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QUATRAIN

We cannot here enter into the applications of Quaternions to Geometry and Mechanics, and must close this very imperfect sketch of the elements of the calculus with the remark that, in it, 1 is the general symbol of rotation through a right angle, and that the decomposition of a quaternion into its scalar and Vector parts at once leads to an expression of the form

q=m (cos 0 + √−1 sin ◊), where m is a pure number, and the angle of the quaternion; whence it will be readily understood that a quaternion may be also represented as a power of a vector, considered as a rectangular versor. As in ordinary algebra, however, this symbol -1 sometimes denotes, in the Calculus of Quaternions, an impossible operation. It then gives rise to what are termed biquaternions, for a definition of which, however, the reader must be referred to the writings of

their eminent inventor.

Quatrain (Ital. quattrino). In Poetry, a piece consisting of four verses, the rhymes being usually alternate, but sometimes, especially in French poetry, intermixed, the first and fourth, second and third, rhyming together.

Quatrefoil (Lat. quatuor, four, and folium, a leaf). In Heraldry and in Mediaeval Sculpture, a flower of four leaves (quatre feuilles).

Quattrocentismo (Ital. quattro cento). A term expressing the peculiar or characteristic taste or so-called purism in art, prevailing in Italy in the fifteenth century. Hard and rigid in its manner, positive in its colouring, but predominating in sentiment; yet aesthetically very imperfect, it is the triumph of the Cinquecento to have supplied the aesthetic qualities wanting in the art of this period, and to have reformed its technical deficiencies, the sensuous being made coordinate with the sentimental. [CINQUECENTO.]

Quaver. In Music, a character, J, whose measure is equal to half a crotchet, or oneeighth of a semibreve.

Quay (Fr. quai, Dutch kaai). An artificial landing place, to enable ships which could not otherwise approach the shore to take in or disembark their cargoes without the intervention of small boats.

Quay Wall. A wall forming the support of ground left at a higher level than that of the roadway, or waterway, of the surrounding surface; thus the walls of a platform or of a dock, or pier, are said to be the quay walls, irrespective of the nature of the element whose force they have to resist. The thickness of quay walls, however, depends greatly upon this condition, which will be found discussed under RETAINING WALL. It may suffice here to mention that in the case of walls intended to protect the earthwork left behind a quay wall erected in dry ground, a thickness equal to one-third of the height would, on the average, be sufficient; but that, in the case of earthwork exposed to alternations of mois

QUEEN

ture and dryness, as in docks or harbours, the thickness to be given to the quay walls should, on the average, be at least one-half the height.

1. A

Queen (A.-Sax. cwen, Gr. yuvh; for the history of the root, see LANGUAGE). female sovereign; entitled queen regnant, or queen regent. She has, in Great Britain, the same power, prerogatives, &c., as a king, which is expressly declared by stat. 1 Mar. I. st. 3. c. i. In France, where females do not succeed to the throne, the title queen regent has been given to the mothers of kings holding sovereign authority, or a portion of it, during the minority of their sons; as Catherine de Médicis in the reign of Francis II.; Mary de Médicis, in that of Louis XIII.

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2. Queen Consort. The wife of a king. Her rights and dignities (in England, as well as most other countries) appear to be similar in many respects to those of the Augusta,' or Piissima regina conjux divi imperatoris, in imperial Rome. The English queen, like the Roman empress, is capable of receiving a grant from her husband, or making one to him; therein differing from all other wives. She can also purchase and convey land, &c., without his concurrence; and sue and be sued alone: in short, she is looked upon in all legal proceedings as a feme sole. But, except where she enjoys specific exemptions, she is only on a footing with other subjects; and this also is according to the Roman maxim, Augusta legibus soluta non est.' By the Statute of Treasons, 25 Edw. III., to compass or imagine the death of the king's companion, and also to violate and defile her, is treason. The queen, if accused of treason herself, is tried by the peers of parliament; as Anne Boleyn in 28 Hen. VIII. The consort of George IV. was proceeded against by the method of a bill of pains and penalties. Queen-gold was a duty amounting to one full tenth of the value of fines, &c. on grants by the crown, anciently due to the queen; which Charles I. purchased of his consort Henrietta, in 1635, for 10,000%., but which was not revived after the Restoration. The queen consort has a separate household, consisting of six ladies of the bed-chamber, a chamberlain, vice-chamberlain, mistress of the robes, master of the horse, and three equerries, attorney and solicitor general, &c.

