The genus _Ceratospyris_ differs from all the other Zygospyrida in the possession of numerous large spines on the surface of the shell, which usually exhibits only a small number of large pores or meshes. The lower spines which cover the inferior or basal face of the shell (usually nine to twelve or more) may be compared to the descending "basal feet" of the other Zygospyrida; the upper spines, however, which cover the superior or coryphal face (usually six to nine, rarely more), may be regarded as "coryphal horns." In many species of this genus the lattice-work of the shell is of a peculiar loose kind, with few large meshes, resembling the wicker-work of the Plectanida. Subgenus 1. _Lophospyris_, Haeckel, 1881, Prodromus, p. 443. _Definition._--Spines simple, not branched. Meshes of the shell usually polygonal, or roundish with polygonal frames. Bars of the network prismatic. 1. _Ceratospyris polygona_, n. sp. (Pl. 86, fig. 1). Shell polyhedral, with deep sagittal stricture, studded with twenty-four to thirty long simple straight slender pyramidal spines, which are as long as the shell or longer. All pores large, polygonal. On the frontal and the occipital face two pairs of very large pores only, the superior {1067}pentagonal, larger than the inferior tetragonal. Basal plate with two triangular pores. Bars of the loose framework three-sided prismatic, thin. _Dimensions._--Shell 0.08 long, 0.12 broad; spines 0.06 to 0.12 long. _Habitat._--Cosmopolitan; Atlantic, Indian, Pacific, surface. 2. _Ceratospyris pentagona_, Ehrenberg. _Ceratospyris pentagona_, Ehrenberg, 1872, Abhandl. d. k. Akad. d. Wiss. Berlin, p. 287, Taf. x. fig. 15. Shell polyhedral, with slight sagittal stricture, studded with twenty-four to thirty small simple conical spines, which are shorter than one-fourth of the shell. Most pores pentagonal. On the frontal and the occipital face two pairs of large pores only, the superior smaller than the inferior. Basal plate with four quadrangular pores. Bars of the network prismatic, thin. _Dimensions._--Shell 0.07 long, 0.11 broad; spines 0.01 to 0.02 long. _Habitat._--Cosmopolitan; Atlantic, Indian, Pacific, surface. 3. _Ceratospyris allmersii_, n. sp. (Pl. 86, fig. 3). Shell polyhedral, with slight sagittal stricture, studded with thirty to forty prismatic spines which are not longer than half the shell. Most pores pentagonal. On the frontal face two, on the occipital three pairs of larger pores; the inferior the largest. Basal plate with two rhomboidal pores (?). Bars of the network three-sided prismatic, thin. Dedicated to my dear friend, the excellent poet and naturalist, Hermann Allmers, of Rechtenfleth. _Dimensions._--Shell 0.08 long, 0.12 broad; spines 0.01 to 0.03. _Habitat._--Tropical Atlantic, Station 347, depth 2250 fathoms. 4. _Ceratospyris mulderi_, n. sp. (Pl. 86, fig. 4).