The Porodiscida are commonly flat or biconvex (rarely biconcave) disks, the central chamber of which is surrounded not by a single, but by a variable number (commonly three to six) of concentric chambered girdles or rings; they arise from Archidiscus by apposition of new concentric chambered rings around the first ring, all lying in the equatorial plane. Afterwards the disk often becomes thickened by apposition of concentric chamber-rings on both flat sides also, so that two to four or more layers are stratified one over the other. The circular concentric rings often become interrupted, or spirally convoluted (wholly or partially); also the chambers sometimes become irregularly crowded. But in all cases both surfaces of the disk (upper and lower) continue to be porous plates or sieve-plates, at least in the centre, but they never become spongy.

The margin of the disk exhibits in the Porodiscida a great variety of different forms, serving for distinction of subfamilies and of genera. In the Trematodiscida the margin remains quite simple, as in the Archidiscida, or is only surrounded by a hyaline equatorial girdle. In the Ommatodiscida it is distinguished by one or two peculiar oscula, surrounded by a corona of spines. The Stylodictyida are distinguished by a number of solid radial spines, and the Euchitonida by a number of chambered, or spongy, radial arms, arising from the margin of the disk and lying in the equatorial plane. The variety of these radial marginal appendages is in the Porodiscida much greater than in the Coccodiscida.

The Pylodiscida (Pl. [48], figs. 12-20) represent a new, small, but very remarkable family of Discoidea, all triradial, and distinguished by the peculiar formation of large open spaces in the latticed discoidal shell, which reappear in a similar shape among the Larcoidea in the Pylonida (Tetrapyle, &c.). We get the best understanding of this peculiar formation if we return to Archidiscus, probably the common ancestral form of all Cyclodiscaria, of the Porodiscida as well as of the Pylodiscida and Spongodiscida. In some species of Archidiscus (Archidiscus hexoniscus, Archidiscus pyloniscus, &c.) the small lenticular shell is composed of a spherical latticed central chamber and of a concentric equatorial girdle composed of six such chambers, either all six equal, or alternately larger and smaller. This latter form is nearly identical with Triodiscus, and if we imagine the lattice-work of only three ring-chambers complete, whilst that of the three alternating chambers is reduced to the marginal ring, we get Triopyle, by loss of this ring Triolene (a disk composed of four simple lattice-chambers, lying in one plane, three radial around one central spherule). The genera mentioned form together the subfamily of Triopylida. In the second subfamily, Hexapylida, the same formation is doubled; here three double arm-chambers are separated by three double spaces (two in each radius). Also here the three distal spaces may be either quite open (Pylolena), or half closed by the marginal girdle (Hexapyle), or quite loosely latticed (Pylodiscus). If the margin of this latter form become surrounded by a perfect chambered equatorial girdle, we get Discozonium, and if this acquire a peculiar marginal ostium (surrounded by a corona of spines) we arrive at Discopyle. These two latter genera form the third subfamily, the Discopylida. The eight genera of Pylodiscida represent therefore a continuous phylogenetic series.

The Spongodiscida are the sixth and last family of the Discoidea, differing from the five other families in the irregular, spongy structure of the discoidal skeleton; both surfaces of the flat disk (upper and lower) are here principally covered with a rough, spongy framework, whilst in the five other families they are covered by the flat and smooth porous plates or sieve-plates. Nevertheless there is no sharp boundary between the Spongodiscida and the closely allied Porodiscida. In these latter also the discoidal shell becomes often more or less spongy (mainly in the peripheral part, e.g., in Myelastrum, Pl. [47]); but at least the central part of the disk here remains constantly covered by sieve-plates. The massive skeleton of the Spongodiscida is either of perfectly irregular structure, only composed of innumerable fine branched siliceous threads, interwoven in all possible directions; or only the outer part of the disk is composed of such spongy framework, whilst the central part is more or less distinctly composed of concentric chambered rings, as in the Porodiscida. These latter forms indeed exhibit an immediate transition to this family, and were formerly (in 1862) separated by me as Spongocyclida. Also the polymorphous shape of the disk margin in the Spongodiscida is quite analogous to that of the Porodiscida. Whilst in the first subfamily, the Spongophacida, the margin is quite simple; in the second, the Spongotrochida, it is armed with solid radial spines; and in the third, the Spongobrachida, it is provided with two, three, or four spongy, radial arms—the former as well as the latter lying in the equatorial plane of the disk, either regularly or irregularly disposed.