3. Queen Dowager. The widow of a deceased king. She continues to enjoy most of the privileges which belonged to her as queen consort. Nor did she, in ancient times, lose her dignity on remarriage; for Catherine, queen dowager of Henry V., after she had married Owen Tudor, maintained an action by the name of Catherine queen of England. But it is held that no man can marry a queen dowager without special license from the king, on pain of forfeiture of lands and goods, according to an Act of 6 Hen. VI., which, however, is not printed among the statutes. The revenue of a queen dowager is settled by statute. By 1 & 2 Wm. IV. c. 11, that king was empowered to settle

QUEEN ANNE'S BOUNTY 100,000l. per annum on his queen, to commence at his decease.

4. Queen Mother. A queen dowager who is
also mother of the reigning sovereign.

Queen Anne's Bounty. [BOUNTY, QUEEN
ANNE'S.]

Queen Post. In Architecture, an upright
post in a roof for suspending the beam when
the principal rafters do not meet in the head
of the king post. A queen-post roof is employed
whenever the span of the assemblage is above
forty feet; it makes, in fact, an arch of the
timber. [ROOF.]

Queen's Advocate. [KING'S ADVOCATE.]
Queen's Bench. [KING'S BENCH.]

the service. Every officer is required to pos-
QUERCUS
acquainted with them.
sess a copy, and to make himself perfectly

iron-ore, a synonym of Limonite or Bog Iron-ore.
Quellerz. A German term signifying brook
ciple of oak bark. It differs from the tannic
Quercitannic Acid. The astringent prin-
acid of oak galls.

talline saccharine matter contained in acorns.
Quercite (Lat. quercus, an oak). A
crys-
ing matter of quercitron bark. It is a crystal-
Quercitrin. Quercitric acid. The colour-
line, yellow, bitter substance.

olive, with iron mordants. It is much used in
calico-printing.

Quercitron Bark or Quercitron TincQueen's Counsel. It has been custom- valuable dye stuff is used in the production of toria. The bark of the Quercus nigra. This ary for a long period to appoint the leading some of the most durable yellows. It contains members of the bar to be the standing a yellow crystallisable principle, Quercitrin, counsel of the crown. This practice appears which is sparingly soluble in water, but is reato have originated in the reign of Charles II., dily solved in weak alkalies. A decoction of and has been gradually extended until the this bark, deprived of its tannic acid by a little position of a queen's counsel has come to be gelatine, produces a good yellow upon fabrics regarded as a professional rank which any bar-mordanted with alumina, or various shades of rister of a certain eminence may claim almost as of right. The functions of queen's counsel as representing the crown by virtue of their office are now merely honorary, though they formerly received a small salary by way of retainer. They receive the usual fees if retained on behalf of the crown on any particular occasion. They cannot be employed in any cause against the crown without a special license, which is never refused, but which involves an expense of about 91. on each occasion. As the crown is the nominal prosecutor in criminal proceedings, no queen's counsel can defend a prisoner without a license, a circumstance which has incidentally a considerable effect in preventing the leading members of the bar from practising in the criminal courts. Queen's counsel have a right of precedence and pre-audience over the other members of the bar (which constitutes the chief advantage of the appointment), and by the etiquette of the profession they are forbidden to conduct causes, or to prepare pleadings or other legal instruments without the assistance of a junior counsel. Their professional robes are of silk instead of stuff (whence the term silk is often used to denote their rank). They are usually elected to be benchers of their respective Inns of Court. [BENCHERS.]

