The genus _Tristylospyris_ exhibits in general the same structure as the typical genus _Tripospyris_, its ancestral form. It differs from the latter in the absence of the apical {1033}horn, which is completely reduced, and may therefore be regarded as the simplest prototype of all tripodal Cyrtellaria without a horn. Subgenus 1. _Tristylospyrula_, Haeckel. _Definition._--Feet simple, not branched nor forked. 1. _Tristylospyris palmipes_, n. sp. (Pl. 84, fig. 14). Shell companulate, smooth, with slight sagittal stricture. Pores irregular roundish, three pairs of larger annular pores on each side of the broad ring. Basal plate with four large collar pores. Feet half as long as the shell, slightly divergent, straight, prismatic, with a broad, hand-like, radially striped plate at the distal end. _Dimensions._--Shell 0.1 long, 0.09 broad; feet 0.06 long. _Habitat._--Equatorial Atlantic, Station 347, depth 2250 fathoms. 2. _Tristylospyris scaphipes_, n. sp. (Pl. 84, fig. 13). Shell nut-shaped, smooth, with sharp sagittal stricture. Pores very small and numerous, circular; two pairs of larger pores on both sides of the ring. Basal plate with four large pores (?). Feet about half as long as the shell, angular, shovel-shaped, straight, parallel, vertical. _Dimensions._--Shell 0.06 long, 0.08 broad; feet 0.04 long. _Habitat._--North Pacific, Station 244, depth 2900 fathoms. 3. _Tristylospyris clavipes_, n. sp. (Pl. 84, fig. 15). Shell nut-shaped, rough, with deep sagittal stricture. Pores small, subregular circular. Basal plate with three large pores. Feet about as long as the shell, slender, straight, divergent, with a spinulate knob at the thickened distal end. _Dimensions._--Shell 0.06 long, 0.08 broad; feet 0.05 long. _Habitat._--Central Pacific, Station 272, depth 2600 fathoms. 4. _Tristylospyris triceros_, Haeckel. _Ceratospyris triceros_, Ehrenberg, 1875, Abhandl. d. k. Akad. d. Wiss. Berlin, p. 66, Taf. xxi. fig. 5. Shell nut-shaped, tuberculate, without external sagittal stricture. Pores circular, not numerous. Basal plate with four large collar pores. Feet large, cylindrical, three to four times as long as the shell, strongly curved and divergent. _Dimensions._--Shell 0.05 long, 0.07 broad; feet 0.15 to 0.2 long. _Habitat._--Fossil in Barbados. {1034}Subgenus 2. _Tristylospyrium_, Haeckel. _Definition._--Feet forked or branched. 5. _Tristylospyris furcata_, n. sp. Shell subspherical, rough, with slight sagittal stricture. Pores subregular circular. Basal plate with three large collar pores. Feet cylindrical, three to four times as long as the shell, strongly curved and divergent, at the distal end forked, with two short (sometimes ramified) branches. _Dimensions._--Cephalis 0.08 long, 0.09 broad; feet 0.2 to 0.3 long. _Habitat._--South Atlantic (off Patagonia), Station 318, surface. 6. _Tristylospyris ramosa_, n. sp. (Pl. 52, fig. 23).