19, 23). The basal ring sometimes bears the three typical feet of Cortina (Pl. 93, figs. 16, 22), one odd caudal foot and two paired pectoral feet. Sometimes a fourth (sternal) foot is developed (Pl. 94, fig. 4), at other times only two lateral feet (Pl. 94, figs. 5, 6).

Synopsis of the Genera of Tympanida.

Subfamily 1. Protympanida, Haeckel.

Definition.—Tympanida with two bisected horizontal rings, connected by the complete vertical sagittal ring. (The upper mitral ring and the lower basal ring become divided by the complete primary or sagittal ring into two horizontal symmetrical gates, two mitral gates on the apical and two basal gates on the basal pole.)

Genus 425. Protympanium,^[44] Haeckel, 1881, Prodromus, p. 447 (sensu emend.).

Definition.—Tympanida with two bisected horizontal rings, connected by two vertical columellæ.

The genus Protympanium, is the most simple form of all Tympanida, and probably the common ancestral form of this family. It arises from Lithocircus by the development of two horizontal rings, perpendicular to the primary sagittal ring. The upper or mitral ring arises by lateral union of two pairs of superior branches, the lower or basal ring by union of two pairs of basal branches of the primary vertical ring.

1. Protympanium primordiale, n. sp.

Mitral and apical ring of equal size, elliptical, smooth, somewhat smaller than the connecting thorny sagittal ring.

Dimensions.—Diameter of the two horizontal rings 0.12, of the sagittal ring 0.15.

Habitat.—Central Pacific, Stations 263 to 274, at various depths.

2. Protympanium amphipodium, n. sp. (Pl. 93, fig. 14).

Mitral and apical rings of equal size, thin, elliptical, smooth, larger than the broad connecting sagittal ring. The latter bears on the apical and on the basal pole two divergent straight spines (lying in the frontal plane), the two apical (or horns) somewhat smaller and not so spiny as the two basal spines (or feet). In the frontal plane there arise from the two horizontal rings on each side two small opposite spines (remnants or beginnings of the lateral frontal ring?).

Dimensions.—Diameter of the two horizontal rings 0.11, of the sagittal ring 0.07.

Habitat.—Central Pacific, Station 271, depth 2425 fathoms.

3. Protympanium trissocircus, n. sp.

Mitral ring smaller than the basal ring; both rings circular, rough. Sagittal ring in size between the two former. All three rings covered with very small thorns.

Dimensions.—Diameter of the mitral ring 0.08, of the sagittal ring 0.1, of the basal ring 0.12.

Habitat.—Central Pacific, Station 268, depth 2900 fathoms.

Genus 426. Acrocubus,^[45] Haeckel, 1881, Prodromus, p. 447.

Definition.—Tympanida with two bisected horizontal rings, connected by four vertical columellæ. No equatorial ring.

The genus Acrocubus is the most primitive of those remarkable Tympanida, the skeleton of which represents more or less exactly the form of a geometrical cube. A simple complete sagittal ring bears on the superior and on the inferior part two opposite pairs of lateral branches; by union of the convergent branches of each side there arise two horizontal parallel quadrangular rings, which are bisected by the sagittal ring. Therefore the superior ring encloses two triangular mitral gates, the inferior two triangular basal gates. The lateral corners of the two gates of each side are connected by a vertical rod or columella. These two parallel columellæ are the remaining middle parts of the secondary or frontal ring, which is incomplete on the superior and on the inferior face of the body. If the sagittal ring also become incomplete, by the loss of the superior and inferior part (the anterior and posterior only remaining), then Acrocubus is transformed into Lithocubus.

Subgenus 1. Apocubus, Haeckel.

Definition.—Basal ring without descending feet.

1. Acrocubus octopylus, n. sp. (Pl. 82, fig. 9).

Mitral ring somewhat smaller than the basal ring; both rings rhombic, with curved outlines. Sagittal ring elliptical, with six pairs of nodulate protuberances. Four columellæ curved. Nodal points without radial spines.

Dimensions.—Height of the frontal ring 0.12, breadth 0.18.

Habitat.—Western Tropical Pacific, Station 225, depth 4475 fathoms.