genus of trees found in the cold countries of the Quercus (Lat.). This is the most important world, on account of its producing the various kinds of timber called OAK. The species are not, however, confined to Europe, or similar latitudes, but occur abundantly in the equinoetial parts of Asia and America. It is usually recognised by the cup in which the acorn is seated; but in some tropical species the acorn is so small as to be buried in the cup, when the fruit nearly resembles that of the chestnut (Castanea). The valuable Oak of Great Britain is obtained from two native trees: the one Q. pedunculata, the long-stalked or white oak; the other Q. sessiliflora, the sessile-fruited or red oak. Oak timber is affected very much by soil and climate; and hence we have oak of bad quality from both our native species. What is called wainscot oak is probably the timber of Q. sessiliflora, grown rapidly in the dense forests of Hungary; by some persons, however, it is supposed to be furnished by an Oriental species called Q. Cerris, or the mossy-cupped. Esculus of Virgil, the acorns of which were eatable, appears to have been a sweet-fruited variety of Q. sessiliflora. Besides those already the Q. Suber, or cork-tree, whose bark is in mentioned, the Quercus Ilex, or European oak, such extensive use, and the Q. Ballota, or Spanish Ilex, whose acorns are sweet and eatable, are the more important species. Those from North Queen's Regulations. The regulations oaks of England as regards their timber, and America, although fine trees, are inferior to the and orders issued by the queen to the army require hotter summers than we have in these (through the commander-in-chief, as distin- islands. Oak galls are produced upon Q. inguished from those issued through the Secretary fectoria, in the Levant, by the puncture of a of State for War, which are War Office re- cynips. The species of Quercus are excessively gulations). They regulate the whole military confused by botanists; but a full popular acsystem, except in matters affecting finance. count of them will be found in Louden's ArboThey interpret the Mutiny Act and Articles retum Britannicum, and a scientific summary of War as regards military discipline, and in the sixteenth volume of De Candolle's furnish the rules for the interior economy of Prodromus. For a few popular details, see OAK.

Queen's Metal. An alloy intermediate between Britannia metal and pewter, used for the manufacture of common spoons and teapots. It consists of nine parts of tin, one of lead, one of antimony, and one of bismuth.

170

The

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Quia Emptores (Lat.). In English Law, the designation (from its first words) of the statute 18 Edward I. (A. D. 1290) which prevented subinfeudation. [FEUDAL SYSTEM.] Quick Match. [MATCH.] Quicklime. [LIME.] Quicksilver. [MERCURY.]

Question (Lat. quæstio). The application of TORTURE to prisoners under criminal accusation, according to the law of France before the Revolution. The question was of two kinds: one, where strong evidence, but insufficient of itself to justify a condemnation to death, existed against a prisoner on a capital charge; he might then be subjected to torture! Quietism. A name generally applied to to produce confession. This was termed the the opinions of enthusiasts, who conceive the question préparatoire. It was abolished by great object of religion to be the absorption of an ordonnance of Louis XVI. in 1780. The all human sentiments and passions into devout other, termed question préalable or definitive, contemplation and love of God. This idea has was applied to the prisoner when convicted of found its admirers in all ages. A sect called a capital offence, in order to make him discover by this name [HESYCHASTS] existed among supposed accomplices. It was abolished by the the religious of Mount Athos; and in the National Assembly. The preparatory question seventeenth century it was given in France was also of two sorts: one, avec réserve de to a class of devout persons with a tendency preuves, in which case, if the criminal did not towards a higher spiritual devotion. A Spanish confess under the torture, the other evidence priest, Molinos, published at Rome a work was considered as still subsisting against him, entitled The Spiritual Guide (1675), of which so as to justify his condemnation to some the ardent language attracted a multitude of lighter punishment; the other, sans réserve de partisans. Its leading feature was the depreuves, in which case, if he persisted in his scription of the happiness of a soul reposing in denial, he was acquitted altogether. It was at perfect quiet on God, so as to become conscious the option of the judges, according to their of His presence only, and untroubled by exteropinion of the amount of evidence, to decide to nal things. He even advanced so far as to which of these questions the accused should be maintain that the soul in its highest state is subjected. The modes of torture applied varied removed even beyond the contemplation of God in France, being fixed by the several parlia- himself, and is solely occupied in the passive ments within their separate jurisdictions. (See reception of divine influences. The work of a very curious dissertation on this horrible Molinos was afterwards condemned on the subject by M. Berriat Saint-Prix, Des Tribunaux application of the Jesuits. Akin to the ideas et de la Procédure du Grand Criminel au 18 of Molinos seem to have been those of the Siècle, 1859.) Those in common use at Paris French Quietists, of whom Madame Guyon were, the question by water, which consisted and Archbishop Fénelon are the most celebrated. in stretching the limbs of the sufferer on a The former was at one time treated as insane; board by means of screws, and forcing him to at another, she was admitted to the intimacy of swallow large quantities of water; and the Madame de Maintenon, and rose high in court boots, in which his legs were enclosed in wooden favour. Fénelon praised her in his treatise cases, the whole tightly compressed with ropes, Sur la Vie Intérieure (1691). The writings of and wedges driven with a mallet between the the latter upon this subject were finally conThe question varied in degree, demned by Innocent XII.; and the example of being ordinary or extraordinary, at the dis- the archbishop in submitting to the decision cretion of the judges. Children and adolescents, has been dwelt on by pious writers as a signal old men, and women with child, were excepted triumph of a religious mind. The dissolute from torture by the French law. And, by an conduct of some hypocritical priests, under the ordonnance of 1670, the second application of pretence of inculcating the tenets and practice the question was forbidden in all cases. [RACK; of Quietism, brought it eventually into disrepute TORTURE.] more than the repeated condemnations of the head of the Roman Catholic church.

