Quadrant. AB, beginning at A; this will terminate in H, allow- ing every small interval four leagues. Then tracing out the parallel HE, from the point H to the thread; the part AE of the thread shows that 125 greater or equi noctial leagues make 60° 15'; and therefore that the 83 lesser leagues AH, which make the difference of longitude of the course, and are equal to the radius of the parallel HE, make 60° 15' of the said parallel.

Fig. 6.

If the ship sails an oblique course, such course, besides the north and south greater leagues, gives lesser leagues easterly and westerly, to be reduced to degrees of longitude of the equator. But these leagues being made neither on the parallel of departure, nor on that of arrival, but in all the intermediate ones, we must find a mean proportional parallel between them. To find this, we have on the instrument a scale of cross latitudes. Suppose then it were required to find a mean parallel between the parallels of 40° and 60°; with your compasses take the middle between the 40th and 60th degree on this scale: the middle point will terminate against the 51st degree, which is the mean parallel required.

The principal use of the sinical quadrant is to form triangles upon, similar to those made by a ship's way with the meridians and parallels; the sides of which triangles are measured by the equal intervals between the concentric quadrants and the lines N and S, E and W: and every fifth line and arch is made deeper than the rest. Now, suppose a ship to have sailed 150 leagues north-east, one-fourth north, which is the third point, and makes an angle of 33° 44' with the north part of the meridian: here are given the course and distance sailed, by which a triangle may be formed on the instrument similar to that made by the ship's course; and hence the unknown parts of the triangle may be found. Thus, supposing the centre A to represent the place of departure, count, by means of the concentric circles along the point the ship sailed on, viz. AD, 150 leagues: then in the triangle AED, similar to that of the ship's course, find AE=difference of latitude, and DE=difference of longitude, which must be reduced according to the parallel of latitude come to.

10. Gunner's quadrant (fig. 6.), sometimes called gunner's square, is that used for elevating and pointing cannon mortars, &c. and consists of two branches either of brass or wood, between which is a quadrantal arch divided into 90 degrees, beginning from the shorter branch, and furnished with a thread and plummet, as represented in the figure. - The use of the gunner's quadrant is extremely easy; for if the longest branch be placed in the mouth of the piece, and it be elevated till the plummet cut the degree necessary to hit a proposed object, the thing is done. Sometimes on one of the surfaces of the long branch are noted the division of diameters and weights of iron bullets, as also the bores of pieces.

QUADRANT of Altitude, is an appendage of the artificial globe, consisting of a lamina, or slip of brass, the length of a quadrant of one of the great circles of the globe, and graduated. At the end, where the division terminates, is a nut rivetted on, and furnished with a screw, by means whereof the instrument is fitted on the meridian, and moveable round upon the rivet to all points of the horizon. Its use is to serve as a scale in

4

measuring altitudes, amplitudes, azimuths, &c. Sce Quadrast ASTRONOMY.

ture,

QUADRANTAL, in Antiquity, the name of a Quadra vessel in use among the Romans for the measuring of liquids. It was at first called amphora; and afterwards quadrantal, from its form, which was square every way like a die. Its capacity was 80 libræ, or pounds of water, which made 48 sextaries, two urnæ, or eight congii.

QUADRAT, a mathematical instrument, called also a Geometrical Square, and Line of Shadows: it is frequently an additional member on the face of the common quadrant, as also on those of Gunter's and Sutton's quadrants.

QUADRAT, in Printing, a piece of metal used to fill up the void spaces between words, &c. There are quadrats of different sizes ; as m-quadrats, n-quadrats, &c. which are respectively of the dimensions of these letters, only lower, that they may not receive the ink.

QUADRATIC EQUATIONS, in Algebra, those wherein the unknown quantity is of two dimensions, or raised to the second power. See ALGEBRA.

QUADRATRIX, in Geometry, a mechanical line, by means whereof we can find right lines equal to the circumference of circles, or other curves, and their several parts.

