The most important element of the skeleton, with which the formation begins, in all Stephoidea is the simple primary or sagittal ring, lying vertically in the sagittal or median plane of the body and surrounding the monaxonian central capsule. This sagittal ring is the only essential element of the skeleton in all Stephanida, and is completely preserved in all Semantida, also in the greater part of the Coronida and Tympanida. It is partially reduced in the small groups of the true Acanthodesmida (subfamily of Coronida) and the Dystympanida and Eutympanida (subfamilies of Tympanida). Here only the vertical parts of it are preserved (dorsal and ventral rod), whilst the horizontal parts are lost (mitral and basal rod).

The sagittal ring lies constantly in the vertical median plane of the body, and therefore divides the enclosed central capsule into a right and a left half. It is rarely regular or subregular, commonly dipleuric or distinctly bilateral, so that we may easily distinguish its dorsal and ventral, apical and basal parts. The most important of these four parts or "rods" is the "basal rod" or the inferior part, because here the ring is in closer connection with the central capsule and its "porous area"; here peculiar spines or branches are commonly developed, which even on the isolated ring immediately determine the basal pole. The opposite upper part, or the "mitral rod," is also often distinguished by the peculiar appendages. The posterior part, or the "dorsal rod" (the anterior rod, a, in the description of Bütschli), is commonly more straight, often quite vertical. The opposite anterior part, or the "ventral rod" (the posterior rod, b, of Bütschli), is usually more convex, and often strongly curved or semicircular.

Whilst this dipleuric or bilateral (commonly obliquely ovate or nearly triangular) form of the sagittal ring is distinctly preserved in by far the greater number of Stephoidea, it is replaced in some few genera by a more regular, amphithect, diphragmatic, or biradial form. In this case we may often suppose a primary regularity to exist, the dorsal and ventral parts being not yet differentiated, as in Archicircus and Lithocircus, Zygostephanus and Protympanium, and perhaps also in some other forms. But in other cases the regularity is, on the contrary, secondary, being derived from original bilateral forms.

The rod of the sagittal ring is either cylindrical (with circular transverse section) or angular (commonly with triangular transverse section). In nearly all Stephoidea (with very few exceptions) branches or apophyses are developed from the ring, regularly disposed and often of great morphological importance. Commonly these apophyses are developed in pairs, growing symmetrically on both sides of the ring. The most important of these apophyses are:—(1) Basal apophyses, arising from the basal hole of the ring; (2) mitral apophyses, arising from the apical pole; (3) dorsal apophyses, arising from the middle of the dorsal rod; and (4) ventral apophyses, arising from the middle of the ventral rod. The two former arise in the principal axis, the two latter in the sagittal axis of the body. Very frequently the latter pair is replaced by two pairs of transverse branches, one inferior (mandibular) and one superior (orbital). The apophyses of the ring are either simple or branched, often very large, richly ramified, and give origin to a number of further products.

Whilst in the Stephanida the primary sagittal ring alone represents the whole skeleton, it produces in all other Stephoidea one or more secondary rings. The most important of these is the horizontal basal ring, appearing first in the Semantida (Pl. [92]). From the base of the sagittal ring there arise in the horizontal basal plane two pairs of lateral branches or "basal apophyses." The curved opposite branches of the corresponding pairs become united on each side of the primary ring (right and left), and so produce a second, horizontal ring, perpendicular to the former. This basal ring encloses two paired basal gates, which are enclosed on the medial side by the basal rod of the sagittal ring, and on the lateral side by two united apophyses (Semantis, Pl. [92], figs. 1, 2). These two primary basal gates are of the greatest morphological importance; we call them the "jugular gates or jugular pores" (in the description of Bütschli, the pores I, loc. cit., p. 498). The dorsal pair of basal apophyses (on their posterior edge) are the coracal rods, e (rods e of Bütschli); the opposite ventral pair (on their anterior edge) are the clavicular or furcular rods, f (rods e1 of Bütschli); compare Pls. [92]-[95], and their explanation.

