_Definition._--#Plectanida# with three radial spines, arising from one common central point and corresponding to the edges of a three-sided pyramid. The genus _Plectophora_ has been derived from _Plagiacantha_ by union of the meeting neighbouring branches of the three radial spines, and exhibits therefore to it the same relation that _Triplecta_ bears to _Triplagia_. The loose framework so produced corresponds to the three sides of a flat pyramid and supports the central capsule. 1. _Plectophora triomma_, n. sp. Spines equal, straight, three-sided prismatic, thorny, connected by three convex bows, the meeting branches of lateral spines arising in one pair from the middle part of each spine. Therefore the skeleton exhibits three large ovate meshes only. _Dimensions._--Length of the spines 0.12, of the meshes 0.08. _Habitat._--North Pacific, Station 238, surface. 2. _Plectophora arachnoides_, Haeckel. _Plagiacantha arachnoides_, var., Claparède, 1858, Études sur les Infusoires et les Rhizopodes, p. 462, Taf. xxii. fig. 9. Spines straight, cylindrical, trifid, with one pair of lateral branches. The nine diverging, straight, and smooth branches are connected in the distal part by slender concave bows, so that the whole skeleton exhibits nine wide meshes, three larger pentagonal and six smaller triangular. _Dimensions._--Length of the spines 0.14, of their branches 0.07. _Habitat._--North Atlantic, west coast of Norway (Claparède), surface. {923}3. _Plectophora novena_, n. sp. Spines slightly curved, three-sided prismatic, thorny, with two pairs of lateral branches. The six smaller distal branches end freely, whilst the six larger basal branches are connected by slender convex bows. There are therefore nine wide meshes, as in the preceding closely allied species. _Dimensions._--Length of the spines 0.18, of the basal branches 0.08. _Habitat._--North Atlantic, Færöe Channel (Gulf Stream) (John Murray), surface. 4. _Plectophora pyramidalis_, n. sp. Spines straight, three-sided prismatic, with three to four verticils of short lateral branches. The branches of the basal verticils are again ramified, and form by connecting bows a delicate loose framework, covering the three sides of a flat pyramid, the three edges of which are the three radial spines. _Dimensions._--Length of the spines 0.2, base of the pyramid 0.16. _Habitat._--Central Pacific, Station 267, surface. Subfamily 2. TETRAPLECTIDA, Haeckel, 1881, Prodromus, p. 424. _Definition._--#Plectanida# with four radial spines. Genus 395. _Tetraplecta_,[14] Haeckel, 1881, Prodromus, p. 424. _Definition._--#Plectanida# with four equal radial spines, arising from one common central point and corresponding to the four axes of a tetrahedron.