The Equatorial Margin of the lenticular disk exhibits in all six families of Discoidea similar characters, mainly serving for the distinction of subfamilies and genera. In the most primitive genera of all six families the margin is simple, without radial prolongations (spines or arms); it is quite simple in Cenodiscus, Sethodiscus, Phacodiscus, Lithocyclia, Coccodiscus, Archidiscus, Porodiscus, Pylodiscus, and Spongodiscus. In some genera the simple margin of the lenticular disk is bordered and surrounded by a thin, hyaline, equatorial girdle of silex, either quite solid or slightly porous (Zonodiscus, Periphæna, Perizona, Perichlamydium, and Spongophacus).

A quite peculiar and remarkable character of few genera is the development of one or two oscula, larger marginal openings, which are surrounded by a corona of spines, and probable are fit for the issue a peculiar bunch of pseudopodia or of a "sarcode flagellum." Such oscula occur only in two families of Cyclodiscaria; in the Porodiscida and Pylodiscida; in the former Ommatodiscus, in the latter Discopyle (Pl. [48], figs. 19, 20) is distinguished by a single marginal osculum; besides this, in the former occurs Stomatodiscus, with two such oscula, opposite on the poles of one axis (Pl. [48], fig. 8). These oscula may be compared with the similar polar formations in some Ellipsida (Lithomespilus) and in many Cyrtoidea; but they do not prove a nearer affinity with the latter, and are only analogous, not homologous.

Radial Spines occur on the margin in the equatorial plane of the Discoidea in the greatest variety of number, form, size, and disposition. If the number be low (between two and eight) they are commonly regularly disposed; if the number be larger (ten to twenty or more) their disposition becomes commonly more or less irregular. The regular disposition is of great promorphological importance, as indicating the axes in which the growth is preponderant, and introduces other peculiar radial formations. Regarding these axes we can generally distinguish two groups, Artiacantha with a paired number (two, four, eight), and Perissacantha with odd numbers (usually three). The section of Artiacantha could be divided into three following groups:—A. Stylodiscida, with two radial spines only, lying opposite on both poles of one equatorial axis (the "first cross axis")—Stylodiscus, Sethostylus, Stylocyclia, Xiphodictya, Spongolonche (Pl. [31], figs. 9-12; Pl. [38], fig. 1; Pl. [42], figs. 10-12, &c.); B. Staurodiscida, with four radial spines, lying opposite in pairs on the poles of two crossed equatorial axes, perpendicular to one another (first and second cross axes)—Crucidiscus, Sethostaurus, Staurocyclia, Staurodictya, Spongostaurus (Pl. [31], figs. 1-8; Pl. [37], figs. 1-4; Pl. [42], figs. 1-6; Pl. [48], fig. 2, &c.); C. Octostylida, with eight radial spines, opposite in pairs in four axes, which are crossed at angles of 45°—Heliosestrum, Astrosestrum, &c. (Pl. [32], figs. 4, 5; Pl. [34], figs. 3, 6); in this latter case sometimes the radial symmetry is the same as in many Medusæ, four larger (perradial) spines alternating with four smaller (interradial), indicating radii of first and second order. The section of Perissacantha is much smaller, and commonly represented only by triradial forms, with three spines at equal distances (120°)—Triactis, Tripocyclia, Tripodictya, Spongotripus, &c. (Pl. [33], fig. 6; Pl. [37], fig. 5; Pl. [42], figs. 7-9).

