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symmetry

symmetry

symmetry Sentence Examples

  • There is symmetry about the initial line and a cusp at the origin.

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  • There is symmetry about the initial line and a cusp at the origin.

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  • 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.

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  • His vanity made him order the surgeons to cut out a bone which protruded below the knee and spoilt the symmetry of his leg.

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  • In the first place, there is necessarily a complete symmetry round the direction of the force.

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  • In the first place, there is necessarily a complete symmetry round the direction of the force.

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  • A factor of considerable importance in determining boiling-points of isomers is the symmetry of the molecule.

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  • But he is always ingenious, often witty, and nobody has carried farther than he the harmony of diction, sometimes marred by an affectation of symmetry and an excessive use of antithesis.

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  • The groups within groups adopted for this purpose were necessarily wanting in symmetry: the whole system presented a strangely irregular character.

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  • The rude symmetry of the feudal system had been long ago destroyed by partial and unskilful adaptations to modern commercial life, effected at various dates and in accordance with various theories.

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  • The plane of the optic axes may be either perpendicular or parallel to the plane of symmetry of the crystal, and according to its position two classes of mica are distinguished.

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  • If we consider for the present only the primary plane of symmetry, the figure is reduced to two dimensions.

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  • If we consider for the present only the primary plane of symmetry, the figure is reduced to two dimensions.

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  • An elaborate symmetry is observable in the construction of many of his elegies, and this has tempted critics to divide a number of them into strophes.

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  • Pierre disturbed the symmetry by moving a chair for himself, and Berg and Vera immediately began their evening party, interrupting each other in their efforts to entertain their guest.

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  • If the symmetry that is so noticeable in geological history had extended to climate as well, many geographical features might now present likenesses instead of contrasts.

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  • Another group of investigations that seems to play an important part in the future development of the theory of evolution relates to the study of what is known as organic symmetry.

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  • Her figure was carelessly wrapped in a loose gown, trimmed with fur; but its grace indicated its symmetry.

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  • Instead, place end tables on the outside of each loveseat with a lamp to repeat your theme of symmetry.

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  • Typically, these cabinets are combined with a wall mirror for symmetry.

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  • Theorem of Symmetry.

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  • Restrictions: The main restriction is related to the assumed spherical symmetry.

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  • The vast quantity of it on the internet attests to an unholy symmetry between click-and-point and the solitary, masturbatory act itself.

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  • Here the gage symmetry is hidden by spontaneous symmetry breaking.

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  • This would be a very weak test, easily satisfied for a single symmetry axis.

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  • Alternatively, the symmetry operators can be input explicitly, each separated with a ' * '.

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  • This option does NOT unlock the symmetry matrices if they are locked !

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  • Progress continues in developing new techniques to match image curves over arbitrary viewpoints for extracting symmetry axes and recognition.

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  • For merged data files, the spacegroup symmetry is used to generate the whole zone.

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  • Symmetry: When you look straight down the centerline of the bike, are items like mirrors and handlebars symmetrical or askew?

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  • Symmetry is critical between both brows to prevent a skewed, disproportionate appearance.

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  • Strange as it may appear, I would refer to an Australian as the finest model of the human proportions I have ever met; in muscular development combining perfect symmetry, activity and strength, while his head might have compared with the antique bust of a philosopher."

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  • He defined them as possessing radial instead of bilateral symmetry, and as apparently destitute of nervous system and sense organs, as having the circulatory system rudimentary or absent, and the respiratory organs on or coextensive with the surface of the body; he included under this title and definition five classes, - Echinodermata, Acalepha, Entozoa, Polypi and Infusoria.

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  • In cases where the development of the embryo is advanced at the resting period, traces run from the cotyledons and determine the symmetry of the stele of the primitive axis, the upperpart of which often shows stem-structure, in some respects at least, and is called the hypocoty- ledonary stem or hypocotyl, while the lower part is the primary root .~-,

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  • Beyond the limits of his personal travels Herodotus applied the characteristically Greek theory of symmetry to complete, in the unknown, outlines The ides of lands and rivers analogous to those which had been of symexplored.

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  • The old instinctive idea of symmetry must often have suggested other oekumene balancing the known world in the other quarters of the globe.

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  • arranged with a certain rough radiate symmetry round the north pole, and extending southwards in three unequal arms which taper to points in the south.

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  • And, if Kant was overridden by a love of symmetry, Reid's indifference to form and system is an even more dangerous defect.

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  • The Gastropoda are mainly characterized by a loss of symmetry, produced by torsion of the visceral sac. This torsion may be resolved into two successive movements.

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  • - These are the most primitive Gastropods, retaining to a great degree the original symmetry of the FIG.

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  • A stair turret breaks the symmetry on the south face.

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  • The graph of the function will have rotational symmetry about the origin (e.g. y = x³).

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  • Symmetry: If you are wearing your blouse under a suit, you probably want a symmetrical design.

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  • Symmetry: A symmetrical tree is one that will look fabulous when viewed from any angle.

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  • Two end tables flanking a sofa will infuse a room with balance and symmetry.

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  • Traditional interiors are characterized by symmetry and lack of clutter.

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  • This gives symmetry in your placement with one loveseat on either side of the fireplace.

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  • The symmetry and shape of well-kept brows are instant beautifiers.

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  • When shooting large groups, which include five or more subjects, symmetry is critical.

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  • Japanese gardens are typically formal gardens that focus on symmetry and symbolism.

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  • The Persian varieties are the finest as regards color, compactness, and symmetry of growth; but the Turban varieties are of hardier constitution and of freer growth, and therefore are better suited for beds, lines, and masses.

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  • Formal or Traditional: Characterized by classic, clean lines and symmetry, a formal or traditional container garden is elegant, simple, and tasteful.

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  • Cut: Gemstone graders evaluate how well the gem was cut in terms of shape, symmetry and finish - overall appearance and workmanship.

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  • Choose summer dresses with bateau, princess or sweetheart, square or V-necklines to show off collarbones and add symmetry.

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  • They're also often available in unusual shapes (and the usual ones!) for additional symmetry and fashion statement.

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  • People with obsessive-compulsive disorder may have an intense preoccupation with order and symmetry or may be unable to throw anything out.

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  • Some patients pull out hairs without regard for symmetry, while others will attempt to follow a pattern or pull out hairs in an effort to maintain symmetry of appearance.

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  • It's the math that holds our universe together because it's responsible for creating balance and symmetry.

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  • People began to apply the symmetry of the Golden Ratio to create buildings, sculpture and other forms of art.

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  • As you can see, by understanding the math behind it, you can measure any object or person to determine if it's symmetry correlates to that dictated by the Golden Ratio.

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  • Symmetry is the art of harmony and balance between the proportions of an object and the space it occupies.

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  • To create a Golden Ratio symmetry design for your fireplace mantle using candles, you'll need to place the same configuration of number, order of height, color of candles and spacing of the arrangement on both sides of the mantle.

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  • To achieve Divine Proportions, architects apply the symmetry of this ratio to buildings and any other structure.

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  • Two important components of the Golden Ratio in a face are symmetry and harmony.

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  • Symmetry is often described as the mirror image and harmony refers to a recurring theme found within the face and the measurements.

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  • The Golden Ratio in humans provides balance, symmetry and beauty, just as it does to other life forms and the universe itself.

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  • Oval faces are blessed with even symmetry, making many hairstyles easy to wear and ultra-flattering.

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  • Achieve the ultimate slimming look by focusing on the symmetry of the face in proportion to the body.

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  • In an academic setting, tea bag folding is sometimes used as a part of a lesson on symmetry.

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  • Crop and Color-change the color and symmetry of your shots with photo tools, then blow them up and frame them.

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  • Suspension bridges are among the most beautiful bridges in the world, representing a symmetry that directly reflects its internal balance.

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  • What you want to be mindful of is sizing and torso length; although this is less a concern with a homemade bikini than a one-piece, you still want to achieve symmetry.

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  • Recognizing that a stone's cut is the only factor created by man, the designer has driven cut standards even higher as it strives for perfection and anatomical symmetry in each stone.

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  • Vintage styles with larger settings, art deco symmetry, and bold use of metal are popular in right hand rings.

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  • Ritani's attention to detail and meticulous eye for form and symmetry have led to dozens of exquisite engagement ring designs.

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  • Less precise detailing in the filigree pattern with minute imperfections in the ring's symmetry or overall pattern due to the lack of machine tooling and the predominance of hand jewelry making decades ago.

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  • Symmetry: A well balanced, symmetrical ring is lovely on the finger.

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  • Proportions: In addition to good symmetry, beautiful rings have appropriate proportions.

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  • Concentric Hearts: Layering heart designs in a filigree or geometric pattern along the ring's band adds symmetry and boldness to the design.

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  • Outlines: If the ring's central diamond is a heart shape, it may be outlined in bold geometric accents such as tapered baguettes or small side stones to emphasize the symmetry and detail of the ring while still highlighting the heart shape.

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  • Art Deco(1915-1938):Geometry, symmetry, and bold design.

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  • "Cut" refers to the proportion, polish, and symmetry of a diamond, all of which contribute to the diamond's sparkle.

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  • Quality diamonds that are less than a one-third carat are rare because getting a quality cut that shows off the heart shape in perfect symmetry is more difficult in smaller stones.

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  • These hand-cut diamonds greatly varied in symmetry and appearance.

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  • Modern cushion cuts have the advantage of today's jewelry technology, which creates smoother, uniform cuts with better symmetry and precise shape than antique cushion cuts.

