To modern science, these assumptions are as much out of date as the equally venerable errors, that the sun goes round the earth every four-and-twenty hours, or that water is an elementary body. The handful of soil is a factory thronged with swarms of busy workers; the rusty nail is an aggregation of millions of particles, moving with inconceivable velocity in a dance of infinite complexity yet perfect measure; harmonic with like performances throughout the solar system. If there is good ground for any conclusion, there is such for the belief that the substance of these particles has existed and will exist, that the energy which stirs them has persisted and will persist, without assignable limit, either in the past or the future. Surely, as Heracleitus said of his kitchen with its pots and pans, "Here also are the gods." Little as we have, even yet, learned of the material universe, that little makes for the belief that it is a system of unbroken order and perfect symmetry, of which the form incessantly changes, while the substance and the energy are imperishable.
No human face is exactly the same in its lines on each side, no leaf perfect in its lobes, no branch in its symmetry.
Who marks in church-time others' symmetry, / Makes all their beauty his deformity.
There is a very important “symmetry,” or ALRROMORPHISM
The first principle of economic symmetry: building the economic power to consume simultaneously with the industrial power to produce.
Up to 1956 it was believed that the laws of physics obeyed each of three separate symmetries called C, P, and T. The symmetry C means that the laws are the same for particles and antiparticles. The symmetry P means that the laws are the same for any situation and its mirror image (the mirror image of a particle spinning in a right-handed direction is one spinning in a left-handed direction). The symmetry T means that if you reverse the direction of motion of all particles and antiparticles, the system should go back to what it was at earlier times; in other words, the laws are the same in the forward and backward directions of time.
there are only four units in the ring R-1 of Gaussian integers, namely ±1 and ±i; multiplication by any of these units effects a symmetry of the infinite square tiling
The essence of affectation is that it be assumed; the character is, as it were, forcibly crushed into some foreign mould, in the hope of being thereby re-shaped and beautified; and the unhappy man persuades himself he has become a new creature of wonderful symmetry, though every movement betrays not symmetry, but dislocation.
=== ALL USERS PLEASE NOTE ======================== CAR and CDR now return extra values. The function CAR now returns two values. Since it has to go to the trouble to figure out if the object is carcdr-able anyway, we figured you might as well get both halves at once. For example, the following code shows how to destructure a cons (SOME-CONS) into its two slots (THE-CAR and THE-CDR): (MULTIPLE-VALUE-BIND (THE-CAR THE-CDR) (CAR SOME-CONS) ...) For symmetry with CAR, CDR returns a second value which is the CAR of the object. In a related change, the functions MAKE-ARRAY and CONS have been fixed so they don't allocate any storage except on the stack. This should hopefully help people who don't like using the garbage collector because it cold boots the machine so often.
Tyger, Tyger, burning bright Where the hammer? Where the chain? In the forests of the night, In what furnace was thy brain? What immortal hand or eye What the anvil? What dread grasp Dare frame thy fearful symmetry? Dare its deadly terrors clasp? Burnt in distant deeps or skies When the stars threw down their spears The cruel fire of thine eyes? And water'd heaven with their tears On what wings dare he aspire? Dare he laugh his work to see? What the hand dare seize the fire? Dare he who made the lamb make thee? And what shoulder & what art Tyger, Tyger, burning bright Could twist the sinews of they heart? In the forests of the night, And when thy heart began to beat What immortal hand or eye What dread hand & what dread feet Dare frame thy fearful symmetry? Could fetch it from the furnace deep And in thy horrid ribs dare steep In the well of sanguine woe? In what clay & in what mould Were thy eyes of fury roll'd? -- William Blake, "The Tyger"
"The old man had, in the meantime, been pensive, but on the appearance of his companions he assumed a more cheerful air, and they sat down to eat. The meal was quickly dispatched. The young woman was again occupied in arranging the cottage, the old man walked before the cottage in the sun for a few minutes, leaning on the arm of the youth. Nothing could exceed in beauty the contrast between these two excellent creatures. One was old, with silver hairs and a countenance beaming with benevolence and love; the younger was slight and graceful in his figure, and his features were moulded with the finest symmetry, yet his eyes and attitude expressed the utmost sadness and despondency. The old man returned to the cottage, and the youth, with tools different from those he had used in the morning, directed his steps across the fields.
So saying, she tumult raised in Helen's mind. Yet soon as by her symmetry of neck, By her love-kindling breasts and luminous eyes She knew the Goddess, her she thus bespake.
