B. The radial structure, indicated by radial apophyses arising from the shell, offers three principal differences, according to which the whole group of Cyrtoidea may be divided into three large groups or sections, viz., (1) Pilocyrtida, or Cyrtoidea triradiata, with three radial apophyses; (2) Astrocyrtida, or Cyrtoidea multiradiata, with numerous radial apophyses (four to nine or more); and (3) Corocyrtida, or Cyrtoidea eradiata, without external radial apophyses. The majority of Cyrtoidea are Pilocyrtida, with three radial apophyses, which are probably homologous to the three primary feet of the Plectoidea and of Cortina (therefore "cortinar feet"). The Astrocyrtida, or the Cyrtoidea with a variable number of radial apophyses (at least four to six) may be derived from the Pilocyrtida by interpolation of secondary or interradial apophyses between the three primary or perradial apophyses. The Corocyrtida, however, or the Cyrtoidea without external radial apophyses, may have originated by reduction and loss of the latter, either from the Pilocyrtida or from the Astrocyrtida.

C. The shape of the basal mouth in the Cyrtoidea exhibits two essential differences only, viz., (1) the terminal mouth of the shell is a simple wide opening in the Stomocyrtida, or (2) the terminal mouth is closed by a lattice-plate, in the Clistocyrtida. As these two different cases occur in all the twelve families, which we have distinguished according to the differences in the number of joints and in the radial structure, we get altogether twenty-four subfamilies which are synoptically arranged in the following table:—

The cephalis, or the first shell-joint of the Cyrtoidea, is in the majority homologous with the cephalis of the Spyroidea, from which it differs in the reduction of the sagittal ring and the absence of the corresponding sagittal constriction; its cavity is therefore simple, not bilocular. Its homology with the original cephalis of the Spyroidea cannot be doubted, when its base exhibits the typical basal pores of the Semantida. But in many cases these are wanting, and in a great number of Cyrtoidea (mainly of Monocyrtida) there is more or less evidence that the original cephalis is lost, and that the real first joint is the thorax, the original second joint. At present it is quite impossible to distinguish between the former and the latter shells, and therefore in the following descriptions the first joint is always named cephalis and the second thorax. In future, when the affinities of the Cyrtoidea become better known, it will be necessary to distinguish the "Archicephalis," or true cephalis of all Spyroidea and of the majority of Cyrtoidea, from the "Pseudocephalis" or the false cephalis of the minority (e.g., of many Monocyrtida aperta, Archipilida, Archiphormida, Archicorida, &c.).

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.

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.

The lattice-work of the shell exhibits in the Cyrtoidea an extraordinary variety, similar to that of the Sphæroidea; it serves in the first place for the distinction of species. The three first joints of the shell are often distinguished by the different character of the lattice-work. The cephalis has usually very small and simple pores. The lattice-work of the thorax is often characterised by radial structures. The pores of the abdomen are usually very numerous and regular. The numerous joints in the annulated abdomen of the Stichocyrtida commonly exhibit little variety.

The closure of the mouth, effected by a convex or horizontal terminal lattice-plate, has a different signification in the Monocyrtida and in the jointed Cyrtoidea. In the Monocyrtida clausa this closing plate is the original cortinar plate or the basal plate of the cephalis. In the jointed Cyrtoidea, however, the lattice-plate which closes the terminal mouth of the thorax or of the abdomen (of the last annular joint in the Stichocyrtida), is produced by central union of the convergent edges, which grow centripetally from the margin of the mouth of the last joint towards its centre.

The radial apophyses arising from the shell of the Cyrtoidea may probably be always derived from that tripodal structure which is found in all Plectoidea, in Cortina and Cortiniscus among the Stephoidea, and in the majority of Spyroidea. Therefore the prototype of this radial structure would be Plagoniscus and Cortina, with four radial spines united in a common point, the cortinar centrum; an ascending apical horn and three descending basal feet. The odd posterior or caudal foot is usually similar in shape to the two paired anterior or pectoral feet, but may be distinguished from these latter by its relation to the apical horn. Very frequently an internal vertical free columella arises in the cephalis, or instead of it an ascending rib in the dorsal wall of the cephalis, which connects the base of the apical horn with the origin of the caudal foot. This is probably the remaining part of the sagittal ring. More rarely also a part of the ventral rod of the latter is preserved, or on the anterior pole of the basal rod of the cephalis an ascending procolumella arises which is inserted on the frontal face of the cephalis, and sometimes prolonged into a nasal horn (the rod, C, of Bütschli). These two odd horns, the posterior apical horn and the anterior nasal horn, are usually different and divergent. In some genera a variable number of accessory radial horns is developed on the convex face of the cephalis. In many hornless genera the free apical horn is lost, but not unfrequently the columella is preserved which connects the caudal foot with that point of the cephalis, in which formerly the apical horn was inserted.

