The Project Gutenberg eBook of Report on the Radiolaria Collected by H.M.S. Challenger During the Years 1873-1876, First Part: Porulosa (Spumellaria and Acantharia), by Ernst Haeckel

33. The Regular Dipyramidal or Quadrilonchial Ground-Form.—The ground-forms whose geometrical type is the regular double pyramid are characterised by a vertical main axis which possesses equal poles, and which is crossed at its centre by several equal transverse axes. The horizontal equatorial plane is therefore a regular polygon, and divides the body into two equal regular pyramids. The simplest and commonest form of this group is the quadratic octahedron, the ground-form of the quadratic crystallographic system; its equatorial plane is a square. This regular dipyramidal ground-form occurs among the Spumellaria in the shells of the Staurosphærida as well as of many Discoidea, in which several equidistant radial spines or arms lie in the quadratic equatorial plane of the body, and project from the margin of the lenticular disc (e.g., Sethostaurus, Pl. 31; Histiastrum, Pl. 46, &c.). It is, however, among the Acantharia that the most important part is played by this ground-form (and especially by the quadratic octahedron); it forms the basis of all those Acanthometra and Acanthophracta in which twenty radial spines are disposed according to the Müllerian Law, and in which the four equatorial spines are of equal dimensions (Icosacantha). (See Gener. Morphol., Bd. i. p. 436-446.)

34. The Amphithect Dipyramidal or Lentelliptical Ground-Forms.—The ground-forms whose geometrical type is the lenticular or "triaxial" ellipsoid, may also be designated amphithect double pyramids; they are characterised by the possession of a vertical main axis which has similar poles, and is crossed at its middle by two transverse axes, unequal but isopolar. The horizontal equatorial plane of the body is therefore an amphithect or elongated polygon (a rhombus in the simplest case possible), and divides the whole body into two equal amphithect pyramids. The simplest and commonest form of this group is the rhombic octahedron, which is also the ground-form of the rhombic crystallographic system. It plays an important part in those Acantharia in which twenty radial spines are disposed according to the Müllerian Law, but in which the two pairs of equatorial spines are unequal (different geotomical and hydrotomical axes, see p. 719); to this category belong the Amphilonchida (Pl. 132), Belonaspida (Pl. 136), Hexalaspida (Pl. 139), and Diploconida (Pl. 140). A form essentially identical obtains also among the Spumellaria in the majority of the Larcoidea, both in their triaxial lattice-shells, and in their lentelliptical central capsules, which present geometrically accurate triaxial ellipsoids, with three unequal isopolar axes at right angles to each other. (See Gener. Morphol., Bd. i. p. 446-452.)

35. The Regular Pyramidal Ground-Forms.—The ground-forms whose geometrical type is the regular pyramid, and which are the most conspicuous in the Medusæ, Polyps, Corals, and regular Echinoderms (the Radiata of earlier authors), are almost confined among the Radiolaria to the legion Nassellaria; they occur, however, in the great majority of these, and especially in those families which may be classed together as "Cyrtoidea triradiata et multiradiata." Strictly speaking, however, almost all these Nassellaria, at all events in their origin, are bilateral or dipleuric, since the primary sagittal ring with its characteristic apophyses marks out the sagittal median plane, and further, since the three feet of the basal tripod are usually divided into an unpaired dorsal (pes caudalis) and two paired ventral or lateral (pedes pectorales, dexter et sinister). On the other hand, it is noteworthy, firstly, that among the primitive Plectoidea there are perfectly regular radial forms, without any indication of an original bilateral symmetry, and secondly, that similar forms are also very common among the Cyrtoidea, probably as secondary radial forms, developed from primitive bilateral ones. Similar cases also occur in certain Phæodaria (e.g., the Medusettida and Tuscarorida, Pls. 100, 120), but they are entirely wanting among the Acantharia and Spumellaria. The multiradial Nassellaria have arisen from the triradial by the interpolation of three, six, nine, or more interradial and adradial secondary apophyses between the three primary perradial ones. (See Gener. Morphol., Bd. i. pp. 459-874.)