They received Pierre in their small, new drawing-room, where it was impossible to sit down anywhere without disturbing its symmetry, neatness, and order; so it was quite comprehensible and not strange that Berg, having generously offered to disturb the symmetry of an armchair or of the sofa for his dear guest, but being apparently painfully undecided on the matter himself, eventually left the visitor to settle the question of selection. 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.
Bourgeois houses only began to spring up there twenty-five years later. The place was unpleasant. In addition to the gloomy thoughts which assailed one there, one was conscious of being between the Salpetriere, a glimpse of whose dome could be seen, and Bicetre, whose outskirts one was fairly touching; that is to say, between the madness of women and the madness of men. As far as the eye could see, one could perceive nothing but the abattoirs, the city wall, and the fronts of a few factories, resembling barracks or monasteries; everywhere about stood hovels, rubbish, ancient walls blackened like cerecloths, new white walls like winding-sheets; everywhere parallel rows of trees, buildings erected on a line, flat constructions, long, cold rows, and the melancholy sadness of right angles. Not an unevenness of the ground, not a caprice in the architecture, not a fold. The ensemble was glacial, regular, hideous. Nothing oppresses the heart like symmetry. It is because symmetry is ennui, and ennui is at the very foundation of grief. Despair yawns. Something more terrible than a hell where one suffers may be imagined, and that is a hell where one is bored. If such a hell existed, that bit of the Boulevard de l'Hopital might have formed the entrance to it.
This cemetery, with its peculiarities outside the regulations, embarrassed the symmetry of the administration. It was suppressed a little later than 1830. The cemetery of Mont-Parnasse, called the Eastern cemetery, succeeded to it, and inherited that famous dram-shop next to the Vaugirard cemetery, which was surmounted by a quince painted on a board, and which formed an angle, one side on the drinkers' tables, and the other on the tombs, with this sign: Au Bon Coing.
Occupied in observing Mr. Bingley's attentions to her sister, Elizabeth was far from suspecting that she was herself becoming an object of some interest in the eyes of his friend. Mr. Darcy had at first scarcely allowed her to be pretty; he had looked at her without admiration at the ball; and when they next met, he looked at her only to criticise. But no sooner had he made it clear to himself and his friends that she hardly had a good feature in her face, than he began to find it was rendered uncommonly intelligent by the beautiful expression of her dark eyes. To this discovery succeeded some others equally mortifying. Though he had detected with a critical eye more than one failure of perfect symmetry in her form, he was forced to acknowledge her figure to be light and pleasing; and in spite of his asserting that her manners were not those of the fashionable world, he was caught by their easy playfulness. Of this she was perfectly unaware; to her he was only the man who made himself agreeable nowhere, and who had not thought her handsome enough to dance with.
In the first place, you are struck by the general contrast between these heads. Both are massive enough in all conscience; but there is a certain mathematical symmetry in the Sperm Whale's which the Right Whale's sadly lacks. There is more character in the Sperm Whale's head. As you behold it, you involuntarily yield the immense superiority to him, in point of pervading dignity. In the present instance, too, this dignity is heightened by the pepper and salt colour of his head at the summit, giving token of advanced age and large experience. In short, he is what the fishermen technically call a "grey-headed whale."
In 1789 a ferment arises in Paris; it grows, spreads, and is expressed by a movement of peoples from west to east. Several times it moves eastward and collides with a countermovement from the east westward. In 1812 it reaches its extreme limit, Moscow, and then, with remarkable symmetry, a countermovement occurs from east to west, attracting to it, as the first movement had done, the nations of middle Europe. The counter movement reaches the starting point of the first movement in the west--Paris--and subsides.
While these two men were manoeuvring, each on his own side, with irreproachable strategy, they approached an inclined plane on the quay which descended to the shore, and which permitted cab-drivers arriving from Passy to come to the river and water their horses. This inclined plane was suppressed later on, for the sake of symmetry; horses may die of thirst, but the eye is gratified.