Radial Arms on the margin of the disk appear in similar variety of number, form, and disposition as the radial spines; but the number is here commonly limited to from two to four, rarely five to six. The arms are absent in the families Cenodiscida and Phacodiscida; in the four other families they return under similar forms. These arms are direct prolongations of the disk, and exhibit the same structure, so that they may be regarded both as centrifugal productions of certain radii, and also inversely as peripheral parts of a disk, the interjacent radii of which are reduced. The regular disposition and shape of the arms, an important character for the distinction of genera and species, is repeated in a quite analogous manner in the four above mentioned families, so that we can distinguish the following groups—A. Amphibrachida, with two radial arms, opposite on the poles of one equatorial axis (the first cross axis)—Diplactura, Amphibrachium, Spongobrachium (Pl. [38], figs. 3-5; Pl. [44], figs. 6-11); B. Triobrachida, with three radial arms; the most important group (with all Pylodiscida); either all three arms are equal and disposed at equal distances (Trigonactura, Dictyastrum, Rhopalodictyum, Pl. [38], figs. 6-9; Pl. [43], figs. 5, 13, 16; Pl. [48], figs. 12-19), or a single odd arm differs in size and position, and is often larger than both the opposite paired arms (Rhopalastrum, Euchitonia, Pl. [43], figs. 6, 10, 15, &c.); C. Tetrabrachida, with four radial arms, opposite in pairs in two crossed axes, commonly perpendicular one to another, Stauractura, Stauralastrum, Spongaster, &c. (Pls. [46], [47]).

The arms are commonly simple, undivided, but sometimes also forked or branched (Pl. [43], figs. 15, 16; Pl. [47]). Their basal parts are either free, separately inserted into the margin of the circular central disk, or they are connected by a "patagium," a peculiar connecticulum, like a web-membrane, which is composed of a chambered, commonly more or less spongy framework, different in texture from the lattice-work of the arms (Pl. [38], figs. 8, 9; Pl. [43], figs. 9-16; Pl. [46]). Sometimes the patagium overgrows the whole shell. A peculiar modification of it appears in Stephanastrum (Pl. [44], fig. 1), where only the distal parts of the arms are connected by the ring-shaped patagium, whilst the basal parts are free; therefore open gates rest between them, like those of the Pylodiscida (Pl. [48], figs. 12-20).

The Central Capsule of the Discoidea is constantly discoidal, more or less lenticular; in some cases more biconvex, with vaulted faces and thin margin; in others more medal-shaped, with flat faces and thick margin. In the Cenodiscida alone the capsule lies freely inside the simple phacoid shell, and is separated from it by the jelly-veil. In the other five families the capsule encloses the central parts of the skeleton, and is enveloped by the superficial parts of it, whilst its membrane is perforated by radial beams connecting the latter with the former. In the Phacodiscida and Coccodiscida the capsule encloses the simple or double medullary shell, but is itself enclosed by the cortical phacoid shell. In all Cyclodiscaria (in the Porodiscida, Pylodiscida, and Spongodiscida) the capsule fills out the greatest part of the chambered or spongy skeleton, and is only protected by the superficial parts of it, in the Porodiscida and Pylodiscida by the covering sieve-plates, in the Spongodiscida by the spongy cortical substance of the shell. The growth of the capsule corresponds to that of the including shell, gradually increasing on the margin in the equatorial plane. Whilst in the greater number of Discoidea its form continues circular, in many forms provided with radial arms it enters into the arms and assumes their form. The protoplasm of the capsule is commonly coloured by brown or red pigment, and often contains many oil-globules. The nucleus is originally enclosed by the medullary shell or the central chamber, and with increasing size enters into the surrounding parts; in the Cyclodiscaria it often fills out the internal concentric rings. The extracapsular jelly or the calymma is commonly thick, and envelops the greater part or the whole body.