_Dimensions._--Shell 0.07 to 0.09 diameter; horn 0.06 long, feet 0.3 to 0.4 long. _Habitat._--Fossil in Tertiary rocks of Barbados. 6. _Tripospyris conifera_, n. sp. (Pl. 84, figs. 7, 7_a_). Shell nearly hemispherical, papillate, with slight sagittal stricture and semicircular internal ring. Basal plate with three large pores (sometimes, as in the figured specimen, with some small accessory peripheral pores). The other lattice-work with subregular circular pores. Apical horn shorter than the three basal feet, but of similar form, like an elegant ovate dimpled cone, spinulate, with a smooth spindle-shaped pedicle, about as long as the shell. _Dimensions._--Shell 0.08 long, 0.1 broad; horn 0.06 long, feet 0.08 long. _Habitat._--Western Tropical Pacific, Station 225, depth 4475 fathoms. 7. _Tripospyris triplecta_, n. sp. (Pl. 95, fig. 2). Shell thorax-shaped, spiny, with deep sagittal stricture and semicircular internal ring. Basal plate with three large collar pores. Facial plate with four pairs, occipital plate with three pairs of large annular pores; the other pores small, subregular, circular. Apical horn and the feet slender, three-sided pyramidal, about as long as the shell. _Dimensions._--Shell 0.1 long, 0.11 broad; horn and feet 0.1 to 0.15 broad. _Habitat._--Mediterranean, Corfu (Haeckel), surface. Subgenus 3. _Tripospyrissa_, Haeckel. _Definition._--Basal plate with two pairs of collar pores (two larger posterior cardinal pores and two smaller anterior jugular pores). 8. _Tripospyris semantrum_, n. sp. (Pl. 95, fig. 3). Shell thorax-shaped, thorny, with deep sagittal stricture and subcircular ring. Basal plate with four large collar pores (two smaller ovate jugular, and two larger pentagonal cardinal pores). Facial and occipital plates also each with two pairs of large annular pores; lateral sides with smaller irregular polygonal pores. Apical horn and the three feet slender, prismatic, divergent, longer than the shell. _Dimensions._--Shell 0.07 long, 0.08 broad; horn and feet 0.11 to 0.13 long. _Habitat._--South Atlantic, Cape of Good Hope (Wilhelm Bleek), surface. {1028}9. _Tripospyris capitata_, n. sp. (Pl. 84, fig. 1). Shell subspherical, spiny, with slight sagittal stricture and ovate internal ring. Basal plate with four large collar pores. Facial plate with three pairs and occipital plate with two pairs of large roundish annular pores; lateral lattice with smaller irregular pores. Apical horn and the three feet subcylindrical, about half as long as the shell, straight, divergent, with a spherical, spinulate knob at the distal end. _Dimensions._--Shell 0.09 long, 0.1 broad; horn and feet 0.05 to 0.06 long. _Habitat._--Central Pacific, Station 266, depth 2750 fathoms. 10. _Tripospyris clavata_, Haeckel. _Ceratospyris clavata_, Bütschli, 1882, Zeitschr. f. wiss. Zool., vol. xxxvi. p. 539, Taf. xxxii. fig. 13, _a-c_.