36. The Amphithect Pyramidal Ground-Forms.—The ground-forms whose geometrical type is the amphithect pyramid, are distinguished from the regular pyramidal forms, just discussed, chiefly by the form of the basal plane, which is not a regular, but an amphithect or elongated polygon (in the simplest case a rhombus). Hence in this case the allopolar main axis of the body is crossed by two transverse axes which are isopolar and at right angles, but are unequal; they cannot, however be distinguished as sagittal and frontal axes as is the case in the zeugites. In the animal as well as in the vegetable kingdom, an important part is played by this ground-form, e.g., in the Ctenophora, where it is the rhombic pyramid. Among the Radiolaria it is not common, though it is clearly expressed among the Nassellaria in a number of Stephoidea (Stephanida and Tympanida), as well as in many Spyroidea (e.g., the bipedal Zygospirida). It is very accurately developed among the Phæodaria in the bivalved Phæoconchia (Pls. [121]-[128]), where the two valves of the shell (dorsal and ventral) are generally exactly alike, their median keels corresponding to the poles of the sagittal axis. In the slit between the two valves lie the two secondary openings (right and left) of the tripylean central capsule, corresponding to the two poles of the frontal axis, and the main axis stands perpendicularly to both these, its oral pole being indicated by the astropyle, or principal aperture. (See Gener. Morphol., Bd. i. pp. 479-494.)
37. The Amphipleural Ground-Forms.—By the term amphipleural ground-forms are to be understood those usually defined as "bilaterally radial"; their geometrical type is a half amphithect pyramid. The best known examples of this form in the animal kingdom are the bilateral five-rayed Echinoderms (Spatangus, Clypeaster), in the vegetable kingdom the symmetrical five-rayed flowers (Viola, Trifolium). The three dimensive axes have the same relation as in the zygopleura, to be next discussed, and which also resemble them in being divisible only by one plane (the sagittal median plane) into two equal halves. They differ, however, the amphipleural body not being made up of two antimeres, but of at least three pairs of antimeres (or three parameres), being therefore primitively radial. Hence each of the symmetrical halves of the body contains more than one antimere. Among the Radiolaria this form does not occur in the Spumellaria, Acantharia, or Phæodaria; it is very common, however, among the Nassellaria; many Cyrtoidea multiradiata and Spyroidea multiradiata show this bilaterally radial ground-form, inasmuch as the body consists of two symmetrical halves, and is also composed of numerous (usually three, six, nine, or more) radial parameres. In the multiradiate Dicyrtida and Tricyrtida the cephalis (the first joint) is usually bilateral, whilst the thorax (the second joint) is multiradial. (See Gener. Morphol., Bd. i. pp. 495-506.)
38. The Zygopleural Ground-Forms.—As zygopleural or dipleural ground-forms, as opposed to the amphipleural, are classed those zeugites or centroplana which are known as "bilaterally symmetrical" in the strictest sense of the term. This is the most important ground-form in the animal kingdom, inasmuch as it obtains almost exclusively among the higher animals (Vertebrata, Articulata, Mollusca, Vermes). The body consists of only two antimeres, which correspond to the two symmetrical halves of the body. Of the three dimensive axes two are allopolar, one isopolar; the oral pole of the longitudinal main axis is different from the aboral; the dorsal pole of the sagittal axis is different from the ventral; but the right pole of the frontal axis is equal to the left. The right antimere is usually precisely similar to the left (Eudipleura), more rarely it is slightly dissimilar or asymmetrical (Dysdipleura). Among the Radiolaria this ground-form is entirely wanting in the Porulosa or Holotrypasta (Spumellaria and Acantharia), but on the contrary it is very common in the Osculosa or Merotrypasta (Nassellaria and Phæodaria). In the Nassellaria it is of special importance, for the typical Cortina (the combination of the primary sagittal ring with the basal tripod) exhibits the zygopleural ground-form clearly sketched out; indeed it is usually clearly seen even in the sagittal ring itself, for its ventral segment is more strongly curved than the dorsal; its basal (or oral) pole is always different from the apical (or aboral). Of the three feet of the basal tripod the unpaired (caudal) one is directed dorsally and backwards, the two paired (pectoral) ones ventrally and forwards. The majority of the Nassellaria may be regarded as modifications of this original ground-form. Its relation to the primitively triradiate tripod presents a still unsolved problem, and the numerous relations of the zygopleural to the multiradiate ground-forms in the Nassellaria are exceedingly complicated. The zygopleural ground-form is less widely distributed among the Phæodaria, though it is very characteristically developed in the rich and varied group of Challengerida (Pl. [99]). (See Gener. Morphol., Bd. i. pp. 507-527.)
