1. _Dictyophimus sphærocephalus_, n. sp. (Pl. 57, fig. 10). Shell smooth, with a deep collar stricture, separating two joints of nearly equal size. Cephalis subglobular, rough, with a stout pyramidal horn of half the length, and regular, circular, hexagonally framed pores. Thorax nearly three-sided prismatic, smooth, with three stout, little divergent or nearly parallel ribs, which are prolonged into conical subvertical feet half as long. Thoracic pores irregular, roundish. _Dimensions._--Cephalis 0.08 long, 0.08 broad; thorax 0.08 long, 0.08 broad. _Habitat._--Western Tropical Pacific, Station 225, depth 4475 fathoms. 2. _Dictyophimus_ tripus, Haeckel. _Dictyophimus tripus_, Haeckel, 1862, Monogr. d. Radiol., p. 306, Taf. vi. fig. 1. Shell with a slight collar stricture, separating two joints of slightly different size. Cephalis nearly ellipsoidal, large, with a slender conical horn of the same length. Thorax truncate three-sided {1196}pyramidal, with three strongly divergent ribs, which are prolonged into three slender conical feet of about the same length. Pores irregular, roundish, of variable size. _Dimensions._--Cephalis 0.032 long, 0.028 broad; thorax 0.34 long, 0.064 broad. _Habitat._--Mediterranean (Messina), Atlantic (Canary Islands), surface. 3. _Dictyophimus plectaniscus_, n. sp. (Pl. 61, figs. 8, 9). Shell flat, pyramidal, smooth, with distinct collar stricture. Cephalis hemispherical, with a conical horn of the same length and numerous small regular pores. Thorax flat, triangular, pyramidal, with three widely divergent ribs, which are prolonged into three cylindrical feet of the same length. Thoracic pores fifteen, very large, subregular, roundish, disposed in two transverse girdles, the inner with six, the outer with nine pores; five pores between every two ribs. _Dimensions._--Cephalis 0.04 long, 0.06 broad; thorax 0.08 long, 0.18 broad. _Habitat._--Central Pacific, Station 265, depth 2900 fathoms. 4. _Dictyophimus craticula_, Ehrenberg. _Dictyophimus craticula_, Ehrenberg, 1875, Abhandl. d. k. Akad. d. Wiss. Berlin, p. 68, Taf. v. figs. 4, 5. _Dictyophimus craticula_, Bütschli, 1882, Zeitschr. f. Wiss. Zool., vol. xxxvi. p. 515, Taf. xxxiii. fig. 35. Shell flat, pyramidal, very similar to the preceding species, but differing in the rudimentary horn, which is smaller than half the cephalis, and in the length of the three cylindrical feet, which are twice to three times as long as the shell. The nine inferior large pores of the thorax are twice to three times as large as the six superior pores. The basal peristome is commonly thorny. _Dimensions._--Cephalis 0.04 long, 0.05 broad; thorax 0.1 long, 0.2 broad. _Habitat._--Fossil in Barbados. 5. _Dictyophimus pyramis_, n. sp. (Pl. 61, fig. 16).