Shell regular, pyramidal, with flat collar stricture. Relative length of the two joints = 1 : 4, breadth = 2 : 6. Cephalis hemispherical, with a stout pyramidal horn of the same length. Thorax triangular pyramidal, with three prominent ribs, which are prolonged into three slender pyramidal feet, half as long. Pores small and very numerous, subregular, circular. _Dimensions._--Cephalis 0.03 long, 0.05 broad; thorax 0.1 long, 0.15 broad. _Habitat._--Central Pacific, Station 266, depth 2750 fathoms. 6. _Dictyophimus challengeri_, Haeckel. _Dictyophimus challengeri_, Haeckel, 1878, Protistenreich, p. 47, fig. 35. Shell campanulate, with sharp collar stricture. Relative length of the joints = 1 : 3, breadth = 1 : 4. Cephalis subspherical, with a stout pyramidal horn of twice the length, and numerous {1197}very small pores. Thorax nearly hemispherical, with three vaulted bosoms between the three decurrent ribs, which are prolonged into three nearly parallel and vertical feet of about the same length. Pores subregular, circular, of medium size. This species is very similar to _Lychnodictyum challengeri_, Haeckel, but differs in the smaller straight horn and the longer solid feet, which are not fenestrated. _Dimensions._--Cephalis 0.03 long, 0.04 broad; thorax 0.09 long, 0.13 broad. _Habitat._--Tropical Atlantic, Station 347, surface. 7. _Dictyophimus lasanum_, n. sp. (Pl. 61, fig. 5). Shell nearly pear-shaped, with distinct collar stricture. Relative length of the two joints = 1 : 3, breadth = 1 : 3. Cephalis hemispherical, with a conical horn of the same length. Thorax nearly spherical, on both poles truncate and constricted, with three decurrent curved ribs and small regular circular pores. The prolongations of the ribs form three divergent pyramidal straight feet, nearly as long as the thorax. _Dimensions._--Cephalis 0.02 long, 0.03 broad; thorax 0.09 long, 0.09 broad. _Habitat._--South Atlantic, Station 332, depth 2200 fathoms. 8. _Dictyophimus longipes_, n. sp. (Pl. 61, fig. 3). Shell three-sided pyramidal, with distinct collar stricture. Relative length of the two joints = 1 : 4, breadth = 2 : 6. Cephalis hemispherical, with a rudimentary pyramidal horn, scarcely one-fourth as long; and with small circular regular pores. Thorax with larger irregular pores, and three vaulted bosoms between the three decurrent ribs, which are prolonged into three very long and slender prismatic feet, S-shaped, curved, and twice to three times as long as the shell. _Dimensions._--Cephalis 0.02 long, 0.04 broad; thorax 0.09 long, 0.13 broad. _Habitat._--South Pacific, Station 300, depth 1375 fathoms. 9. _Dictyophimus gracilipes_, Bailey. _Dictyophimus gracilipes_, Bailey, 1856, Amer. Journ. Sci. and Arts, vol. xxii. p. 4, pl. i. fig. 8.