Shell nearly spherical, tuberculate, a little broader than long. Pores regular, circular, as broad as the bars. Mouth constricted, half as broad as the shell. Apical feet and the three divergent feet of equal size and similar form, about as long as the shell, straight, in the basal half smooth, cylindrical, in the distal half club-shaped, dimpled. (Very similar to _Tripospyris conifera_ and _Tripospyris eucolpos_, Pl. 84, figs. 7 and 4; but the spherical shell exhibits no trace of sagittal ring or constriction, and the simple shell-cavity has a wide open mouth, and is not closed by a basal plate.) _Dimensions._--Shell 0.1 diameter, horn and feet 0.08 to 0.09 long. _Habitat._--Central Pacific, Station 268, depth 2900 fathoms. 6. _Tripilidium costatum_, n. sp. (Pl. 98, figs. 8, 8_a_, 8_b_). Shell ovate, spinulate and costate, nearly twice as broad as long. Surface with fifteen to twenty prominent longitudinal ribs, which are convergent towards each pole and elegantly denticulate. The deep furrows between them are divided by delicate, parallel, transverse ribs into numerous short and broad dimples (thirty to forty in each furrow); each dimple contains a small pore, like a transverse {1142}fissure. The apex bears a short and stout, three-sided pyramidal horn, the hollow base of which is closed by a small cortinar septum with three collar pores (fig. 8_b_). This seems to indicate a rudimentary cephalis and the derivation of this species from _Lychnocanium_ (Pl. 61). Peristome constricted, only one-fourth as broad as the shell, with three short, conical, nearly vertical feet. The central capsule (fig. 8_a_) in the specimen examined was well preserved, hemispherical, not lobate, and filled up the upper half of the shell-cavity (beyond the rudiment of the cortinar septum). _Dimensions._--Shell 0.2 long, 0.12 broad; horn 0.01 long, feet 0.02 long. _Habitat._--Tropical Atlantic, Station 348, depth 2450 fathoms. 7. _Tripilidium elongatum_, n. sp. Shell elongate, smooth, nearly cylindrical, in the upper third conical. Pores small and numerous, regular, circular, half as broad as the bars, disposed in about thirty longitudinal alternating rows. Peristome scarcely constricted. The apical horn and the three parallel feet are of equal size and similar form, straight, conical, one-sixth as long as the shell. _Dimensions._--Shell 0.12 long, 0.06 broad; horn and feet 0.02 long. _Habitat._--Fossil in Barbados. Subgenus 2. _Tripodocorys, Haeckel_, 1881, Prodromus, p. 428. _Definition._--Feet forked or branched. 8. _Tripilidium dichopodium_, n. sp.