The three primary radial beams, corresponding to the three basal feet of Plectaniscus and Cortina, exhibit in the Cyrtoidea the greatest variety in form and size, and chiefly in their relation to the shell, the latter serving mainly for the distinction of genera. Originally these three cortinar beams arise from the basal plate of the cephalis, the odd caudal foot appearing as a prolongation of the basal rod of that plate, and the paired pectoral feet as prolongations of its coracal rods (between the jugular and cardinal pores). The lattice-work of the thorax is developed usually between the three cortinar feet, more rarely inside or outside of them. Therefore the three beams appear commonly as three divergent ribs in the wall of the thorax, and continue over its basal mouth as three free terminal feet. With the increasing length of the shell and the number of its joints the three radial ribs are also prolonged, and their free distal ends may be prominent at very different points, either as three lateral wings or as three terminal feet. These are either solid spines or lattice-plates, sometimes more or less ramified.

The three radial apophyses are prevalent in the majority of the Cyrtoidea, which we call "Pilocyrtida" (or Cyrtoidea triradiata). Their number increases in the Astrocyrtida (or Cyrtoidea multiradiata). The most frequent cases of multiplication are here caused by the development of six or nine radial apophyses; these may be enclosed ribs, or lateral wings, or terminal feet. In the sexradial Cyrtoidea there are three secondary or interradial apophyses interpolated between the three primary or perradial; in the nine-radial Cyrtoidea, however, there are six adradial apophyses interpolated.

A third and last great group is formed by the Corocyrtida or Cyrtoidea eradiata. These exhibit no radial apophyses, neither enclosed ribs, nor free lateral wings, nor terminal feet. But in a great number of them internal traces of an original triradiate structure are visible, mainly in the cortinar septum between cephalis and thorax; this often exhibits three or four, and sometimes six cortinar or collar pores, of the same typical shape as in the triradial Spyroidea. Sometimes even an internal columella with three radial branches is preserved, as in Axocorys. It is therefore very probable that a great part of these Cyrtoidea eradiata (if not all) may be derived from triradiate or multiradiate ancestral forms, by reduction and loss of the radial apophyses. In another part of this group, mainly in the Monocyrtida eradiata (Cyrtocalpida) it is possible, or even probable, that their eradiate shell has originated independently from Nassellida, and that they have no true relation to radial Cyrtoidea.

The Central Capsule of the Cyrtoidea, first observed by J. Müller (1858), and more fully described in my Monograph (1862), was very accurately examined by Richard Hertwig (1879). His observations were confirmed by numerous new forms, which I was able to examine in well-preserved preparations of the Challenger. The central capsule, according to these, exhibits the same typical shape, which is characteristic of all Monopylea (with porochora and podoconus), and may be derived with the latter from the common ancestral forms, Cystidium and Nassella (= the skeletonless Nassellida). In the majority, however, of Cyrtoidea, the capsule develops on its basal face a number of depending lobes, as were also found in some Spyroidea (and probably also Botryodea). In this respect we may distinguish two main forms of the capsule in the Cyrtellaria, viz., the primary simple, not lobate form, and the secondary lobate form. The central capsule is originally always enclosed in the cephalis, and has there a simple, subspherical, ellipsoidal or ovate form. As soon as their growth increases, and the enclosing cephalis becomes too narrow, it sends out prolongations in the form of basal lobes, which depend from its base, and proceed through the pores of the basal lattice of the cephalis, or the cortinar pores. In the great majority of Cyrtoidea in which the capsule was observed, either three or four such lobes were seen (already described by J. Müller). Of course this number depends upon the number of cortinar pores, which is either three or four; therefore in the Cyrtoidea with three pores in the cortinar plate, we find three lobes of the central capsule (an odd posterior and two paired anterior); in the Cyrtoidea, however, with four pores in the cortinar plate (the majority) we find four lobes of the central capsule (two smaller anterior jugular and two larger posterior cardinal lobes). Usually each lobe is ovate or pear-shaped and encloses a large oil-globule, and often also an apophysis of the cell-nucleus.

Section I. MONOCYRTIDA, Haeckel, 1862, Monogr. d. Radiol., pp. 280, 281.

Definition.—Cyrtoidea monothalamia, with simple, not jointed shell (or cephalis), without transverse constrictions.

Synopsis of the three Families and six Subfamilies of Monocyrtida.