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.	brace	I. Homaxonia. All axes equal	brace	1. Sphere,	brace	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.	brace	2. Endospherical polyhedron,	brace	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).	brace	III. Monaxonia. Uniaxial ground-forms or centraxonia without transverse axes. The transverse planes (perpendicular to the main axis) are circles.	brace	8. Monaxonia isopola. (Spheroids and ellipsoids; both poles of the main axis similar.)	brace	Central capsule and lattice-shell of of many Discoidea (lenses) and Prunoidea (ellipsoids), Belonaspida, &c.
			brace	9. Monaxonia allopola. (Cone, ovoid and hemisphere; the two poles of the axis dissimilar.)	brace	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.	brace	10. Dipyramides regulares. (Quadratic octahedron, or quadrilonchial forms and regular double pyramids.)	brace	Acantharia with twenty radial spines, the four equatorial being equal. Multiradial Discoidea and Staurosphærida.
				11. Dipyramides amphithectæ. (Rhombic octahedron, lentellipsoid, and amphithect double pyramids.)	brace	Acantharia with twenty radial spines, whose four equatorial spines are unequal but paired. Many Larcoidea.
				12. Pyramides regulares. (Regular pyramids.)	brace	Many Nassellaria (triradial and multiradial). Medusettida and Tuscarorida.
				13. Pyramides amphithectæ. (Rhombic pyramids.)	brace	Phæoconchia. Bipedal Spyroidea and Stephoidea.
III. Centroplana. The geometrical centre of the body is a plane (the sagittal plane).	brace	V. Bilateralia (or Zeugita). Bilateral forms in the general sense, with right and left halves.	brace	14. Amphipleura (Bilaterally radial ground-form.)	brace	Many Cyrtoidea and Spyroidea multiradiata.
	brace		brace	15. Zygopleura. (Bilaterally symmetrical ground-form.)	brace	Most Nassellaria (primitively at least), many Challengerida.
IV. Acentra. There is no geometrical centre.	brace	VI. Anaxonia. No definite axes can be determined.	brace	16. Irregularia. (Absolutely irregular ground-forms.)	brace	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.
	I. Homaxonia. All axes equal.
		1. Sphere,
		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,
		2. Endospherical polyhedron,
			Lattice-spheres of the Sphæroidea, Sphærophracta, and Phæosphæria.
		3. Icosahedron,
		3. Icosahedron,
			Circogonia.
		4. Dodecahedron,
		4. Dodecahedron,
			Circorrhegma.
		5. Octahedron,
		5. Octahedron,
			Cubosphærida, Circoporus.
		6. Cube,
		6. Cube,
			Centrocubus, Lithocubus, &c.
		7. Tetrahedron,
		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.)
		12. Pyramides regulares. (Regular pyramids.)
			Many Nassellaria (triradial and multiradial). Medusettida and Tuscarorida.
		13. Pyramides amphithectæ. (Rhombic pyramids.)
		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.)
		14. Amphipleura (Bilaterally radial ground-form.)
			Many Cyrtoidea and Spyroidea multiradiata.
		15. Zygopleura. (Bilaterally symmetrical ground-form.)
		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.
	VI. Anaxonia. No definite axes can be determined.
		16. Irregularia. (Absolutely irregular ground-forms.)
		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.

44. Principal Axes.—From the foregoing consideration of the statical conditions and their direct causal connection with the geometrical ground-forms of the Radiolaria, the great mechanical significance of the differentiation of definite axes in these unicellular free-swimming organisms will be manifest. The most important of these is the primary main axis (axis principalis, or protaxon), which in all cases has a vertical direction. It is wanting in the Centrostigma (spheres and endospherical polyhedra), and in the Anaxonia (acentra). It is isopolar in the phacotypic forms (Monaxonia isopola), and in the double pyramids (Stauraxonia isopola). It is allopolar in all monastatic ground-forms, in the conotypic forms (Monaxonia allopola), pyramids (Stauraxonia allopola), and the Centroplana (or bilateral forms).

