The genus _Tholospyris_ is probably the common ancestral form of the Tholospyrida, and has arisen from _Tripospyris_ by development of a galea or cupola; this is composed of the apical horn, the lateral branches of which become connected with lateral spines arising from the coryphal face of the cephalis, and of lattice-work developed between the former and the latter. The three descending feet of the basal face are the typical cortinar feet (one odd caudal and two paired pectoral), the same as in the old ancestral genera _Cortina_, _Plagoniscus_, _Tripospyris_, &c. Subgenus 1. _Tholospyrium_, Haeckel. _Definition._--Basal feet simple, neither forked nor branched. {1079}1. _Tholospyris tripodiscus_, n. sp. (Pl. 89, fig. 1). Shell campanulate, smooth, as broad as long, with deep sagittal stricture. Cephalis compressed, with irregular roundish pores; two or three pairs of larger annular pores on each side of the ring. Basal plate with four large pores. Galea with two very large opposite holes (an occipital and a frontal opening). A slender free perpendicular columella connects the uppermost part of the sagittal ring with the strong three-sided pyramidal apical horn. All three feet of equal length, half as long as the ring, three-sided, prismatic, divergent, with three dentated edges. _Dimensions._--Shell 0.13 diameter, ring 0.08 long, feet 0.05 long. _Habitat._--Central Pacific, Station 272, depth 2600 fathoms. 2. _Tholospyris fenestrata_, n. sp. (Pl. 89, fig. 2). Shell roundish polyhedral, smooth, with slight sagittal stricture. Cephalis nearly cubical, with irregularly roundish pores; two or three pairs of larger pores on each side of the ring. Basal plate with two very large pores. Galea pyramidal, with two large occipital holes. Columella enclosed in the dorsal wall of the galea, prolonged into an oblique pyramidal spine of the same length. Two pectoral feet pyramidal, nearly vertical and as long as the ring, twice as long as the caudal foot. _Dimensions._--Shell 0.12 diameter, ring 0.07, pectoral feet 0.05 long. _Habitat._--Central Pacific, Station 266, depth 2750 fathoms. 3. _Tholospyris galeata_, n. sp. Shell helmet-shaped, thorny, with deep sagittal stricture. Cephalis campanulate, with subregular circular pores. Basal plate with three large pores. Galea hemispherical, separated from the cephalis by a sharp horizontal stricture; pores smaller. A slender free columella connects the apex of the ring with the strong conical apical horn, which is half as long as the ring. All three feet of equal length, divergent conical, as long as the horn. _Dimensions._--Shell 0.14 diameter, ring 0.09 long, feet 0.08 long. _Habitat._--Central Pacific, Station 263, depth 2650 fathoms. Subgenus 2. _Tholospyridium_, Haeckel. _Definition._--Basal feet forked or branched. 4. _Tholospyris ramosa_, n. sp. (Pl. 89, fig. 3).