The skeleton of Semantis, the prototype of the Semantida, thus assumes the characteristic form of a signet-ring. The basal ring enclosing the two jugular pores corresponds to the seal-plate. It is commonly more or less horizontal; but often the apophyses descend obliquely (Pl. [92], figs. 1, 2, 13, &c.), more rarely laterally (Pl. [29], fig. 11). The further development of this typical form is essentially effected by the production of new basal pores in the horizontal seal-plate. In Semantrum (Pl. [92], figs. 3, 4, 5) we find already four basal gates. Behind the jugular gates is formed a second pair, the "cardinal gates" (pores II of Bütschli). These are enclosed on the anterior margin by the coracal rods (e), on the posterior margin by the scapular rods (d), a third pair of basal apophyses, arising behind the former from the sagittal ring and uniting with them (the rods e2 of Bütschli). Commonly the two posterior, or cardinal gates are much larger than the two anterior, jugular gates. This characteristic basal plate of Semantrum, with two pairs of basal pores, is of the greatest morphological importance, as it is inherited in by far the greater number of the Nassellaria, though not so generally as Bütschli supposes. The basal ring of Semantrum is either more circular or elliptical, or more polygonal, and is connected with the basal rod of the sagittal ring by three pairs of radial apophyses, the anterior furcular, the middle coracal, and the posterior scapular rods.

A third important form of Semantida is Semantidium (Pl. [92], figs. 6, 7). Here we find three pairs of basal pores in the seal-plate; the third pair, newly formed, consists of the cervical gates (e), bounded in front by the scapular rods (d), behind by a fourth pair of basal apophyses, the cervical rods.

The basal apophyses of the sagittal ring are not only of great morphological importance, because they produce by their union three typical pairs of basal gates or "collar pores," but also because their prolongations often appear as typical basal feet. The distal prolongations of the coracal rods appear in Semantiscus (Pl. [92], figs. 16-18) as two pectoral feet, those of the scapular rods as two tergal feet, whilst the opposite prolongations of the basal rod of the sagittal ring appear as two "sagittal feet" (in front an anterior or sternal, and behind a posterior or caudal foot). In the typical Cortiniscus (Pl. [92], figs. 11-13) only three feet are developed; an odd caudal and two paired pectoral feet (compare above, p. [891]). The typical basal ring of the Semantida, with its paired basal gates (Semantis), reappears in the majority of the Coronida, differing from the former in the development of a second vertical ring, which lies in the frontal plane (perpendicular to the sagittal ring), and which we therefore call the frontal ring. In only one small group of the Coronida the basal ring is absent, namely, in the Zygostephanida, and here the frontal ring appears in the simplest form, as a complete elliptical meridian ring, crossing the sagittal ring perpendicularly on the two poles of the main axis (Zygostephanus, Pl. [93], figs. 1-4), Four large lateral gates between the two rings remain open. This form may be derived directly from the Stephanida in the following way; from both poles of a simple sagittal ring there arise two opposite lateral apophyses, which in the frontal plane become curved one towards the other, and united in the poles of the transverse axis. The basal apophyses would be the coracal rods. But it is also possible that Zygostephanus was derived from Semantis by the loss of the furcular rods.

The three typical rings (or the "dimensive rings") of the Stephoidea appear in their most complete form in the subfamily Trissocyclida (Pl. [93], figs. 7, 13). Here all three rings are undivided and completely developed in the three dimensive planes, perpendicular one to another. Between them there remain eight large open gates; the four superior are the four "lateral gates" of Zygostephanus, the four inferior are the four basal gates of Semantrum. The four latter are originally much smaller than the four former; but in Trissocircus and Trissocyclus (Pl. [93], figs. 10-12) they reach the same size. Therefore all eight gates are here of equal form and similar size, and the basal ring, now a true equatorial ring, divides the two meridional rings into two equal halves.

In the Eucoronida, a third subfamily of Coronida, the sagittal and the basal rings are complete, but the frontal ring is incomplete, its basal part being wanting (Pl. [82], figs. 4-6). Therefore we find here six large gates between the three rings; four upper lateral gates (between the two crossed vertical rings) and two lower basal gates (between the basal rod of the sagittal ring and the two halves of the basal ring). Eucoronis, the type of this subfamily, may be derived either directly from Semantis by development of a frontal ring, or from Tristephanium by loss of the basal part of the frontal ring.