2. Acrocubus tesseralis, n. sp.

Mitral ring of the same size as the basal ring; both rings square, smooth, with straight outlines. Sagittal ring also square, smooth. Four columellæ straight. Nodal points without radial spines. The shell has the form of a regular geometrical cube, the edges of which are represented by the rings.

Dimensions.—Height of the frontal ring 0.1, breadth 0.11.

Habitat.—Tropical Atlantic, Station 348, depth 2450 fathoms.

Subgenus 2. Dipocubus, Haeckel.

Definition.—Basal ring with two descending feet.

3. Acrocubus brachiatus, n. sp.

Mitral ring smaller than the basal, both rings square, with thick straight rods. Sagittal ring tuberculate, square, equatorial part thinner. Four columellæ curved, the two lateral ones prolonged downwards into two vertical parallel straight feet of half their length.

Dimensions.—Diameter of the cube 0.12; length of the feet 0.06.

Habitat.—North Pacific, Station 244, depth 2900 fathoms.

4. Acrocubus amphistylus, n. sp.

Mitral and basal rings of nearly equal size, square, with thick curved rods. Sagittal ring elliptical, in the equatorial part thinner. Frontal ring tuberculate. Four columellæ curved, the two lateral ones prolonged downwards into two vertical, tuberculate feet of half their length.

Dimensions.—Diameter of the cube 0.13; length of the feet 0.07.

Habitat.—Central Pacific, Station 268, depth 2900 fathoms.

5. Acrocubus arcuatus, n. sp. (Pl. 93, fig. 15).

Mitral and basal rings, as well as the sagittal ring, of the same form as in the preceding nearly allied species. The two lateral columellæ are prolonged not only downwards into two short vertical feet, but also upwards into two curved bows, which are united in a vertical ascending horn, arising from the apical pole of the sagittal ring.

Dimensions.—Diameter of the cube 0.14; total height 0.21.

Habitat.—Central Pacific, Station 265, depth 2900 fathoms.

Subgenus 3. Tripocubus, Haeckel.

Definition.—Basal ring with three descending feet (one odd caudal and two paired lateral).

6. Acrocubus lasanum, n. sp.

Mitral ring smaller than the basal, both rings square, with curved rods. Sagittal ring ovate, prolonged upwards into an occipital simple horn, downwards into a caudal foot. Two lateral columellæ prolonged downwards into two pectoral feet. All three feet conical, about as long as the height of the cube.

Dimensions.—Diameter of the cube 0.08; length of the feet 0.07.

Habitat.—North Pacific, Station 241, depth 2300 fathoms.

7. Acrocubus cortina, n. sp. (Pl. 93, fig. 16).

Mitral ring smaller than the basal, both rings elliptical, with curved rods. Sagittal ring ovate, prolonged upwards into an occipital horn, downwards into a caudal foot, as in the preceding species. As in the latter, also, the two lateral columellæ are prolonged downwards into two pectoral feet, but also upwards into two convergent horns, which are united with the occipital horn (commencing the formation of a galea). Rings and feet somewhat thorny.

Dimensions.—Diameter of the cube 0.16; total height 0.2.

Habitat.—Central Pacific, Station 266, depth 2750 fathoms.

Subgenus 4. Tetracubus, Haeckel.

Definition.—Basal ring with four descending feet (two sagittal and two lateral).

8. Acrocubus tetrapodius, n. sp.

Mitral and basal rings of the same size, square, with straight rods, sagittal ring also square. The four vertical columellæ are nearly parallel and straight, prolonged upwards into four short conical horns, downwards into four longer conical feet. (The shell has nearly the form of a geometrical cube, the eight corners of which are prolonged into eight vertical conical spines, four smaller ascending and four larger descending.)

Dimensions.—Diameter of the cube 0.09; length of the feet 0.06.

Habitat.—South Atlantic, Station 332, depth 2200 fathoms.