QUADRATURE, in Geometry, denotes the squaring, or reducing a figure to a square. Thus, the finding of a square, which shall contain just as much surface or area as a circle, an ellipsis, a triangle, &c. is the quadrature of a circle, ellipsis, &c. The quadrature, especially among the ancient mathematicians, was a great postulatum. The quadrature of rectilineal figures is easily found, for it is merely the finding their areas or surfaces, i. e. their squares; for the squares of equal areas are easily found by only extracting the roots of the areas thus found. The quadrature of curvilinear spaces is of more difficult investigation; and in this respect extremely little was done by the ancients, except the finding the quadrature of the parabola by Archimedes. In 1657, Sir Paul Neil, Lord Brouncker, and Sir Christopher Wren, geometrically demonstrated the equality of some curvilinear spaces to rectilinear spaces; and soon after the like was proved both at home and abroad of other curves, and it was afterwards brought under an analytical calculus; the first specimen of which was given to the public in 1688 by Mercator, in a demonstration of Lord Brouncker's quadrature of the hyperbola, by Dr Wallis's reduction of a fraction into an infinite series by division. Sir Isaac Newton, however, had before discovered a method of attaining the quantity of all quadruple curves analytically by his fluxions before 1668. It is disputed between Sir Christopher Wren and Mr Huyghens which of them first discovered the quadrature of any determinate cycloidal space. Mr Leibnitz afterwards found that of another space; and in 1669 Bernoulli discovered the quadrature of an infinity of cycloidal spaces both segments and sectors, &c. See SQUARING the Circle.

QUADRATURE, in Astronomy, that aspect of the moon when she is 90o distant from the sun; or when she is in a middle point of her orbit, between the points of conjunction and opposition, namely, in the first and third quarters. See ASTRONOMY Index.

QUADRATUS,

Quadratus
QUADRATUS, in Anatomy, a name given to seve-
ral muscles on account of their square figure. See
Quadrille. ANATOMY, Table of the Muscles.

QUADREL, in Building, a kind of artificial stone, so called from its being perfectly square. The quadrels are made of a chalky earth, &c. and dried in the shade for two years. These were formerly in great request among the Italian architects.

QUADRIGA, in Antiquity, a car or chariot drawn by four horses. On the reverses of medals, we frequently see the emperor or Victory in a quadriga, holding the reins of the horses; whence these coins are, among the curious, called nummi quadrigati, and vic

toriati.

QUADRILATERAL, in Geometry, a figure whose perimeter consists of four sides and four angles; whence it is also called a quadrangular figure.

QUADRILLE, a little troop or company of cavaliers, pompously dressed, and mounted for the performance of carousals, justs, tournaments, runnings at the ring, and other gallant divertisements.

QUADRILLE, a game played by four persons, with 40 cards; which are the remains of a pack after the four tens, nines, and eights are discarded; these are dealt three and three, and one round four, to the righthand player; and the trump is made by him that plays with or without calling, by naming spades, clubs, diamonds, or hearts, and the suit named is tramps. If the person who names the trump should mistake, and say spades instead of clubs, or if he name two suite, the first named is the trump.

In this game the order of the cards, according to their natural value, is as follows: of hearts and diamonds, king, queen, knave, ace, deuce, three, four, five, six, seven; in all 10: of spades and clubs, king, queen, knave, seven, six, five, four, three, deuce; in all 9. The reason why the ace of spades and ace of clubs are not mentioned, is, because they are always trumps in whatever suit that is played. The ace of spades being always the first, and the ace of clubs the third trump, for the cards ranked according to their value when trumps stand in the following order.

Hearts and diamonds, SPADILL, or the ace of spades; MANILL, the seventh of the two red suits; BASTO, the ace of clubs; PONTO, the ace of hearts and diamonds ; king, queen, knave, deuce, three, four, five, six; in all 12. Spades and clubs, SPADILL, the ace of spades, MANILL, the deuce of spades and clubs, BASTO the ace of clubs, king, queen, knave, seven, six, five, four, three; in all 11. It is here to be observed, that the card which is manill and the second trump, is always the lowest in its suit when not trumps; and that the ace of hearts or diamonds, which when trump is above the king, is below the knave when not trump.