39. Synopsis of the Geometrical Ground-Forms:—
| Principal Groups of Ground-Forms. | Subsidiary Groups of Ground-Forms. | Geometrical Type. | Examples. | |||
I. Centrostigma. The geometrical centre of the body is a point. Main axis wanting. |  | I. Homaxonia. All axes equal |  | 1. Sphere, |  | Central capsule of the Sphæroidea and of many Acantharia. |
II. Polyaxonia. Endospherical polyhedra. All the angles of the body lie on the surface of a sphere. Numerous isopolar axes. |  | 2. Endospherical polyhedron, | | Lattice-spheres of the Sphæroidea, Sphærophracta, and Phæosphæria. | ||
| 3. Icosahedron, | Circogonia. | |||||
| 4. Dodecahedron, | Circorrhegma. | |||||
| 5. Octahedron, | Cubosphærida, Circoporus. | |||||
| 6. Cube, | Centrocubus, Lithocubus, &c. | |||||
| 7. Tetrahedron, | Tetraplagia, Tetraplecta, &c. | |||||
II. Centraxonia. The geometrical centre of the body is a straight line (the vertical main axis).
Constant transverse axes (perpendicular to the main axis) are wanting in the Monaxonia (which have circular transverse sections); on the contrary they are differentiated in the Stauraxonia (which have polygonal transverse sections). |  | III. Monaxonia. Uniaxial ground-forms or centraxonia without transverse axes. The transverse planes (perpendicular to the main axis) are circles. |  | 8. Monaxonia isopola. (Spheroids and ellipsoids; both poles of the main axis similar.) |  | Central capsule and lattice-shell of of many Discoidea (lenses) and Prunoidea (ellipsoids), Belonaspida, &c. |
9. Monaxonia allopola. (Cone, ovoid and hemisphere; the two poles of the axis dissimilar.) | | Central capsule and lattice-shell of many Nassellaria, especially the Cyrtoidea eradiata (Cyrtocalpida, &c.). | ||||
IV. Stauraxonia. Pyramidal ground-forms or centraxonia with transverse axes. The transverse planes (perpendicular to the main axis) are either regular or amphithect polygons. | | 10. Dipyramides regulares. (Quadratic octahedron, or quadrilonchial forms and regular double pyramids.) | | Acantharia with twenty radial spines, the four equatorial being equal. Multiradial Discoidea and Staurosphærida. | ||
11. Dipyramides amphithectæ. (Rhombic octahedron, lentellipsoid, and amphithect double pyramids.) | | Acantharia with twenty radial spines, whose four equatorial spines are unequal but paired. Many Larcoidea. | ||||
12. Pyramides regulares. (Regular pyramids.) | | Many Nassellaria (triradial and multiradial). Medusettida and Tuscarorida. | ||||
13. Pyramides amphithectæ. (Rhombic pyramids.) | | Phæoconchia. Bipedal Spyroidea and Stephoidea. | ||||
III. Centroplana. The geometrical centre of the body is a plane (the sagittal plane). |  | V. Bilateralia (or Zeugita). Bilateral forms in the general sense, with right and left halves. | | 14. Amphipleura (Bilaterally radial ground-form.) | | Many Cyrtoidea and Spyroidea multiradiata. |
15. Zygopleura. (Bilaterally symmetrical ground-form.) | | Most Nassellaria (primitively at least), many Challengerida. | ||||
IV. Acentra. There is no geometrical centre. | | VI. Anaxonia. No definite axes can be determined. | | 16. Irregularia. (Absolutely irregular ground-forms.) | | Collodastrum, Collosphæra, Phorticida, Soreumida. |
| Principal Groups of Ground-Forms. | |||||
| Subsidiary Groups of Ground-Forms. | |||||
| Geometrical Type. | |||||
| Examples. | |||||
I. Centrostigma. The geometrical centre of the body is a point. Main axis wanting. | |||||
I. Homaxonia. All axes equal. | |||||
| 1. Sphere, | |||||
| Central capsule of the Sphæroidea and of many Acantharia. | |||||
II. Polyaxonia. Endospherical polyhedra. All the angles of the body lie on the surface of a sphere. Numerous isopolar axes. | |||||
| 2. Endospherical polyhedron, | |||||
