Shell nut-shaped, spiny, with deep sagittal stricture. Pores irregular polygonal or roundish. Basal plate with two large semicircular pores. Three horns slender, simple, about half as long as the shell. Three feet of the same length, slender, divergent, irregularly branched like coral. _Dimensions._--Shell 0.06 long, 0.09 broad; horn and feet 0.03 to 0.05 long. _Habitat._--South Atlantic, Station 332, depth 2200 fathoms. 8. _Triceraspyris maniculata_, n. sp. Shell subspherical, smooth, without external sagittal stricture. Pores subregular circular. Basal plate with four large pores (?). Three horns simple, straight, divergent, spindle-shaped, half {1032}as long as the shell. Caudal foot of the same form, twice as long. Two pectoral feet cylindrical, curved, twice as long as the shell, palmate, divided at the distal end into five short fingers. _Dimensions._--Shell 0.08 diameter; horns 0.04 long; lateral feet 0.12 long. _Habitat._--North Pacific, Station 241, depth 2300 fathoms. 9. _Triceraspyris longicornis_, n. sp. Shell nut-shaped, papillate, with deep sagittal stricture. Pores irregular roundish. Basal plate with six pores (?). Apical horn short, conical, two frontal horns very large, curved, widely divergent, longer than the shell. Three feet of about the same length, irregularly branched. _Dimensions._--Shell 0.08 long, 0.12 broad; lateral horns and feet 0.15 to 0.2 long. _Habitat._--Tropical Atlantic, Station 348, depth 2450 fathoms. Subgenus 3. _Triospyridium_, Haeckel. _Definition._--Horns and feet forked or branched. 10. _Triceraspyris damaecornis_, n. sp. Shell nut-shaped, smooth, compressed, with broad sagittal ring. Pores irregular roundish; one pair of very large pores on each side of the ring. Basal plate with four large collar pores. Three horns and three feet short, divergent, slightly curved, about half as long as the shell, irregularly branched. (In general form very similar to _Elaphospyris damaecornis_, Pl. 84, fig. 10, with which I formerly confounded it.) _Dimensions._--Shell 0.08 long, 0.12 broad; horns and feet 0.04 long. _Habitat._--South Pacific, Station 295, depth 1500 fathoms. 11. _Triceraspyris arborescens_, n. sp. Shell subspherical, with deep sagittal stricture. Pores irregular roundish; three pairs of larger pores on both sides of the ring. Basal plate with two large collar pores. Three horns about half as long as the shell, with few irregular terminal branches. (Beginning of a cupola.) Three feet strong, cylindrical, twice as long as the shell, richly branched, arborescent. _Dimensions._--Shell 0.09 long, 0.1 broad; horns 0.05 long, feet 0.2 long. _Habitat._--Indian Ocean (Madagascar), Rabbe, surface. Genus 443. _Tristylospyris_,[61] Haeckel, 1881, Prodromus, p. 441. _Definition._--#Zygospyrida# with three basal feet, without apical horn.