844 MORPHOLOGY I. HOMAXONIA all axes equal. (a) Spheres, where an indefinite number of equal axes can be drawn through the middle point, e.g., Sphserozoum. (b) Polyhedra, with a definite number of like axes. Of these a considerable number occur in nature, for example, many Radiolarians (fig. 3), pollen-grains, &c., and they are again classifiable by the number and regularity of their faces. II. PIIOTAXONIA, where all the parts are arranged round a main axis, and of these we distinguish 1. Afonaxonia,v, r iih not more than one definite axis. Here are distinguished (a) those with similar poles, spheroid (Coccodiscus) and cylinder (Pyrosoma) and (b) those with dissimilar poles, cone (Conulina). 2. Stauraxonia where besides the Flo 3 . _ Radiolarian (Ethmo- mam axes, a definite number of second- sp ha>ra), an irregular endo- ary axes are placed at right angles, and spharic polyhedron with equi- the stereometric ground-form becomes angular faces. Type of Hom- a pyramid. Here, again, may be distin guished () those with poles similar, Stauraxonia homopola, where the stereometric form is the double pyramid (fig. 4), and (b) those with poles dissimilar, Stauraxonia hctero- pola, where the stereometric form is the single pyramid, and where we distin guish a basal, usually oral, pole from an apical, aboral, or anal pole. The bases of these may be either regular or irre gular polygons, and thus a new classi fication into Homostaura and Hctcro- staura naturally arises. The simpler group, the Homostaura, may have either an even or an odd number of sides, and thus among the Homostaura we have even-sided and odd-sided, single and double pyramids. In those Homostaura with an even number of sides, such as Medusae, the radial and inter-radial axes have simi lar poles ; but in the series with an odd number of sides, like most Echi- noderms, each of the transverse axes is half radial and half semi-radial (fig. 5). Of the group of regular double pyra- Flo 4 .__ Po]lenofPassi0 n Flower, mids the twelve-sided pollen-gram of as example of Stauraxonia ho- Passiflora (fig. 4) may be taken as an mopola. Ground-form a regu- example, having the ground-form of lar double pyramid of six sides, the hexagonal system, the hexagonal dodecahedron. Of the equal even-sided single pyramids (Heteropola homostaura), Alcyonium, Geryonia, Aurelia may be taken as ex amples of the eight-sided, six-sided, and four-sided pyramids, while those with an odd number of sides may be illustrated by Ophiura or Primula with five sides, and the flower of Lily or Rush with three sides. In the highest and most complicated group, the Heterostaura, the basal poly gon is no longer regular but amphithect (afj.<j>lt)r]KTos = double-edged). Such a polygon has an even number of sides and Flo . 5 ._ 8tarfi8h an example can be divided into symmetrical halves of Heteropola homostaura. by each of two planes intersecting at right Ground-form a regular single angles in the middle point, and thus divid- Py rami d of five sides. ing the whole figure into four congruent polygons. The longer of these axes may be termed lateral, the shorter the equatorial or dorso- ventral ; 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 amphi thect pyramids. In these forms the poles of the dorso-ventral 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 Centrazonia, while the Pro taxonia, which are defined by their central point, are called Ccntrostigma. 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 Centropipcda. 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 con veniently 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 Amyliiplcura and Zygoplcura, the former in cluding 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 Fig. 6. Fig. 7. Fia. 0. Ctenophore (Eucharis). Ground-form an eight-sided double amphithect pyramid. Fio. 7. Spatangus. Ground-form a five-sided half amphithect pyramid. 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 Diplcura. 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 peculi arities, and its greater adaptability to the environment. The classification into bilateral and radiate forms which usually does duty for more precise promorphological conceptions must bo aban doned as hopelessly confusing essentially different forms, or at least must be rigidly restricted, the terra 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. 6. Nature of Morphological Changes. The main forms of organic structure being analysed and classified and their stage of individu ality being ascertained, the question next arises, by what morpho logical 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 meta morphosis, 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 "dedoublements," metamorphosis and displace ment 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 fertili zation. These are obviously too numerous, as may best be shown by a single comparison with the view of an animal morphologist. Thus Huxley, in discussing the arrangement of the "Vertebra ta, recognizes only three processes of modification, not only in the ancestral evolution of the Equidte, but in the individual develop ment of animals generally ; these are "(1) excess of development of some parts in relation to others, (2) partial or complete suppres sion of certain parts, (3) coalescence of parts originally distinct." It is probable that this "threefold law of evolution " may include all observed cases of change, even in the flower ; thus Chorisis and Peloria may be regarded as peculiar forms of excess, while displace ment is probably in all cases only apparent, and really due to adhesion or coalescence (see BIOLOGY, vol. iii. p. 681 sq. ). i 7. Nature of Morphological Correspondence Categories of Homology. To indicate all the steps by which the idea of mor phological has been distinguished from that of physiological resemblance would be to examine the whole history of morphology; it must suffice to discuss the terminology of the subject which lias, 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 estab lished 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) ; tho second as a part or organ in one animal which has the same function 1 Compare A. de St-IIilaire, Morphologie ; Gray, Manual, p. 179 (1808) ;
Huxley, 1 roc. Zool. Society, p. 019, Lond., 18SO.