9. Cannopylea or Phæodaria.—Those Radiolaria which we call "Cannopylea" from the constitution of their central capsule, or "Phæodaria" on account of their peculiar phæodium, are distinguished from the other three legions by the combination of the following characters:—(1) The Membrane of the central capsule is double, consisting of a strong outer and delicate inner capsule, and has only one principal opening (osculum) at the basal pole of the vertical main axis; this osculum is closed by a radiate cover (astropyle or operculum radiatum), from the centre of which arises an external tubular spout (proboscis). Occasionally a few small accessory openings (parapylæ) are present besides the principal opening. (2) The Nucleus lies centrally or subcentrally in the capsule (in the vertical main axis), and is serotinous, inasmuch as it only divides at a late period into spore-nuclei. (3) The Pseudopodia are usually very numerous and arise from a thick sarcomatrix, formed by the spreading out of a thick stem of sarcode, which issues from the astropyle. (4) The Calymma always contains a phæodium or peculiar voluminous excentric mass of pigment. (5) The Skeleton (very rarely absent) is never centrogenous, always extracapsular and formed of a silicate of carbon. (6) The Ground-form of the central capsule is always monaxon (with a vertical allopolar main axis) and generally spheroidal; that of the skeleton is very varied.
10. Synopsis of the Subclasses and Legions:—
| First Subclass. | Second Subclass. | ||
|
Porulosa vel Holotrypasta. Central capsule originally spherical, without osculum or principal opening, with innumerable fine pores. |
Osculosa vel Merotrypasta. Central capsule originally monaxon, with an osculum at the basal pole of the vertical main axis. |
||
| Legion I. Spumellaria. (Peripylea). |
Legion II. Acantharia. (Actipylea). |
Legion III. Nassellaria. (Monopylea). |
Legion IV. Phæodaria. (Cannopylea). |
| Central capsule originally spherical, homaxon. | Central capsule originally spherical, homaxon. | Central capsule originally ovoid, monaxon. | Central capsule always spheroidal, monaxon. |
| Capsule-membrane single, pores innumerable, distributed all over. |
Capsule-membrane single, pores numerous, regularly distributed. |
Capsule-membrane single, a porous area (porochora) at the oral pole of the main axis. |
Capsule-membrane always double, an astropyle (with radiate operculum) at the oral pole of the main axis. |
| Nucleus central, originally spherical (usually dividing late). | Nucleus excentric, (usually dividing early). | Nucleus excentric, near the aboral pole (dividing late). | Nucleus always spheroidal, in the main axis (dividing late). |
| Skeleton absent or siliceous, never centrogenous. | Skeleton always of acanthin, always centrogenous. | Skeleton siliceous, usually monaxon, extracapsular. | Skeleton of a silicate, always extracapsular. |
| Calymma always without phæodium. | Calymma always without phæodium. | Calymma always without phæodium. | Calymma always with phæodium. |
| First Subclass. | |
|---|---|
|
Porulosa vel Holotrypasta. Central capsule originally spherical, without osculum or principal opening, with innumerable fine pores. |
|
| Legion I. Spumellaria. (Peripylea). |
Legion II. Acantharia. (Actipylea). |
| Central capsule originally spherical, homaxon. | Central capsule originally spherical, homaxon. |
| Capsule-membrane single, pores innumerable, distributed all over. | Capsule-membrane single, pores numerous, regularly distributed. |
| Nucleus central, originally spherical (usually dividing late). | Nucleus excentric, (usually dividing early). |
| Skeleton absent or siliceous, never centrogenous. | Skeleton always of acanthin, always centrogenous. |
| Calymma always without phæodium. | Calymma always without phæodium. |
| Second Subclass. | |
|
Osculosa vel Merotrypasta. Central capsule originally monaxon, with an osculum at the basal pole of the vertical main axis. |
|
| Legion III. Nassellaria. (Monopylea). |
Legion IV. Phæodaria. (Cannopylea). |
| Central capsule originally ovoid, monaxon. | Central capsule always spheroidal, monaxon. |
| Capsule-membrane single, a porous area (porochora) at the oral pole of the main axis. | Capsule-membrane always double, an astropyle (with radiate operculum) at the oral pole of the main axis. |
