In my Monograph of the Radiolaria (1862, pp. 265-345) forty-four genera of Nassellaria were enumerated (six Acanthodesmida and thirty-eight Cyrtida), whilst the total number of genera in the whole class of Radiolaria at that time amounted to one hundred and thirteen. But owing to the astonishing number of new and interesting forms of this legion which I afterwards detected in the collection of the Challenger, in 1881 I distinguished in my Prodromus not less than three hundred and seventeen genera. These were disposed in five large main groups, retained in the present Report, with twenty-six families, viz., (1) Plectoidea (with three families), (2) Stephoidea (with four families), (3) Spyroidea (with four families), (4) Botryodea (with three families), and (5) Cyrtoidea (with twelve families). The first two groups have an incomplete or rudimentary skeleton, and may be united in the order Plectellaria, whilst the other three families possess a complete latticed shell, and may be united as Cyrtellaria. The former correspond to the Acanthodesmida, the latter to the Cyrtida in my Monograph.

The character common to all Monopylea or Nassellaria, which separates them from all other Radiolaria, was first recognised by Richard Hertwig in 1879, and consists in the singular structure of the monaxonian central capsule, bearing on the basal pole a peculiar porous area or operculum, the "Porenfeld;" we call it shortly the "porochora." It represents a circular or elliptical porous plate on the basal pole of the vertical main axis of the central capsule, and bears a peculiar "podoconus" or "Pseudopodien-Kegel," a conical body of singular structure, protruding inside the membrane into the capsule. The pseudopodia arising from this peculiar "podoconus" proceed from the capsule piercing the "porochora," whilst the other parts of the capsule are not perforated.

The Monopylea are therefore "Merotrypasta," like the following fourth legion, the Phæodaria or Cannopylea. But in these latter we find on the basal pole of the monaxonian capsule only one single large main opening, prolonged into a peculiar tube, and there is no trace of the typical "podoconus," characteristic of all Nassellaria. The latter agree, however, with the former in the possession of a basal opening, serving for the emission of the pseudopodia, and in the monaxonian fundamental form, arising from this structure. Therefore these two legions of "Merotrypasta" exhibit a wider divergence from the Acantharia and Spumellaria, the two legions of "Holotrypasta," in which the central capsule is everywhere perforated by innumerable small pores (compare above, pp. [5], [6], [716]).

The Skeleton in all Nassellaria consists either of pure silica, or of a peculiar silicate; never of acanthin (as in all Acantharia). The siliceous bars and beams constituting it are invariably solid (as also in the Spumellaria); never hollow (as in the Phæodaria). In the small family of Nassellida alone (with the two genera Cystidium and Nassella) the skeleton is entirely absent. In all other genera of Nassellaria the siliceous skeleton is more or less developed; imperfect, or quite rudimentary in the Plectellaria (Plectoidea and Stephoidea), but perfect and forming a regular lattice-shell in the Cyrtellaria (Spyroidea, Botryodea, and Cyrtoidea). The different forms of this skeleton exhibit an extraordinary variety, but may be reduced to a few very simple fundamental forms, or even to a single, most simple original form. The comparative morphology is more interesting, but also more difficult to understand than in any other Radiolaria.

The geometrical fundamental form of the skeleton is in all Nassellaria monaxonial, the vertical main axis of the body, which is already indicated by the axis of the central capsule with two different poles, being also expressed constantly in the form of the skeleton. The lower or basal pole of the latter always exhibits a different shape from that of the upper or apical pole. This difference is so striking in nearly all Monopylea, that the two poles may be determined on the first view.

In the great majority of Nassellaria not only is the monaxonial fundamental form expressed, but also the dipleuric or bilateral, so that the symmetrical halves of the body may be easily determined; the right and left halves exhibit the same symmetry as in the vertebrates, so that we may distinguish an anterior ventral and a posterior dorsal face of the body. The whole form is in this case determined by three dimensive axes, perpendicular to one another, two of which are heteropolar, the third is homœopolar. The apical pole of the vertical main axis (principal or longitudinal axis) is different from the basal pole. The ventral pole of the horizontal sagittal axis (or dorso-ventral axis) is different from the dorsal pole. The right pole of the horizontal transverse axis (lateral or frontal axis) is equal to the left pole. Therefore the sagittal or median plane of the body (in which the principal and the sagittal axis are crossed) divides it into symmetrical equal halves and is perpendicular to the frontal axis.

Three different original elements of structure are recognisable in the majority of Nassellaria, viz., (1) a vertical simple ring, the primary or sagittal ring, placed vertically in the sagittal plane and enclosing the median plane of the central capsule; (2) a basal tripod, composed of three diverging radial rods, which are united on the basal pole of the central capsule and are either expanded horizontally or descend; (3) an ovate or subspherical, simple lattice-shell, the cephalis or capitulum, which surrounds the central capsule and exhibits a peculiar structure on its basal pole.

These three important original elements of structure—the sagittal ring, the basal tripod, and the latticed cephalis—are so united in the majority of Nassellaria that the cephalis rests upon the tripod and includes the sagittal ring wholly or partially. The simplest realisation of this typical union is afforded by the Archiperida and Tripospyrida, and these may be derived from the simpler important Stephanid Cortina (Pl. [83], fig. 9; Pl. [92], fig. 21; Pl. [97], fig. 1). In this and in all other tripodal Nassellaria, the three basal rods or the "cortinar feet" are constantly so arranged that an odd or posterior rod, the "caudal foot" (c) is opposed to the two anterior paired rods, the "pectoral feet" (one right, p″, and one left, p′). The caudal foot lies in the sagittal plane, and is prolonged upwards into the dorsal rod of the sagittal ring (b), and over this in a free ascending spine, the "apical horn" (a). The curved ventral rod of the ring (r) is united above with the base of the apical horn, below with the common centre of the tripod or the "cortinar centrum." The characteristic position of the central capsule in this skeleton of Cortina is such that its basal pole (with the porochora) rests upon the centre of the tripod, whilst its sagittal perimeter is separated from the surrounding ring by the calymma; the numerous pseudopodia arising from its base diverge downwards and are supported and protected by the three basal feet of the tripod (Pl. [97], fig. 1). Compare also Pls. [51], [53], [84], [95], [98].

The typical skeleton of Cortina, a tripodal ring, becomes more developed in the Semantid Cortiniscus, in which the basal parts of the three diverging feet are united by a second horizontal ring, the cortinar or basal ring (Pl. [92], figs. 11-13). The pores between the former and the latter, or the "cortinar pores," may be regarded as the first beginning of the lattice-plate, composing the "cephalis" or the simple primordial shell in the Archiperida and Tripospyrida, and transmitted from these by heredity to the great majority of Nassellaria.

The "cephalis or capitulum" (the "Köpfchen" of the German authors) is therefore the most important part of the skeleton in all Cyrtellaria, or in all Nassellaria possessing a complete lattice-shell. In the Plectellaria, however, or in those Nassellaria which do not possess a complete fenestrated shell, the "cephalis" is either imperfect or totally wanting. The cephalis surrounds the enclosed central capsule on all sides in the form of an ovate or subspherical lattice-shell, and is separated from it only by the jelly-like calymma. The sagittal ring is either enclosed in the wall of the cephalis (whole or partially), separating its two lateral halves, or it is enclosed in the cavity of the cephalis and connected with its sagittal perimeter by short beams. The base of the cephalis (with the cortinar plate) often rests immediately upon the centre of the tripod; in the majority of Nassellaria, however, this near relation is altered by reason of later changes and secondary modifications.