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  • If your kids thrive on order and symmetry, consider the Mandalas Stained Glass Coloring Book.

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  • Beyond their beauty, symmetry of shape and limitless pattern varieties, here are some other reasons women commonly choose a butterfly design.

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  • In statuary, heads and bodies usually face the same direction, emphasizing symmetry and stillness.

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  • One of the purposes of multiple belly button piercings is to create a look of symmetry.

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  • The beauty of Celtic knots lies in their symmetry.

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  • Scherenschnitte is a German form of paper cutting characterized by symmetry within the design.

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  • While performing bicep exercises will enhance bicep size and definition, remember that health and muscular symmetry come from total body workouts.

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  • As if these benefits were not enough, an upper body workout plan adds symmetry to your body.

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  • However, in order to maintain or enhance muscle symmetry, it's important to spend equal time on each muscle group.

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  • Remember as you do triceps exercises, spend equal time exercising your biceps and shoulders to achieve muscle symmetry.

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  • Star Trek fans everywhere enjoyed the symmetry that the first space passenger vehicle would be named for the Starship that served as the flagship of the Federation.

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  • Drills are judged on precision and symmetry.

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  • Pectinibranchia.-In this order there is no longer any trace of bilateral symmetry in the circulatory, respiratory and excretory organs, the topographically right half of the pallial complex having completely disappeared, except the right kidney, which is FIG.

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  • Where the modification is carried to its extreme degree, not only the shell but the pallial cavity, ctenidium and visceral hump disappear, and the body acquires a simple elongated form and a secondary external symmetry, as in Pterotrachaea and in Doris, Eolis, and other Nudibranchia.

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  • The facade is a triumph of graceful elegance; so light is the tracery, so rich the decoration, so successful the breach of symmetry which gives us a wing upon the left-hand side but none upon the right.

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  • The symmetry of the second pair was also established in 1878 by E.

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  • 149, p. 20) established the symmetry of the naphthalene nucleus, and showed that whichever half of the molecule be oxidized the same phthalic acid results.

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  • Mag., 18 93 [5), 35, p. 45 8) has shown that, while an increase in molecular weight is generally associated with a rise in the boiling-point, yet the symmetry of the resulting molecule may exert such a lowering effect that the final result is a diminution in the boiling-point.

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  • The series H 2 S = - 61°, CH 3 SH = 21 °, (C 11 3) 2 S=41 ° is an example; in the first case, the molecular weight is increased and the symmetry diminished, the increase of boiling-point being 82°; in the second case the molecular weight is again increased but the molecule assumes a more symmetrical configuration, hence the comparatively slight increase of 20°.

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  • 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.

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  • The measure of the loss of symmetry associated with the introduction of alkyl groups depends upon the relative magnitudes of the substituent group and the rest of the molecule; and the larger the molecule, the less would be the morphotropic effect of any particular substituent.

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  • 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.

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  • The nitro group behaves very similarly to the hydroxyl group. The effect of varying the position of the nitro group in the molecule is well marked, and conclusions may be drawn as to the orientation of the groups from a knowledge of the crystal form; a change in the symmetry of the chemical molecule being often attended by a loss in the symmetry of the crystal.

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  • r is bounded by the basal pinacoid c (ooi) parallel to which is the perfect cleavage, the clinopinacoid b ((D10) parallel to the plane of symmetry, and the pyramids m (221) and o (112).

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  • To the first class, with the optic axial plane perpendicular to the plane of symmetry, belong muscovite, lepidolite, paragonite, and a rare variety of biotite called anomite; the second class includes zinnwaldite, phlogopite, lepidomelane and most biotites.

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  • Dark coloured micas are strongly pleochroic. Accurate determinations of the optical orientation, as well as the symmetry of the etching figures on the cleavage planes, seem to suggest that the micas, except muscovite, may be anorthic rather than monoclinic in crystallization.

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  • aj Hence the system of values also causes to vanish in this case; dx and by symmetry aj and Fz also vanish.

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  • Hence, finally, the resultant is expressed in terms of the coefficients of the three equations, and since it is at once seen to be of degree mn in the coefficient of the third equation, by symmetry it must be of degrees np and pm in the coefficients of the first and second equations respectively.

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  • A table may be formed expressing the k expressions Pa l), P(2),...P(1) as linear functions of the k expressions (m"`'sm�2sm�3s...), s =1, 2, ...k, and the numbers BSc occurring therein is 2s 3s possess row and column symmetry.

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  • According to his view, all mountain ranges parallel to the same great circle of the earth are of strictly contemporaneous origin, and between the great circles a relation of symmetry exists in the form of a pentagonal reseau.

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  • Intended to evolve a history of jurisprudence from the truthful portraits of England's greatest lawyers, it merely exhibits the ill-digested results of desultory learning, without a trace of scientific symmetry or literary taste, without a spark of that divine imaginative sympathy which alone can give flesh and spirit to the dead bones of the past, and without which the present 1 See thereon J.

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  • Even in ordinary algebra the notation for powers and roots disturbs the symmetry of the rational theory; and when a schoolboy illegitimately extends the distributive law by writing -V (a+b)a+J b, he is unconsciously emphasizing this want of complete harmony.

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  • The part corresponding to negative values of u is similar, OA being a line of symmetry.

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  • The phase of the resultant effect is by symmetry that of the component which comes from the middle of a.

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  • When the plane zx is not a plane of symmetry, we have to consider the terms in xy, 2 y, and y 3 .

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  • The other coefficients in (8) vanish in virtue of the symmetry.

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  • - 47rb 2 ' The occurrence of sin 4 shows that there is no disturbance radiated in the direction of the force, a feature which might have been anticipated from considerations of symmetry.

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  • Generally, by making a' = -oo, the line x'A' may be taken as a straight stream line of infinite length, forming an axis of symmetry; and then by duplica tion the result can be ob A tained, with assigned n, a, and b, of the efflux from a symmetrical converging FIG.

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  • preserves its original direction, if a principal axis of the body; otherwise the axis describes a cone, right circular if the body has uniaxial symmetry, and a Poinsot cone in the general case.

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  • ideas of symmetry, so different from ours, from a close study of nature and her processes in the attainment of endless variety.

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  • Her artists and artisans alike aim at symmetry, not by an equal division of parts, as we do, but rather by a certain balance of corresponding parts, each different from the other, and not numerically even, with an effect of variety and freedom from formality.

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  • By repeated hammering and polishing the expert obtains such control of the wood-grain pattern that its sinuosities and eddies seem to have developed symmetry without losing anything of their fantastic grace.

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  • Thus the two images under measurement are not defined with equal sharpness and symmetry.

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  • The value n = 2 is appropriate to bodies of which the shape is that of a solid of revolution, so that there is no rotation about the axis of symmetry.

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  • the Prussian intervention deranged the symmetry of Napoleon's battle-array.

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  • The medusa has a pronounced radial symmetry, and the positions of the primary tentacles, usually four in number, mark out the so-called radii, alternating with which are four interradii.

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  • Geranium, Cardamine pratensis, mallows, Rubus, Oxalis, Epilobium, &c., but many species show more or less well-marked median symmetry (zygomorphism) as Euphrasia, Orchis, thyme, &c., and red, blue and violet are the usual colours.

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  • The mastery which he had obtained over the mathematical symbols was so complete that he never shrank from the use of expressions, however complicated - nay, the more complicated they were the more he seemed to revel in them - provided they did not sin against the ruling spirit of all his work - symmetry.

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  • To a mind imbued with the love of mathematical symmetry the study of determinants had naturally every attraction.

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  • Its nest, which is a model of neatness and symmetry, it builds on trees and bushes, preferring such as are overgrown with moss and lichens.

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  • Here the barns, granaries, stables, shambles, workshops and workmen's lodgings were placed, without any regard to symmetry, convenience being the only consideration.

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  • These digressions at times interrupt the symmetry of his plan; but Strabo had all the Greek love of legendary lore, and he discusses the journeyings of Heracles as earnestly as if they were events within recent history.

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  • The Lamellibranchia are mainly characterized by the rudimentary condition of the head, and the retention of the primitive bilateral symmetry, the latter feature being accentuated by the lateral compression of the body and the development of the shell as two bilaterally symmetrical plates or valves covering each one side of the animal.

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  • The chief points in which they vary are - (1) in the structure of the ctenidia or branchial plates; (2) in the presence of one or of two chief muscles, the fibres of which run across the animal's body from one valve of the shell to the other (adductors); (3) in the greater or less elaboration of the posterior portion of the mantle-skirt so as to form a pair of tubes, by one of which water is introduced into the sub-pallial chamber, whilst by the other it is expelled; (4) in the perfect or deficient symmetry of the two valves of the shell and the connected soft parts, as compared with one another; (5) in the development of the foot as a disk-like crawling organ (Arca, Nucula, Pectunculus, Trigonia, Lepton, Galeomma), as a simple plough-like or tongueshaped organ (Unionidae, &c.), as a re-curved saltatory organ (Cardium, &c.), as a long burrowing cylinder (Solenidae, &c.), or its partial (Mytilacea) or even complete abortion (Ostraeacea).

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  • As a result, the Coelomata, and with them the Mollusca, present (in the first instance) the general condition of body known as bilateral symmetry; the dorsal is differentiated from the ventral surface, whilst a right and a left side similar to, or rather the complements of, one another are permanently established.

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  • The original form was bilaterally symmetrical, and this symmetry is retained in all the classes except the Gastropoda.