two cases.

Question, Previous. [PREVIOUS QUESTION.]

Questmen (Lat. quæstus, a secking). Parochial officers sometimes appointed in large parishes to assist the churchwardens in enquiring into abuses, making presentments, &c. Qui pro Quo or Quid pro Quo (Lat.). A conventional term borrowed from the French, who apply it to an error committed by mistaking one thing or person for another. In England it is used also in the sense of an equivalent.

Qui Tam (Lat. who as well). In Law, a penal action, in which half the penalty is given to the crown and the rest to the informer. The plaintiff, while Latin forms were in use, described himself as A. B. 'qui tam pro domino rege quam pro se ipso who sues as well for the king as himself.

Quilted Armour. Armour formed of soft material padded, and stitched at regular intervals, so as to keep the padding in its place. This armour is also called pourpointed, and was much worn in the middle ages.

Quincite. A hydrated silicate of magnesia and protoxide of iron, of a carmine-red colour, found disseminated in a fresh-water limestone, near Quincey, in the Département du Cher.

Quincunx. The Latin term properly for that disposition of five objects in which they are made to occupy the four corners and point of intersection of the diagonals of a square; but the word is extended to any number of things so arranged in lines that the members of each succeeding line stand behind the spaces between those of the preceding one. Troops

QUINDECAGON

QUINTAIN

were frequently drawn up in this order, which | consequently about the fiftieth day before that was also a favourite arrangement for planta- festival; whence the origin of the term, from tions of vines. Lat. quinquagesimus, fiftieth.

Quindecagon. In Geometry, a plane figure bounded by fifteen sides. The regular quindecagon is inscribable in a circle by elementary geometry. (Euclid, book iv.) Quindecemviri. Roman magistrates, whose duty it was to take care of and to consult the Sibylline books.

Quinquatrus. In Roman Antiquities, the feast of Minerva, which began on March 19, and lasted five days.

Quinquennalia or Ludi Quinquennales. In Classical Antiquity, public games celebrated every five years. Tacitus (Ann. xiv. 20) says that they were introduced at Rome by Nero.

