QUADRIENNIUM UTILE—QUADRILLE. in the form of an infinite continued fraction, during minority. The injury or lesion must have thus: This was appropriated by Leibnitz, and formed perhaps the first of that audacious series of peculations from English mathematicians which have for ever dishonoured the name of a man of real genius. T If we notice that, by ordinary trigonometry, the arc whose tangent is unity (the arc of 45° or) 4' falls short of four times the arc whose tangent is by an angle whose tangent is, we may easily calculate to any required number of decimal places by calculating from Gregory's formula the values of the arcs corresponding to and as tangents. And it is, in fact, by a slight modification of this process (which was originally devised by Machin), that has been obtained, by independent calculators, to 600 decimal places. 4 9 It is not yet proved, and it may not be true, that the area or circumference of a circle cannot be expressed in finite terms; if it can be, these must (of course) contain irrational quantities. The integral calculus gives, among hosts of others, the following very simple expression in terms of a definite integral : Xx been caused, not by an accident, but by the imprudence or negligence of themselves or of their curators. The proceeding, therefore, must be commenced before the minor attains 25, after which it is too late to seek restitution. See INFANT. QUADRI'GA. See CHARIOT. QUADRILATERAL, in Military Language, is an expression designating a combination of four fortresses, not necessarily connected together, but mutually supporting each other; and from the fact that if one be attacked, the garrisons of the others, unless carefully observed, will harass the besiegers, rendering it necessary that a very large army should be employed to turn the combined position. As a remarkable instance, and a very √x + √y, where and are irrational numbers. Such an expression, if discovered, would undoubtedly be hailed as a solution of the grand problem. But this, we need hardly say, is not the species of solution attempted by squarers.' We could easily, from our own experience alone, give numerous instances of their helpless absurdities, but we spare the reader, and refer him, for further information on this painful yet ridiculous subject, to a recent series of papers by De Morgan in the Athenæum; and to the very interesting work of Montucla, His toire des Recherches sur la Quadrature du Cercle. QUADRIE'NNIUM U'TILÉ, in Scotch Law, means the four years after majority during which a person is entitled to reduce or set aside any deed made to his prejudice during_minority. This protection was also given by the Roman law to minors, to enable them to neutralise any unfair advantage that may have been taken of their inexperience The Venetian Quadrilateral. powerful one, may be cited the celebrated quadrilateral in Venetia, comprising the four strong posts of Mantua, Verona, Peschiera, and Legnago. These form a sort of outwork to the bastion which the southern mountains of the Tyrol constitute, and divide the north plain of the Po into two sections by a most powerful barrier. Napoleon III., in 1859, even after the victories of Magenta and Solferino, hesitated to attack this quadrilateral. QUADRI'LLE, a dance of French origin, consisting of consecutive dance movements, generally five in number, danced by couples, or sets of couples, opposite to, and at right angles to each other. The namie seems to be derived from its having been originally danced by four couples. QUADRILLE is a card game, which, as its name denotes, is played by four persons. The number of cards employed is forty, the tens, nines, and eights being discarded from the pack. The rank and order of the cards in each suit vary according as they are or are not trumps, and are different in the black and red is always the highest trump, and is called spadille; suits. The ace of spades, whatever suit be trumps, the ace of clubs is always the third highest trump, and is known as basto; while the second highest and is known as basto; while the second highest trump, or manille, is the deuce of spades or clubs, or the seven of hearts or diamonds, according to the the seven of hearts or diamonds, according to the suit which is trumps, it being always of the trump suit. When the black suits are not trumps, the black cards rank as in whist; and when they are trumps, the order is the same, with the exception, as above mentioned, of the deuce, which then (in the trump suit only) becomes manille, the deuce of the black suit which is not trumps retaining its position as the lowest card. When the red suits are not trumps, the order of rank is as follows: QUADRIVIUM-QUÆSTOR. King, queen, knave, ace, deuce, three, four, five, six, seven; but when they are trumps, the ace (of the trump suit only) is raised to the position of the fourth highest trump, under the name of ponto or punto, and the seven (of the trump suit only) becomes, as previously stated, manille. A little consideration will shew, that when the black suits are trumps, the number of