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 {892}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.

The number of various forms, developed from these simple original structural elements of the skeleton, is astonishing, and there are described more than three hundred genera and nearly two thousand species of this legion in the following pages. This large number may be easily increased by subsequent observers. Since in all these MONOPYLEA the characteristic structure of the central capsule is identical, and also the structural elements of the siliceous skeleton are similar, it is very probable that they may have arisen from a single common stock. But it is very difficult (and at present impossible) to explain a natural monophyletic system of this large legion. The greatest difficulty is presented by the fact that the three structural elements mentioned above, viz., the sagittal ring, the basal tripod, and the latticed cephalis, are not constantly united, but each alone may also constitute the skeleton by itself. In this respect the following seven cases are possible, and are actually realised.

A. The skeleton is composed of the sagittal ring only and of its spiny appendages, without basal tripod and without latticed cephalis. This is the case in the majority of #Stephoidea# (Stephanida, Semantida, Coronida, and Tympanida).

B. The skeleton is composed of a basal tripod only (Plagiacantha), or of a tripod in the centre of which arises a vertical apical horn (Plagoniscus), and often of an irregular framework, arising from the rods of the tripod; but there is neither a trace of a sagittal ring nor a complete latticed cephalis. This is the case in the remarkable suborder #Plectoidea# (Plagonida and Plectanida).

C. The skeleton is composed of a latticed cephalis only, a simple ovate or subspherical fenestrated shell, which encloses the monopylean central capsule; there is no {893}trace of a sagittal ring nor of a basal tripod. This is the case in the remarkable family of Cyrtocalpida (Archicorida and Archicapsida), in numerous #Botryodea# and in other #Cyrtellaria#.

D. The skeleton is composed of a sagittal ring and a basal tripod, without latticed cephalis. This is the case in a few, but very important forms of #Stephoidea#: Cortina, Stephanium, Cortiniscus, Stephaniscus, Podocoronis, and some allied genera.

E. The skeleton is composed of a sagittal ring and a latticed cephalis, but without basal tripod. This is the case in numerous #Cyrtellaria#, in the Circospyrida (or Zygospyrida apoda: Dictyospyris, Circospyris) and some other #Spyroidea#; and in a large number of #Botryodea# and Cyrtoidea eradiata (a part of the Sethocyrtida, Theocyrtida, Lithocampida, and others).

F. The shell is composed of a basal tripod and a latticed cephalis, but without any trace of the sagittal ring. This is the case in numerous Cyrtoidea triradiata and multiradiata, and perhaps in the majority of the following families--Tripocalpida, Tripocyrtida, Podocyrtida, and Podocampida.

G. The shell is composed of all three above-mentioned elements, of a sagittal ring, a basal tripod, and a latticed cephalis. This is the case in the great majority of #Spyroidea# (with a few exceptions only), and perhaps also in the majority of #Cyrtoidea#.

The survey of these seven groups, A to G, each of which is represented by numerous living forms, shows clearly how difficult and complicated the morphology and phylogeny of the numerous NASSELLARIA must be. For all possible combinations of the three original structural elements are realised abundantly, and in such complicated relations, and so intermingled in the different orders and families, that it seems nearly hopeless to answer the question of their true origin. The identity in the structure of the central capsule, however, in all these MONOPYLEA, makes it probable that they have all arisen originally from the skeletonless Nassellida (Cystidium, Nassella), either in a monophyletic or in a polyphyletic way. In this respect the following phylogenetical hypotheses are possible.

1. Monophyletic hypothesis, deriving all NASSELLARIA from a simple sagittal ring (Archicircus, Lithocircus, &c., Pl. 81). The groups A, D, E, and G may be derived easily from such a ring, but the groups B, C, and F only by means of the hypothesis that the original ring may be completely reduced and finally lost. This hypothesis was stated by me in the years 1877 to 1879, when I had got the first general survey of the astonishing number of new NASSELLARIA in the Challenger collection, and as I had found the sagittal ring in the majority of them. This, my former hypothesis, is mentioned by Richard Hertwig (1879, loc. cit., pp. 68, 126). It was afterwards supported with particular energy by O. Bütschli (1882, Zeitschr. für wiss. Zool., Bd. XXXVI.).

2. Monophyletic hypothesis, deriving all NASSELLARIA from a basal tripod (Triplagia, Plagoniscus, &c., Pl. 91). The groups B, D, F, and G, all triradiate, may {894}be derived easily from such a tripod; but the groups A, C, and E only by means of the hypothesis that the original tripod may be completely reduced and finally lost. This hypothesis was employed in 1881 in my Prodromus, since I had convinced myself that the "triradial structure" is prevalent in the great majority of NASSELLARIA, and is perhaps more important than the sagittal ring.

3. Monophyletic hypothesis, deriving all NASSELLARIA from a latticed cephalis, a simple ovate or subspherical fenestrated shell without ring and tripod (Cyrtocalpis, Archicapsa, &_c._). The groups C, E, F, and G may be derived easily from such a cephalis, but the groups A, B, and D only by means of the hypothesis that the sagittal ring as well as the basal tripod may remain as the last remnants of a reduced cephalis. This hypothesis was given in 1862 in my Monograph, where I constructed the first pedigree of Radiolaria (p. 234). I there derived all the Cyrtida from the #Sphæroidea# (Cyrtidosphæra), supposing that Cyrtocalpis and some other Monocyrtida may form a direct phylogenetical passage from the #Sphæroidea# to the #Cyrtoidea#.