Quinia or Quinine. An alkaline base obtained chiefly from yellow bark, Cinchona Quinquereme (Lat. quinqueremis, Gr. Calisaya, and other species. This substance, TeVThons). The name of a class of Roman combined with sulphuric acid, forms the sul-war ships rowed by five banks of oars. The phate of quinine, now extensively used as a introduction both of quadriremes and quinmedicine, and as a substitute for the various queremes is attributed to the Syracusan tyrant forms of Peruvian bark. To obtain quinine, Dionysius the Elder; while the younger Dionybruised yellow bark is boiled in repeated por- sius is said to have possessed hexeres, or ships tions of water, acidulated by sulphuric acid, till with six sets of rowers. Polybius says that all its soluble matters are extracted; a little ex- the first Punic war was carried on chiefly with cess of quicklime is then added to the strained quinqueremes. At Athens vessels larger than decoction, and the precipitate which is formed is triremes were not introduced till about the collected, washed, and carefully dried; it is then time of Alexander the Great; and we first hear digested in alcohol, which takes up the quinine, of a quinquereme in a document of B. c. 325. and from which the latter may be obtained in It is a matter of dispute how the banks of oars the form of a yellowish substance by careful were disposed: some maintaining that they evaporation. It is dissolved in dilute sulphuric were above each other, others that such an acid, and the sulphate of quinine crystallises arrangement must involve an impossible length from its concentrated solution in fine silky of oar for the upper bank. Yet in works of prisms, which effloresce on exposure to air. art the ranks of oars appear one above another, Sulphate of quinine is not easily soluble in although not perpendicularly; and thus more water, and is intensely bitter. It is admi- room was furnished for the various classes of nistered as a tonic and febrifuge in doses of rowers. In the ships ranging from the monfrom one to five or six grains. eris (or ship with one bank of oars on each side) up to the quinquereme, each oar is said to have been managed by one man; but it is obviously impossible that one man could manage the long oars of a Teσσapakovτhpns, thirty-eight cubits in length. For further details see Smith's Dictionary of Greek and Roman Antiquities, art Navis.' [TRIREME; GALLEY.]

The composition of quinine, in its anhydrous state, is represented by the formula C,,H2104N, and the crystallised sulphate, as sold for medical use, is a compound of one atom of sulphuric acid, one of quinine, and fourteen of water. Its high price renders it liable to various adulterations. Quinine appears to be associated in the barks which afford it with some other analogous alkaloid, and the mixture is called quinoidine, and is said to contain two bases isomeric with quinine which have been termed quinidine and quinicine.

Quinicine. An alkaloid much resembling quinine and quinidine, from either of which it may be prepared by applying a temperature below their fusing point for a few hours.

Quinidine. One of the cinchona alkaloids. It is an isomer of quinine, which it much resembles; but it more readily crystallises, a much larger quantity of it is required to be taken into the system before an effect is produced equal to that obtained by a given amount of quinine, and finally its solutions have an opposite action on a ray of polarised light. Under the names of quinidine and quinoidine, various substances are sometimes sold for medical use, as comparatively cheap substitutes for sulphate of quinine, but on account of their indefinite composition they cannot be relied on.

Quinoidine. [QUINIDINE.] Quinquagesima Sunday. In the Calendar, the seventh Sunday before Easter, and

Quinquina. Peruvian bark. The bark of various species of CINCHONA.

Quinsey (Ital. squinanzia, Gr. kuvάyxn). Inflammation of the tonsils. This is common inflammatory sore-throat: it is not infectious. It begins with pain on one side of the throat, and swelling of the tonsil, or of both tonsils at the same time, attended by febrile symptoms, which sometimes run high, especially as the tumefaction advances; there is great restlessness and anxiety, and often the utmost difficulty of swallowing even liquids, and of breathing. The disease has proved fatal by producing suffocation, but it generally terminates in resolution or suppuration: in the latter case the abscess breaks, a good deal of pus is discharged, and the patient is at once relieved of all his urgent symptoms.

Quintain (Fr. quintaine). An ancient pastime, in which a post was erected, with a crosspiece, turning upon a pivot on the top of it, to one end of which a sand-bag was suspended, and a board fixed at the other. The play consisted in riding or tilting against the boarl with a lance, and passing without being struck behind by the sand-bag.

QUINTAL

Quintal. An old denomination of weight, being the same with the hundred weight, or equal to 112 pounds.

Quintessence (Lat. quinta essentia). A term applied by the older chemists to alcoholic tinctures or essences, made by digestion at common temperatures or in the sun's heat. In Alchemy it denoted the fifth or highest essence of power in a natural body.

