Two species only of Plagonida have been hitherto known. The first form described is the _Plagiacantha arachnoides_, discovered thirty years ago (1855) by Claparède on the western shore of Norway. Another species of the same genus, from the Mediterranean, was very accurately described by Richard Hertwig in 1879 in his Organismus der {907}Radiolarien (_Plagiacantha abietina_). Upon these two species the latter founded his family Plagiacanthida, a term which was afterwards employed by Bütschli and others, for the whole group of #Plectoidea#. Many new forms are contained in the collection of the Challenger, so that we may describe here nine genera and thirty-four species. The family Plagonida may be divided into four different subfamilies, according to the numbers of the radial spines which compose the skeleton: Triplagida with three, Tetraplagida with four, Hexaplagida with six, and Polyplagida with numerous (seven to nine or more) radial spines. These are united commonly in one common central point, upon which rests the basal pole of the central capsule, with the porochora. More rarely (in the genera _Plagonidium_, _Plagiocarpa_, and _Plagonium_) the spines arise in two opposite groups (each with two or three spines) from the two poles of a common central rod; in this case the basal pole of the central capsule with the porochora rests upon the horizontal common rod, which corresponds probably to the basal part of the sagittal ring of the #Stephoidea# and #Cyrtellaria#. The different forms which the skeleton of the Plagonida assumes in the different genera of this family, and the important relations which these exhibit on the one hand to the spicula of the #Beloidea#, and on the other hand to the shell of some #Stephoidea# (_Cortina_, _Cortiniscus_, &c.) and #Cyrtoidea# (_Pteroscenium_, _Clathrocorys_, &c.), have been already pointed out in the preceding description of the suborder #Plectoidea#. There it is also demonstrated, that all these different forms may be derived from the simplest triradial forms, _Triplagia_ and _Plagiacantha_ (compare above, pp. 900-904). Whilst the genera of the Plagonida are characterised by the number of the radial spines and the peculiar mode of junction in a common central point or at the two poles of a common central rod, the different species of this family may be defined by the peculiar form of the spines and their branches. These morphological characters have also been already described above. We repeat here only that the radial spines in the majority of species are three-sided prismatic and verticillate, each verticil commonly with three branches. The distal ends of these branches remain constantly free, and are never united, as is always the case in the following family.