| Nucleus excentric, near the aboral pole (dividing late). | Nucleus always spheroidal, in the main axis (dividing late). |
| Skeleton siliceous, usually monaxon, extracapsular. | Skeleton of a silicate, always extracapsular. |
| Calymma always without phæodium. | Calymma always with phæodium. |
11. Individuality of the Radiolaria.—Like other Protozoa the Radiolaria are unicellular organisms, the whole fully developed organisation of which falls under the category of a single cell, both morphologically and physiologically. Since this view is based upon the composition of the individual body out of two different morphological elements, nucleus and protoplasm, it is at once justified in the case of the majority of Radiolaria, in which the plasmatic body encloses only a single nucleus (the so-called "Binnen-Bläschen"); such is the case in all the Spumellaria monozoa, Nassellaria and Phæodaria. This aspect of the case might appear doubtful in those Radiolaria in which the simple primary cell-nucleus divides early into numerous small secondary nuclei, as is the case in the Spumellaria polyzoa and most Acantharia. Strictly speaking, the multinucleate central capsule should in such cases be regarded as a syncytium; but since the individual unity of the unicellular organism is as clearly defined in these precocious multinuclear Radiolaria as in the ordinary serotinous forms, the former must be considered unicellular Rhizopods just as are the latter. This mode of regarding the case is the more necessary, inasmuch as the early division of the nucleus has no further influence upon the organisation. Just as in many other classes of the Protista there are monozootic (solitary) and polyzootic (social) forms, so also in the Radiolaria there are in addition to the ordinary monozootic or monobious forms certain families in which colonies or cœnobia are formed by the association of individuals; this distinction may be expressed by the terms "Monocyttaria" and "Polycyttaria."
The unicellular nature of the Radiolaria was first established by Richard Hertwig in 1879 (L. N. 33),[1] and brought into conformity with our present histiological knowledge and the new reform of the cell-theory. Huxley, however, who was in 1851 the first to examine living Radiolaria accurately, declared Thalassicolla nucleata to be a unicellular Protozoon, and the individual central capsules of Sphærozoum punctatum to be cells, but, owing to the then condition of the cell-theory, he was unable to give a conclusive demonstration of this view. Later, when Johannes Müller in 1858 and myself in 1862 recognised the peculiar "yellow cells" which occur in large numbers in many Radiolaria as true nucleated cells, it appeared impossible any longer to maintain the unicellular nature of the Radiolaria; also the great complication which I showed to exist in the structure of Thalassicolla appeared to contradict it. Only after Cienkowski (1871) and Brandt (1881) had shown that the "yellow cells" do not belong to the Radiolarian organism, but are symbiotic unicellular algæ, was it possible to revive and demonstrate anew the unicellular nature of the Radiolaria.
12. Morphological Individuality.—From the morphological standpoint the individuality of the unicellular elementary organism is obvious in the ordinary solitary Radiolaria (Monobia), and is to be so regarded that the whole body with all its constituent parts, and not merely the central capsule, is to be regarded as a cell. Naturally the xanthellæ or yellow cells (§§ 76, 90), which as independent algæ live in symbiosis with many Radiolaria, must be excluded. The unicellular organisation of the Radiolaria is further to be distinguished from that of the other Protista, inasmuch as an internal membrane (capsule-membrane) separates the central (medullary) from the peripheral (cortical) portion. In the cœnobia of the social Radiolaria (or Polycyttaria), the morphological individuality persists only as regards the medullary portions of the aggregated cells (the individual central capsules), while the cortical portions fuse completely to form a common extracapsulum. Hence in these Spumellaria polyzoa two different stages of morphological individuality must be distinguished, the Cell as a Morphon of the first stage, and the Cœnobium as a Morphon of the second stage.
