_Definition._--#Archiphormida# (vel Monocyrtida multiradiata aperta) with simple, slender, pyramidal shell, and numerous radial beams (six to nine or more). Network double, with a delicate arachnoidal fenestration, filling up the large quadrangular meshes. The genus _Cinclopyramis_ differs from the preceding _Bathropyramis_ in the development of a very delicate secondary network, filling up the large quadrangular meshes, which are produced by the crossing of the radial beams and the parallel horizontal rings. It therefore bears the same relation to the preceding genus that _Plectopyramis_ does to _Sethopyramis_; it is perhaps derived directly from the former by loss of the small cephalis. 1. _Cinclopyramis cribellum_, n. sp. _Cinclopyramis cribellum_ = "Ladder of lattice-shape," Bury, 1862, Polycystins of Barbados, pl. xii. fig. 6. Shell slender, pyramidal, with six strong radial ribs, which are connected by twelve to sixteen complete horizontal rings. Meshes trapezoidal, filled up by a very delicate and regular secondary network with square porules (two to four horizontal threads in each larger mesh). _Dimensions._--Shell 0.2 to 0.3 long, 0.12 to 0.16 broad. _Habitat._--Fossil in Barbados. 2. _Cinclopyramis infundibulum_, n. sp. (Pl. 54, fig. 7). Shell slender, pyramidal, with nine strong radial ribs, which are connected by eighteen to twenty-four complete horizontal rings. Meshes subregular square, filled up by a very delicate and regular secondary network with square porules (ten to twelve horizontal threads in each larger mesh). Apex of the pyramid with three very small cortinar pores. _Dimensions._--Shell 0.3 to 0.4 long, 0.2 to 0.25 broad. _Habitat._--Tropical Atlantic, Station 338, depth 1990 fathoms. {1162}3. _Cinclopyramis lithosestrum_, n. sp. Shell slender, pyramidal, with twelve strong radial ribs (six primary longer and six secondary shorter) connected by twelve to fifteen interrupted irregular rings. Meshes irregular square or trapezoidal, filled up by a delicate secondary network with irregular polygonal porules. _Dimensions._--Shell 0.4 to 0.5 long, 0.2 to 0.3 broad. _Habitat._--Fossil in Barbados. Genus 513. _Peripyramis_,[130] Haeckel, 1881, Prodromus, p. 428. _Definition._--#Archiphormida# (vel Monocyrtida multiradiata aperta) with double, slenderly pyramidal shell, and numerous radial beams (six to nine or more). Network double, with an external arachnoidal or spongy envelope around the primary lattice-shell. The genus _Peripyramis_ differs from its probable ancestral form, _Bathropyramis_, by development of a delicate external envelope around the primary shell, and therefore bears to it the same relation that _Spongopyramis_ among the Dicyrtida does to _Sethopyramis_. It may also be derived directly from the former by loss of the cephalis. 1. _Peripyramis circumtexta_, n. sp. (Pl. 54, fig. 5).