Many of the physical properties of crystals vary with the direction in the material, but are the same in certain directions; these directions obeying the same laws of symmetry as do the faces on the exterior of the crystal. The symmetry of the internal structure of crystals is thus the same as the symmetry of their external form. Entry: II
According to their action on transmitted plane-polarized light (see POLARIZATION OF LIGHT) all crystals may be referred to one or other of the five groups enumerated below. These groups correspond with the six systems of crystallization (in the second group two systems being included together). The several symmetry-classes of each system are optically the same, except in the rare cases of substances which are circularly polarizing. Entry: II
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. When the resolution is effected in a perfectly periodic manner, each drop is in the same phase of its vibration as it passes through a given point of space; and thence arises the remarkable appearance of alternate swellings and contractions described by Savart. The interval from one swelling to the next is the space described by the drop during one complete vibration, and is therefore (as Plateau shows) proportional _ceteris paribus_ to the square root of the head. Entry: ____
Here there is only one dyad axis in which two planes of symmetry intersect. The crystals are usually so placed that the dyad axis coincides with the vertical crystallographic axis, and the planes of symmetry are also vertical. Entry: PYRAMIDAL
With a one-circle goniometer, such as is described above, it is necessary to mount and re-adjust the crystal afresh for the measurement of each zone of faces (i.e. each set of faces intersecting in parallel edges); with very small crystals this operation takes a considerable time, and the minute faces are not readily identified again. Further, in certain cases, it is not possible to measure the angles between zones, nor to determine the position of small faces which do not lie in prominent zones on the crystal. These difficulties have been overcome by the use of a two-circle goniometer or theodolite-goniometer, which as a combination of a vertical-circle goniometer and one with a horizontal-circle was first employed by W. H. Miller in 1874. Special forms have been designed by E. S. Fedorov (1889), V. Goldschmidt (1893). S. Czapski (1893) and F. Stoeber (1898), which differ mainly in the arrangement of the optical parts. In these instruments the crystal is set up and adjusted once for all, with the axis of a prominent zone parallel to the axis of either the horizontal or the vertical circle. As a rule, only in this zone can the angles between the faces be measured directly; the positions of all the other faces, which need be observed only once, are fixed by the simultaneous readings of the two circles. These readings, corresponding to the polar distance and azimuth, or latitude and longitude readings of astronomical telescopes, must be plotted on a projection before the symmetry of the crystal is apparent; and laborious calculations are necessary in order to determine the indices of the faces and the angles between them, and the other constants of the crystal, or to test whether any three faces are accurately in a zone. Entry: A
The observance of the Ember days is confined to the Western Church, and had its origin as an ecclesiastical ordinance in Rome. They were probably at first merely the fasts preparatory to the three great festivals of Christmas, Easter and Pentecost. 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." An earlier mention of these fasts, as four in number--the first known--is in the writings of Philastrius, bishop of Brescia, in the middle of the 4th century. He also connects them with the great Christian festivals (_De haeres._ 119). In Leo's time, A.D. 440-461, Wednesday, Friday and Saturday were already the days of special observance. From Rome the Ember days gradually spread through the whole of Western Christendom. Uniformity of practice, however, was of somewhat slow growth. Neither in Gaul nor Spain do they seem to have been generally recognized much before the 8th century. Their introduction into Britain appears to have been earlier, dating from Augustine, A.D. 597, acting under the authority of Gregory the Great. The general period of the four fasts being roughly fixed, the precise date appears to have varied considerably, and in some cases to have lost its connexion with the festivals altogether. The _Ordo Romanus_ fixes the spring fast in the first week of March (then the first month); the summer fast in the second week of June; the autumnal fast in the third week of September; and the winter fast in the complete week next before Christmas eve. Other regulations prevailed in different countries, until the inconveniences arising from the want of uniformity led to the rule now observed being laid down under Pope Urban II. as the law of the church, in the councils of Piacenza and Clermont, A.D. 1095. Entry: EMBER
