A further morphological differentation takes place in the remarkable genera Lonchostaurus and Zygostaurus. In the former (Pl. [131], figs. 4-6) the four larger equatorial spines becomes differentiated in pairs, so that the opposite equal spines of one pair, c1, c3 (in the longitudinal or hydrotomical axis), are larger, and often also of another form, than the opposite equal spines of the other pair, c2, c4 (in the transverse or geotomical axis). The most peculiar form is the rather common Zygostaurus (Pl. [131], figs. 7, 8). Here the two opposite spines of one equatorial axis (of the longitudinal axis) become very different, so that the anterior or frontal spine (c1) is very unequal to the posterior or caudal spine (c3), whereas the two opposite spines, of the other equatorial axis (of the transverse axis) remain equal (c2, c4). Therefore the fundamental forms become here "amphithect," as in the Ctenophora.
The numerous Quadrilonchida may be disposed in two different subfamilies: in the Acanthostaurida all twenty radial spines are simple, without apophyses; in the Lithopterida all twenty spines (or only one part of them) bear two opposite apophyses (or lateral transverse processes). The former correspond to the Zygacanthida, the latter to the Phractacanthida among the Astrolonchida. The two opposite apophyses are simple in Quadrilonche (Pl. [133], fig. 1). In Xiphoptera they are provided on their distal side with lateral branches which are parallel to the spine itself. In Lithoptera the spines bear two to four parallel pairs of transverse apophyses, and these are crossed by perpendicular branches, parallel to the spine itself, so that there arise fenestrated wings or latticed plates, comparable to the sails of a wind-mill. The lattice-work of these plates lies in the same meridian plane with the radial spine itself, and is therefore not comparable to the fenestrated apophyses of Doracantha, of Phatnacantha, and of the Dorataspida; in these the lattice-plates lie in tangential planes, perpendicular to the radial spine.
The apophyses of the Lithopterida may be developed either on all twenty spines equally, or only on twelve spines (four equatorial and eight tropical, whilst the eight polar spines are simple, Pl. [131], fig. 10), or only on the four equatorial spines (whilst the sixteen others are simple, Pl. [131], fig. 9).
The Central Capsule of the Quadrilonchida is rarely spherical, commonly more or less compressed from both poles of the spineless axis, lenticular or discoidal, sometimes square. It is enveloped by a voluminous calymma constantly bearing coronals of "Myophrisca" (compare p. [724]).
Synopsis of the Genera of Quadrilonchida.
II. Subfamily Acanthostaurida. All twenty spines simple, without lateral apophyses (sometimes forked, but neither branched nor latticed). |  | Four equatorial spines of equal size and form. |  | Eight tropical and eight polar spines nearly equal, | 334. Acanthostaurus. |
| Eight tropical and eight polar spines very different, | 335. Belonostaurus. | ||||
| Four equatorial spines of very different size or form (the two lateral constantly equal). | | Two principal spines of equal size and form, | 336. Lonchostaurus. | ||
| Two principal spines (frontal and caudal) very different, | 337. Zyostaurus. | ||||
II. Subfamily Lithopterida. Either all twenty spines or a part of them provided with two opposite lateral branches or apophyses. | | Apophyses simple, neither branched nor latticed, | 338. Quadrilonche. | ||
| Apophyses branched or pinnate, but not latticed, | 339. Xiphoptera. | ||||
| Apophyses latticed, with fenestrated network, | 340. Lithoptera. | ||||
| I. Subfamily Acanthostaurida. All twenty spines simple, without lateral apophyses (sometimes forked, but neither branched nor latticed). | ||||||||
| Four equatorial spines of equal size and form. | ||||||||
| Eight tropical and eight polar spines nearly equal, | ||||||||
| 34. Acanthostaurus. | ||||||||
| Eight tropical and eight polar spines very different, | ||||||||
| 35. Belonostaurus. | ||||||||
| Four equatorial spines of very different size or form (the two lateral constantly equal). | ||||||||
| Two principal spines of equal size and form, | ||||||||
| 336. Lonchostaurus. | ||||||||
| Two principal spines (frontal and caudal) very different, | ||||||||
| 337. Zyostaurus. | ||||||||
| II. Subfamily Lithopterida. Either all twenty spines or a part of them provided with two opposite lateral branches or apophyses. | ||||||||
| Apophyses simple, neither branched nor latticed, | ||||||||
| 338. Quadrilonche. | ||||||||
| Apophyses branched or pinnate, but not latticed, | ||||||||
| 339. Xiphoptera. | ||||||||
| Apophyses latticed, with fenestrated network, | ||||||||
| 340. Lithoptera. | ||||||||
Subfamily 1. Acasthostaurida, Haeckel, 1881, Prodromus, p. 466.
Definition.—Quadrilonchida with simple radial spines, without apophyses.