| Lattice-spheres of the Sphæroidea, Sphærophracta, and Phæosphæria. | |||||
| 3. Icosahedron, | |||||
| Circogonia. | |||||
| 4. Dodecahedron, | |||||
| Circorrhegma. | |||||
| 5. Octahedron, | |||||
| Cubosphærida, Circoporus. | |||||
| 6. Cube, | |||||
| Centrocubus, Lithocubus, &c. | |||||
| 7. Tetrahedron, | |||||
| Tetraplagia, Tetraplecta, &c. | |||||
II. Centraxonia. The geometrical centre of the body is a straight line (the vertical main axis). Constant transverse axes (perpendicular to the main axis) are wanting in the Monaxonia (which have circular transverse sections); on the contrary they are differentiated in the Stauraxonia (which have polygonal transverse sections). | |||||
III. Monaxonia. Uniaxial ground-forms or centraxonia without transverse axes. The transverse planes (perpendicular to the main axis) are circles. | |||||
8. Monaxonia isopola. (Spheroids and ellipsoids; both poles of the main axis similar.) | |||||
| Central capsule and lattice-shell of of many Discoidea (lenses) and Prunoidea (ellipsoids), Belonaspida, &c. | |||||
9. Monaxonia allopola. (Cone, ovoid and hemisphere; the two poles of the axis dissimilar.) | |||||
| Central capsule and lattice-shell of many Nassellaria, especially the Cyrtoidea eradiata (Cyrtocalpida, &c.). | |||||
IV. Stauraxonia. Pyramidal ground-forms or centraxonia with transverse axes. The transverse planes (perpendicular to the main axis) are either regular or amphithect polygons. | |||||
10. Dipyramides regulares. (Quadratic octahedron, or quadrilonchial forms and regular double pyramids.) | |||||
| Acantharia with twenty radial spines, the four equatorial being equal. Multiradial Discoidea and Staurosphærida. | |||||
11. Dipyramides amphithectæ. (Rhombic octahedron, lentellipsoid, and amphithect double pyramids.) | |||||
| Acantharia with twenty radial spines, whose four equatorial spines are unequal but paired. Many Larcoidea. | |||||
12. Pyramides regulares. (Regular pyramids.) | |||||
| Many Nassellaria (triradial and multiradial). Medusettida and Tuscarorida. | |||||
13. Pyramides amphithectæ. (Rhombic pyramids.) | |||||
| Phæoconchia. Bipedal Spyroidea and Stephoidea. | |||||
III. Centroplana. The geometrical centre of the body is a plane (the sagittal plane). Constant transverse axes (perpendicular to the main axis) are wanting in the Monaxonia (which have circular transverse sections); on the contrary they are differentiated in the Stauraxonia (which have polygonal transverse sections). | |||||
V. Bilateralia (or Zeugita). Bilateral forms in the general sense, with right and left halves. | |||||
14. Amphipleura (Bilaterally radial ground-form.) | |||||
| Many Cyrtoidea and Spyroidea multiradiata. | |||||
15. Zygopleura. (Bilaterally symmetrical ground-form.) | |||||
| Most Nassellaria (primitively at least), many Challengerida. | |||||
IV. Acentra. There is no geometrical centre. | |||||
VI. Anaxonia. No definite axes can be determined. | |||||
16. Irregularia. (Absolutely irregular ground-forms.) | |||||
| Collodastrum, Collosphæra, Phorticida, Soreumida. | |||||
40. Mechanical Causes of the Geometrical Ground-Forms.—The great variety of ground-forms exhibited by the Radiolaria is of special interest, since in most instances their causes admit of recognition, and since they are so intimately related to each other that even in the remaining cases the assumption that they have arisen by purely mechanical causæ efficientes seems justified. In this respect the first rank is taken by statical conditions, especially the indifferent or stable equilibrium of the whole organism, which floats freely in the water. With regard to these fundamental statical relations, three principal groups of ground-forms may be distinguished, pantostatic, polystatic, and monostatic.