45. Secondary or Transverse Axes.—In contrast to the vertical main axis all the other constant axes differentiated in the body may be called "secondary axes," or "transverse axes," since they cross the former at definite points. All ground-forms whose vertical axis is crossed by a fixed number of such axes at definite angles may be called "Stauraxonia." They are divided into two groups, double pyramids and single pyramids; in the former the two poles of the main axis (or the two halves of the body separated by the equatorial plane) are similar (Stauraxonia homopola), in the latter dissimilar (Stauraxonia heteropola). If all the secondary axes be equal, the stauraxon ground-form is regularly radial. If some of them be unequal they are arranged in certain relations towards two primary transverse axes, perpendicular to each other, to which all the other secondary axes are subsidiary; the ground-forms are then either amphithect or bilateral. The two primary transverse axes, which may also be designated "ideal transverse axes" (euthyni), divide the vertical main axis in its centre; one of them is the sagittal, the other the frontal. These three dimensive axes give the factors which accurately determine the ground-form and the dimensions in most Radiolaria; the vertical main axis determines the length (principal axis); one horizontal transverse axis determines the thickness (sagittal axis), and the other the breadth (frontal axis). Those ground-forms in which the transverse axes are isopolar are termed "amphithect," and those in which the one (frontal or lateral) is isopolar and the other (sagittal or dorso-ventral) is allopolar, are termed "bilateral," or better "zeugitic."

46. Primary and Secondary Ground-Forms.—The geometrical sphere must be regarded as the original ground-form of the Radiolaria; it being understood that its monophyletic derivation from a single stem-form, Actissa, is correct. The simplest forms of Actissa (Procyttarium, Pl. 1, fig. 1) are in fact geometrically perfect spheres; indeed even the individual parts which compose their unicellular bodies (nucleolus, nucleus, central capsule and calymma) are concentric spheres. But in addition the central capsules of most other Spumellaria, especially the Sphæroidea, as well as of many Acantharia are true spheres. Furthermore the simple or concentrically composed lattice-spheres of Sphæroidea, Sphærophracta, and Phæosphæria may be regarded as spheres, although strictly speaking they are endospherical polyhedra. From the primary spherical form of the Radiolaria all other secondary forms may be derived in the following order:—1. By the development of a main axis the Monaxonia arise. 2. By the development of transverse axes the Stauraxonia arise. 3. In both groups (Monaxonia and Stauraxonia) the two poles (or upper and lower halves of the body) are at first similar (Isopola). 4. By differentiation in the two poles or halves of the body (distinction between the basal pole and the apical) the forms with different poles (Allopola) arise. 5. The transverse axes of the Stauraxonia are at first equal (regular pyramids and double pyramids). 6. By differentiation in the transverse axes (distinction between the sagittal and the frontal axis) the amphithect pyramids and double pyramids arise. 7. From the amphithect pyramids the Amphipleura arise by differentiation of both poles of the sagittal axis. 8. The zygopleural ground-form appears last, as the simplest form of the Amphipleura.

47. The Ground-Forms of the Spumellaria.—The Spumellaria, being the oldest and most primitive Radiolaria, have for the most part either indifferent or multistable equilibrium; e.g., all Colloidea and Beloidea which have a spherical central capsule, and also most Sphæroidea. Among these primitive Centrostigma true spheres and endospherical polyhedra are represented in the utmost variety, and the regular polyhedra in particular. By the development of a vertical main axis these Centrostigma have also given rise to very numerous Centraxonia, which are usually isopolar, very rarely allopolar. Sometimes they are Monaxonia (circular in transverse section), sometimes Stauraxonia (polygonal in transverse section). The vertical main axis is longer in the Prunoidea, shorter in the Discoidea than any of the other axes. The Larcoidea are distinguished by their lentelliptical or triaxial ellipsoid form; the three different but isopolar axes corresponding with those of the rhombic octahedron; but even among the Sphæroidea, Prunoidea, and Discoidea, this form is sometimes produced by the differentiation of two different transverse axes at right angles to each other. Whilst these ground-forms (Centraxonia and Centrostigma) occur in the utmost variety among the Spumellaria, the centroplanar (or true bilateral) ground-form is entirely wanting.

