Cephalis nut-shaped, with deep sagittal stricture, and three short apical horns of half its length; the middle odd horn is straight, the two paired lateral horns are curved outwards. Thorax somewhat larger than the cephalis, dilated around the wide open mouth, with a coronet of twenty-five to thirty slender basal feet, which are slightly curved and convergent, about as long as the thorax. Pores small, numerous and circular. _Dimensions._--Cephalis 0.05 long, 0.07 broad; thorax 0.06 long, 0.08 broad; horns 0.02 long, feet 0.06 long. _Habitat._--Indian Ocean, Madagascar (Rabbe), surface. 2. _Rhodospyris triceros_, n. sp. Cephalis nut-shaped, with deep sagittal and deep collar stricture, and with three stout divergent horns of nearly equal length. Thorax cylindrical, twice as long as the cephalis, and of the same breadth, with a coronet of twelve to sixteen broad, lamellar, rectangular, perpendicular feet around the mouth, about as long as the cephalis. Pores rather large, subregular, circular. _Dimensions._--Cephalis 0.06 long, 0.08 broad; thorax 0.12 long, 0.09 broad. _Habitat._--Indian Ocean, Singapore (Trebing), surface. Genus 478. _Desmospyris_,[96] Haeckel, 1881, Prodromus, p. 443. _Definition._--#Phormospyrida# with numerous basal feet (nine to twelve or more), without a coryphal horn. The genus _Desmospyris_ differs from the two preceding polypodal genera in the complete absence of horns on the coryphal face of the cephalis. It therefore corresponds to _Gorgospyris_ among the Zygocyrtida, and arises when the numerous basal feet of the latter become connected by lattice-work. 1. _Desmospyris mammillata_, n. sp. (Pl. 83, fig. 14). Shell mammillate, with deep sagittal and slight collar constriction. Pores irregular, roundish. Cephalis nut-shaped, larger than the inversely conical thorax, and twice as broad as the constricted {1090}mouth. Coronet of the peristome with twelve to fifteen short conical convergent feet, shorter than half the thorax. _Dimensions._--Cephalis 0.06 long, 0.09 broad; thorax 0.04 long, 0.06 broad. _Habitat._--Central Pacific, Station 272, depth 2600 fathoms. 2. _Desmospyris cyrtocolpos_, n. sp. Shell smooth, with deep sagittal and collar strictures. Pores subregular, circular, double-contoured, very small and numerous. Cephalis nut-shaped, larger than the short truncate thorax. Coronet with eighteen to twenty-four slender, irregular, pointed, convergent feet, about twice as long as the thorax. _Dimensions._--Cephalis 0.08 long, 0.12 broad; thorax 0.04 long, 0.1 broad. _Habitat._--Western Tropical Pacific, Station 225, depth 4475 fathoms. 3. _Desmospyris anthocyrtoides_, Haeckel. _Petalospyris anthocyrtoides_, Bütschli, 1882, Zeitschr. f. wiss. Zool., vol. xxxvi. pp. 533, 539, Taf. xxxii. fig. 19, _a-c_.