Quintic. In the Higher Algebra, this term denotes a homogeneous function of the fifth order in the variables. [QUANTIC.] The theory of binary quintics has been most studied on account of its connection with algebraical equations of the fifth degree, the most general form of which is

x23+ ax1+ bx3 + cx2 + dx+e=0.

QUIRITES

x2 + dx + e=0 x2 + cx2 + e = 0 x3 + a x1 + e = 0)

2 + bx3 + e = 0.

In any one of these four forms we may make either the last coefficient e, or the intermediate coefficient a or b or c or d equal to unity or to any other assumed number except zero; so that the general quintic equation may, by the aid of lower equations, be reduced to a trinomial form involving only a single variable parameter. (See Jerrard's Essay on the Resolution of Equations, London 1859; also an historical paper by Harley in the Quart. Journ. of Math. vol. vi. 1863.)

Availing himself of this reduction of the general quintic to a trinomial form, involving Various attempts have been made by mathe-only one parameter, M. Hermite, in his Essai maticians to effect a finite algebraic solution of sur la Théorie des Equations modulaires et la Résolution de l'Equation du Cinquième Degré the quintic equation, i.e. to express a root of it by means of finite combinations of radicals (Paris 1859), has succeeded in expressing the and rational functions, as can be done for quad-roots of the quintic in terms of elliptic functions, and M. Kronecker, in Crelle's Journal, has In ratic, cubic, and biquadratic equations. shown that the same thing can be done for the particular cases such solutions have been discovered. Thus, De Moivre found that when equation in its complete form. the quintic takes the form

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These and other cases have been shown by Harley to be included in a large class of solvable forms. (Manchester Memoirs, vol. xv. second series, pp. 172-219.)

But all the attempts of mathematicians to discover a finite algebraical solution of the general quintic have hitherto failed. Abel, indeed (Euvres complètes, Christiana 1839), has demonstrated that it is impossible, except in particular cases, to effect a finite algebraic solution of any equation of a higher degree than the fourth. His argument has been reproduced and modified by Sir W. R. Hamilton. (Trans. Royal Irish Acad. vol. xviii.; Abstract of Hamilton's Exposition by Cockle, Quart. Journ. of Math. vol. v.) A shorter and more simple demonstration of Abel's theorem has been given by Wantzel, and reproduced in Serret's excellent Cours d'Algèbre Supérieure.

Another important discovery which has been recently made in the theory of quintic equations is that the general quintic equation can be deprived of any three of its four middle terms by the aid of equations of inferior degrees, and so reduced to one of the following four trinomial

forms:

Attacking the problem from a different point, Harley, in vol. v. of the Quart. Journ. of Math., has calculated a certain linear differential equation of the fourth order and remarkably simple in form, whose solution is shown to embrace the solution of the general quintic equation. [DIFFERENTIAL RESOLVENT.]

Quintile. In Astronomy, an aspect of two planets distant from each other the fifth of the zodiac, or 72°.

Quintine (Lat. quintus). In Botany, a name given to the fifth or innermost envelope of the vegetable ovule, the most external being the first or primine.

Quintuple. In Music, a species of time, now seldom used, containing five crotchets in a bar.

Quinzaine. In Chronology, the fourteenth day after a feast day, or the fifteenth if the day of the feast be included. But a different rule seems to have prevailed on the Continent. (Sir H. Nicolas, Chronology of History, p. 105.)

Quire. In Printing, a bundle of paper consisting of twenty-four sheets. A quire of newspapers consists of twenty-five sheets.

Quirinus. According to Dionysius of Halicarnassus, this is a Sabine word, derived, perhaps, from quiris or curis, a spear, with which some have connected the word curia, a senate house. Under this name ROMULUS was worshipped by the Romans after his deification.

Quirites. In Roman Antiquities, this name occurs in the expression Populus Romanus Quirites. By some it has been supposed that this phrase refers to a coalition of two tribes, the Romans and the Quirites, the latter belonging, perhaps, to a town called Cures or Quirium. But in the absence of all historical evidence, these suppositions can neither be proved nor refuted. According to Bekker, the name Roman denoted the people in its rela

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