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. {992}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_.