There are three matadores; spadill, manill, and basto; the privilege of which is, that when the player has no other trumps but them, and trumps are led, he is not obliged to play them, but may play what card he thinks proper, provided, however, that the trump led is of an inferior rank; but if spadill should be led,

he that has manill or basto only is obliged to play it; Quadrille. it is the same of manill basto, with respect to the supe rior matadore always forcing the inferior. Though there are properly but three matadores, nevertheless all those trumps which follow the three first without interruption, are likewise called matadores; but the three first only enjoy the privilege above mentioned.

Each person is to play as he judges most convenient for his own game. He is not to encourage his friend to play; but each person ought to know what to do when it is his turn to play. The stakes consist of seven equal mils or contrats, as they are sometimes called, comprising the ten counters and fishes, which are given to each player. A mil is equal to ten fish, and each fish to ten counters: the value of the fish is according to the players agreement, as also the number of tours, which are generally fixed at ten, and marked by turning the corners of a card.

If the cards should happen not to be dealt right, or that there should be two cards of the same sort, as two deuces of spades, for example, there must be a new deal; provided it is discovered before the cards are all played. The cards must likewise be dealt over again in case a card is turned in dealing, as it might be of prejudice to him who should have it, and of course if there should be several cards turned. There is no penalty for dealing wrong, he who does so must only deal again.

When each player has got his ten cards, he that is on the right hand of the dealer, after examining his game, and finding his hand fit to play, asks if they play; or if he has not a good hand, he passes, and so the second, third, and fourth. All the four may pass; but he that has spadill, after having shown or named it, is obliged to play by calling a king. Whether the deal is played in this manner, or that one of the players has asked leave, nobody choosing to play without calling, the eldest hand must begin the play, first naming the suit, and the king which he calls; he who wins the trick plays another card, and so of the rest till the game is finished. The tricks then are counted; and if the ombre, that is, he who stands the game, has together with him who is the king called, six tricks, they have won and are paid the game, the consolation, and the matadores, if they have them, and divide what is upon the game, and the beasts if there are any. But if they make only five tricks, it is a remise, and they are beasted, what goes upon the game, paying to the other players the consolation and the matadores. If the tricks are equally divided betwixt them, they are likewise beasted; and if they make only four tricks between them, it is a remise; if they make less they lose codill (A), and in that case they pay to their adversaries what they should have received if they had won; that is, the game, the consolation, and the matadores, if they have them, and are beasted what is upon the game: they who win codill, divide the stakes. The beast and every thing else that is paid, is paid equally betwixt the two losers; one half by him that calls, and the other half by him that is called, as well in case of codill as a remise;

Quadrille. mise; unless the ombre does not make three tricks, in which case he that is called is not only exempted from paying half the beast, but also the game, the consolation, and the matadores if there are any, which the ombre in that case pays alone; and as well in case of a codill as a remise. This is done in order to oblige players not to play games that are unreasonable. There is nevertheless, one case in which if the ombre makes only one trick, he is not beasted alone, and that is, when not having a good hand he passes, and all the other players have passed likewise; he having spadillis obliged to play. Here it would be unjust to oblige him to make three or four tricks; in this case, therefore, he that is called pays one half of the losings. For which reason he that has spadill with a bad hand, should pass, that if he is afterwards obliged to play by calling a king (which is called forced spadill), he may not be beasted alone. He that has once passed cannot be admitted to play; and he that has asked leave cannot refuse to `play, unless any one should offer to play without calling.