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  • The Freiburg minster is considered one of the finest of all the Gothic churches of Germany, being remarkable alike for the symmetry of its proportions, for the taste of its decorations, and for the fact that it may more correctly be said to be finished than almost any other building of the kind.

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  • The grounds for this view are the radial symmetry of several Polyclads and the supposed origin of gonads and excretory flame-cells from the walls of gut, the occurrence of nematocysts in Anonymus, one of the most radially constructed Polyclads, and lastly the presence of two peculiar animals Ctenoplana and Coeloplana, which suggests a transition from Ctenophora to Polyclads.

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  • The symmetry is remarkable, and the reverberations are strangely musical.

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  • 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.

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  • The Viennese are successful in dyeing marmot well, and their cleverness in colouring it with a series of stripes to represent the natural markings of sable which has been done after the garments have been made, so as to obtain symmetry of lines, has secured for them a large trade among the dealers of cheap furs in England and the continent.

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  • 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.

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  • Crystals exhibit pyroelectrical characters, since they possess four uniterminal triad axes of symmetry.

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  • C. t is on symmetry and proportion; c. 2 on various forms of Greek temples, e.g.

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  • Thus regarded, even without remarking that the Novels, never having been officially collected, much less incorporated with the Codex, mar the symmetry of the structure, Justinian's work may appear to entitle him and Tribonian to much less credit than they have usually received for it.

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  • It shows the pope and emperor, with a lute-playing angel between them, kneeling to right and left of the enthroned Virgin and Child, who crown them with rose garlands, with a multitude of other kneeling saints disposed with free symmetry in the background, and farther in the background portraits of the donor and the painter, and a flutter of wreath-carrying cherubs in the air.

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  • 3), or with a symmetry in the median plane as in Gladiolus.

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  • And similarly in the development of a complicated organism, the suppression or doubling of a single cell or group of cells may bring about striking differences in the symmetry of the adult, or the reduction or increase in the number of metameric organs.

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  • The quality of .the surface left by the skilled artist or artisan is more regarded than symmetry of design, or even than correct modelling.

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  • Cooke's mounting is admirable for its symmetry and simplicity of design, its just apportioning of strength, and a general suitability of means to ends.

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  • Boltzmann Suggested That A Diatomic Molecule Regarded As A Rigid Dumb Bell Or Figure Of Rotation, Might Have Only Five Effective Degrees Of Freedom, Since The Energy Of Rotation About The Axis Of Symmetry Could Not Be Altered By Collisions Between The Molecules.

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  • Kobold, using a peculiar and ingenious method, found for it a declination - 3°, which disagrees very badly with all other determinations; but it is a peculiarity of Kobold's method that it gives the line of symmetry of motion, which joins the apex and antapex, without indicating which end is the apex.

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  • Now the position of this line, as found by Kobold, actually is a (properly weighted) mean between the corresponding lines of symmetry of the two drifts, but naturally it lies in the acute angle between them, whereas the line of the solar motion is also a weighted mean between the two lines of drift, but lies in the obtuse angle between them.

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  • Hence, and in this lies the main element of the symmetry and simplicity of the quaternion calculus, all systems of three mutually rectangular unit lines in space have the same properties as the fundamental system i, j, k.

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  • But, as yet, we have not taken advantage of the perfect symmetry of the method.

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  • But every quaternion formula is a proposition in spherical (sometimes degrading to plane) trigonometry, and has the full advantage of the symmetry of the method.

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  • Here the symmetry points at once to the selection of the three principal axes as the directions for i, j, k; and it would appear at first sight as if quaternions could not simplify, though they might improve in elegance, the solution of questions of this kind.

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  • Since I~=Ii., I~=o, we deduce 100=3/4Ma2, ~ =4MaZ; hence the value of the squared radius of gyration isfora diameter 3/4ai, and for the axis of symmetry 3/4af.

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  • in the case of symmetry about an axis it appears that the ratio of the polar to the equatorial diameter of the ellipsoid cannot be less than I/~2.

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  • The mass-system is then said to possess kinetic symmetry about 0.

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  • where K is the radius of gyration about the axis of symmetry, a is the constant distance of G from the plane, and R, F are the normal and tangential components of the reaction of the plane, as shown in fig.

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  • If a be the inclination of the instantaneous axis to the axis of symmetry, (3 the inclination of the latter axis to the invariable line, we have rcosfl=Cw cos a, r sin ~3 = Aw sin a, (6) whence tan ~ =~ tan a.

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  • It frequently happens that the extraneous forces have zero moment about the axis of symmetry, as e.g.

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  • For we have seen that r is constant when there are no extraneous forces; and r is evidently not affected by an instantaneous impulse which leaves the angular momentum Cr, about the axis of symmetry, unaltered.

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  • The components of angular momentum about the axis of the flywheel and about the vertical will be Cn and A ~ respectively, where A is the moment of inertia about any axis through the masscentre (or through the fixed point 0) perpendicular to that of symmetry.

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  • If the direction of the axis of kinetic symmetry be specified by means of the angular co-ordinates 0, ~

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  • We can hence deduce the condition of steady precessional motion in a top. A solid of revolution is supposed to be free to turn about a fixed point 0 on its axis of symmetry, its masscentre G being in this axis at a distance h from 0.

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  • Hence, and b~ symmetry, we obtain -~ ru +qv ~P~+rX=M, (I)

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  • Again, a vertical plane passing, through O and a point where the motion is horizontal is evidently a plane of symmetry as regards the path.

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  • Since 8, o, are the polar co-ordinates (in a horizontal plane) of a point on the axis of symmetry, relative to an initial line which revolves with constant angular velocity P/2A, we see by comparison with 14 (i5) (16) that the motion of such a point will be elliptic-harmonic superposed on a uniform rotation e/2A, provided v2 >4AMgh.

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  • The result, owing to its symmetry, must still hold if we interchange accented and unaccented Greek letters, and by comparison we deduce (15) and (16), provided cr2 and Cr~2 are unequal.

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  • On assuming the directorship of the Nautical Almanac he became very strongly impressed with the diversity existing in the values of the elements and constants of astronomy adopted by different astronomers, and the injurious effect which it exercised on the precision and symmetry of much astronomical work.

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  • In the other pyro-electric crystals above mentioned, Hatly detected the same deviation from the rules of symmetry in their secondary crystals which occurs in tourmaline.

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  • In a corresponding manner the right side of the animal's body is somewhat less developed than the left, and to this extent there is a departure from the bilateral symmetry characteristic of Lamellibranchs.

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  • The optic figure seen in convergent polarized light through a section cut parallel to the plane of symmetry of a borax crystal is symmetrical only with respect to the central point.

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  • In regard to colour and design the Taj ranks first in the world for purely decorative workmanship; while the perfect symmetry of its exterior once seen can never be forgotten, nor the aerial grace of its domes, rising like marble bubbles into the azure sky.

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  • Suppose, therefore, that the equation of the boundary is r =a+a cos kz, (I) where a is a small quantity, the axis of z being that of symmetry.

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  • The detached masses into which a jet is resolved do not at once assume and retain a spherical form, but execute a series of vibrations, being alternately compressed and elongated in the direction of the axis of symmetry.

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  • A fourth was subsequently added, for the sake of symmetry, to make them correspond with the four seasons, and they became known as the jejunium vernum, aestivum, autumnale and hiemale, so that, to quote Pope Leo's words, "the law of abstinence might apply to every season of the year."

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  • Apart from the numerous parasitic forms, the only Crustacea which have adopted a strictly sedentary habit of life are the Cirripedia, and here, as elsewhere, profound modifications of structure have resulted, leading ultimately to a partial assumption of the radial type of symmetry which is so often associated with a sedentary life.

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  • 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.

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  • Most living bodies, it is true, are capable of reproduction, but there are many without this capacity, whilst, on the other hand, it would be difficult to draw an effective distinction between that reproduction of simple organisms which consists of a sub-division of their substance with consequent resumption of symmetry by the separate pieces, and the breaking up of a drop of mercury into a number of droplets.

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  • Such a model, properly constructed, that is to say, with the vesicles of the foam microscopic in size, is a marvellous imitation of the appearance of protoplasm, being distinguishable from it only by a greater symmetry.

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  • Leonardo, though no special student of the Greeks, has perfectly carried out the Greek principle of expressive variety in particulars subordinated to general symmetry.

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  • The crisis of his mental conflict had just been passed in Tirol, and he was now beginning to let his creed grow again from the one fixed point which nothing had availed to shift: "The one great certainty to which, in the midst of the darkest doubt, I never ceased to cling - the entire symmetry and loveliness and the unequalled nobleness of the humanity of the Son of Man."

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  • 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.

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  • Crystals of this class possess neither planes nor centre of symmetry, but only axes of symmetry: perpendicular to the principal triad axis there are three uniterminal dyad axes of symmetry.

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  • Usually, however, this lower degree of symmetry is not indicated by the faces developed on the crystals.

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  • 4 and 5), which indicate the true degree of symmetry of quartz, are of comparatively rare occurrence except on crystals from certain localities.

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  • The pyro-electric characters of quartz are closely connected with its peculiar type of symmetry and especially with the three uniterminal dyad axes.

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  • A similar distribution of electric charges is produced when a crystal is subjected to pressure; quartz being thus also piezo-electric. Etched figures, both natural and artificial (in the latter case produced by the action of hydrofluoric acid), on the faces of the crystals are in accordance with the symmetry, and may serve to distinguish leftand righthanded crystals.

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  • This phenomenon is connected with the symmetry of the crystals, and is also shown by the crystals of certain other substances in which there are neither planes nor centre of symmetry.

