The genus _Triplagia_ and the following closely allied _Plagiacantha_ may be regarded as the simplest and most primitive forms of the #Plectoidea#, perhaps as the common ancestral stock of this suborder. The skeleton is composed of three simple or branched radial spines, arising from one common central point. These three spines in _Triplagia_ lie in one and the same plane, whilst in _Plagiacantha_ they lie in different planes. Therefore the former exhibits the simplest type of the triradial structure, common to the majority of NASSELLARIA. {909}1. _Triplagia primordialis,_ n. sp. (Pl. 91, fig. 2). Spines straight, of equal size and similar form, equidistant, three-sided prismatic, each with two pairs of opposite lateral branches, which are correspondingly parallel to the two other spines; the proximal branches twice as long as the distal branches. _Dimensions._--Length of each spine 0.2, of the basal branches 0.07. _Habitat._--Central Pacific, Station 271, depth 2425 fathoms. 2. _Triplagia triradialis,_ n. sp. Spines straight, of equal size and similar form, equidistant, three-sided prismatic, regularly pinnate, with six pairs of opposite pinnulæ, tapering gradually towards the distal ends; the basal pinnulæ are again branched, with straight ramules. _Dimensions._--Length of each spine 0.27, of the basal branches 0.08. _Habitat._--North Pacific, Station 256, surface. 3. _Triplagia horizontalis,_ n. sp. Spines curved, cylindrical, irregularly branched, with three primary and nine to twelve secondary branches, which are also slightly curved. The angles between the bases of the three spines are equal, but the size and form of the branches different. _Dimensions._--Length of the three spines 0.15 to 0.25, of the basal branches 0.05 to 0.08. _Habitat._--West Tropical Pacific, Station 226, depth 4475 fathoms. Genus 385. _Plagiacantha_,[4] Claparède, 1856, Monatsber. d. k. preuss. Akad. d. Wiss. Berlin, November 13. _Definition._--#Plagonida# with three radial spines, arising from one common central point and corresponding to the edges of a three-sided pyramid. The genus _Plagiacantha_ agrees with the preceding _Triplagia_ in the simple structure of the triradial skeleton, composed of three diverging radial spines, which are united in a common centre at the oral pole of the central capsule. But whilst the three radial rods of _Triplagia_ lie in one horizontal plane, here they lie in different planes and correspond to the three edges of a flat pyramid. _Plagiacantha arachnoides_, described in 1856 by Claparède, was the earliest known form of all #Plectoidea#. {910}1. _Plagiacantha arachnoides_, Claparède. _Plagiacantha arachnoides_, Claparède, 1856, Monatsber. d. k. preuss. Akad. d. Wiss. Berlin, November 13. _Plagiacantha arachnoides_, Claparède, 1858, Études sur les Infusoires et les Rhizopodes, p. 462 (pl. xxii. fig. 8).