_Definition._--#Archicorida# with conical shell, gradually dilated towards the wide open mouth. Apex armed with a horn. The genus _Cornutella_ is one of the three oldest genera of Polycystina, described by Ehrenberg, in 1838 (_Cornutella_, _Lithocampe_, and _Haliomma_). He afterwards enumerated, in 1872 and 1875, a large number of fossil and living species, the majority of which, however, belong to other genera of Monocyrtida and Dicyrtida (at least six or seven different genera). We retain here as the true type of the genus the oldest known species:--_Cornutella clathrata_, and the nearly allied forms _Cornutella stylophæna_, _Cornutella mitra_, _Cornutella circularis_, &c. The simple conical shell exhibits no distinct trace of an original cephalis, excepting the apical horn; it may have originated either independently, or been derived from _Sethoconus_, by loss of the cephalis. Subgenus 1. _Cornutellium_, Haeckel. _Definition._--Axis of the conical shell straight. Pores polygonal, or roundish with polygonal frames. 1. _Cornutella hexagona_, n. sp. (Pl. 54, fig. 9). Shell slender, conical, with straight outlines. Pores subregular, hexagonal, gradually increasing in size towards the mouth; in about ten to twelve longitudinal series, in the upper part very small. Horn slenderly conical, nearly bristle-shaped, long. _Dimensions._--Shell 0.1 to 0.15 long, 0.04 to 0.06 broad. _Habitat._--Central Pacific, Stations 265 to 274, surface, and at different depths. 2. _Cornutella sethoconus_, n. sp. (Pl. 54, fig. 10). Shell slender, conical, with undulate outlines. Pores subregular, hexagonal, gradually increasing in size towards the mouth, in about fifteen to eighteen longitudinal series, in the upper part circular. Horn small, conical, short. The network is not so delicate as in the preceding similar species. _Dimensions._--Shell 0.12 to 0.16 long, 0.06 to 0.08 broad. _Habitat._--South Atlantic, Station 332, depth 2200 fathoms. {1181}3. _Cornutella distenta_, Ehrenberg. _Cornutella distenta_, Ehrenberg, 1872, Abhandl. d. k. Akad. d. Wiss. Berlin, p. 287, Taf. vi. III. fig. 3. Shell slender, conical, with straight outlines. Pores small, circular, regularly disposed in six to eight alternating longitudinal rows, each pore surrounded by a large rhombic frame. The connected frames form together a regular rhombic framework with obliquely crossed crests. Horn conical, stout, large. _Dimensions._--Shell 0.1 to 0.15 long, 0.04 to 0.06 broad. _Habitat._--North Pacific, Californian Sea, depth 2600 fathoms, Ehrenberg. 4. _Cornutella stiligera_, Ehrenberg. _Cornutella stiligera_, Ehrenberg, 1854, Mikrogeol., Taf. xxxvi. fig. 1; Abhandl. d. k. Akad. d. Wiss. Berlin, 1875, p. 68, Taf. ii. fig. 3.