13. Physiological Individuality.—From the physiological standpoint also the individuality of the unicellular organism is immediately obvious in the case of the ordinary solitary Radiolaria (Monobia); as in other Protista it fulfils all the functions of life by itself alone. This physiological individuality of the monobious Radiolarian cell is furthermore not influenced by the xanthellæ, which live as independent algæ in symbiosis with many Radiolaria; even though these often by the production of starch assist in the nourishment of the Radiolaria, yet they are by no means indispensable to them. On the other hand, the physiological individuality offers more complicated relations in the social Radiolaria (Polycyttaria) which live united in colonies or cœnobia. Here the actual Bion (or the fully developed physiological individual) is not represented by the individual cells, but by the whole multicellular cœnobium, which in each species has a definite form and size. In these cœnobia, which are usually spherical or cylindrical jelly-like masses, several millimeters in diameter, numerous cells are so intimately united that only their medullary portions (the central capsule with the endoplasm) remain independent; the cortical portions (calymma and exoplasm) on the contrary uniting into a common extracapsulum. This discharges, as a whole, the functions of locomotion, sensation, and inception of nutriment, while the separate central capsules act in the main only as reproductive organs (forming spores) and partly also as the central organs of metastasis (digestion). Each cœnobium may also be regarded as a polycyttarium, i.e., a "multicellular Radiolarian," whose numerous central capsules represent so many sporangia or spore-capsules.
On this head compare the section in my monograph of 1862 (L. N. 16), entitled Die Organisation der Radiolarien-Colonien; Polyzoen oder Polycyttarien? (pp. 116 to 126); and also R. Hertwig, Zur Histologie der Radiolarien, 1876 (L. N. 26, p. 23).
14. Monocyttaria and Polycyttaria.—In the majority of the Radiolaria each unicellular organism passes its individual life in an isolated condition (as a Monocyttarium). Only in a part of the Spumellaria numerous unicellular individuals are united into societies which are regarded as cœnobia or colonies (Polycyttaria). This is the case in three different families belonging to the Peripylea, in the Collozoida (without a skeleton, Pl. 3), the Sphærozoida (with a Beloid skeleton, Pl. 4), and the Collosphærida (with a Sphæroid skeleton, Pls. 5-8). All three families of Polycyttaria (or social Radiolaria), agree in their mode of forming colonies, since the central capsules of the social individuals remain separate and lie in a common jelly-like mass, which is formed by the fusion of their extracapsulum. The chief part of the voluminous colonies, which attain a diameter of several millimetres (sometimes more than 1 cm.), and are generally spherical, ellipsoidal or cylindrical, consists therefore of the jelly-like calymma, and this is penetrated by a sarcoplegma, to whose meshes all the individual organisms contribute by means of the pseudopodia, which radiate from their sarcomatrix. A further peculiarity in which the social Spumellaria differ from the solitary consists in the fact that the former are precocious and the latter serotinous in the division of the nucleus (§ 64). Whilst in the solitary or monozootic Spumellaria the middle of the central capsule is occupied by the simple nucleus, and this divides only at a late period (immediately before the formation of spores) into the numerous spore nuclei, in the colonial or polyzootic Spumellaria this division takes place very early, and the middle of each central capsule is usually occupied by an oil-globule.
The colonial Radiolaria were described as early as the year 1834 by Meyen, the first investigator of the class, under the name Sphærozoum, and, as Palmellaria, compared with the gelatinous colonies of the Nostochineæ. The first accurate observations upon their structure were, however, made in 1851 by Huxley, who described examples of all three families under the name Thalassicolla punctata. More extended, however, were the investigations of Johannes Müller, who in his fundamental work (1858) divided the whole class Radiolaria into Solitaria and Polyzoa. The Radiolaria solitaria he divided into Thalassicolla, Polycystina and Acanthometra, the Radiolaria polyzoa into Sphærozoa (without a shell) and Collosphæra (with a shell). The most accurate delineation of the Polycyttaria was given by Hertwig in his beautiful memoir, Zur Histologie der Radiolarien (1876). Quite recently, however (1886), since the completion of my manuscript upon the Challenger Radiolaria, a very complete Monograph of the Polycyttaria has appeared by Karl Brandt, Die colonie-bildenden Radiolarien (Sphærozoen) des Golfes von Neapel und der angrenzenden Meeres-Abschnitte (276 pp., 8 pls., Berlin). It contains in particular most valuable contributions to the physiology and histology.