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  • It is chiefly built of outlayer granite, and, though the plainest cathedral in Scotland, its stately simplicity and severe symmetry lend it unique distinction.

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  • The elongation of the mouth and stomodaeum confer a bilateral symmetry on the body of the zooid, which is extended to other organs of the body.

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  • A pause in the development follows, during which no new mesenteries are formed, and then the six-rayed symmetry characteristic of a normal Actinian zooid is completed by the formation of the mesenteries V, V in the lateral chambers, and VI, VI in the sulcolateral chambers, their muscle-banners being so disposed that they form couples respectively with II, II and I, I.

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  • In many of these so-called rugose forms the septa have a characteristic arrangement, differing from that of recent corals chiefly in the fact that they show a tetrameral instead of a hexameral symmetry.

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  • This arrangement, however, is by no means characteristic even of the Zaphrentidae, and in the family Cyathophyllidae most of the genera exhibit a radial symmetry in which no trace of the bilateral arrangement described above is recognizable, and indeed in the genus Cyathophyllum itself a radial arrangement is the rule.

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  • The general structure of this coral leaves no doubt that it is closely allied to the Astraeidae, but in the young calicles a tetrameral symmetry is indicated by the presence of four large septa placed at right angles to one another.

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  • The orocentral was, it must be admitted, a theoretical conception due to a desire for symmetry, and was not confirmed by anything 1p _.

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  • 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.

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  • The different extent of quinqueradiate symmetry in the different classes would thus depend on the period at which they diverged from the sedentary stock.

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  • It might be possible to prove the origin of all classes from Pelmatozoa, without thereby explaining the origin of such fundamental features as radial symmetry, the developmental metamorphosis, and the torsion that affects both gut and body-cavities during that process; but the acceptance of a Dipleurula as the common ancestor necessitates an explanation of these features.

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  • Although, in the extreme correlation of the radial food-grooves, nerves, watervessels, and so forth, with a radiate symmetry of the theca, such a type differs from the Cystidea, while in the possession of jointed processes from the radial plates, bearing the grooves and the various body-systems outwards from the theca, it differs from all other Echinoderms, nevertheless ancient forms are known which, if they are not themselves the actual links, suggest how the crinoid type may have been evolved from some of the more regular cystids.

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  • So too the explanation of radial symmetry and torsion of organs as due to a Pelmatozoic mode of life finds confirmation in many other phyla.

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  • Since this must have, on our theory, enclosed the parietal canal from the anterior coelom, it is possible that the genital products were developed from the lining cells of that cavity, and that the genital pore was nothing but its original pore not yet united with that from the water-sac. The concrescence of these pores can be traced in other cystids; but as the genital organs became affected by radial symmetry the original function of the duct was lost, and the reproductive elements escaped to the exterior in another way.

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  • At last a quinqueradiate symmetry influenced the plates of the theca, partly through the development of a plate at the end of each groove (terminal), partly through plates at the aboral pole of the theca (basals and infrabasals) arising in response to mechanical pressure, but soon intimately connected with the cords of an aboral nervous system.

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  • 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.

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  • All living, and most extinct, Echinoderms show the following features, almost certainly due to an ancestral pelmatozoic stage: - An incomplete radial symmetry, of which five is usually the dominant number, is superimposed on the secondary bilateralism, owing to the outgrowth from the mouth region of one unpaired and two paired ciliated grooves; these have a floor of nervous epithelium, and are accompanied by subjacent radial canals from the water-ring, giving off lateral podia and thus forming ambulacra, and by a perihaemal system of canals apparently growing out from coelomic cavities.

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  • - Pelmatozoa in which radial polymeric symmetry of the theca is developed either not at all or not in complete correlation with the radial symmetry of the ambulacra (such as obtains in Blastoidea and Crinoidea); in which extensions of the food-grooves are exothecal or epithecal or both combined, but neither endothecal nor pierced by podia (as in some Edrioasteroidea).

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  • - Radial symmetry has affected neither food-grooves nor thecal plates; nor, probably, nerves, ambulacral vessels, nor gonads.

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  • - Radial symmetry affects the food-grooves and, in the more advanced families, the thecal plates; probably also the nerves and ambulacral vessels, but not the gonads.

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  • - Pentamerous symmetry affects the foodgrooves and thecal plates; probably also the nerves and ambulacral vessels, but not the gonads.

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  • - Radial symmetry affects the food-grooves, and by degrees the thecal plates connected therewith, but not the interradial thecal plates; probably also the nerves and ambulacral vessels, but not the gonads.

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  • The thecal plates, however irregular in some species, always show defined basals and a distinct plate ("radial") at the end of each ambulacrum; they are in all cases so far affected by pentamerous symmetry that their sutures never cross the ambulacra.

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  • - Eleutherozoa with a depressed stellate body composed of a central disk, whence radiate five or more rays; this radiate symmetry affects all the systems of organs, including the genital.

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  • - Eleutherozoa with a test of roughly circular, subpentagonal or elliptical outline, spheroidal, domed or flattened, of primary pentameric symmetry affecting all systems of organs except the gut.

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  • 12, D); the ambulacra thus formed are continuous from the peristome to the apical system of plates; the hydropore is connected with a definite plate of that system, and thus marks a secondary bilateral symmetry.

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  • 19, 7), thus initiating yet another bilateral symmetry.

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  • Of the primary, secondary and tertiary alcohols having the same empirical formula, the primaryhave the highest, and the tertiary the lowest boiling point; this is in accordance with the fairly general rule that a gain is symmetry is attended by a fall in the boiling point.

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  • Owing largely to the simplicity and symmetry of the syllogism it has been a commonplace of logic to make the syllogistic form the type of all thought.

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  • It was built in1888-1895from plans by Ludwig Hoffmann, and is distinguished for the symmetry and harmony of its proportions.

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  • By symmetry the polarization-vector must be either parallel or perpendicular to the plane of polarization: which of these directions is assumed depends upon the physical characteristic that is attributed to the vector.

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  • This state of things may, however, be considerably departed from if the axes of optical symmetry of the crystal are different for the various colours.

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  • This refractive index should be equal to the greatest index of the plate, and with a biaxal plate the mean axis of optical symmetry should be parallel to its faces and in the normal section of the prisms, while with an uniaxal plate the optic axis should be in a plane perpendicular to this normal section.

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  • By these momentous inductions the geometrical theory of the solar system was perfected, and a hitherto unimagined symmetry was perceived to regulate the mutual relations of its members.

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  • With its symmetry, activity, strength and endurance the Clydesdale is easily broken to harness, and makes an excellent draught horse.

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  • Owing to the approximate symmetry of the American and Asiatic continents it does not seem likely that the inequality of snowfall would produce an appreciable effect.

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  • In Symmetry contrast to the cyclic flowers are those, as in Magnoli of the flower.

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  • In such circumstances, however, a flower has been called symmetrical, provided the parts of the other whorls are normal, - the permanent state of the pistil not being taken into account in determining symmetry.

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  • Symmetry, then, in botanical language, has reference to a certain definite numerical relation of parts.

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  • The symmetry which is most commonly met with is trimerous and pentamerous - the former occurring generally among monocotyledons, the latter among dicotyledons.

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  • Dimerous and tetramerous symmetry occur also among dicotyledons.

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  • In contrast with this are polysymmetrical or actinomorphic flowers, which have a radial symmetry and can be divided by several planes into several exactly similar portions; such are all regular, symmetrical flowers.

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  • This want of symmetry may be brought about in various ways.

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  • By suppression or non-appearance of a part at the place where it ought to appear if the structure was normal, the symmetry or completeness of the flower is disturbed.

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  • In all these cases the want of symmetry is traced to the suppression of certain parts.

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  • Degeneration, or the transformation of parts, often gives rise either to an apparent want of symmetry or to irregularity in form.

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  • Cohesion, or the union of parts of the same whorl, and adhesion, or the growing together of parts of different whorls, are causes of change both as regards form and symmetry.

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  • The symmetry in the flower is evidently dimerous, and the abnormality in the androecium, where the four long stamens are opposite the posterior sepals, takes place by a splitting, at a very early stage of development, of a single outgrowth into two.

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  • Branching of stamens also produces apparent want of symmetry; thus, in the so-called polyadelphous stamens of Hypericaceae there are really only five stamens which give off numerous branches, but the basal portion remaining short, the branches have the appearance of separate stamens, and the flower thus seems asymmetrical.

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  • the flower is perfect, and has pentamerous symmetry, the whorls being isomerous.

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  • Many other forms of seed, and especially those which show radial symmetry, as for example Trigonocarpus, Stephanospermum and Lagenostoma belonged, as we have seen, to some of the plants grouped under Pteridospermeae, though other Pteridosperms had flattened seeds not as yet distinguishable from those of Cordaitales.

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  • Relatively minor variation from perfect symmetry is called fluctuating asymmetry.

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  • axis of symmetry.

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  • bicyclic ring junction, whilst that with C 2 symmetry has trans stereochemistry.

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  • How reliable could this Rfree be to point me that there really is a symmetry breakage?

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  • One particularly expressive picture captures a tailback of oil tankers stood bumper-to-bumper in symmetry with a line of sheep led by a farmer.

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  • cylindrical symmetry, the changes in radius can also be calculated.

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  • deviation from symmetry is at most rank two.

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  • dihedral symmetry, and the symmetry is used to block diagonalize the relevant matrices, enabling their eigenvalues to be calculated.

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  • electron diffraction pattern by noting its symmetry.

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  • electroweak symmetry breaking.