41. Pantostatic Ground-Forms.—By pantostatic or indifferently stable ground-forms are meant those in which the centre of gravity coincides with the centre of the body, so that they are in equilibrium in any given position. Strictly speaking, the only form which possesses perfectly indifferent equilibrium is the sphere, that being the only truly homaxon and perfectly regular form. Nevertheless, in a somewhat wider sense many Polyaxonia, especially the endospherical polyhedra with very numerous sides, may be included in this category. Such indifferently stable bodies are found among the Spumellaria in many Collodaria and Sphæroidea, as well as in the Astrolophida among the Acantharia. On the contrary they are entirely wanting among the Nassellaria and Phæodaria, since their central capsule constantly presents a main axis with a differentiated basal pole, and determines the position of stable equilibrium.
42. Polystatic Ground-Forms.—Those ground forms are defined as polystatic or multistable in which the body is in equilibrium in several different positions (though not in an infinite number). The number of these positions is usually twice as many as that of the constant equal isopolar axes exhibited by the form. Hence the regular polyhedra have as many positions of equilibrium as they have angles or sides, the icosahedron twenty, dodecahedron twelve, octahedron eight, cube six, tetrahedron four. The isopolar monaxon ground-forms (lens, ellipsoid, cylinder) and the diplopyramidal ground forms (quadrilonchial and lentelliptical) have two positions of stable equilibrium, since the two poles of the vertical axis are equal and similar and the body is divided into equal halves by the equatorial plane. This is the case in many Spumellaria (especially Discoidea, Prunoidea, and Larcoidea), as well as in the great majority of Acantharia. Perhaps the same holds good also in certain Nassellaria (e.g., isopolar Tympanida) and Phæodaria (e.g., isopolar Phæosphæria), though here unistable equilibrium appears to be necessitated by the constant main axis of the central capsule and the differentiated basal pole of the main axis.
43. Monostatic Ground-Forms.—Those ground-forms are classed as monostatic or unistable in which the body is in equilibrium only in one position, since the centre of gravity of the body lies in a constant vertical axis below its centre. This fixed position is only rarely and exceptionally found among the Spumellaria (e.g., in Xiphostylus, Sphærostylus, Lithomespilus, Lithapium) and among the Acantharia (e.g., in Zygostaurus and Amphibelone). On the contrary it is quite usual among the Nassellaria and Phæodaria (with but few exceptions); for here a vertical main axis, with a differentiated basal pole, is determined even by the formation of the central capsule, and usually also by the corresponding structure of the skeleton. Among the Nassellaria this basal pole, with the porochora of the central capsule, appears always to be the lower; as also in most Phæogromia among the Phæodaria. In the peculiar bivalved Phæoconchia, on the other hand, the basal pole with the cannopyle is directed upwards; as also in the Challengerida and Tuscarorida. The Phæosphæria and Phæocystina are probably to a large extent polystatic. In general unistable equilibrium may be assumed in the following categories of ground-forms:—(1) Allopolar monaxon (conical and ovoid); (2) pyramidal (regular and amphithect); (3) Centroplana (amphipleura and zygopleura); (4) Anaxonia.