48. The Ground-Forms of Acantharia.—In the small family Astrolophida, which contains the most archaic forms of the legion (Actinelius, Astrolophus), the Acantharia show a direct relation to the most primitive Spumellaria (Actissa), and like these have indifferent equilibrium; their central capsule is a sphere, their calymma an endospherical polyhedron, whose angles are indicated by the distal ends of the numerous equal radial spines. In the great majority of Acantharia, however (all Acanthonida and Acanthophracta), twenty radial spines are present, regularly distributed, according to Müller's icosacanthan law, in five parallel circles, each containing four crossed spines (p. 717). Usually the twenty spines are equal, and the ground-form is the quadratic octahedron, or a regular double pyramid with sixteen sides. But in some groups (the Amphilonchida and Prunophracta) two opposite equatorial spines are much more strongly developed than the other eighteen, and therefore the hydrotomical axis in the equatorial plane is larger than the geotomical axis (p. 719); the isopolar stauraxonian form passes over into the allopolar, and the ground-form becomes the rhombic octahedron or the amphithect double pyramid (compare §§ 33 and 34, and p. 720). The centroplanar ground-form is entirely wanting in the Acantharia.

49. The Ground-Forms of the Nassellaria.—The Nassellaria all possess monostatic ground-forms, inasmuch as by the very structure of their monopylean central capsule a vertical main axis is necessitated, whose basal pole occupies the porochora. The same arrangement is also for the most part clearly recognisable in the corresponding structure of the skeleton, which is generally either centraxon or centroplanar. Among their manifold skeletal forms different larger groups of ground-forms may be recognised according as the vertical allopolar main axis is crossed by differentiated transverse axes or not (Stauraxonia or Monaxonia); the former are either triradial or multiradial. The triradial, with three lateral or terminal radial apophyses, constitute the greater part of the Nassellaria, and have probably been derived originally from the triradial Plectoidea (Triplagia, Triplecta); a more careful examination, however (especially with reference to the structure of the cortinar septum), reveals the fact that the ground-form is not strictly regularly pyramidal (with three equal radii), but amphipleural (with two paired ventral and one unpaired dorsal radius), and that it usually passes over into a distinctly zygopleural form. The same holds true of the multiradial Nassellaria, where for the most part three interradial or six adradial (sometimes more) apophyses are intercalated between the three primary perradial ones; sometimes here also the ground-form is a quite regular hexagonal or nonagonal pyramid, but usually it is more or less amphithect or amphipleural. Among the eradial Nassellaria, which have no radial apophyses, the ground-form is sometimes allopolar monaxon (conical, ovoid, hemispherical, &c.), sometimes amphithect pyramidal (even in the simplest Stephanida, Archicircus, &c.), or sometimes distinctly zygopleural or bilateral (many Plectellaria).

50. The Ground-Forms of the Phæodaria.—The Phæodaria agree with the Nassellaria in the possession of a primitively centraxon ground-form, and like them are monostatic, since a vertical main axis whose basal pole passes through the astropyle is present, owing to the characteristic structure of their cannopylean central capsule. In the great majority of Phæodaria the spheroidal central capsule also possesses a pair of parapylæ near the opposite apical pole of the main axis (Tripylea), and these determine (as the right and left secondary openings) an isopolar frontal axis. Hence, strictly speaking, in most Phæodaria the central capsule has the geometrical ground-form of the amphithect pyramid (as in the Ctenophora), with an allopolar vertical main axis, and two unequal, but isopolar, horizontal transverse axes. In many Phæodaria the skeleton also has this amphithect pyramidal ground-form, e.g., the bivalved Phæoconchia and part of the Phæogromia. On the contrary, in the rest of the Phæodaria the skeleton exhibits very various geometrical ground-forms, independent of that of the central capsule. In the Phæosphæria it forms preferably spheres or endospherical polyhedra, as also in the Castanellida and Circoporida among the Phæogromia; among the Circoporida there are also seen with remarkable distinctness the regular polyhedra (especially the dodecahedron and icosahedron). Isopolar monaxonia are found among the Aulosphærida (Aulatractus) and Orosphærida; allopolar monaxonia among the Challengerida (Lithogromia). The Medusettida and Tuscarorida show various forms of regular pyramids (allopolar Stauraxonia); and finally, the Challengerida are for the most part centroplanar or bilateral. Thus the Phæodaria present a great wealth of different geometrical ground-forms in the development of their skeleton, not in that of their central capsule.

Chapter II.—THE CENTRAL CAPSULE.