Definition.—Acantharia with a simple ellipsoidal lattice-shell, composed of the branched apophyses of twenty radial spines meeting in its centre and disposed according to the Müllerian law of Icosacantha. Two opposite equatorial spines larger than the two others. Central capsule ellipsoidal, enclosed in the fenestrated shell.

The family Belonaspida, formerly united by me with the Dorataspida (in the Prodromus, 1881, p. 468), differs from it in the ellipsoidal form of the lattice-shell and the enclosed central capsule. In the spherical Dorataspida, their ancestral family, all twenty radial spines are of equal size, whilst here in the Belonaspida two opposite spines are larger than the eighteen others. These two larger or principal spines are both equatorial spines, placed in the longitudinal or major axis of the ellipsoid, or the "hydrotomical axis" (compare above, p. [719]). The two other equatorial spines are constantly smaller, and lie in the transverse or minor axis of the ellipsoid, or the "geotomical axis." The geometrical proportion of these two determining axes of the ellipsoidal shell is very variable (even in one and the same species), commonly 4 : 3 or 3 : 2, rarely 2 : 1, often only 5 : 4 or 6 : 5. All meridian planes, passing through the principal spines (or the longitudinal axis of the shell) are elliptical, and of equal size. All transverse planes, perpendicular to that axis, are circular; the largest of these circular parallel planes is the geotomical plane, which passes through the smaller equatorial spines and the spineless axis.

In the spherical Dorataspida the internal length of the radial spines (or the distance between the shell and the centre) is equal in all twenty spines. In the ellipsoidal Belonaspida this internal length is different, and commonly exhibits four different degrees; in the two principal spines it is of first rank, in the eight tropical spines of second rank, in the four (hydrotomical) polar spines of third rank, and in the six spines (four geotomical polar spines and two transverse equatorial spines) of fourth rank. These differences of the internal length become more important the more the hydrotomical axis is prolonged. Regarding all other qualities (in form, disposition, and mode of junction at the centre) the ellipsoidal Belonaspida do not differ from their ancestral group, the spherical Dorataspida (compare above, p. [802]). In both families the pyramidal central bases of the twenty spines are commonly supported one upon another with their triangular neighbouring faces; but sometimes also here (particularly in Phatnaspis) the central bases are perfectly grown together. In this case also the sutures of the meeting branches of the apophyses are obliterated, whilst usually they remain open. Such forms, with spines and plates perfectly grown together, form a single piece of acanthin, and were formerly separated by me as a peculiar genus Haliommatidium (Monogr. d. Radiol., 1862, p. 419). But as I now find this concrescence to be an accidental and inconstant peculiarity of some species, it no longer seems to me to be of generic importance.

The apophyses of the twenty radial spines, the branches of which compose the ellipsoidal lattice-shell, exhibit in all Belonaspida the same appearance as in the Diporaspida (and especially the Ceriaspida) among the spherical Dorataspida. Everywhere each radial spine gives off only two opposite primary apophyses, the fork-branches of which unite together and form a plate or shield with two aspinal pores (as in Dorataspis). Commonly the shell exhibits only these forty parmal pores, the other meshes between them being sutural pores. Only in one genus, Phatnaspis (Pl. [136], figs. 6-9), is this number multiplied; the two opposite primary apophyses are here crossed by numerous perpendicular lateral branches, and these are again united by secondary perpendicular ramules which are parallel to the apophyses themselves; therefore each plate here forms a rhombic shield pierced by very numerous (often more than one hundred) small quadrangular or circular pores. Only two of these numerous parmal pores are the primary aspinal pores (sometimes, as in Pl. [136], fig. 8, distinguished by their larger size); all others are secondary or coronal pores. Therefore Phatnaspis repeats the characteristic formation of Coscinaspis, from which it differs in its ellipsoidal shell.

Moreover, the four other genera of the ellipsoidal Belonaspida correspond perfectly to certain genera of the spherical Dorataspida, and may be derived from these by hypertrophy or stronger development of two opposite equatorial spines. In Thoracaspis and Belonaspis (Pl. [139], figs. 8, 9) the surface of the shell-plates is without crests and dimples (in the former without, in the latter with accessory by-spines); they thus correspond to Dorataspis and Diporaspis among the Dorataspida. In two other genera the surface of the shell-plates bears a network of elevated crests, separating funnel-shaped dimples, in Dictyaspis without, in Coleaspis with by-spines; these correspond to Ceriaspis and Hystrichaspis among the Dorataspida. The small by-spines, covering the surface, exhibit the same forms as in the Dorataspida; but they are usually smaller, and less developed in the Belonaspida.

The twenty radial spines are commonly more or less compressed or two-edged, sometimes very flat, broad, and triangular (Pl. [139], figs. 8, 9). In some species (mainly of Phatnaspis) they are very long, thin, and needle-shaped (Monogr. d. Radiol., 1862, Taf. xxii. figs. 10-12). Rarely they are cylindrical, four-edged, or prismatic. The Belonaspida testify by this and other peculiarities to their near relation to the Diporaspida and Phractacanthida and their older origin from Zygacantha.

The Central Capsule is in the Belonaspida ellipsoidal, and more or less prolonged in the hydrotomical or longitudinal axis of the shell. It is constantly smaller than the enveloping ellipsoidal shell, and separated from it by the calymma. Its structure and the shape of its nucleus are the same as in the nearly allied Dorataspida.

Synopsis of the Genera of Belonaspida.

II. Subfamily Coleaspida.

Forty parmal pores (two aspinal pores on each plate, no coronal pores).

Plates not dimpled, without prominent crests.No by-spines,371. Thoracaspis.
With by-spines,372. Belonaspis.
Plates dimpled, with a network of prominent crests,No by-spines,373. Dictyaspis.
With by-spines,374. Coleaspis.

II. Subfamily Phatnaspida.

Eighty to two thousand or more parmal pores (two aspinal pores on each plate, surrounded by two to one hundred or more coronal pores).

No by-spines (plates not dimpled),375. Phatnaspis.
I. Subfamily Coleaspida. Forty parmal pores (two aspinal pores on each plate, no coronal pores).
Plates not dimpled, without prominent crests.
No by-spines,
371. Thoracaspis.
With by-spines,
372. Belonaspis.
Plates dimpled, with a network of prominent crests,
No by-spines,
373. Dictyaspis.
With by-spines,
374. Coleaspis.
II. Subfamily Phatnaspida. Eighty to two thousand or more parmal pores (two aspinal pores on each plate, surrounded by two to one hundred or more coronal pores).
No by-spines (plates not dimpled),
375. Phatnaspis.