MORPHOLOGY 843 form higher aggregates which he terms zoides. Such zoides may be irregular, radiate, or linear aggregates, of which the two former classes especially are termed demcs. The organ Haeckel s idorgan is excluded, since tissues and organs result from division of labour in the anatomical elements of the me rides, and so have only a .secondary individuality, "carefully to be distinguished from the individuality of those parts whose direct grouping has formed the organism, and which live still, or have lived, isolated from one another." Perrier further points out that undifferentiated colonies are sessile, as Sponges and Corals, while a free state of existence is -associated with the concentration and integration of the colony into fin individual of a higher order. So far the various theories of the subject ; detailed criticism is impossible, but some synthesis and reconciliation must be attempted. Starting from the cell as the morphological unit, we find these forming homogeneous aggregates in some Protozoa and in the early development of the ovum. But integration into a whole, not merely aggregation into a mass, is essential to the idea of individu ality ; the earliest secondary unit, therefore, is the gastrula or me ride. This stage is permanently represented by an unbranched J lydra or Sponge or by a Planarian. These secondary units may, however, form aggregates either irregular as in most Sponges, in definitely branched as in the Hydroids and Actinozoa, or linear as in such Planarians as Catenula. Such aggregations, colonies, or denies, not being aggregated, do not fully reach individuality of the third order. This is attained, however, for the branched series by such forms as Siphonophores among Hydrozoa, or Renilla or Pennatula among Actinozoa ; for linear aggregates again by the higher Worms, and still more fully by Arthropods and Vertebrates. Aggregates of a yet higher order may occur, though rarely. A longitudinally dividing Nais or laterally branched Syllis are obviously aggregates of these tertiary units, which, on Haeckel s view, become integrated in the Echinoderm, which would thus reach a complete indivi duality of the fourth order. A chain of Salpae or a colony of Pyro- soma exhibits an approximation to the same rank, which is more nearly obtained by a radiate group of Botryllus around their central cloaca, while the entire colony of such an Ascidian would represent the individual of the fifth order in its incipient and unintegrated state, these and the preceding intermediate forms being, of course, readily intelligible, and indeed, as Spencer has shown, inevitable on the theory of evolution. The exclusion of tissues and organs from rank in this series is thus seen to necessarily follow. Ectoderm and endoderm cannot exist alone ; they and the organs into which they differentiate arise merely, as Jager expresses it, from that concentric lamination, or, with Perrier, from that polymorphism of the members of the colony, which is associated with organic and social existence. The idea of the antimere is omitted, as being essentially a promorpho- logical conception (for a Medusoid or a Star-fish, though of widely distinct order of individuality, are equally so divisible) ; that of the metamere is convenient to denote the secondary units of a linear tertiary individual ; the term persona, however, seems un likely to survive, not only on account of its inseparable psycho logical connotations, but because it has been somewhat vaguely applied alike to aggregates of the second and third order ; and the term colony, corm, or deme may indifferently be applied to those aggregates of primary, secondary, tertiary, or quaternary order which are not, however, integrated into a whole, and do not reach the full individuality of the next higher order. The term zooid is also objectionable as involving the idea of individualized organs, a view natural while the medusoid gonophores of a Hydrozoori were looked at as evolved of its homologue in Hydra, whereas the latter is really a degenerate form of the former. Passing to the vegetable world, here as before the cell is the unit of the first order, while aggregates representing almost every stage in the insensible evolu tion of a secondary unit are far more abundant than among animals. Complete unity of the second order can hardly be allowed to the thallus, which Spencer proposes to compound and integrate into tertiary aggregates the higher plants ; as in animals the embryo- logical method is preferable, both as avoiding gratuitous hypothesis and as leading to direct results. Such a unit is clearly presented by the embryo of higher plants in which the cell-aggregate is at once differentiated into parts and integrated into a whole. Such an embryo possesses axis and appendages as when fully developed (fig. 2). The latter, however, being as organs mere lateral expan sions of the concentric layers into which the plant embryo, like the animal, is differentiated, and so neither stages of evolution nor capable of separate existence, are not entitled to individual rank. The embryo, the bud, shoot, or uni-axial plant, all thus belong to the second order of individuality, like the Hydroid they resemble. Like the lower Ccelenterates, too, aggregates of such axes are formed by branching out from their low degree of integration. Such colonies can hardly be termed individuals of the third, much less of higher order, at least without somewhat