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  • equations of motion is integrated under the assumption of axial symmetry.

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  • fearful symmetry?

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  • fivefold axes of symmetry.

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  • fluctuateely minor variation from perfect symmetry is called fluctuating asymmetry.

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  • If the output symmetry is a he output symmetry is a higher symmetry, then all input reflections will output, with more observations per h k l set.

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  • If the output symmetry is a he output symmetry is a higher symmetry, then all input reflections will output, with more observations per h k l set.

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  • If the output symmetry is a he output symmetry is a higher symmetry, then all input reflections will output, with more observations per h k l set.

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  • hexagonal symmetry.

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  • homologues of the gene CYCLOIDEA that has been shown to be involved in setting floral symmetry in snapdragon flowers.

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  • We have identified homologues of the gene CYCLOIDEA that has been shown to be involved in setting floral symmetry in snapdragon flowers.

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  • If the output symmetry is a higher symmetry, then all input reflections will output, with more observations per h k l set.

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  • If the output symmetry is a higher symmetry, then all input reflections will output, with more observations per h k l set.

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  • Even in the dim lamplight he could see the ornamental plantings, the blooms, the symmetry.

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  • Combining the primitive lattice vectors with spacegroup symmetry will effectively generate the crystal lattice.

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  • We consider the phenomenon of forced symmetry breaking in a symmetric Hamiltonian system on a symplectic manifold.

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  • Strategies include mechanical locking with lead ' fishtails ' and die pad perforations, and improving the overall package symmetry by using depressed pads.

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  • Benefits of sitting in the Saddle Seat position - A clear midline assists maintenance of balance and symmetry.

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  • mirror symmetry.

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  • mops up sweat, whilst maintaining a lack of symmetry.

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  • If the symmetry of the SI joints are incorrect, it can prevent the pelvic floor musculature from working properly.

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  • nucleon density distribution that deviates appreciably from spherical symmetry.

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  • This axis of symmetry is called the optic axis.

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  • orthorhombic crystallographic symmetry might exhibit this behavior.

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  • perfectible beauty ' is open to challenge, just as erstwhile requirements for symmetry or circles were.

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  • What, then, are the physical properties of such structures lacking periodicity but with a hierarchical symmetry?

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  • pleasing symmetry is found in the latter idea.

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  • An alternative method to create parts or features that have rotational symmetry is to form a protrusion by revolving rather than extruding.

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  • name a quadrilateral with no lines of symmetry and order of rotational symmetry of 2 Coordinates Co-ordinates.. .

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  • The anticlockwise rotation of the galaxy may stretch out the plumes to contribute to the rough rotational symmetry of the DRAGN.

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  • rotation The rotation symmetry operation rotates an object about an axis.

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  • As a closed shell singlet, 7 is planar and aromatic, with C 2v symmetry.

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  • stereochemistry of each reaction also reflects its symmetry.

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  • The system with C s has cis stereochemistry at the bicyclic ring junction, whilst that with C 2 symmetry has trans stereochemistry.

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  • The system with C s has cis stereochemistry at the bicyclic ring junction, whilst that with C 2 symmetry has trans stereochemistry at the bicyclic ring junction, whilst that with C 2 symmetry has trans stereochemistry.

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  • A very interesting symmetry, called supersymmetry, is essentially the unique way to connect bosons with fermions, or equivalently forces with matter.

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  • Arnold's report shows a bilaterally symmetrical craft that travels in the direction of the axis of symmetry.

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  • Remember that " cell " maps will obey crystal symmetry and unit cell repeats; " work " maps do not.

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  • This did, however, spoil the original symmetry of the frontage.

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  • Note there is rotational symmetry of this pattern around the line joining the elements.

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  • There are two modes to deal with non-crystallographic symmetry.

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  • For each peak, peaks related by crystallographic symmetry are also listed.

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  • Several options are available for applying less than full icosahedral symmetry.

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  • Restrictions: The main restriction is related to the assumed spherical symmetry.

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  • The vast quantity of it on the internet attests to an unholy symmetry between click-and-point and the solitary, masturbatory act itself.

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  • Here the gage symmetry is hidden by spontaneous symmetry breaking.

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  • symmetry breakage?

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  • symmetry axis.

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  • symmetry operators can be input explicitly, each separated with a ' * ' .

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  • symmetry matrices if they are locked!

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  • symmetry axes and recognition.

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  • symmetry between click-and-point and the solitary, masturbatory act itself.

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  • For merged data files, the spacegroup symmetry is used to generate the whole zone.

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  • The tetrahedral structuring possesses five-fold symmetry, which prevents easy freezing in line with the pronounced supercooling found for intracellular water.

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  • A particle viewed down, for example, the three-fold symmetry axis can be readily identified by the three-fold symmetry of the projection.

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  • The crystal symmetry will be used to generate atom positions from a unique molecule.

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  • symmetry &and transformations is available from MicroSMILE Isaac Newton Center 108a Lancaster Rd.

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  • trigonal space groups, symmetry equivalents do not seem as " natural " as in other systems.

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  • trimmed with fur; but its grace indicated its symmetry.

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  • A stair turret breaks the symmetry on the south face.

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  • unholy symmetry between click-and-point and the solitary, masturbatory act itself.

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  • The.g.aph of the function will have rotational symmetry about the origin (e.g. ymmetry about the origin (e.g. y = x³ ).

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  • The disturbance, consisting of transverse vibrations, is propagated outwards in all directions from the centre; and, in consequence of the symmetry, the direction of vibration in any ray lies in the plane containing the ray and the axis of symmetry; that is to say, the direction of vibration in the scattered or diffracted ray makes with the direction of vibration in the incident or primary ray the least possible angle.

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  • The symmetry also requires that the intensity of the scattered light should vanish for the ray which would be propagated along the axis; for there is nothing to distinguish one direction transverse to the ray from another.

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  • An elaborate symmetry is observable in the construction of many of his elegies, and this has tempted critics to divide a number of them into strophes.

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  • 7, and believed that by the use of wires,, much thicker than spider webs, the eye could estimate more accurately the symmetry of the star-images with respect to the wires.

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  • The crystals possess a perfect cleavage parallel to the plane of symmetry and are usually bladed, in habit; they are soft (H= 2), flexible and sectile.

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  • But he is always ingenious, often witty, and nobody has carried farther than he the harmony of diction, sometimes marred by an affectation of symmetry and an excessive use of antithesis.

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  • Strange as it may appear, I would refer to an Australian as the finest model of the human proportions I have ever met; in muscular development combining perfect symmetry, activity and strength, while his head might have compared with the antique bust of a philosopher."

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  • The main difference between symphonic and modern dramatic orchestration depends on this: that in a symphony any important incident will probably be heard again within five minutes, in every circumstance of formal symmetry and preparation that can attract the attention.

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  • Another group of investigations that seems to play an important part in the future development of the theory of evolution relates to the study of what is known as organic symmetry.

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  • Closely allied to the study of symmetry is the study of the direct effect of the circumambient media on embryonic young and adult stages of living beings (see Embryology: Physiology; Heredity; and Variation And Selection), and a still larger number of observers have added to our knowledge of these.

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  • He defined them as possessing radial instead of bilateral symmetry, and as apparently destitute of nervous system and sense organs, as having the circulatory system rudimentary or absent, and the respiratory organs on or coextensive with the surface of the body; he included under this title and definition five classes, - Echinodermata, Acalepha, Entozoa, Polypi and Infusoria.

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  • In cases where the development of the embryo is advanced at the resting period, traces run from the cotyledons and determine the symmetry of the stele of the primitive axis, the upperpart of which often shows stem-structure, in some respects at least, and is called the hypocoty- ledonary stem or hypocotyl, while the lower part is the primary root .~-,

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  • Beyond the limits of his personal travels Herodotus applied the characteristically Greek theory of symmetry to complete, in the unknown, outlines The ides of lands and rivers analogous to those which had been of symexplored.

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  • Symmetry was in fact the first geographical metry.

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  • The old instinctive idea of symmetry must often have suggested other oekumene balancing the known world in the other quarters of the globe.

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  • arranged with a certain rough radiate symmetry round the north pole, and extending southwards in three unequal arms which taper to points in the south.

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  • And, if Kant was overridden by a love of symmetry, Reid's indifference to form and system is an even more dangerous defect.

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  • The rude symmetry of the feudal system had been long ago destroyed by partial and unskilful adaptations to modern commercial life, effected at various dates and in accordance with various theories.

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  • The Gastropoda are mainly characterized by a loss of symmetry, produced by torsion of the visceral sac. This torsion may be resolved into two successive movements.

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  • - These are the most primitive Gastropods, retaining to a great degree the original symmetry of the FIG.

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  • Pectinibranchia.-In this order there is no longer any trace of bilateral symmetry in the circulatory, respiratory and excretory organs, the topographically right half of the pallial complex having completely disappeared, except the right kidney, which is FIG.

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  • Where the modification is carried to its extreme degree, not only the shell but the pallial cavity, ctenidium and visceral hump disappear, and the body acquires a simple elongated form and a secondary external symmetry, as in Pterotrachaea and in Doris, Eolis, and other Nudibranchia.

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  • The facade is a triumph of graceful elegance; so light is the tracery, so rich the decoration, so successful the breach of symmetry which gives us a wing upon the left-hand side but none upon the right.

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  • His vanity made him order the surgeons to cut out a bone which protruded below the knee and spoilt the symmetry of his leg.

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  • The symmetry of the second pair was also established in 1878 by E.