trump cards is eleven, and twelve when a red suit is trumps. The three highest trumps, spadille, manille, and basto, are called matadores, and the player who possesses one of them can, if he have no other trumps in his hand, decline to follow suit if trumps are led, provided the trump led is not a matadore of value superior to his own. After the cards have been shuffled, cut, and dealt, the elder hand, on looking at his cards, may, if his hand be weak, decline to play (or pass); the next player may do the same, and so on all round; in which case the elder hand must commence, naming the suit which he wishes to be trumps, and the cards are laid, and tricks taken, as in ordinary card games. If a player does not pass, but commences the game by naming trumps and playing a card, he must himself make six tricks to win; and if he succeeds, he obtains the whole of the winnings; but if he loses, he pays the whole of the losses. If he commences the game by asking leave'—i. e., to have a partner-which is done by calling a king, the player who holds the king of the suit led must play it when his turn arrives; and he who asked leave, or l'hombre (in England generally called ombre), along with him who had the king called, or the friend, are from this time partners in the game, and divide either the gains or the losses, as the case may be. The ombre and the friend win the game if they make six tricks between them. This game is complicated by a number of conditions, which, under certain circumstances, modify the ordinary mode of playing. A modification of this game, under the name of preference, is much in vogue in Lancashire; and in this country in the beginning of last century, and on the continent--especially in France-the game of l'hombre, which is nothing more than quadrille played by three persons, was exceedingly fashionable. L'hombre is now quite obsolete, but a most accurate description of the mode in which it was played will be found in Pope's Rape of the Lock. L'hombre was the immediate predecessor of quadrille in popular favour. Collectively they differ from other Mammalia in having 4 or 5 elongate more or less prehensile toes, with generally flat nails, and the molar teeth all tubercular; feet all plantigrade. The limbs are formed for grasping; the hands are sometimes imperfect, through the want or rudimentary character of the thumb. None of the Q., except man, are naturally adapted for an erect posture. The differences between man and the apes which most nearly approach him in form, are pointed out in the articles MONKEY, CHIMPANZEE, GORILLA, and ORANG. The Q. resemble man in their dentition more than any other animals. Their other digestive organs also exhibit a general similarity to those of man. The similarity is further apparent in the brain and in the reproductive organs; but in the Lemuridæ, a gradual departure from the human form and characters is manifested, with an approach to the ordinary quadruped type. QUA'DRUPEDS (Lat. four-footed), a term employed both popularly and by scientific writers to designate four-footed animals. It is not, however, the name of a class or order in systems of zoology. Popularly, it is almost always limited to those Mammalia which have four limbs well developed and formed for walking, and is scarcely ever applied to the Cetacea, and rarely even to Seals or to the Quadrumana (q. v.). The full development of the limbs, with their termination in. feet properly so called, thus appears to be by no means one of the most important characters by which groups of animals are distinguished; and this further appears when the same character is found again, in great perfection, in a lower class of vertebrate animals in Chelonian and Saurian Reptiles, as tortoises and lizards. But the four-limbed type prevails among vertebrate animals, from man downwards; so that even in serpents, in which it is least notable, traces of it appear on anatomical examination, as in Boas (q. v.); links as to this character between serpents and and there are many creatures which form connecting those reptiles as crocodiles and lizards — which possess it in greatest perfection. The homology of certain fins of fishes with the limbs of quadrupeds is noticed in the article FISHES. No approach to the four-limbed type is found among Invertebrate animals. QUA'DRUPLE ALLIANCE. See ALLIANCE. QUÆ'STOR (Lat. contr. from quæsitor, a searcher or investigator, from quæro, to seek or search into) was anciently the title of a class of Roman magistrates, reaching as far back, according to all accounts, as the period of the Kings. The oldest quaestors were the quæstores parricidii ("trackers of murder,' Their office was to conduct the prosecution of persons ultimately public accusers), who were two in number. accused of murder, and to execute the sentence that QUADRI'VIUM (Lat. quatuor, four, and via, a road), the name given, in the language of the schools of the West, to the higher course of the medieval studies, from its consisting of four branches, as the lower course for an analogous reason, was called TRIVIUM (q. v.), or Three Roads.' The quadrivium consisted of arithmetic, music, geometry, and astronomy. It would carry might be pronounced. They ceased to exist as early us beyond our limits to detail the nature and as 366 B. C., when their functions were transferred extent of each of these branches as pursued into the Triumviri Capitales. But a far more importthe medieval schools. The reader will find much ant though later magistracy was the questores clascurious and new matter on all questions of this nature in the volumes of the works of Roger Bacon, lately edited in the series issued under authority of the Master of the Rolls, as also in the Introduction prefixed to the volumes. sici, to whom was intrusted the charge of the public not be ascertained, but it was subsequent to the treasury. The exact date of their institution canexpulsion of the kings. They appear to have derived the epithet of classici from their having been originally elected by the centuries. At first they were only two in number, but in 421 B. C. two more were added. Shortly after the breaking out of the first Punic War, the number was increased to eight; and as province after province was added to the Ro man Republic, they amounted, in the time of Sulla, to twenty, and in the time of Cæsar to forty. On its first institution the quæstorship (quæstura) was open only to patricians; but after 421 B. C., plebeians also QUADRU'MANA (Lat. four-handed), in the zoological system of Cuvier an order of Mammalia, which he places next after Bimana (q. v.), and which contains the animals most nearly resembling man in their form and anatomical characters-viz., the monkey and lemur families. The order Q., as now received by naturalists, includes both these groups, as sub-orders, under the names of Anthropoilea and Simioidea, and a third, the Lemuroidea. I became eligible. QUAGGA-QUAKING GRASS. QUA'GGA (Equus—or Asinus-Quagga), an animal of the family Equidæ (q. v.), a native of the southern parts of Africa, rather smaller than the Zebra (q. v.), with the hinder parts higher, and the ears shorter; the head, mane, neck, and shoulders blackish-brown, banded with white; similar bands towards the rump, gradually becoming less Quagga (Asinus Quagga). distinct; a black line running along the spine. The Q. receives its name from its voice, which somewhat resembles the barking of a dog. It is more easily domesticated than the zebra, and a curricle drawn by quaggas has been seen in Hyde Park. In its wild state it does not associate with the zebra, although inhabiting the same plains. Hybrids, or mules, have been produced between the horse and quagga. QUAIL (Coturnix), a genus of gallinaceous birds of the family Tetraonida, nearly allied to partridges, but having a more slender bill, a shorter tail, longer wings, no spur, and no red space above the eye. The first and second quills of the wing are about as long as the third, which is the longest in the more rounded wing of the partridges. Quails, therefore, Common Quail (Coturnix vulgaris). far excel partridges in their power of flight. The tail is very short. They never perch on trees, but always alight on the ground. They are among the smallest of gallinaceous birds.-The COMMON Q. (C. vulgaris or C. dactylisonans) is found in most parts of Europe, Asia, and Africa. In India and other warm countries, it is a permanent resident; but in many countries it is a bird of passage; and thus it visits the north of Europe, and at certain seasons appears in vast multitudes on the coasts and islands of the Mediterranean, so that quails are there taken in hundreds of thousands in their northern and southern migrations. The Q. is not plentiful at any season in any part of Britain; but sometimes appears even in the northern parts of Scotland, and more frequently in the south of England, where it is sometimes seen even in winter. There is reason to believe that the food miraculously supplied to the Israelites in the wilderness was this very species of bird, to which the name Selav, used in the Mosaic narrative, seems to belong.-The Q. is fully 7 inches in entire length; of a brown colour, streaked with different shades, and the wings mottled with light-brown; the throat white, with dark-brown bands in the male, and a black patch beneath the white, the lower parts yellowish-white. The Q. is polygamous. The nest is a mere hole in the ground, with 7 to 12 eggs. The Q. is highly esteemed for the table. Great numbers of quails are brought from the continent to the London market. Other species of Q. are found in different parts of Asia, although no other is so abundant as the Common Q., and none migrates as it does. The Coromandel Q. (C. textilis) is a very pretty little bird, rather smaller than the Common Quail. The Chinese Q. (C. excalfactoria), a very beautiful little species, only about 4 inches long, is abundant in China, and is there kept for fighting, the males being very pugnacious, like those of other polygamous birds, and much money is lost and won on the combats of these quails. It is also used for a singular purpose-the