Originally the two horizontal rings of these "drum-shells" are both bisected by the complete sagittal ring, each provided with two lateral gates (Protympanida). But in the Eutympanida both rings exhibit one simple gate only, the apical and the basal rod of the sagittal ring being lost. In the Paratympanida both rings are closed by a secondary lattice-plate whilst in the Dystympanida the upper (mitral) ring alone is closed by such a plate, the lower (basal) ring is open. In some Eutympanida the shell assumes the strange form of a regular geometrical cube, the twelve edges of which are represented by thin rods of silex (_Lithocubus_)--its four upper edges represent the mitral ring, the four lower the basal ring; two opposite of the four vertical {937}cube-edges are the lateral halves of the frontal ring, the two other alternate ones are the remaining halves of the reduced sagittal ring (dorsal and ventral rod) (Pl. 82, fig. 12). In many Tympanida and Coronida a loose irregular lattice or framework is developed, which partly closes the large open gates. But this never reaches the completeness of a true lattice-shell, such as we find in the #Spyroidea#, #Botryodea#, and #Cyrtoidea#. In by far the greater number of #Stephoidea# the corners, and partly also the rods, of the shell are armed with numerous irregular spines, often forked or richly branched. Among these spines the descending "basal apophyses" possess a peculiar importance, since by their regular number and disposition they correspond to the radial rods of the #Plectoidea#, and to the typical "feet" of the #Spyroidea# and #Cyrtoidea#. The most important of them are the three cortinar feet (one caudal and two pectoral) of _Cortina_, _Cortiniscus_, &c. (compare above, p. 891). _The Central Capsule_ exhibits in the #Stephoidea# the same characteristic structure as in all other MONOPYLEA, first exactly pointed out by Richard Hertwig in 1879 (Organismus der Radiol., p. 71, Taf. vii. figs. 4, 5). Its form is commonly ovate or ellipsoidal, sometimes also lentelliptical or nearly spherical. It exhibits constantly on the basal pole the porochora or porous area, and in the basal half the podoconus or pseudopodial cone. From the surrounding sagittal ring it is separated by a thick jelly-like calymma, which commonly exhibits numerous zooxanthellæ. The numerous pseudopodia are commonly branched, with rather rare anastomoses. The membrane of the central capsule is thick. _Synopsis of the Families of_ #Stephoidea#. I. Skeleton composed of the simple vertical sagittal ring only, without secondary rings, 1. STEPHANIDA. II. Skeleton composed of two crossed rings, a vertical sagittal and a horizontal basal ring, 2. SEMANTIDA. III. Skeleton composed of two crossed vertical meridional rings (a primary sagittal and a secondary frontal ring), commonly also with a horizontal basal ring, 3. CORONIDA.