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  • 149, p. 20) established the symmetry of the naphthalene nucleus, and showed that whichever half of the molecule be oxidized the same phthalic acid results.

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  • A factor of considerable importance in determining boiling-points of isomers is the symmetry of the molecule.

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  • Mag., 18 93 [5), 35, p. 45 8) has shown that, while an increase in molecular weight is generally associated with a rise in the boiling-point, yet the symmetry of the resulting molecule may exert such a lowering effect that the final result is a diminution in the boiling-point.

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  • The series H 2 S = - 61°, CH 3 SH = 21 °, (C 11 3) 2 S=41 ° is an example; in the first case, the molecular weight is increased and the symmetry diminished, the increase of boiling-point being 82°; in the second case the molecular weight is again increased but the molecule assumes a more symmetrical configuration, hence the comparatively slight increase of 20°.

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  • Broadly this phenomenon is termed polymorphism; however, it is necessary to examine closely the diverse crystal modifications in order to determine whether they are really of different symmetry, or whether twinning has occasioned the apparent difference.

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  • 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.

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  • Attempts to connect a change of symmetry with stability show equally a lack of generality.

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  • The measure of the loss of symmetry associated with the introduction of alkyl groups depends upon the relative magnitudes of the substituent group and the rest of the molecule; and the larger the molecule, the less would be the morphotropic effect of any particular substituent.

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  • 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.

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  • The nitro group behaves very similarly to the hydroxyl group. The effect of varying the position of the nitro group in the molecule is well marked, and conclusions may be drawn as to the orientation of the groups from a knowledge of the crystal form; a change in the symmetry of the chemical molecule being often attended by a loss in the symmetry of the crystal.

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  • r is bounded by the basal pinacoid c (ooi) parallel to which is the perfect cleavage, the clinopinacoid b ((D10) parallel to the plane of symmetry, and the pyramids m (221) and o (112).

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  • When a cleavage flake of mica is struck a sharp blow with a blunt needle-point a six-rayed star of cracks or "percussion figure" is developed: the rays intersect at angles of approximately 60°, and the pair most prominently developed are parallel to the plane of symmetry of the crystal.

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  • The plane of the optic axes may be either perpendicular or parallel to the plane of symmetry of the crystal, and according to its position two classes of mica are distinguished.

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  • To the first class, with the optic axial plane perpendicular to the plane of symmetry, belong muscovite, lepidolite, paragonite, and a rare variety of biotite called anomite; the second class includes zinnwaldite, phlogopite, lepidomelane and most biotites.

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  • Dark coloured micas are strongly pleochroic. Accurate determinations of the optical orientation, as well as the symmetry of the etching figures on the cleavage planes, seem to suggest that the micas, except muscovite, may be anorthic rather than monoclinic in crystallization.

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  • aj Hence the system of values also causes to vanish in this case; dx and by symmetry aj and Fz also vanish.

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  • Hence, finally, the resultant is expressed in terms of the coefficients of the three equations, and since it is at once seen to be of degree mn in the coefficient of the third equation, by symmetry it must be of degrees np and pm in the coefficients of the first and second equations respectively.

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  • A table may be formed expressing the k expressions Pa l), P(2),...P(1) as linear functions of the k expressions (m"`'sm�2sm�3s...), s =1, 2, ...k, and the numbers BSc occurring therein is 2s 3s possess row and column symmetry.

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  • Theorem of Symmetry.

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  • The one-sided specialization and the peculiar metallic colouring of the lateral tail feathers mark them as the extreme terms of a degenerative series, whilst the symmetry, likeness of constituent parts inter se, and absence of specialized pigment, as well as the fact that they differ little from any average feather of birds in general, mark the contour feather as primitively simple, and as the starting-point from which the highly elaborated eye-painted tail feather has gradually evolved.

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  • According to his view, all mountain ranges parallel to the same great circle of the earth are of strictly contemporaneous origin, and between the great circles a relation of symmetry exists in the form of a pentagonal reseau.

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  • Intended to evolve a history of jurisprudence from the truthful portraits of England's greatest lawyers, it merely exhibits the ill-digested results of desultory learning, without a trace of scientific symmetry or literary taste, without a spark of that divine imaginative sympathy which alone can give flesh and spirit to the dead bones of the past, and without which the present 1 See thereon J.

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  • Even in ordinary algebra the notation for powers and roots disturbs the symmetry of the rational theory; and when a schoolboy illegitimately extends the distributive law by writing -V (a+b)a+J b, he is unconsciously emphasizing this want of complete harmony.

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  • The groups within groups adopted for this purpose were necessarily wanting in symmetry: the whole system presented a strangely irregular character.

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  • The part corresponding to negative values of u is similar, OA being a line of symmetry.

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  • The phase of the resultant effect is by symmetry that of the component which comes from the middle of a.

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  • When the plane zx is not a plane of symmetry, we have to consider the terms in xy, 2 y, and y 3 .

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  • If Q be on the circle described upon OA as diameter, so that u = a cos 4,, then Q' lies also upon the same circle; and in this case it follows from the symmetry that the unsymmetrical aberration (depending upon a) vanishes.

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  • The other coefficients in (8) vanish in virtue of the symmetry.

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  • - 47rb 2 ' The occurrence of sin 4 shows that there is no disturbance radiated in the direction of the force, a feature which might have been anticipated from considerations of symmetry.

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  • With the values above of u, v, w, u', v', w', the equations become of the form p x + 4 7rpAx -Fax -{-hy-}-gz =o, - p - dy+ 4?pBy + hx+ay+fz =o, P d p + TpCZ +f y + yz = o, and integrating p p 1+27rp(Ax2+By2+CZ2) +z ('ax e +ay e + yz2 2 f yz + 2gzx + 2 hx y) = const., (14) so that the surfaces of equal pressure are similar quadric surfaces, which, symmetry and dynamical considerations show, must be coaxial surfaces; and f, g, h vanish, as follows also by algebraical reduction; and 4c2 (c 2 - a2)?

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  • Generally, by making a' = -oo, the line x'A' may be taken as a straight stream line of infinite length, forming an axis of symmetry; and then by duplica tion the result can be ob A tained, with assigned n, a, and b, of the efflux from a symmetrical converging FIG.

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  • preserves its original direction, if a principal axis of the body; otherwise the axis describes a cone, right circular if the body has uniaxial symmetry, and a Poinsot cone in the general case.

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  • The symmetry of the cone is marred by a con vexity on the seaward (S.) side.

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  • ideas of symmetry, so different from ours, from a close study of nature and her processes in the attainment of endless variety.

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  • Her artists and artisans alike aim at symmetry, not by an equal division of parts, as we do, but rather by a certain balance of corresponding parts, each different from the other, and not numerically even, with an effect of variety and freedom from formality.

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  • By repeated hammering and polishing the expert obtains such control of the wood-grain pattern that its sinuosities and eddies seem to have developed symmetry without losing anything of their fantastic grace.

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  • 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.

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  • Thus the two images under measurement are not defined with equal sharpness and symmetry.

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  • The value n = 2 is appropriate to bodies of which the shape is that of a solid of revolution, so that there is no rotation about the axis of symmetry.

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  • If the symmetry that is so noticeable in geological history had extended to climate as well, many geographical features might now present likenesses instead of contrasts.

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  • the Prussian intervention deranged the symmetry of Napoleon's battle-array.

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  • His natural idiom in short was that of a heightened and ennobled folk-song, and one of the most remarkable evidences of his genius was the power with which he adapted all his perfection and symmetry of style to the requirements of popular speech.

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  • In some domes, for instance in a dome at the university of Birmingham, a sound from one end of a diameter is heard very much more loudly quite close to the other end of the diameter than elsewhere, but in St Paul's Lord Rayleigh found that " the abnormal loudness with which a whisper is heard is not confined to the position diametrically opposite to that occupied by the whisperer, and therefore, it would appear, does not depend materially upon the symmetry of the dome.

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  • The medusa has a pronounced radial symmetry, and the positions of the primary tentacles, usually four in number, mark out the so-called radii, alternating with which are four interradii.

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  • Geranium, Cardamine pratensis, mallows, Rubus, Oxalis, Epilobium, &c., but many species show more or less well-marked median symmetry (zygomorphism) as Euphrasia, Orchis, thyme, &c., and red, blue and violet are the usual colours.

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  • The mastery which he had obtained over the mathematical symbols was so complete that he never shrank from the use of expressions, however complicated - nay, the more complicated they were the more he seemed to revel in them - provided they did not sin against the ruling spirit of all his work - symmetry.

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  • To a mind imbued with the love of mathematical symmetry the study of determinants had naturally every attraction.

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  • In the genus Rhizostoma, common on the British coasts and conspicuous on account of its large size, the oral arms, originally distinct and four in number, undergo concrescence, so that the entrance to the mouth is reduced to numerous fine pores and canals.2 Like the external structure, the internal anatomy of the medusa shows a complete radial symmetry, and is simple in plan but often complicated in detail (see fig.

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  • Its nest, which is a model of neatness and symmetry, it builds on trees and bushes, preferring such as are overgrown with moss and lichens.

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  • Here the barns, granaries, stables, shambles, workshops and workmen's lodgings were placed, without any regard to symmetry, convenience being the only consideration.

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  • These digressions at times interrupt the symmetry of his plan; but Strabo had all the Greek love of legendary lore, and he discusses the journeyings of Heracles as earnestly as if they were events within recent history.

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  • The Lamellibranchia are mainly characterized by the rudimentary condition of the head, and the retention of the primitive bilateral symmetry, the latter feature being accentuated by the lateral compression of the body and the development of the shell as two bilaterally symmetrical plates or valves covering each one side of the animal.

