Nine equal and equidistant, straight, cylindrical radial spines, lying nearly in one plane, arise from an irregular spongy central framework; six of them seem to be secondary, intercalated between three equidistant primary spines, which are united in the centre. (This species resembles in the nine-radial structure the remarkable _Enneaphormis rotula_, Pl. 57, fig. 9, and may perhaps be derived from a similar species; but it has no regular latticed shell.) _Dimensions._--Length of the spines 0.22, diameter of the framework 0.17. _Habitat._--Central Pacific, Station 266, depth 2750 fathoms. {930}3. _Polyplecta decacantha_, n. sp. _Pentaplegma decacantha_, Haeckel, Prodromus, p. 425. Ten radial spines, curved, cylindrical, irregularly branched, diverge in different directions and seem to arise in pairs from an irregular central framework, in the centre of which five primary spines are united; the latter correspond probably to the five spines of _Pentaspyris_, &c. The density of the spongy central framework did not allow of an accurate investigation, and makes it doubtful whether this species is not a _Spongiomma_. _Dimensions._--Length of the spines 0.3 to 0.4, diameter of the framework 0.18. _Habitat._--Tropical Atlantic, Station 338, depth 1990 fathoms. 4. _Polyplecta polybrocha_, Haeckel. ? _Acanthodesmia polybrocha_, Haeckel, 1865, Zeitschr. f. wiss. Zool., Bd. xv. p. 368, Taf. xxvi. fig. 3. _Plegmosphæra polybrocha_, Haeckel, 1881, Prodromus, p. 455. Numerous (twenty to thirty or more) radial spines, thin, cylindrical, curved and irregularly branched, arising from an irregular central spongy framework, are connected by numerous slender arches. The specimen observed by me in 1880 in Portofino was a true _Polyplecta_, with three primary spines centrally united, between which numerous other spines were intercalated. The similar specimen, however, observed in 1864 in Villafranca, and figured, _loc. cit._, was perhaps a _Plegmosphæra_. _Dimensions._--Length of the radial spines 0.05 to 0.1, diameter of the framework 0.16. _Habitat._--Mediterranean (Villafranca, Portofino), surface. 5. _Polyplecta dumetum_, Haeckel. _Acanthodesmia dumetum_, J. Müller, 1868, Abhandl. d. k. Akad. d. Wiss. Berlin, p. 30, Taf. i. Fig. 3. Numerous (ten to twelve or more) radial spines, thin and straight, with a few straight lateral branches, diverge in different directions and are connected by a few slender curved arches. Some similar forms, but more developed, with numerous branches and curved rods, are found in the Pacific Radiolarian ooze, and represent probably different species. _Dimensions._--Length of the radial spines 0.05 to 0.08, of the branches 0.02 to 0.03. _Habitat._--Mediterranean, French shore (Cette and Saint Tropez), Johannes Müller, surface. {931}---- Suborder III. STEPHOIDEA, Haeckel.