Crystals, like other bodies, are either paramagnetic or diamagnetic, i.e. they are either attracted or repelled by the pole of a magnet. In crystals other than those belonging to the cubic system, however, the relative strength of the induced magnetization is different in different directions within the mass. A sphere cut from a tetragonal or hexagonal (uniaxial) crystal will if freely suspended in a magnetic field (between the poles of a strong electro-magnet) take up a position such that the principal axis of the crystal is either parallel or perpendicular to the lines of force, or to a line joining the two poles of the magnet. Which of these two directions is taken by the axis depends on whether the crystal is paramagnetic or diamagnetic, and on whether the principal axis is the direction of maximum or minimum magnetization. The surface expressing the magnetic character in different directions is in uniaxial crystals a spheroid; in cubic crystals it is a sphere. In orthorhombic, monoclinic and anorthic crystals there are three principal axes of magnetic induction, and the surface is an ellipsoid, which is related to the symmetry of the crystal in the same way as the ellipsoids expressing the thermal and optical properties. Entry: _
The grand characteristic of Chinese architecture is the pre-eminent importance of the roof. The _t'ing_ is the commonest model of building. The roof is the main feature; in fact the _t'ing_ consists of this roof, massive and immense, with recurved edges, and the numerous short columns on which the roof rests. The columns are of wood, the straight stems of the _nanmu_ being specially used for this purpose. The walls are not supports, but merely fill in, with stone or brickwork, the spaces between the columns. The scheme of construction is thus curiously like that of the modern American steel-framed building, though the external form may be derived from the tent of primitive nomads. The roof, being the preponderant feature, is that on which the art of the architect has been concentrated. A double or a triple roof may be devised; the ridges and eaves may be decorated with dragons and other fantastic animals, and the eaves underlaid with carved and lacquered woodwork; the roof itself is often covered with glazed tiles of brilliant hue. In spite of efforts, sometimes desperate, to give variety and individual character by ornament and detail, the general impression is one of poverty of design. "Chinese buildings are usually one-storeyed and are developed horizontally as they are increased in size or number. The principle which determines the plan of projection is that of symmetry" (Bushell). All important buildings must face the south, and this uniform orientation increases the general architectural monotony produced by a preponderance of horizontal lines. Entry: 3
It is doubtful indeed whether any general conclusions can yet be drawn as to the relations between crystal structure and scalar properties and the relative stability of polymorphs. As a general rule the modification stable at higher temperatures possesses a lower density; but this is by no means always the case, since the converse is true for antimonious and arsenious oxides, silver iodide and some other substances. Attempts to connect a change of symmetry with stability show equally a lack of generality. It is remarkable that a great many polymorphous substances assume more symmetrical forms at higher temperatures, and a possible explanation of the increase in density of such compounds as silver iodide, &c., may be sought for in the theory that the formation of a more symmetrical configuration would involve a drawing together of the molecules, and consequently an increase in density. The insufficiency of this argument, however, is shown by the data for arsenious and antimonious oxides, and also for the polymorphs of calcium carbonate, the more symmetrical polymorphs having a lower density. Entry: A
Swimming is perhaps the commonest mode of locomotion, but numerous forms have taken to creeping or walking, and the robber-crab (_Birgus latro_) of the Indo-Pacific islands even climbs palm-trees. None has the power of flight, though certain pelagic Copepoda are said to leap from the surface of the sea like flying-fish. 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. Entry: CRUSTACEA
As regards the most general motion of a spherical pendulum, it is obvious that a particle moving under gravity on a smooth sphere cannot pass through the highest or lowest point unless it describes a vertical circle. In all other cases there must be an upper and a lower limit to the altitude. 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. Hence the path will be confined between two horizontal circles which it touches alternately, and the direction of motion is never horizontal except at these circles. In the case of disturbed steady motion, just considered, these circles are nearly coincident. When both are near the lowest point the horizontal projection of the path is approximately an ellipse, as shown in § 13; a closer investigation shows that the ellipse is to be regarded as revolving about its centre with the angular velocity 2/3 ab[Omega]/l², where a, b are the semi-axes. Entry: 2
All the forms are open, being either pinacoids or prisms; the former consisting of a pair of parallel faces, and the latter of four faces intersecting in parallel edges and with a rhombic cross-section. The pair of faces parallel to the plane of symmetry is distinguished as the "clino-pinacoid" and has the indices {010}. The other pinacoids are all perpendicular to the plane of symmetry (and parallel to the ortho-axis); the one parallel to the vertical axis is called the "ortho-pinacoid" {100}, whilst that parallel to the clino-axis is the "basal pinacoid" {001}; pinacoids not parallel to the arbitrarily chosen clino- and vertical axes may have the indices {101}, {201}, {102} ... {hol} or {1´01}, {2´01}, {1´02} ... {h´ol}, according to whether they lie in the obtuse or the acute axial angle. Of the prisms, those with edges (zone-axis) parallel to the clino-axis, and having indices {011}, {021}, {012} ... {okl}, are called "clino-prisms"; those with edges parallel to the vertical axis, and with the indices {110}, {210}, {120} ... {hko}, are called simply "prisms." Prisms with edges parallel to neither of the axes OX and OY have the indices {111}, {221}, {211}, {321} ... {hkl} or {1´11} ... {h´kl}, and are usually called "hemi-pyramids" (fig. 62); they are distinguished as negative or positive according to whether they lie in the obtuse or the acute axial angle ß. Entry: HOLOSYMMETRIC