15. The Central Capsule and Extracapsulum.—The special peculiarity of the unicellular Radiolarian organism, by which it is clearly distinguished from all other Rhizopoda (and indeed from most other Protista), is its differentiation into two separate chief constituents, the central capsule and extracapsulum, and the formation of a special membrane which separates them. This, the capsule-membrane, is not to be compared with an ordinary cell-membrane, as an external layer, but rather to be regarded as an internal differentiated product. The extracapsulum or external (cortical) portion of the body is in most Radiolaria more voluminous than the central capsule or inner (medullary) portion. The exoplasm of the former (the cortical or extracapsular protoplasm) is emphatically different from the endoplasm of the latter (the medullary or intracapsular protoplasm). Besides the most important vital processes are distributed by division of labour so completely between them that they appear most distinctly co-ordinated. The central capsule is on the one hand the general central organ of the "cell-soul" for the discharge of its sensory and motor functions (comparable to a ganglion-cell), on the other hand the special organ of reproduction (sporangium). The extracapsulum, also, is not less significant, since on the one hand its calymma acts as a protecting envelope to the central capsule, as a support to the pseudopodia, and a foundation for the skeleton or a matrix for the development of the shell, and on the other hand its pseudopodia are of the utmost importance as peripheral organs of movement and sensation as well as of nutrition and respiration. The central capsule and the extracapsulum are therefore to be regarded both morphologically and physiologically as the two characteristic co-ordinated principal parts of the unicellular Radiolarian organism.
In most of the more modern delineations of the Radiolaria the central capsule is regarded as the "cell proper" and its membrane as the "cell-wall." The following facts are opposed to the correctness of this interpretation:—1. In most Radiolaria the exoplasm is clearly different from the endoplasm, and the former is more voluminous than the latter. 2. In all Radiolaria the division of labour is so carried out between the central capsule and the extracapsulum, that the physiological significance and independence of both principal parts of the cell is almost equally great. 3. It is only in the Acantharia that the formation of the skeleton takes place within the central capsule; in all the other three legions it is quite independent of it.
16. The Malacoma and Skeleton.—Whilst the division of the unicellular organism into central capsule and extracapsulum is undoubtedly the most important character of the Radiolarian organism, the development of a skeleton of peculiar and most varied form is of very striking significance. This skeleton is always a secondary product of the cell, but is always anatomically so independent, and so clearly marked off from the soft parts or malacoma, that it seems advisable to regard both separately in a general morphological survey. The skeleton stands in a different relation to each of the two principal constituents of the malacoma. Only in the Acantharia is it centrogenous and developed from the central capsule outwards. In the other three legions the skeleton never arises in the centre of the capsule; in the Nassellaria and Phæodaria it is always extracapsular; in the Spumellaria it is also outside the central capsule originally, but afterwards becomes often surrounded by it, and finally lies in most cases partly within and partly without the central capsule. The chemical basis of the skeleton in the Acantharia is the curious acanthin (an organic substance allied to chitin), in the Phæodaria a silicate of carbon, and in the Nassellaria and Spumellaria silica.
17. Ground-Forms of the Radiolaria (Promorphology).—The ground-forms of the Radiolaria exhibit a greater variety than those of any other class in the organic world, greater indeed than is to be found in all the remaining groups together. For every conceivable ground-form which can be defined in the system of promorphology is actually present in the Radiolaria; their skeleton exhibits, as it were, in material existence, certain geometrical ground-forms which are found in no other organisms. The cause of this unexampled richness in different forms lies chiefly in the static relations of the Radiolaria, which swim freely in the sea, partly also in the peculiar plasticity of their protoplasm and the material of their skeletons.