warming of the hands of its owner. As QUAKERS; the ordinary designation of the Society of Friends (q. v.). In respect of law, Quakers differ from the rest of their fellow-citizens chiefly as regards their marriages and their taking of oaths. Thus, though the English marriage acts required all marriages to take place in a consecrated church of the establishment, before the dissenters obtained a relaxation of the law, the Quakers' marriages were excepted, and marriages between two Quakers were allowed to be solemnised regards Quakers in the matter of taking oaths, it according to the usages of their own sect. is expressly provided by several statutes, that instead of taking an oath in the usual way, they witness in a court of justice, or as holding a civil may make an affirmation instead, whether as office, the qualification for which office is the taking of an oath. The penalties of perjury, however, attach to a false affirmation in the same way as to a false oath. With regard to church-rates, it has been recently decided that Quakers stand on the same footing as other people in respect of their liability pay church-rates, and the mode of disputing the validity of the rate. to QUAKING GRASS (Briza), a genus of grasses, having a loose panicle; drooping spikelets, generally remarkable for their broad and compressed form, suspended by most delicate footstalks, and tremulous in every breath of wind; the spikelets with two glumes and numerous florets, the florets having each two awnless paleæ, which become incorporated with the seed. The species are few, and mostly European. They are all very beautiful. B. maxima, a native of the south of Europe, is often planted in flower-gardens. B. media, the only species common in Britain, growing in almost all kinds of poor soil, from the sea-coast to an elevation of 1500 feet, is of some value as a pasture-grass, being very nutritious, although the quantity of herbage is scanty. The value of many poor pastures very much depends on it; but when they are enriched by manures, it generally disappears. It is sometimes sown by farmers, but not nearly to such an extent as it would be if its seed did not QUAMASH-QUAQUAVERSAL. lose vitality so quickly that only a small proportion matter is all gravitating things,' a kind of proposi Quaking Grass (Briza media). grows, if it is not sown in autumn when newly ripened. QUAMASH, or BISCUIT ROOT (Camassia esculenta), a plant of the natural order Liliacea, nearly allied to squills and hyacinths. It is a North American plant, abounding on the great prairies west of the Mississippi. The roasted bulbs are agreeable and nutritious, and are much used as an article of food. QUANTIFICATION OF THE PREDICATE, a phrase belonging to Logic, and introduced by Sir W. Hamilton to express the characteristic feature of certain logical doctrines of his respecting the Proposition and the Syllogism. According to the Aristotelian Logic, propositions are divided, according to their quality, into affirmative and negative (The sun has set," The sun has not set'); and, according to their QUANTITY, into universal and particular (All men are mortal, 'Some men live eighty years'). If we combine the two divisions, we obtain four kinds of propositions-Affirmative Universal ('All men are mortal'), Affirmative Particular ('Some men live to eighty'), Negative Universal (No men are omnipotent'), Negative Particular (Some men are not wise'). Now, it is remarked by Sir W. Hamilton, that the statement of the QUANTITY of these various propositions is left incomplete; only the subject of each has its quantity expressed (all men, some men, no men); while there is implied or understood in every case a certain quantity of the predicate. Thus, All men are mortal,' is not fully stated. The meaning is, that all men are a part of mortal things, there being (possibly and probably) other mortal things besides men. Let this meaning be expressed, and we have a complete proposition to this effect: 'All men are some (or part of) mortals,' where quantity is assigned, not only to the subject, but also to the predicate. It might be that the predicate contained under it only the subject, as in the proposition: All matter gravitates.' There is no other thing in the universe except matter that obeys the law of gravitation. Knowing this, we might quantify the predicate accordingly: All tion not recognised in the old logic. Another original form of proposition, brought out by supplying the quantity of the predicate, is, 'Some A is all B; Some men are all Englishmen.' So that, instead of two kinds of propositions under affirmation, Sir W. Hamilton's system gives four. In the same way, he increases the number of negative propositions. 1. For 'No man is omnipotent,' he writes, quantifying the predicate, Any man is not any omnipotent; or, All men are out of all omnipotent things.' 2. 