The thorax, or the second shell-joint of the #Cyrtoidea#, is in the majority homologous with the thorax of the Phormospyrida and Androspyrida, and therefore developed by apophyses, which arise from the base of the cephalis and become united by transverse branches forming a lattice-plate. Its size is generally in inverse proportion to that of the cephalis. The more the cephalis becomes reduced, the more the thorax is developed. Its form is very variable, usually three-sided pyramidal or prismatic in the triradiate, polyhedral in the multiradiate, and conical or cylindrical in the eradiate #Cyrtoidea#. Its terminal mouth is either a simple wide opening, or closed by a lattice-plate. In the majority of #Cyrtoidea# the thorax is separated from the cephalis not only by the external collar constriction, but also by the internal cortinar septum, a horizontal lattice-plate which exhibits the typical basal pores of the Semantida (usually two smaller jugular and two larger cardinal pores). But this septum is often reduced or perfectly lost, and then the external collar constriction alone indicates the separation of the cephalis and the thorax. The abdomen, or the third shell-joint of the #Cyrtoidea#, absent in the Monocyrtida and Dicyrtida (as also in all #Spyroidea#), occurs constantly in all Tricyrtida and Stichocyrtida. It is a simple large chamber in the Tricyrtida, but forms an annulated body, composed of a variable number of successive joints, in the Stichocyrtida. The constrictions between these joints, and also the lumbar constriction, between abdomen and thorax, are usually provided with a lattice-girdle, projecting into the cavity of the shell, like a diaphragm. Usually this horizontal girdle bears only a single circle of pores, rarely two or more. In many #Cyrtoidea# it is replaced by a solid horizontal ring of silex, and often it is wanting. It originates by the insertion of the following shell-joint, which takes place not on the terminal mouth of the preceding joint, but somewhat above it. {1131}The annular joints of the Stichocyrtida succeeding the third joint, and very variable in number, may be regarded either as a series of new postabdominal chambers, succeeding the true abdomen, or as secondary joints of the annulated abdomen itself. The latter view may be sustained by the fact that these joints are usually of an indifferent shape, and do not possess the characteristic features which we find in the first three joints, the abdomen, the thorax and the cephalis.