Regarding the general system of ground-forms compare my Generelle Morphologie (1866, Bd. i. pp. 375-552; Bd. iv., Allgemeine Grundformenlehre). The ground-forms there proposed and systematically defined have, however, found but little acceptance (chiefly, no doubt, owing to the difficult and complicated nomenclature); but having now, twenty years after their publication, anew carefully revised and critically studied them, I can find no sufficient reason for abandoning the principles there adopted. On the contrary the study of the Challenger Radiolaria during the last ten years, with its incomparable wealth of forms, has only confirmed the accuracy of my system of ground-forms. The customary treatment of these in zoological and botanical handbooks (such as those of Claus and Sachs) is quite insufficient.
18. The Principal Groups of Geometrical Ground-Forms.—The great variety of the geometrical ground-forms which are actually realised in the variously shaped bodies of the Radiolaria, renders it desirable to classify these in as small a number as possible of principal groups and a larger number of subdivisions. As extensive principal groups four at least must be distinguished; the Centrostigma or Sphærotypic, the Centraxonia or Grammotypic, the Centroplana or Zygotypic, and the Acentrica or Atypic. The natural centre of the body, about which all its parts are regularly arranged, is in the first group a point (stigma), in the second a straight line (principal axis), in the third a plane (sagittal plane), in the fourth a centre is of course wanting.
19. The Centrostigma or Sphærotypic Ground-Forms.—The first group of geometrical ground-forms, here distinguished as sphærotypic or the centrostigma, is undoubtedly the most important among the Radiolaria, inasmuch as if these be considered monophyletic, it must be the original one from which all the other ground-forms have been derived. The common character of all these sphærotypic ground-forms is that their natural centre is a point (stigma); thus there is no single principal axis (or protaxon) such as is characteristic of the two following groups. The sphærotypic ground-forms are subdivided into two important smaller groups, the spheres (Homaxonia) and the endospherical polyhedra (Polyaxonia). The spherical ground-forms, fully developed in the central capsule and calymma of Actissa and the Sphæroidea as well as in many Acantharia, present no different axes; all possible axes passing through the centre of the body are equal (Homaxonia). In the endospherical polyhedra, on the contrary, numerous axes (three at least) may be distinguished, which are precisely equal to each other and different from all the remaining axes (Polyaxonia). If the extremities of these axes, or the poles, which are all equidistant from the common centre, be united by straight lines, a polyhedral figure is produced whose angles all lie in the surface of the sphere. According as the poles of the axes are at equal, subequal, or at different distances from each other, we may divide the endospherical polyhedra into regular, subregular and irregular. (See Gener. Morphol., Bd. i. pp. 404-416.)
20. The Centraxonia or Grammotypic Ground-Forms.—The second principal group of organic ground-forms, here called grammotypic or centraxonia, is characterised by the fact that a straight line (gramma) or a single principal axis (protaxon) forms the natural centre of the body. This important and extensive group is divided into two subgroups, those with one axis (Monaxonia) and those with crossed axes (Stauraxonia); in the latter different secondary transverse or cross-axes may be distinguished, but not in the former. In the Monaxonia, therefore, every transverse section of the body perpendicular to the principal axis is a circle, in the Stauraxonia, on the contrary, a polygon. The Monaxonia are further subdivided into two groups, in one of which the two poles of the principal axis are equal and similar (Isopolar), in the other of which they are different (Allopolar); in the former the two halves of the body, which are separated by the equatorial plane (or the largest transverse plane, perpendicular to the principal axis), are equal, in the latter unequal. Among the isopolar uniaxial ground-forms (Monaxonia isopola) may be mentioned the ellipsoidal, spheroidal, lenticular, &c.; to the allopolar uniaxial forms (Monaxonia allopola) belong the conical, hemispherical, ovoid, &c. In the same way the pyramidal ground-forms with crossed axes are divisible into two groups, according as the two poles of the principal axis are equal or not. The ground-form of the former is the double pyramid, that of the latter the single pyramid. Both the double and the single pyramids may again be subdivided, each into two important lesser groups, the regular and the amphithect. In the first division the equatorial plane of the double and the basal plane of the single pyramid is a regular polygon (square, &c.), whilst in the other division it is an elongated or amphithect polygon (rhombus, &c.); the crossed axes are equal in the former, unequal in the latter. (See Gener. Morphol., Bd. i. pp. 416-494.)