'Some men are not young is fully quantified; 'Some men are not any young things;"Some men are out of all young things.' These two (in their unquantified shape) are the ordinarily recognised propositions of the negative class. To them Sir W. Hamilton adds—3. · All men are not some animals,'' All men are excluded from a certain uivision of the class animal;' and 4. Some animals are not some men;''A portion of the animals is not included in a portion of men.' The The first result, therefore, of completing the statement of a proposition by inserting what Hamilton considers as implied in the thoughtnamely, the quantity of the predicate-is to give eight kinds of propositions instead of four. next result is to modify the process called the Conversion of Propositions. See CONVERSE. The kind of conversion called limitation (All A is B, some B is A) is resolved into simple conversion, or mere transposition of premises without further change. 'All A is some B;''Some B is all A.’ The multiplication of varieties of propositions is attended with the further consequence of greatly increasing the number of syllogisms, or forms of deductive reasoning. See SYLLOGISM. In the scholastic logic, as usually expounded, there are nineteen such forms, distributed under four figures (four in the first, four in the second, six in the third, five in the fourth). By ringing the changes on eight sorts of propositions, instead of the old number, four, thirty-six valid syllogisms can be formed in the first figure. Whether the increase serves any practical object, is another question. Sir W. Hamilton also considers that he has been led, by the new system, to a simplification of the fundamental laws of the syllogism, or, as he expresses it, the reduction of all the General Laws of Categorical Syllogisms to a Single Canon."' Professor De Morgan, in his elaborate system of Formal Logic, has also invented and carried out into great detail a plan of expressing the quantity of the predicate; but he does not admit the whole of Hamilton's eight propositional forms, rejecting in particular the last mentioned in the above enumeration. He also increases the number of valid syllogisms as compared with the old logic. Not content with indicating that the predicate has quantity as well as the subject, he supposes the possibility of a numerical estimate of quantity in both terms of the proposition, and from this draws a new set of inferences. Thus, if 60 per cent. of B are included in C, and 70 per cent. in A, 30 per cent. at least of B must be found both in A and in C.-See Sir W. Hamilton's Discussions; Spencer Baynes's New Analytic of Logical Forms; De Morgan's Formal Logic; Mill's Logic, under the Syllogism; and his Examination of Sir W. Hamilton's Philosophy. QUAQUAVE'RSAL (Lat. turning every way), a term applied in Geology to the dip of the Stratified rocks when arranged in dome-shaped elevations, or basin-shaped depressions, whereby the beds have an inclination on all sides to one point, that point being the summit of the dome in the one case, and the lowest level of the basin in the other. QUARANTINE-QUARRY. Of the more celebrated quarries of the British Islands, we may mention those of Cornwall, Aberdeen, and Wicklow for granite; those in the neighbourhood of Edinburgh, Glasgow, and Newcastle, for sandstone; those near Bristol and Doncaster, and in the Isle of Portland, for limestone ; those of Derbyshire, Devonshire, Kilkenny and Galway, for marbles; and those of North Wales and Argyleshire for slates. QUA'RANTINE (from the Fr. quarantaine, a period of 40 days) is a forced abstinence from communication with the shore, which ships are compelled to undergo when they are last from some port or country where certain diseases held to be infectious, as yellow fever, plague, or cholera, are or have been raging. Where a quarantine is established, it is a high misdemeanour for any person in the suspected ship to come on shore, or for any one to disembark any merchandise or goods from her. The countries To understand the operations of the quarryman, on the eastern and southern shores of the Mediter- it is necessary to bear in mind that all rocks belong ranean are those most commonly held to be infec- to one or other of two great classes, namely, the tious, and, as a regular arrangement, ships from them stratified and the unstratified. The former are have to pass quarantine at Malta, or some French, sedimentary rocks, occurring in parallel beds or Italian, or Spanish port. In England, the quarantine strata, and consist chiefly, in so far as we are at laws were, until about 20 years ago, enforced with present concerned, of sandstone and limestone. severity; but now a quarantine is an unusual occur- Unstratified or igneous rocks, which include greenrence, although the power to enact it rests with stone or whinstone, granite, porphyry, &c., have no the crown, and it is occasionally imposed by an distinct bedding, that is, they do not lie in separate order in Council. In Mediterranean ports, quaran- layers. Roofing-slate is a stratified rock, but it tine ordinarily lasts from 6 to 15 days, though it splits into thinner laminæ in the direction of its sometimes extends to a much longer period, during cleavage than in the direction of its bedding, the which the passengers are