To a mind imbued with the love of mathematical symmetry the study of determinants had naturally every attraction.
Regarding the Echinoderms as a whole in the light of the foregoing account, we may give the following analytic summary of the characters that distinguish them from other coelomate animals: They live in salt or brackish water; a primitive bilateral symmetry is still manifest in the right and left divisions of the coelom; the middle coelomic cavities are primitively transformed into two hydrocoels communicating with the exterior indirectly through a duct or ducts of the anterior coelom; stereom, composed of crystalline carbonate of lime, is, with few exceptions, deposited by special amoebocytes in the meshes of a mesodermal stroma, chiefly in the integument; reproductive cells are derived from the endothelium, apparently of the anterior coelom; total segmentation of the ovum produces a coeloblastula and gastrula by invagination; mesenchyme is formed in the segmentation cavity by migration of cells, chiefly from the hypoblast.
Their bilateral symmetry is obviously to be regarded as primitive, and the nervous system shows an original condition from which that of the asymmetrical twisted Gastropods can be derived.
His fine appearance, his flexible and sympathetic voice, his manifest sincerity, the perfect lucidity and artistic symmetry of his address, and the brilliance with which he illustrated his points would have attracted hearers even had he had little to say.
In the article Crystallography the nature and behaviour of twinned crystals receives full treatment; here it is sufficient to say that when the planes and axes of twinning are planes and axes of symmetry, a twin would exhibit higher symmetry (but remain in the same crystal system) than the primary crystal; and, also, if a crystal approximates in its axial constants to 'a higher system, mimetic twinning would increase the approximation, and the crystal would be pseudo-symmetric.
The hydroxyl group also resembles the methyl group in its morphotropic effects, producing, in many cases, no change in symmetry but a dimensional increase in one direction.
The simplicity and symmetry of his sentences, the modulations of his thrilling voice, the radiance of his fine face, even his slight hesitations and pauses over his manuscript, lent a strange charm to his speech.
Crystals of blende belong to that subclass of the cubic system in which there are six planes of symmetry parallel to the faces of the rhombic dodecahedron and none parallel to the cubic faces; in other words, the crystals are cubic with inclined hemihedrism, and have no centre of symmetry.
A remarkable feature of the solar system, which distinguishes it from all other known systems in the universe, is the symmetry of arrangement and motion of its greater bodies.
Study of the earliest larval stages has always led to the conclusion that the Echinoderms must have descended from some freely-moving form with a bilateral symmetry, and, connecting this with the ideas just mentioned, we reach the conception that this supposed bilateral ancestor (or Dipleurula) may have become fixed, and may have gradually acquired a radial symmetry in consequence of its sedentary mode of life.