21. The Centroplana or Zygotypic Ground-Forms.—The third principal group of ground-forms includes those which are bilaterally symmetrical in the ordinary sense, or zeugitic or zygotypic; the natural centre of their body is a plane. These forms are the only ones in which the distinction between right and left is possible, since their body is divided by the median plane (planum sagittale) into two symmetrical halves (right and left). In all these zeugites the position of every part is determined by three axes perpendicular to each other, and of these three dimensive axes two are allopolar, one is isopolar. The two unlike poles of the principal (or longitudinal) axis are the oral and aboral, the two unlike poles of the sagittal (or vertical) axis are the dorsal and ventral; the two similar poles of the frontal (or transverse) axis, however, are the right and left. This important group of zeugitic or bilateral forms may also be divided into two clearly distinct lesser groups, the Amphipleura and the Zygopleura. In the Amphipleura (or bilaterally radial ground-forms) the "radial two-sided" body is produced by modification of a regular pyramid (as Spatangus from Echinus), and hence is composed of several (not less than three) antimeres. In the Zygopleura (or bilaterally symmetrical ground-forms) on the other hand, the bodies consist of two antimeres (as in all the higher animals, Vertebrata, Arthropoda, &c.). (See Gener. Morphol., Bd. i. pp. 495-527.)
22. The Acentrica or Atypic Ground-Forms.—Among the acentrica or anaxonia are included all those ground-forms which are absolutely irregular, and in which neither a definite centre nor constant axes can be distinguished (e.g., most Sponges). These quite irregular ground-forms are very rare among the Radiolaria, but nevertheless there may be referred to them the amœboid central capsule of some Colloidea (Collodastrum, p. 27, Pl. 3, figs. 4, 5) among the Spumellaria, the irregular shells of many Collosphærida (Pl. 8, fig. 2), and the absolutely irregular shells of the Phorticida and Soreumida among the Larcoidea. (See Gener. Morphol., Bd. i. p. 400.)
23. The Subsidiary Groups of Geometrical Ground-Forms.—The four natural principal groups of ground-forms, which have just been defined according to the nature of the centre of their bodies, may be divided again into numerous subsidiary groups, defined by the relations of the constant axes and the two poles of each axis, as well as by the number of the axes and the differentiation of the secondary with respect to the principal axis. The most important of these subsidiary groups into which the principal ones are immediately divided are the following:—(1) The Centrostigma (or sphærotypic) are divided into spheres (Homaxonia) and endospherical polyhedra (Polyaxonia). (2) The Centraxonia (or grammotypic) into uniaxial (Monaxonia) and those with crossed axes (Stauraxonia); among the former of these may be distinguished the isopolar (phacotypic) and the allopolar (conotypic); among the latter the double and single pyramids. (3) The Centroplana (or bilaterals) are divided into amphipleura (or bilaterally radial) and zygopleura (or bilaterally symmetrical). (4) The Acentrica (or Anaxonia) or absolutely irregular ground-forms, present no special subdivisions.
For a complete system of the geometrical ground-forms and their relation to promorphological classification, see Gener. Morphol., Bd. i. pp. 555-558.
24. The Spherical or Homaxon Ground-Form.—The spherical is the only absolutely regular ground-form, since only in it are all axes which pass through the centre equal; it is very often realised among the Radiolaria, especially in the Spumellaria and Acantharia, where it furnishes the common original ground-form, but it is often to be seen in the shells of many Phæodaria (in most Phæosphæria); on the other hand, it is never found among the Nassellaria. Geometrical spheres, in the strict sense of the term, are only to be found among the Spumellaria and Acantharia, namely, in the central capsule of many Collodaria (Pls. 1, 2) and all Sphæroidea (Pls. 11-30) as well as many Acanthometra and Acanthophracta (Pls. 128-138). Nevertheless, speaking generally, one includes those central capsules and skeletons which have been distinguished here as endospherical polyhedra. (On these ground-forms see Gener. Morphol., Bd. i. pp. 404-406.)
