Shell three-sided pyramidal, thorny, about as long as broad, with three dentate edges. Framework very loose, with irregular polygonal meshes; in the middle of each of the three triangular sides a horizontal band of denser network. Basal plate with three very large simple collar-holes. The apical horn and the three feet are three-sided pyramidal, about half as long as the columella, with three prominent irregularly dentate edges. The horn is straight, whilst the three feet are hook-shaped, its distal end being curved downwards and inwards. _Dimensions._--Shell 0.11 long, 0.13 broad. _Habitat._--Central Pacific, Station 274, depth 2750 fathoms. 2. _Euscenium archicyrtis_, n. sp. Shell three-sided pyramidal, smooth, nearly as long as broad, with three straight edges connected by irregular loose framework with polygonal meshes. Basal plate with three very large {1147}simple collar-holes. The apical horn and the three feet are three-sided prismatic, smooth, about twice as long as the columella, straight and widely divergent. _Dimensions._--Shell 0.08 long, 0.1 broad. _Habitat._--Tropical Pacific, Station 225, depth 4475 fathoms. 3. _Euscenium hemisphæricum_, n. sp. Shell hemispherical smooth, half as long as broad, with small and numerous subregular circular pores. Basal plate with three large triangular simple collar-holes. Horn slender, three-sided prismatic, twice as long as the columella. Feet very slender, with three denticulate edges, widely divergent and curved like the quadrant of a circle. _Dimensions._--Shell 0.04 long, 0.06 broad. _Habitat._--North Pacific, Station 244, depth 2900 fathoms. 4. _Euscenium tricolpium_, n. sp. (Pl. 53, fig. 12). _Archiscenium tricolpium_, Haeckel, 1881, Prodromus et Atlas, _loc. cit._ Shell cap-shaped, nearly hemispherical, with three vaulted hemispherical bosoms between the three arches ascending from the feet to the horn. Network very irregular, with polygonal meshes, of different form and size. Basal plate with three large primary and some smaller irregular accessory collar-holes. Horn slender, straight, twice as long as the columella. Feet of the same length, slender, widely divergent, slightly curved. The three edges of the horn and the feet are elegantly denticulated. _Dimensions._--Shell 0.04 long, 0.08 broad. _Habitat._--Central Pacific, Station 266, depth 2750 fathoms. 5. _Euscenium tripospyris_, n. sp. (Pl. 84, fig. 8). _Tripospyris euscenium_, Haeckel, 1881, Prodromus et Atlas. Shell nearly spherical, smooth, with numerous small circular pores. Basal plate also with numerous small pores. Horn and feet stout, three-sided prismatic, straight or slightly curved, about as long as the thin, somewhat curved columella. This species is closely allied to Tripospyris. _Dimensions._--Shell 0.11 to 0.12 diameter, horn and feet 0.08 to 0.1 long. _Habitat._--South Pacific, Station 298, depth 2225 fathoms. Subgenus 2. _Euscenidium_, Haeckel.