Family LIX. Tripocalpida, n. fam.

Definition.—Monocyrtida triradiata. (Cyrtoidea with a simple, not jointed shell, representing a simple cephalis, with three radial apophyses.)

The family Tripocalpida, composed of the Archipilida and Archiperida of my Prodromus, comprises those Cyrtoidea in which the lattice-shell is quite simple, without transverse constriction, and bears three radial apophyses. The two subfamilies differ in the shape of the basal mouth, which in the Archipilida is a simple wide opening, in the Archiperida closed by a lattice-plate; the former are here divided into eight, the latter into seven different genera.

Only three species of this family were hitherto described, all three belonging to the Archipilida, viz., (1) Tripocalpis galea (fossil in Barbados, figured by Ehrenberg, 1875, as Halicalyptra galea), (2) Tripodiscium campanula (fossil in Sicily, figured by Stöhr, 1880, as Carpocanium); and (3) Tridictyopus elegans, of which Richard Hertwig gave an excellent description in 1879, with an accurate figure of the central capsule. All the other species of the family (seventy) are new.

The shell in the majority of Tripocalpida is ovate or campanulate, sometimes conical or three-sided pyramidal. Three radial apophyses are constantly distinct, either three lateral wings or three terminal feet; these are usually solid spines, rarely lattice-plates. The top of the shell usually bears an apical horn, rarely two or more horns; often the horn is wanting. The lattice-work of the shell is very various in the different species, and often of a remarkable structure (Pl. 51, figs. 6-8; Pl. 98, figs. 4-8). The cavity of the shell is in all Archipilida, and in a part of the Archiperida (Peridium, Archipera, Archibursa) quite simple. In the other part of the Archiperida, however, constituting the peculiar group of Euscenida (genera 504-507), a vertical columella arises in the centre of the basal plate, and is prolonged upwards in the apical horn; this columella is either simple (Euscenium, Archiscenium) or branched (Cladoscenium, Pteroscenium); in the latter case the ascending branches are disposed in triradiate verticils and are inserted on the inner face of the shell (compare Pl. 53, figs. 11-16, and Pl. 98, figs. 1-4).

The phylogenetic origin of the Tripocalpida may be very divergent, and their morphological affinity to the other Nassellaria is a very complicated problem. The Euscenida (genera 504-507) may be derived directly from the Plagonida (Plagoniscus) or Plectanida (Plectaniscus). The Archibursida (genera 508-510) however, manifest a closer affinity to the Tripospyrida, and may be derived from them by reduction of the sagittal ring and constriction. In these two groups of Archiperida the shell may be regarded as a true cephalis. In the Archipilida, however, where the shell has a wide basal opening and the three radial ribs arise originally from the base of the apical horn, the shell itself may correspond to the thorax of the Dicyrtida, and may be derived from these by loss of the cephalis. This is the more probable, as sometimes a small remnant of the reduced cephalis is preserved (Pl. 98, fig. 8). None of these difficult questions can be answered until a much closer morphological knowledge of the Tripocalpida is acquired.

Synopsis of the Genera of Tripocalpida.

Subfamily 1. Archipilida, Haeckel, 1881, Prodromus, p. 427.

Definition.—Tripocalpida with the basal mouth of the shell open (vel Monocyrtida triradiata aperta).

Genus 496. Tripocalpis,^[113] Haeckel, 1881, Prodromus, p. 428.

Definition.—Archipilida (vel Monocyrtida triradiata aperta) with three lateral ribs prolonged into three terminal feet. Apex with a horn.

The genus Tripocalpis opens the series of Archipilida, or of those Monocyrtida in which the monothalamous shell exhibits a distinct triradial structure, and a simple open mouth, without cortinar lattice. Tripocalpis is probably the most primordial of the Archipilida, and has three lateral ribs, which are prolonged into three free terminal feet, and connected in the apex of the pyramidal or campanulate shell with the apical horn. It may probably be derived from Dictyophimus by loss of the cephalis. The central capsule is simple, spherical, or ellipsoidal.

1. Tripocalpis plectaniscus, n. sp.

Shell three-sided pyramidal, smooth, about as long as broad, with irregular polygonal pores and thin bars. Apical horn stout, three-sided pyramidal, about as long as the shell. From the three edges of its base arise three prominent straight radial ribs, which are prolonged into three large divergent feet, of equal size and the same form as the horn.

Dimensions.—Shell 0.1 diameter, horn and feet 0.12.

Habitat.—Tropical Pacific (Philippine Sea), Station 206, depth 2100 fathoms.

2. Tripocalpis galea, Haeckel.