25. The Endospherical Polyhedral Ground-Form.—The endospherical polyhedron or polyaxon ground-form naturally follows the spherical or homaxon. Under it are included all polyhedra whose angles fall in the surface of a sphere; this ground-form is especially common among the Spumellaria, especially in the shells of Sphæroidea, but is also found among the Acantharia (especially in the Astrolophida and Sphærophracta), as well as among the Phæosphæria (in most genera of the Orosphærida, Sagosphærida, and Aulosphærida). Strictly speaking, all those lattice-shells which have been incorrectly called "spherical" belong to this category, for they are none of them true spheres in the geometrical sense (like the central capsules of the Sphæroidea), but rather endospherical polyhedra, whose angles are indicated by the nodal points of the lattice shell, or the radial spines which spring from them. These endospherical polyhedra may be divided into three groups, the regular, subregular, and irregular. Of regular polyhedra, properly so-called, it may be shown geometrically that only five can exist, namely, the regular tetrahedron, cube, octahedron, dodecahedron, and icosahedron. All these are actually manifested among the Radiolaria, although but seldom. Much more common are the subregular endospherical polyhedra, e.g., spherical lattice-shells with regular hexagonal meshes of equal size; they are never exactly equal nor perfectly regular, but the divergences are so insignificant that they escape superficial observation (Pl. 20, figs. 3, 4; Pl. 26, figs. 1-3). On the contrary in the irregular endospherical polyhedra the meshes of the lattice-sphere are more or less different in size and often in form also (Pl. 28, figs. 4, 8; Pl. 30, figs. 4, 6). The five truly regular polyhedra require separate notice on account of their importance. (See Gener. Morphol., Bd. i. p. 406.)
26. The Regular Icosahedral Ground-Form.—The ground-form whose geometrical type is the regular icosahedron (bounded by twenty equilateral triangles) is rarely exemplified, but it occurs among the Phæodaria in the Circoporid genus Circogonia (Pl. 117, fig. 1), and also in certain Aulosphærida, but, apparently, only as an accidental variation (e.g., Aulosphæra icosahedra). Furthermore, this ground-form may also be assumed to occur in those Sphæroidea whose spherical lattice-shells bear twelve equidistant radial spines (e.g., many species of Acanthosphæra, Heliosphæra, and other Astrosphærida); the basal points of these spines indicate the twelve angles of the regular icosahedron. (See on this head Gener. Morphol., Bd. i. p. 411.)
27. The Regular Dodecahedral Ground-Form.—The ground-form whose geometrical type is the regular dodecahedron (or pentagonal dodecahedron), bounded by twelve equilateral and equiangular pentagons, is very rarely found perfectly developed, as in Circorrhegma dodecahedra (Pl. 117, fig. 2). This form is by no means so common among the Radiolaria as in the pollen grains of plants (e.g., Buchholzia maritima, Fumaria spicata, Polygonum amphibium, &c.). It can, however, be regarded as present in all those Sphæroidea whose spherical lattice-shells bear twenty equal and equidistant radial spines (e.g., many species of Acanthosphæra, Heliosphæra, and other Astrosphærida); the basal points of these spines mark out the twenty angles of the regular pentagonal dodecahedron. (See Gener. Morphol., Bd. i. p. 412.)
28. The Regular Octahedral Ground-Form.—The ground-form whose geometrical type is the regular octahedron (bounded by eight equilateral triangles), commonly appears among the Spumellaria in the family Cubosphærida (p. 169, Pls. 21-25). In these Sphæroidea the typical ground-form is usually indicated by six equal radial spines, which are opposed to each other in pairs, and lie in three similar axes perpendicular to each other; these are the three axes of the tesseral crystallographic system; one of them is vertical, whilst the other two cross each other at right angles in its centre. Occasionally, too, the spherical form of the lattice-shell passes over into that of the regular octahedron (Pl. 22, figs. 8, 10). The same form recurs in Circoporus (Pl. 117, fig. 6) among the Phæodaria. In the vegetable kingdom it is exhibited by the antheridia of Chara. It is not found in the Nassellaria and Acantharia. (See Gener. Morphol., Bd. i. p. 412.)