abandoning that unity of treatment of plants and animals without which philosophi cal biology disappears. Individuality of the second order is most fully reached by the flower, the most highly differentiated and integrated form of axes and appendages. Such a simple inflores cence as a raceme or umbel approximates to unity of the third order, to which a composite flower-head must be admitted to have attained, while a compound inflorescence is on the way to a yet higher stage. If, as seems probable, a nomencla ture be indispensable for clear ex pression, it may be simply arranged in conformity with this view. Start ing from the unit of the first order, the plastid or monad, and terming any undifferentiated aggregate a deme, we have a monad-dcme integrating into a secondary unit or dyad, this Fl / a ,, 2 " o El ? b f yo of . Dicot > le(1 n rising through dyad-dones into a ffJBfSpSSR S S! triad, this forming triad-denies, and the three concentric embryonic these when differentiated becoming la yers. tetrads, the Botryllus-colony with which the evolution of compound individuality terminates being a tetrad-deme. The separate living form, whether monad, dyad, triad, or tetrad, requires also some dis tinguishing name, for which persona will probably ultimately be found most appropriate, since such usage is most in harmony with its inevi table physiological and psychological connotations, while the genea logical individual of Gallesio and Huxley, common also to all the cate gories, may be designated with Haeckel the ovum-product or ovum- cycle, the complete series of forms needed to represent the species being the species-cycle (though this coincides with the former save in cases where the sexes are separate, or polymorphism occurs). For such a peculiar case as Diplozoon paradoxum, where two separate forms of the same species coalesce, and still more for such heterogeneous individuality as that of a Lichen, where a composite unit arises from the union of two altogether distinct forms Fungus and Alga, yet additional categories and terms are required. 1 5. Fromorphology. Just as the physiologist constantly seeks to interpret the phenomena of function in terms of mechanical, physical, and chemical laws, so the morphologist is tempted to inquire whether organic as well as mineral forms are not alike reducible to simple mathematical law. And just as the crystallo- grapher constructs an ideally perfect mathematical form from an imperfect or fragmentary crystal, so the morphologist has frequently attempted to reduce the complex-curved surfaces of organic beings to definite mathematical expression. 2 Canon Moseley (Phil. Trans., 1838) succeeded in showing, by a combination of measurement and mathematical analysis, that the curved surface of any turbinated or discoid shell might be considered as generated by the revolution, about the axis of the shell, of a curve, which continually varied its dimensions according to the law of the logarithmic spiral. For Goodsir this logarithmic spiral, now carved on his tomb, seemed a fundamental expression of organic curvature and the dawn of a new epoch in natural science that of the mathematical investiga tion of organic form and his own elaborate measurements of the body, its organs, and even its component cells seemed to yield, now the triangle, and again the tetrahedron, as the fundamental form. But such supposed results, savouring more of the Natur- philosophie than of sober mathematics, could only serve to dis courage further inquiry and interest in that direction. Thus we find that even the best treatises on botany and zoology abandon the subject, satisfied with merely contrasting the simple geometrical ground-forms of crystals with the highly curved and hopelessly complicated lines and surfaces of the organism. But there are other considerations which lead up to a mathe matical conception of organic form, those namely of symmetry and regularity. These, however, are usually but little developed, botanists since Schleiden contenting themselves with throwing organisms into three groups first, absolute or regular ; second, regular and radiate ; third, symmetrical bilaterally or zygomorphic the last being capable of division into two halves only in a single plane, the second in two or more planes, the first in none at all. Burmeister, and more fully Bronn, introduced the fundamental improvement of defining the mathematical forms they sought not by the surfaces but by axes and their poles ; and Haeckel has developed the subject with an elaborateness of detail and nomen clature which seems unfortunately to have impeded its study and acceptance, but of which the main results may, with slight varia tions chiefly due to Jager (Lehrb. d. Zool, i. 283), be briefly out lined. A. ANAXONIA forms destitute of axes, and consequently wholly irregular in form, e.g., Amoebae and many Sponges. B. AXOXIA forms with definite axes. 1 See Haeckel, Gen. Morph. i., Kalkschu-cimme i., and Jena. Ztitschr. x. ; also Sachs, Geschichte d. Bot. ; Fisch, Aufzdhlung u. Kritik, ic., Rostock, 18SO ; Perrier, Les Colonies Animates, 1882, as from these all other references can be obtained. 8 The sciences of organic and mineral form would thus (as Haeckel points out) become thoroughly analogous, for, as promorphology develops the crystallo graphy of organic form, so mineralogy.in th study of such phenomena as those
of pseudomorphism or of mineral development, becomes parallel to morphology.