Definition.—Stephoidea with two parallel horizontal rings, an upper mitral and a lower basal ring; both connected by complete or incomplete vertical rings, or by parallel vertical columellæ.
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).