He that has four kings, may call a queen to one of his kings, except that which is trump. He that wants one or more kings, may call one of those kings; but in that case, he must make six tricks alone, and consequently he wins or loses alone. The king of that suit in which he plays cannot be called. No one should play out of his turn, although he is not beasted for so doing. If he who is not the eldest hand has the king called, and plays spadill, manill, or basto, or even the king called in order to show that he is the friend, having other kings that he fears the ombre should trump, he is not to be allowed to go for the vole; he is even beasted, if it appears to be done with that intent. It is not permitted to show a hand though codill may already be won; that it may be seen whether the ombre is beasted alone. If the ombre or his friend shows their cards before they have made six tricks, thinking that they have made them, and there appears a possibility of preventing their making them, the other players can oblige them to play their cards as they think

proper.

A player need only name his suit when he plays, without calling a king. He who plays without calling must make six tricks alone to win; for all the other players are united against him, and they are to do what they can to prevent his winning. He who plays without calling, is admitted to play in preference to him who would play with calling; however, if he that has asked leave will play without calling, he has the preference of the other who would force him. These are the two methods of play without calling that are called forced.

As he who plays without calling does not divide the winnings with any person, he consequently, when he loses, pays all by himself: if he loses by remise he is beasted, and pays each of the other players the consolation, the sans appeller (which is commonly, but improperly, called the sans prendre), and the matadores if there are any; if he loses codill he is likewise beasted and pays to each player what he would have received from each if he had won. They who win codill divide what there is; and if there are any counters remaining, they belong to him of the three who shall have spadill or the highest trump the next deal. It

is the same with regard to him who calls one of his own quadrille kings; he wins alone or loses alone as in the other case, except the sans appeller, which he does not pay if he loses, or receive if he wins, aithough he plays alone.

If he plays sans appeller, though he may have a sure game, he is obliged to name his suit; which if he neglects to do, and shows his cards, and says " I play sans appeller;" in that case neither of the other players can oblige him to play in what suit he pleases, although he should not have one trump in that suit.

He who has asked leave is not permitted to play sans appeller, unless he is forced; in which case, as was said before, he has the preference of the other that forces him.

A player is not obliged to trump when he has none of the suit led, nor play a higher card in that suit if he has it, being at his option although he is the last player, and the trick should belong to the ombre; but he is obliged to play in the suit led if he can, otherwise he renounces. If he separates a card from his game and shows it, he is obliged to play it, if by not doing it the game may be prejudiced, or if he can give any intelligence to his friend; but especially if it should be a matadore. He that plays sans appeller, or by calling himself, is not subject to this law. He may turn the tricks made by the other players, and count what has been played as often as it is his turn to play, but not otherwise. If instead of turning a player's tricks, he turns and see his game, or shows it to the other players, he is beasted, together with him whose cards he turned; and each of them must pay one half of the beast.

If any one renounces, he is beasted as often as he has renounced and it is detected; but a renounce is not made till the trick is turned. If the renounce is discovered before the deal is finished, and has been detrimental to the game, the cards must be taken up again, and the game replayed from that trick where the renounce was made; but if the cards are all played, the beast is still made, and the cards must not be replayed; except there should be several renounces in the same deal: then they are to be played again, unless the cards should be mixed. If several beasts are made in the same deal, they all go together, unless it is otherwise agreed at the beginning of the party; and when there are several beasts, the greatest always goes first.

A great advantage accrues from being eldest hand at quadrille, which often renders it very disagreeable to the rest of the players, being obliged to pass with a good hand unless they choose to play alone; and when it happens that the eldest hand having asked leave, the second player has three matadores, several trumps in back, and all small cards, he cannot then even play alone; and having no chance of being called, he must pass with this good hand. On account of which, this method has been thought expedient to remedy this defect of the game; each player having an opportunity of availing himself of the goodness of his game, by adding to the usual method of playing the game that of the mediateur, and the favourite suit.

The first thing to be observed is that of drawing for places, which is done in this manner: One of the players takes four cards; a king, a queen, a knave, and an ace; each player draws one of these cards; and commonly he who comes in last, draws first. The per

son