In the continuous-current dynamo it may be, and usually is, necessary to move the brushes forward from the interpolar line of symmetry through a small angle in the direction of rotation, in order to avoid sparking between the brushes and the commutator (_vide infra_). When the dynamo is giving current, the wires on either side of the diameter of commutation form a current-sheet flowing along the surface of the armature from end to end, and whatever the actual end-connexions of the wires, the wires may be imagined to be joined together into a system of loops such that the two sides of each loop are carrying current in opposite directions. Thus a number of armature ampere-turns are formed, and their effect on the entire system of magnet and armature must be taken into account. So long as the diameter of commutation coincides with the line of symmetry, the armature may be regarded as a cylindrical electromagnet producing a flux of lines, as shown in fig. 30. The direction of the self-induced flux in the air-gaps is the same as that of the lines of the external field in one quadrant on one side of DC, but opposed to it in the other quadrant on the same side of DC; hence in the resultant field due to the combined action of the field-magnet and armature ampere-turns, the flux is as much strengthened over the one half of each polar face as it is weakened over the other, and the total number of lines is unaffected, although their distribution is altered. The armature ampere-turns are then called _cross-turns_, since they produce a cross-field, which, when combined with the symmetrical field, causes the leading pole-corners ll to be weakened and the trailing pole-corners tt to be strengthened, the neutral line of zero field being thus twisted forwards in the direction of rotation. But when the brushes and diameter of commutation are shifted forward, as shown in fig. 31, it will be seen that a number of ampere-turns, forming a zone between the lines Dn and mC, are in effect wound immediately on the magnetic circuit proper, and this belt of ampere-turns is in direct opposition to the ampere-turns of the field, as shown by the dotted and crossed wires on the pole-pieces. The armature ampere-turns are then divisible into the two bands, the _back-turns_, included within twice the angle of lead [lambda], weakening the field, and the cross-turns, bounded by the lines Dm, nC, again producing distortion of the weakened symmetrical field. If, therefore, a certain flux is to be passed through the armature core in opposition to the demagnetizing turns, the difference of magnetic potential between the pole-faces must include not only X_a, X_t, and X_g, but also an item X_b, in order to balance the "back" ampere-turns of the armature. The amount by which the brushes must be shifted forward increases with the armature current, and in corresponding proportion the back ampere-turns are also increased, their value being c[tau]2[lambda]/360°, where c = the current carried by each of the [tau] active wires. Thus the term X_b, takes into account the effect of the armature reaction on the total flux; it varies as the armature current and angle of lead required to avoid sparking are increased; and the reason for its introduction in the fourth place (X_p = X_g + X_t + X_a + X_b), is that it increases the magnetic difference of potential which must exist between the poles of the dynamo, and to which the greater part of the leakage is due. The leakage paths which are in parallel with the armature across the poles must now be estimated, and so a new value be derived for the flux at the commencement of the _iron-magnet_ path. If P = their joint permeance, the leakage flux due to the difference of potential at the poles is z_l = 1.257X_p × P, and this must be added to the useful flux Z_a, or Z_p = Z_a + Z_l. There are also certain leakage paths in parallel with the magnet cores, and upon the permeance of these a varying number of ampere-turns is acting as we proceed along the magnet coils; the magnet flux therefore increases by the addition of leakage along the length of the limbs, and finally reaches a maximum near the yoke. Either, then, the density in the magnet B_m = Z_m/A_m will vary if the same sectional area be retained throughout, or the sectional area of the magnet must itself be progressively increased. In general, sufficient accuracy will be obtained by assuming a certain number of additional leakage lines z_n as traversing the entire length of magnet limbs and yoke (= l_m), so that the density in the magnet has the uniform value B_m = (Z_p + z_n)/A_m. The leakage flux added on actually within the length of the magnet core or z_n will be approximately equal to half the total M.M.F. of the coils multiplied by the permeance of the leakage paths around one coil. The corresponding value of H can then be obtained from the (B, H) curve of the material of which the magnet is composed, and the ampere-turns thus determined must be added to X_p, or X = X_p + X_m, where X_m = f(B_m)l_m. The final equation for the exciting power required on a magnetic circuit as a whole will therefore take the form Entry: A