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  • The chief points in which they vary are - (1) in the structure of the ctenidia or branchial plates; (2) in the presence of one or of two chief muscles, the fibres of which run across the animal's body from one valve of the shell to the other (adductors); (3) in the greater or less elaboration of the posterior portion of the mantle-skirt so as to form a pair of tubes, by one of which water is introduced into the sub-pallial chamber, whilst by the other it is expelled; (4) in the perfect or deficient symmetry of the two valves of the shell and the connected soft parts, as compared with one another; (5) in the development of the foot as a disk-like crawling organ (Arca, Nucula, Pectunculus, Trigonia, Lepton, Galeomma), as a simple plough-like or tongueshaped organ (Unionidae, &c.), as a re-curved saltatory organ (Cardium, &c.), as a long burrowing cylinder (Solenidae, &c.), or its partial (Mytilacea) or even complete abortion (Ostraeacea).

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  • The swan-mussel has superficially a perfectly developed bilateral symmetry.

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  • As a result, the Coelomata, and with them the Mollusca, present (in the first instance) the general condition of body known as bilateral symmetry; the dorsal is differentiated from the ventral surface, whilst a right and a left side similar to, or rather the complements of, one another are permanently established.

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  • The original form was bilaterally symmetrical, and this symmetry is retained in all the classes except the Gastropoda.

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  • The Freiburg minster is considered one of the finest of all the Gothic churches of Germany, being remarkable alike for the symmetry of its proportions, for the taste of its decorations, and for the fact that it may more correctly be said to be finished than almost any other building of the kind.

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  • The grounds for this view are the radial symmetry of several Polyclads and the supposed origin of gonads and excretory flame-cells from the walls of gut, the occurrence of nematocysts in Anonymus, one of the most radially constructed Polyclads, and lastly the presence of two peculiar animals Ctenoplana and Coeloplana, which suggests a transition from Ctenophora to Polyclads.

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  • His commanding stature, the symmetry of his form, the dark and melancholy beauty of his countenance, rather rendered piquant than impaired by an obliquity of vision, produced an imposing impression even before his deep and powerful voice had given utterance to its melodious thunders; and harsh and superficial half-truths enunciated with surpassing ease and grace of gesture, and not only with an air of absolute conviction but with the authority of a prophetic messenger, in tones whose magical fascination was inspired by an earnestness beyond all imitation of art, acquired a plausibility and importance which, at least while the orator spoke, made his audience entirely forgetful of their preconceived objections against them.

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  • The symmetry is remarkable, and the reverberations are strangely musical.

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  • Barcelona thus comprises an old town, still consisting for the most part of irregular and narrow streets, and a new town built with all the symmetry and precision of a premeditated scheme.

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  • 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.

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  • The Viennese are successful in dyeing marmot well, and their cleverness in colouring it with a series of stripes to represent the natural markings of sable which has been done after the garments have been made, so as to obtain symmetry of lines, has secured for them a large trade among the dealers of cheap furs in England and the continent.

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  • The perfection and finish of every line, the correspondence of sense and sound, the incomparable command over all the most delicate resources of verse, and the exquisite symmetry of the complete odes which are extant, raise her into the very first rank of technical poetry at once, while her painting of passion, which caused Longinus to quote the ode to Anactoria as an example of the sublime, has never been since surpassed, and only approached by Catullus and in the Vita Nuova.

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  • 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.

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  • Crystals exhibit pyroelectrical characters, since they possess four uniterminal triad axes of symmetry.

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  • C. t is on symmetry and proportion; c. 2 on various forms of Greek temples, e.g.

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  • Thus regarded, even without remarking that the Novels, never having been officially collected, much less incorporated with the Codex, mar the symmetry of the structure, Justinian's work may appear to entitle him and Tribonian to much less credit than they have usually received for it.

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  • It shows the pope and emperor, with a lute-playing angel between them, kneeling to right and left of the enthroned Virgin and Child, who crown them with rose garlands, with a multitude of other kneeling saints disposed with free symmetry in the background, and farther in the background portraits of the donor and the painter, and a flutter of wreath-carrying cherubs in the air.

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  • 3), or with a symmetry in the median plane as in Gladiolus.

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  • And similarly in the development of a complicated organism, the suppression or doubling of a single cell or group of cells may bring about striking differences in the symmetry of the adult, or the reduction or increase in the number of metameric organs.

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  • Fortunately, however, the Gregorian canto fermo associated with it is of exceptional beauty and symmetry; and the great 16th century masters either, like Palestrina, left it to be sung as plain-chant, or obviated all occasion for dramatic expression by setting it in versicles (like their settings of the Magnificat and other canticles) for two groups of voices alternatively, or for the choir in alternation with the plain chant of the priests.

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  • The quality of .the surface left by the skilled artist or artisan is more regarded than symmetry of design, or even than correct modelling.

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  • Cooke's mounting is admirable for its symmetry and simplicity of design, its just apportioning of strength, and a general suitability of means to ends.

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  • Boltzmann Suggested That A Diatomic Molecule Regarded As A Rigid Dumb Bell Or Figure Of Rotation, Might Have Only Five Effective Degrees Of Freedom, Since The Energy Of Rotation About The Axis Of Symmetry Could Not Be Altered By Collisions Between The Molecules.

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  • Kobold, using a peculiar and ingenious method, found for it a declination - 3°, which disagrees very badly with all other determinations; but it is a peculiarity of Kobold's method that it gives the line of symmetry of motion, which joins the apex and antapex, without indicating which end is the apex.

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  • Now the position of this line, as found by Kobold, actually is a (properly weighted) mean between the corresponding lines of symmetry of the two drifts, but naturally it lies in the acute angle between them, whereas the line of the solar motion is also a weighted mean between the two lines of drift, but lies in the obtuse angle between them.

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  • Hence, and in this lies the main element of the symmetry and simplicity of the quaternion calculus, all systems of three mutually rectangular unit lines in space have the same properties as the fundamental system i, j, k.

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  • But, as yet, we have not taken advantage of the perfect symmetry of the method.

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  • But every quaternion formula is a proposition in spherical (sometimes degrading to plane) trigonometry, and has the full advantage of the symmetry of the method.

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  • Here the symmetry points at once to the selection of the three principal axes as the directions for i, j, k; and it would appear at first sight as if quaternions could not simplify, though they might improve in elegance, the solution of questions of this kind.

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  • Since I~=Ii., I~=o, we deduce 100=3/4Ma2, ~ =4MaZ; hence the value of the squared radius of gyration isfora diameter 3/4ai, and for the axis of symmetry 3/4af.

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  • in the case of symmetry about an axis it appears that the ratio of the polar to the equatorial diameter of the ellipsoid cannot be less than I/~2.

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  • The mass-system is then said to possess kinetic symmetry about 0.

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  • where K is the radius of gyration about the axis of symmetry, a is the constant distance of G from the plane, and R, F are the normal and tangential components of the reaction of the plane, as shown in fig.

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  • If a be the inclination of the instantaneous axis to the axis of symmetry, (3 the inclination of the latter axis to the invariable line, we have rcosfl=Cw cos a, r sin ~3 = Aw sin a, (6) whence tan ~ =~ tan a.

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  • If the instantaneous axis only deviate slightly from the axis of symmetry the angles a, (3 are small, and ~ = (AC) A .fa; the instantaneous axistherefore completes its revolution in the body in the period 2,rAC

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  • It frequently happens that the extraneous forces have zero moment about the axis of symmetry, as e.g.

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  • For we have seen that r is constant when there are no extraneous forces; and r is evidently not affected by an instantaneous impulse which leaves the angular momentum Cr, about the axis of symmetry, unaltered.

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  • The components of angular momentum about the axis of the flywheel and about the vertical will be Cn and A ~ respectively, where A is the moment of inertia about any axis through the masscentre (or through the fixed point 0) perpendicular to that of symmetry.

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  • If the direction of the axis of kinetic symmetry be specified by means of the angular co-ordinates 0, ~

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  • We can hence deduce the condition of steady precessional motion in a top. A solid of revolution is supposed to be free to turn about a fixed point 0 on its axis of symmetry, its masscentre G being in this axis at a distance h from 0.

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  • Hence, and b~ symmetry, we obtain -~ ru +qv ~P~+rX=M, (I)

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  • Again, a vertical plane passing, through O and a point where the motion is horizontal is evidently a plane of symmetry as regards the path.

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  • Since 8, o, are the polar co-ordinates (in a horizontal plane) of a point on the axis of symmetry, relative to an initial line which revolves with constant angular velocity P/2A, we see by comparison with 14 (i5) (16) that the motion of such a point will be elliptic-harmonic superposed on a uniform rotation e/2A, provided v2 >4AMgh.

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  • The result, owing to its symmetry, must still hold if we interchange accented and unaccented Greek letters, and by comparison we deduce (15) and (16), provided cr2 and Cr~2 are unequal.

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  • On assuming the directorship of the Nautical Almanac he became very strongly impressed with the diversity existing in the values of the elements and constants of astronomy adopted by different astronomers, and the injurious effect which it exercised on the precision and symmetry of much astronomical work.

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  • In the other pyro-electric crystals above mentioned, Hatly detected the same deviation from the rules of symmetry in their secondary crystals which occurs in tourmaline.

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  • In a corresponding manner the right side of the animal's body is somewhat less developed than the left, and to this extent there is a departure from the bilateral symmetry characteristic of Lamellibranchs.