29. The Regular Cubic Ground-Form.—The ground-form whose geometrical type is that of a die or cube, is actually presented in a very striking manner by various Radiolaria. Among the Spumellaria it occurs in certain Sphæroidea, e.g., in the Astrosphærid genera Centrocubus and Octodendron (Pl. 18, figs. 1-3); in these the central medullary shell is a complete cube, bounded by six equal squares, from the eight angles of which eight equal radial spines project. This form can also be regarded as present in those Sphæroidea whose spherical lattice-shell bears eight equal and equidistant radial spines (many Astrosphærida). Besides these the cubic ground-form is to be seen in certain Nassellaria of the family Tympanida, especially in Lithocubus (Pl. 82, fig. 12; Pl. 94, fig. 13), in many species of Acrocubus, Microcubus, &c.; the twelve bars of its lattice-skeleton correspond often exactly to the edges of the cube. (See Gener. Morphol., Bd. i. p. 413.)
30. The Regular Tetrahedral Ground-Form.—The ground-form whose geometrical type is the regular tetrahedron, bounded by four equilateral triangles, occurs less frequently in the Radiolaria than the other four regular polyhedra. Among the Spumellaria it is found in the Beloidea, and especially in those members of the Thalassosphærida and Sphærozoida whose spicules bear four equal branches, diverging at equal angles from a common centre. Precisely the same structure is seen also among the Nassellaria in some Plectoidea, as in Tetraplagia among the Plagonida, and Tetraplecta among the Plectanida. The skeleton of both these genera consists of four equal rods, which radiate at equal angles from a common centre, just as do the axes of the regular tetrahedron. The tetrahedral form of these Plectoidea is the more important and interesting since on the one hand it is related to the similar spicular form of the Beloidea, and on the other perhaps furnishes the starting point from which Cortina among the Nassellaria may be derived (Plagoniscus, Plectaniscus). (See Gener. Morphol., Bd. i. p. 415.)
31. The Isopolar-Monaxon or Phacotypic Ground-Form.—The isopolar uniaxial or phacotypic ground-form is characterised by the possession of a vertical main axis with equal poles, whilst no transverse axes are differentiated. All horizontal planes which cut the axis at right angles are circles, and increase in size from the poles towards the equator. The most important ground-forms of this group are the phacoid (the lens or oblate spheroid) and the ellipsoid (or prolate spheroid). Phacoids (or geometrical lenses with blunt margins) are very often presented by the central capsules of the Discoidea and of many Acantharia (Quadrilonchida and Hexalaspida), but the lattice-shells of many Spumellaria and Acantharia exhibit the same form, as also do a few Phæodaria (e.g., Aulophacus). True geometrical ellipsoids are seen in the central capsules of many Prunoidea among the Spumellaria, and of many Amphilonchida and Belonaspida among the Acantharia. Furthermore, the lattice shells of many species of these groups retain the same essential form, e.g., many Ellipsida, Druppulida, and Spongurida (Pls. 13-17, and 39), as well as most Belonaspida. (See Gener. Morphol., Bd. i. p. 422.)
32. Allopolar-Monaxon or Conotypic Ground-Form.—The allopolar uniaxial or conotypic ground-form is characterised by the possession of a vertical main axis whose two poles are unlike, while no transverse axes are differentiated. All horizontal planes cutting the main axis at right angles are circles, and decrease more rapidly from the largest plane towards the basal than towards the apical pole. The most important ground-forms of this group are the ovoid, the cone, and the hemisphere. They often occur (and in geometrical perfection) in the egg-shaped central capsule and podoconus of the Nassellaria, as well as in the shells of several groups of this legion, particularly in the Cyrtocalpida or Monocyrtida eradiata (Pl. 51, figs. 10-13), and in many Stichocyrtida eradiata; furthermore, they are also seen among the Phæodaria, e.g., certain Challengerida (Pl. 99, figs. 19-22). (See Gener. Morphol., Bd. i. p. 426.)