The family #Lithobotryida# comprises those #Botryodea# in which the shell is divided by a transverse annular constriction into a lobate cephalis and a simple thorax. They correspond therefore to the Dicyrtida among the #Cyrtoidea#, and to the Phormospyrida among the #Spyroidea#. The thorax, or the second shell-joint, is in all these three families a secondary production, arising from the base of the cephalis; therefore the Lithobotryida must be phylogenetically derived from the Cannobotryida. Several species of _Lithobotrys_ were first described by Ehrenberg as _Lithobotrys_ and _Lithocorythium_. These two genera are, however, identical, as has been {1112}demonstrated by Bütschli (1882, _loc. cit._, p. 519). Some other species united by Ehrenberg with _Lithobotrys_ belong to other genera. The number of Lithobotryida found in the "Radiolarian ooze" of the Challenger collection, is far greater than that of the Cannobotryida and Pylobotryida. But only a small part of them could be thoroughly examined and described here, so that their number may be greatly augmented by further accurate researches. We here arrange those forms in four genera, representing two different subfamilies. The terminal mouth of the thorax remains open in the Botryopylida, whilst it becomes closed by a lattice-plate in the Botryocellida. In each group there are shells with and without porous tubes. The number of these tubes, and also the number of lobes of the cephalis, is very variable, and may in future serve for the distinction of more genera. _Synopsis of the Genera of Lithobotryida._ {Cephalis without porous I. Subfamily Botryopylida. { tubes, 488. _Botryopyle_. { Mouth of the thorax open. {Cephalis with a { variable number of { porous tubes, 489. _Acrobotrys_. {Cephalis without II. Subfamily Botryocellida. { porous tubes, 490. _Botryocella_. { Mouth of the thorax closed {Cephalis with a by a lattice-plate. { variable number of { porous tubes, 491. _Lithobotrys_. Genus 488. _Botryopyle_, Haeckel, 1881, Prodromus, p. 440. _Definition._--#Lithobotryida# without tubes on the cephalis, and with the mouth of the thorax open. The genus _Botryopyle_ comprises the simplest forms of Lithobotryida, the lobate cephalis bearing no tubes and the basal mouth of the thorax remaining open. It may be derived either from _Dictyocephalus_ or from _Desmospyris_, by development of lobes on the cephalis and of an internal frontal septum, separating the larger occipital lobe from the smaller frontal half of the shell. The latter may be divided again into anterior frontal lobes, lateral buccal lobes, &c. 1. _Botryopyle sethocorys_, n. sp. (Pl. 96, fig. 7).