_Definition._--Ring polygonal, with four to six or more prominent corners (and commonly with simple spines arising from the corners). 6. _Archicircus quadratus_, n. sp. Gate square. Ring square, with three edges and four short simple pyramidal spines on the four corners, opposite in pairs in two perpendicular diameters. Transverse section triangular. _Dimensions._--Diameter of the gate 0.08; thickness of the ring 0.008. _Habitat._--Central Pacific, Station 265, depth 2900 fathoms. {942}7. _Archicircus rhombus_, n. sp. (Pl. 81, fig. 7). Gate rhombic. Ring rhombic, with four prominent edges and four pairs of short, divergent, pyramidal spines on the four corners, arising from the lateral edges of the four rods, about as long as the radius of the gate. _Dimensions._--Diameter of the gate 0.04 to 0.08; thickness of the ring 0.007 to 0.01. _Habitat._--North Pacific, Station 244, depth 2900 fathoms. 8. _Archicircus duodenus_, n. sp. Gate square or rhombic. Ring rhombic, with three prominent edges and twelve stout and straight pyramidal spines, about as long as the radius of the gate. In each of the four corners are three divergent spines, arising from the three edges of each two meeting rods. _Dimensions._--Diameter of the gate 0.08; thickness of the ring 0.012. _Habitat._--North Atlantic, surface (Rabbe). 9. _Archicircus primordialis_, n. sp. (Pl. 81, fig. 1). Gate ovate. Ring hexagonal, with three prominent edges and six short pyramidal thorns at the six corners; the basal thorn is either simple or forked. _Dimensions._--Diameter of the gate 0.07; thickness of the ring 0.01 to 0.015. _Habitat._--Central Pacific, Stations 265 to 274, depth 2350 to 2925 fathoms. 10. _Archicircus hexacanthus_, n. sp. (Pl. 81, fig. 4). Gate subregular, hexagonal. Ring hexagonal, with three sharp edges and six equal radial pyramidal spines, arising from the six corners and placed in the plane of the ring, about as long as the diameter of the gate. _Dimensions._--Diameter of the gate 0.05 to 0.07; thickness of the ring 0.01. _Habitat._--South Pacific, Station 295, depth 1500 fathoms. 11. _Archicircus hertwigii_, Haeckel. _Lithocircus annularis_, R. Hertwig (_non_ J. Müller), 1879, Organismus der Radiol., p. 69. Taf. vii. fig. 5. Gate hexagonal, with prolonged main axis. Ring hexagonal, with two prominent edges and six pairs of equal, short, conical spines, arising from the two edges of the six rods at the six corners and divergent on each side of the plane of the ring. The basal spine-pair is doubled, therefore there are in all fourteen spines. _Dimensions._--Diameter of the gate 0.05 to 0.07; thickness of the ring 0.005 to 0.006. _Habitat._--Mediterranean (Messina), Hertwig, surface. {943}12. _Archicircus triglyphus_, n. sp.