the basal polygon is no longer regular but amphithect ἀμφίθηκτςο＝double-edged). Such a polygon has an even number of sides,
and can be divided into symmetrical halves by each of two
planes intersecting at right angles in the middle point, and
thus dividing the whole figure into four congruent polygons.
The longer of these axes may be termed
lateral, the shorter the equatorial or dorsoventral;
and these two axes, along with
the main axes, always define the three
dimensions of space. Ctenophores (fig. 6)
furnish examples of eight-sided amphithect
pyramids, some Madrepore Corals
of six-sided, Crucifers, some Medusae,
and Cestodes of four-sided amphithect
pyramids.
| Fig. 5.—Starfish, an example of Heteropola homostaura. Ground-form a regular single pyramid of five sides. | | Fig. 6.—Ctenophore (Eucharis). Ground-form an eight-sided double amphithect pyramid. | | Fig. 7.—Spatangus. Ground form a five-sided half amphithect pyramid. |
In these forms the poles of the dorsoventral and lateral axes are similar, and, as in the preceding Monaxonia and Stauraxonia, the centre of the body is defined by a line; and they are therefore termed Centraxonia, while the Protaxonia which are defined by their central point are called Centrostigma. There are, however, other forms, and these the most complicated, in which the poles of at least the dorso-ventral axis are unlike, and in which the body is thus defined not with reference to a line but to a median plane, and these have accordingly received the name of Centropipeda. Their ground-form is a polygon with an even number of sides, which can only be divided into two symmetrical halves by the one median plane. It can be obtained by halving an amphithect pyramid of double the number of sides, and is consequently termed a half amphithect pyramid (fig. 7). The whole amphithect pyramid may be most conveniently obtained by the reduplication of the ground-form as if in a mirror. Of half amphithect pyramids there are again two forms, termed by Haeckel Amphipleura and Zygopleura, the former including the “bilaterally symmetrical” or irregularly radiate forms of previous authors, such as Spatangus Viola, Orchis, while the Zygopleura include forms bilaterally symmetrical in the strictest sense, in which not more than two radial planes, and these at right angles to each other, are present. The stereometric ground-form is a half rhombic pyramid. Haeckel again divides these, according to the number of antimeres, into Tetrapleura and Dipleura.
Promorphology has thus shown that the reigning dogma of the fundamental difference of organic and mineral forms is false, and that a crystallography of organic forms is possible—the form of the cell or the cell-aggregate differing from the crystal merely by its more or less viscous state of aggregation, its inherited peculiarities, and its greater adaptability to the environment. The classification into bilateral and radiate forms which usually does duty for more precise promorphological conceptions must be abandoned as hopelessly confusing essentially different forms, or at least must be rigidly restricted—the term radial to regular and double pyramids, the term bilateral to the Centropipeda if not indeed to dipleural forms. Similarly the topographical and relative terms, anterior and posterior, upper and under, horizontal and vertical, must be superseded by the terms above applied to the axes and their poles, oral and aboral, dorsal and ventral, right and left.
Nature of Morphological Changes.—The main forms of organic structure being analysed and classified and their stage of individuality being ascertained, the question next arises, by what morphological changes have they arisen, and into what categories can these modes of differentiation be grouped? They at first sight seem innumerable, yet in reality are few. Goethe somewhat vaguely generalized them for the flower as ascending and descending metamorphosis, expansion and contraction of organs, &c.; but the first attempt at careful enumeration seems to be that of Auguste de St Hilaire, who recognized defects of development, adherences, excesses of production or “dédoublements,” metamorphosis and displacement of organs. Subsequent authors have variously treated the subject; thus Asa Gray enumerates as modifications of the flower—coalescence, adnation, irregularity, abortion, non-alternation or anteposition, multiplication, enation, unusual development of the axis, and other morphological modifications connected with fertilization. These are obviously too numerous, as may be best shown by a single comparison with the view of an animal morphologist. Thus Huxley, in discussing the arrangement of the Vertebrata, recognizes only three processes of modification, not only in the ancestral evolution of the Equidae, but in the individual development of animals generally; these are “(1) excess of development of some parts in relation to others, (2) partial or complete suppression of certain parts, (3) coalescence of parts originally distinct”. The particular form of excess of development which results in the repetition of parts, and the morphological changes due to partial or complete fusion of such repeated parts receive special treatment in the article Metamerism.