9. Acrocubus amphithectus, n. sp. (Pl. 93, fig. 17).

Mitral ring smaller than the basal, both rings elliptical, with curved rods. Four columellæ thorny, also curved, divergent downwards, prolonged upwards into four thorny convergent horns, downwards into four larger branched divergent feet. The two sagittal horns and feet (anterior and posterior) are smaller than the two lateral (right and left); therefore the fundamental form of this species is distinctly amphithect (as in the Ctenophora).

Dimensions.—Breadth of the cube 0.12; total height 0.2.

Habitat.—South Pacific, Station 289, depth 2550 fathoms.

Genus 427. Toxarium,^[46] n. gen.

Definition.—Tympanida with two bisected horizontal rings, connected by four vertical columellæ. In the frontal plane two galear bows project upwards, and two thoracal bows downwards.

The genus Toxarium differs from its ancestral form Acrocubus in the development of two pairs of peculiar bows, placed in the lateral or frontal plane; the upper pair projects above the mitral gates, and may be called the "galear bows," the lower pair projects below the basal gates of the cubical shell, and may be called the "thoracal bows." Both pairs are produced originally by the development of two forked vertical spines, arising in the frontal plane on both poles of the principal axis from the sagittal ring (compare Protympanium amphipodium, Pl. 93, fig. 14). The apical fork-branches become connected with the lateral corners of the mitral gates, the basal branches with those of the basal gates. By development of lattice-work between the bows and the rings some Spyroidea (Amphispyris, &c.) may have arisen. The important genus Toxarium may be divided into three subgenera. In Toxellium all the bows are simple, in Toxonium, all are forked; in Toxidium, the galear bows are simple, the thoracal bows forked.

Subgenus 1. Toxellium, Haeckel.

Definition.—Galear and thoracal bows simple.

1. Toxarium circospyris, n. sp. (Pl. 88, fig. 1).

Galear and thoracal bows simple, of about the same size as the frontal bows between them; all bows armed with scattered simple conical spines. Sagittal constriction deep, half as long as the whole shell. Lateral outlines of the shell nearly parallel.

Dimensions.—Length of the shell 0.16, breadth 0.13.

Habitat.—Central Pacific, Stations 265 to 274, depth 2350 to 2925 fathoms.

2. Toxarium subcirculare, n. sp.

Galear and thoracal bows simple, armed with scattered simple spines of about equal size, smaller than the smooth frontal bows between them. Sagittal constriction very flat. Therefore the frontal perimeter of the shell is nearly circular.

Dimensions.—Length of the shell 0.15, breadth 0.14.

Habitat.—North Atlantic (Antilles), Weber, surface.

3. Toxarium thorax, n. sp. (Pl. 93, fig. 18).

Galear bows simple, smaller than the frontal bows, and these again smaller than the simple thoracal bows; therefore the shell increases in breadth towards the base, and resembles the skeleton of the thorax of one of the higher vertebrates (the bow-pairs corresponding to rib-pairs, the ventral part of the sagittal ring to the sternum, the dorsal part to the vertebral column). Sagittal constriction very deep. All bows are armed with scattered, irregularly branched spines.

Dimensions.—Length of the shell 0.17, breadth 0.2.

Habitat.—Central Pacific, Station 265, depth 2900 fathoms.

4. Toxarium constrictum, n. sp.

Galear and thoracal bows simple, of nearly equal size, larger than the frontal bows between them. Therefore the shell is constricted in the equatorial plane. Sagittal constriction also deep. All bows armed with scattered, irregularly branched spines.

Dimensions.—Length of the shell 0.14, breadth 0.12.

Habitat.—North Pacific, Station 236, surface.

Subgenus 2. Toxidium, Haeckel.

Definition.—Galear bows simple, thoracal bows forked.

5. Toxarium cordatum, n. sp. (Pl. 93, fig. 19).

Galear bows simple, thoracal bows forked, both somewhat smaller than frontal bows; all bows armed with scattered simple conical spines, mostly developed at the thoracal bows. Both galear bows are united in a central vertical columella, which arises from the apex of the sagittal ring, and is prolonged into an apical horn. Therefore the sagittal constriction exists only in the basal half of the inversely cordate shell.

Dimensions.—Length of the shell 0.18, breadth 0.16.

Habitat.—South Atlantic, Station 348, depth 2450 fathoms.