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  • The optic figure seen in convergent polarized light through a section cut parallel to the plane of symmetry of a borax crystal is symmetrical only with respect to the central point.

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  • In regard to colour and design the Taj ranks first in the world for purely decorative workmanship; while the perfect symmetry of its exterior once seen can never be forgotten, nor the aerial grace of its domes, rising like marble bubbles into the azure sky.

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  • Suppose, therefore, that the equation of the boundary is r =a+a cos kz, (I) where a is a small quantity, the axis of z being that of symmetry.

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  • The detached masses into which a jet is resolved do not at once assume and retain a spherical form, but execute a series of vibrations, being alternately compressed and elongated in the direction of the axis of symmetry.

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  • A fourth was subsequently added, for the sake of symmetry, to make them correspond with the four seasons, and they became known as the jejunium vernum, aestivum, autumnale and hiemale, so that, to quote Pope Leo's words, "the law of abstinence might apply to every season of the year."

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  • Apart from the numerous parasitic forms, the only Crustacea which have adopted a strictly sedentary habit of life are the Cirripedia, and here, as elsewhere, profound modifications of structure have resulted, leading ultimately to a partial assumption of the radial type of symmetry which is so often associated with a sedentary life.

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  • 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.

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  • Most living bodies, it is true, are capable of reproduction, but there are many without this capacity, whilst, on the other hand, it would be difficult to draw an effective distinction between that reproduction of simple organisms which consists of a sub-division of their substance with consequent resumption of symmetry by the separate pieces, and the breaking up of a drop of mercury into a number of droplets.

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  • Such a model, properly constructed, that is to say, with the vesicles of the foam microscopic in size, is a marvellous imitation of the appearance of protoplasm, being distinguishable from it only by a greater symmetry.

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  • Leonardo, though no special student of the Greeks, has perfectly carried out the Greek principle of expressive variety in particulars subordinated to general symmetry.

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  • The crisis of his mental conflict had just been passed in Tirol, and he was now beginning to let his creed grow again from the one fixed point which nothing had availed to shift: "The one great certainty to which, in the midst of the darkest doubt, I never ceased to cling - the entire symmetry and loveliness and the unequalled nobleness of the humanity of the Son of Man."

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  • 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.

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  • Crystals of this class possess neither planes nor centre of symmetry, but only axes of symmetry: perpendicular to the principal triad axis there are three uniterminal dyad axes of symmetry.

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  • Usually, however, this lower degree of symmetry is not indicated by the faces developed on the crystals.

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  • 4 and 5), which indicate the true degree of symmetry of quartz, are of comparatively rare occurrence except on crystals from certain localities.

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  • The pyro-electric characters of quartz are closely connected with its peculiar type of symmetry and especially with the three uniterminal dyad axes.

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  • A similar distribution of electric charges is produced when a crystal is subjected to pressure; quartz being thus also piezo-electric. Etched figures, both natural and artificial (in the latter case produced by the action of hydrofluoric acid), on the faces of the crystals are in accordance with the symmetry, and may serve to distinguish leftand righthanded crystals.

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  • This phenomenon is connected with the symmetry of the crystals, and is also shown by the crystals of certain other substances in which there are neither planes nor centre of symmetry.

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  • It is chiefly built of outlayer granite, and, though the plainest cathedral in Scotland, its stately simplicity and severe symmetry lend it unique distinction.

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  • The elongation of the mouth and stomodaeum confer a bilateral symmetry on the body of the zooid, which is extended to other organs of the body.

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  • A pause in the development follows, during which no new mesenteries are formed, and then the six-rayed symmetry characteristic of a normal Actinian zooid is completed by the formation of the mesenteries V, V in the lateral chambers, and VI, VI in the sulcolateral chambers, their muscle-banners being so disposed that they form couples respectively with II, II and I, I.

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  • In many of these so-called rugose forms the septa have a characteristic arrangement, differing from that of recent corals chiefly in the fact that they show a tetrameral instead of a hexameral symmetry.

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  • This arrangement, however, is by no means characteristic even of the Zaphrentidae, and in the family Cyathophyllidae most of the genera exhibit a radial symmetry in which no trace of the bilateral arrangement described above is recognizable, and indeed in the genus Cyathophyllum itself a radial arrangement is the rule.

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  • The general structure of this coral leaves no doubt that it is closely allied to the Astraeidae, but in the young calicles a tetrameral symmetry is indicated by the presence of four large septa placed at right angles to one another.

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  • Thus, about 1875, the distinction of Echinoderms from such radiate animals as jelly-fish and corals (see Coelentera), by their possession of a body-cavity ("coelom") distinct from the gut, was fully realized; while their severance from the worms (especially Gephyrea), with which some Echinoderms were long confused, had been necessitated by the recognition in all of a radial symmetry, impressed on the original bilateral symmetry of the larva through the growth of a special division of the coelom, known as the "hydrocoel," and giving rise to a set of water-bearing canals - the watervascular or ambulacral system.

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  • The orocentral was, it must be admitted, a theoretical conception due to a desire for symmetry, and was not confirmed by anything 1p _.

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  • The Pentactaea again suggested a search for some primitive type in which quinqueradiate symmetry was exhibited in circumoral appendages, but had not affected the nervous, water-vascular, muscular or skeletal systems to any great extent, and the generative organs not at all.

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  • 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.

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  • The different extent of quinqueradiate symmetry in the different classes would thus depend on the period at which they diverged from the sedentary stock.

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  • It might be possible to prove the origin of all classes from Pelmatozoa, without thereby explaining the origin of such fundamental features as radial symmetry, the developmental metamorphosis, and the torsion that affects both gut and body-cavities during that process; but the acceptance of a Dipleurula as the common ancestor necessitates an explanation of these features.

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  • In this way the many highly modified orders of Cystidea may be traced back to a simple, many-plated ancestor with little or no radiate symmetry (see below).

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  • Although, in the extreme correlation of the radial food-grooves, nerves, watervessels, and so forth, with a radiate symmetry of the theca, such a type differs from the Cystidea, while in the possession of jointed processes from the radial plates, bearing the grooves and the various body-systems outwards from the theca, it differs from all other Echinoderms, nevertheless ancient forms are known which, if they are not themselves the actual links, suggest how the crinoid type may have been evolved from some of the more regular cystids.

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  • So too the explanation of radial symmetry and torsion of organs as due to a Pelmatozoic mode of life finds confirmation in many other phyla.

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  • Since this must have, on our theory, enclosed the parietal canal from the anterior coelom, it is possible that the genital products were developed from the lining cells of that cavity, and that the genital pore was nothing but its original pore not yet united with that from the water-sac. The concrescence of these pores can be traced in other cystids; but as the genital organs became affected by radial symmetry the original function of the duct was lost, and the reproductive elements escaped to the exterior in another way.

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  • At last a quinqueradiate symmetry influenced the plates of the theca, partly through the development of a plate at the end of each groove (terminal), partly through plates at the aboral pole of the theca (basals and infrabasals) arising in response to mechanical pressure, but soon intimately connected with the cords of an aboral nervous system.

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  • 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.

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  • All living, and most extinct, Echinoderms show the following features, almost certainly due to an ancestral pelmatozoic stage: - An incomplete radial symmetry, of which five is usually the dominant number, is superimposed on the secondary bilateralism, owing to the outgrowth from the mouth region of one unpaired and two paired ciliated grooves; these have a floor of nervous epithelium, and are accompanied by subjacent radial canals from the water-ring, giving off lateral podia and thus forming ambulacra, and by a perihaemal system of canals apparently growing out from coelomic cavities.

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  • - Pelmatozoa in which radial polymeric symmetry of the theca is developed either not at all or not in complete correlation with the radial symmetry of the ambulacra (such as obtains in Blastoidea and Crinoidea); in which extensions of the food-grooves are exothecal or epithecal or both combined, but neither endothecal nor pierced by podia (as in some Edrioasteroidea).

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  • - Radial symmetry has affected neither food-grooves nor thecal plates; nor, probably, nerves, ambulacral vessels, nor gonads.

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  • - Radial symmetry affects the food-grooves and, in the more advanced families, the thecal plates; probably also the nerves and ambulacral vessels, but not the gonads.

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  • - Pentamerous symmetry affects the foodgrooves and thecal plates; probably also the nerves and ambulacral vessels, but not the gonads.

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  • - Radial symmetry affects the food-grooves, and by degrees the thecal plates connected therewith, but not the interradial thecal plates; probably also the nerves and ambulacral vessels, but not the gonads.

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  • The thecal plates, however irregular in some species, always show defined basals and a distinct plate ("radial") at the end of each ambulacrum; they are in all cases so far affected by pentamerous symmetry that their sutures never cross the ambulacra.

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  • - Eleutherozoa with a depressed stellate body composed of a central disk, whence radiate five or more rays; this radiate symmetry affects all the systems of organs, including the genital.

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  • - Eleutherozoa with a test of roughly circular, subpentagonal or elliptical outline, spheroidal, domed or flattened, of primary pentameric symmetry affecting all systems of organs except the gut.

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  • 12, D); the ambulacra thus formed are continuous from the peristome to the apical system of plates; the hydropore is connected with a definite plate of that system, and thus marks a secondary bilateral symmetry.

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  • 19, 7), thus initiating yet another bilateral symmetry.

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  • Of the primary, secondary and tertiary alcohols having the same empirical formula, the primaryhave the highest, and the tertiary the lowest boiling point; this is in accordance with the fairly general rule that a gain is symmetry is attended by a fall in the boiling point.

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