Nature of Morphological Correspondence—Categories of Homology.—To indicate all the steps by which the idea of morphological resemblance has been distinguished from that of physiological would be to examine the whole history of morphology; it must suffice to discuss the terminology of the subject which has, as ever, served not only as an index but as an engine of progress. For these two distinct forms of resemblance the terms homology and analogy gradually became specialized, and were finally established and clearly defined by Owen in 1843—“the former as the same organ in different animals under every variety of form and function (e.g. fore-limbs of Draco volans and wings of Bird); the second as a part or organ in one animal which has the same function as another part or organ in a different animal (e.g. parachute of Draco and wings of Bird).” He further distinguishes three kinds of homology: (1) special, being “that above defined, namely, the correspondence of a part or organ determined by its relative position and connexions with a part or organ in a different animal, the determination of which homology indicates that such animals are constituted on a common type,” e.g. basilar process of human occipital with basi-occipital of fish; (2) general, that “higher relation in which a part or series of parts stands to the fundamental or general type, involving a knowledge of the type on which the group in question is constituted,” e.g. the same human bone and centrum of the last cranial vertebra; (3) serial homology, “representative or repetitive relation in the segments of the same skeleton” (demonstrated when general and special homologies have been determined); thus usually the basi-occipital and basi-sphenoid are “homotypes.” These terms were henceforth accepted by naturalists; but the criterion of analogy and homology became for L. Agassiz and other embryologists developmental as well as comparative, reference to the ideal archetype becoming less and less frequent. Passing over the discussions of L. Agassiz and Bronn, of which the latter is criticized and partly incorporated by Haeckel, we find the last-named (1) placing serial under general homology; (2) erecting categories of homology partially corresponding to those of individuality—(a) homotypy (of antimeres), hence distinct from that of Owen, (b) homodynamy (of metameres), (c) homonomy (of parts arranged on transverse axes); (3) defining special homology in terms of identity of embryonic origin. In 1870 this latter point was more fully insisted upon by Ray Lankester, who, decomposing it into two others, proposed to supersede the term homology by homogeny, being the correspondence of common descent, and homoplasy, denoting any superinduced correspondence of position and structure in parts embryonically distinct. Thus, the fore-limb of a mammal is homogenous with that of a bird, but the right and left ventricles of the heart in both are only homoplastic, these having arisen independently since the divergence of both groups from a uni-ventriculate ancestor in relation to similarity of physiological needs. St G. Mivart next proposed to retain homology as a generic term, with homogeny and homoplasy as two species under it, and carried the analysis into great detail, distinguishing at first twenty-five, but later fifteen, kinds of correspondence: (1) parts similar in function only, e.g. legs of lizard and lobster; (2) parts similar both in function and relative position, wings of bat and bird; (3) parts of common descent, fore-limb of horse and rhinoceros; (4) parts of similar embryonic origin, whatever be their racial genetic relations, e.g. occipitals of panther and perch; (5) parts of dissimilar embryonic origin, whatever be their racial genetic relations, e.g. legs of Diptera; (6, 7, 8, 9, 10) laterally, vertically, serially, anteroposteriorly and radially homologous parts; (11) subordinate serial homologues, e.g. joints of antenna; (12 and 13) secondary and tertiary subordinate serial homologues; (14 and 15) special and general homologies (in Owen’s sense). In his Kalkschwämme Haeckel proposed to term homophyly the truly phylogenetic homology in opposition to homomorphy, to which genealogic basis is wanting; and finally Von Jhering has published a repetition of Lankester’s view.
In this discussion, as in that of individuality, it is evident that we are dealing with numerous logical cross-divisions largely corresponding, no doubt, to the complex web of inter-relations presented by nature, yet remaining in need of disentanglement. Though we must set aside analogies of functional activity, the resemblances in external shape or geometric ground-form which correspond to
these, e.g. Hydrozoa and Bryozoa, Fishes and Cetaceans, mimetic