imprisoned in a sort of former being often at right angles to the latter. barrack called a 'lazaretto,' and the contents of the Granite and other igneous rocks have also a natural ship-animals, goods, and letters-are fumigated, jointage or cleavage, although they are not stratified. punctured, sometimes immersed in water, or even Advantage is taken of these peculiarities in quarryacid, and all possible means are adopted to destroying the different rocks, but in the main the systems infection. adopted do not greatly differ. Quarantine is not of necessity limited to a seafrontier; and it is enforced-often with absurd rigour at the frontiers between contiguous states, especially in Eastern Europe, to the annoyance of travellers, and to the serious detriment of commerce. History declares quarantine regulations for maritime intercourse to have been first established by the Venetians in 1127 A. D.; but the practice must have been greatly older on land-frontiers; and the precautions of the Jews against leprosy indicate that a species of quarantine was enforced by them. The law for regulating quarantine, when imposed in England, is 6 Geo. IV. c. 78. QUA'RÉ I'MPEDIT is the title of an English action, whereby a person who has purchased an advowson, or right of presentation to an ecclesiastical benefice, sues any one who disturbs or hinders him in the exercise of his legal right. QUA'RREL, or QUARRY, a pane of glass of a lozenge or diamond shape. The name is also applied to a perforation or window of this form, and to square or diamond-shaped paving-stones or tiles. QUA'RRY (Fr. carrière). When any useful rock is worked in an open manner at the surface of the earth, the excavation is called a quarry. Quarrying differs little from mining in principle, except that the latter is essentially an underground operation. From a very remote period, famous granite quarries have been worked at Syene, and others of sandstone and limestone, along the banks of the Nile, for the temples and monuments of ancient Egypt. Greece found the materials for her white marble temples in the quarries of Mount Pentelicus, near Athens, and in those of the islands of the Archipelago. It was from the quarries of Travertine (a kind of limestone), at Tibur, that ancient Rome was chiefly built. Italy has long been celebrated for her marble quarries, those of Tuscany yielding the most esteemed kinds. The fine saccharoid marbles for statuary and other fine-art purposes, are exclusively obtained from the Apuan Alps, which rise around Carrara, Massa, and Seravezza. Those of Carrara, especially, are highly prized all over the world. From the quarries at Seravezza, marble to the value of £150,000 has been recently taken for the splendid cathedral of St Isaac at St Petersburg alone. Stones are most frequently separated from their native rock by blasting with gunpowder. This operation is described in detail under BLASTING; see also GALVANISM and SAFETY-FUSE. Of late the practice of boring jumper-holes with engine-power has been introduced, and wherever it can be conveniently applied, must be a great improvement on the slow and tedious process of boring by hand. See Tunnel. With some stratified rocks, such as sandstone, a good many of the best stones are procured without the aid of gunpowder. Hand-tools are alone used, because blasting is apt to cause rents, and otherwise shatter portions which it is desirable to keep solid. By this method, the quarryman makes a number of small holes with a pick, along a certain length of rock, into which steel wedges are inserted. After a succession of blows with heavy hammers, the wedges at length cut through the stratum. Blocks for columns, obelisks, tombstones, &c., are best procured in this way. It may also be stated that these are obtained from those more valuable parts of sandstone deposits technically termed liver rock,' which consist of the thicker and more consolidated strata. Flagstones and other pieces of limited thickness are quarried from the thinner beds termed ‘bed rock.’ When stones are removed in masses by blasting or otherwise, they have still to be quarried into shape, according to the purpose for which the various pieces are best suited. Thus, in an ordinary building-stone quarry, the larger stones (after those of unusual size and quality are selected for the purposes named above) are roughly formed into ashlar, window-sills, lintels, rybats, corners, steps, and the like, by means of such tools as picks, hammers of various kinds, and wedges. The small irregular-shaped pieces are called rubble, and are used for the commonest kind of building. Slates are split up into the thickness used for roofing, by means of a mallet and broad chisel. In granite quarries worked for paving-stones, as has been incidentally alluded to above, the loss of material in reducing the blocks to the size and shape required, is enormous, as much as four-fifths of the whole being commonly wasted. Besides the tools already mentioned, long iron bars called pinches, and powerful cranes for turning and lifting the larger stones, |