QUART-QUARTERING.

QUARTERMASTER-QUARTER SESSIONS.

The Quartermaster Depart ant of the Army of the United States provides the quarters and transportation of the army; storage and transportation for all army supplies; army clothing; camp and garrison equipage; cavalry and artillery horses; fuel; forage; straw materials for bedding, and stationery. The incidental expenses of the army are paid through the Q. M. Department, and include per diem and extra-duty men; postage on public service; expenses of courts-martial, pursuit and apprehension of deserters, burial of officers and soldiers; expenses of hired escorts, interpreters, spies, and guides, of veterinary surgeons, supply of water at posts, and generally the proper and authorized expenses for the movements and operations of the army not expressly assigned to any other department. The Q. M. Department includes 85 commissioned officers, viz., 1 brigadier-general, 6 colonels, 10 lieutenant-colonels, 15 majors, 37 captains, and 16 military storekeepers.

Ponthieu are similarly quartered on the same monu-coiling ropes, attending to the steering, keeping time ment, and on the crosses erected to Queen Eleanor's by the sand-glasses, &c. memory. The received rule regarding the quartering of the ensigns of different states is, that precedence is given to the most ancient, unless it be inferior in importance. Feudal arms are sometimes quartered in the same way by subjects. 2. Arms of augmentation or special concession accorded to a subject by his sovereign, by way of honour, are sometimes granted to be borne quarterly with the paternal arms. These generally contain a portion of the royal insignia, and have precedence of the paternal coat. 3. The most usual reason for quartering is to indicate descent from an heiress who has intermarried into the family. Where there is but one heiress, her coat occupies the second and | third quarter of the shield, and the paternal arms the first and fourth. Where there are more than one, they are marshalled in the successive quarters in the order of the intermarriages. Where more than four coats have to be marshalled, the number of vertical lines is increased, and the divisions, though more than four, are still called quarters. Where there is an odd number of coats, the last quarter is usually filled up by repeating the first. One of the quarters may itself he quartered, when the heiress was entitled to bear a quartered coat; the shield is then said to be counter-quartered, and its primary quarters are called grand quarters. Quarterings are not allowed to be added to the paternal coat without the sanction of the heraldic authorities.

The expression 'quarterings' is often loosely used for descents in cases where there is no right to quarter from representation. The eight or sixteen quarterings which are sometimes ranged round the Scottish funeral escutcheon, and which are still important for many purposes in Germany, have no reference to representation, but imply purity of blood for four or five generations; i. e., that the father and mother, the two grandmothers, and four great-grandmothers, as also in the case of sixteen quarterings. the eight great-great-grandmothers, have all been entitled to coat-armour.

QUAʼRTERMASTER. In the British Army, the quartermaster-general is a staff-officer of high rank, whose duty it is to arrange the marches, quarters, and internal arrangements of the army to which he belongs. Every army has some officer of this department; from a brigade with a deputy-assistant-quartermaster-general, receiving £173, 7s. 6d. a year, besides regimental pay, up to a complete army under a commander-in-chief, with a quartermaster-general, who is usually a general officer, and receives £691, 19s. 7d. per annum, besides his other pay. At headquarters, there is a permanent quartermaster-general, responsible for all the movements of the army, the organisation of expeditions, camps of instruction,

&c.

QUARTERS, in Naval and Military affairs, are, generally, the positions assigned to persons or bodies of men. In a more special sense, the quarters in the army are the places of lodging assigned to officers or men when not actually on duty. Headquarters is the quarter of the commanding officer of a force, or of a section of a force. The headquarters of the whole British army is at the Horse Guards, where the commander-in-chief has his permanent offices.

In the Navy, quarters has the special meaning of the positions to be taken by every man in actual combat.

QUARTERS, the upright posts of timber-partitions, &c., used for lathing upon. They are generally about 4 or 4 inches by 3 inches, and are placed from 12 to 14 inches or farther apart. In America they are termed studding.

QUARTER SESSIONS, in England, is a court or meeting of justices of the peace, who assemble every quarter of the year, for judicial as well as miscellaneous business. The meetings are fixed by statute to be held in the first full week after December 28, March 31, June 24, and October 11, respectively; often otherwise called the Epiphany, Easter, Trinity, and Michaelmas Sessions. The chief officer of the Court of Quarter Sessions is the custos rotulorum, so called because he is intrusted with the custody of the records and rolls. He is always one of the justices of the peace of the county or riding, nominated by the crown, and appointed by the commission. His deputy is the clerk of the peace, who acts also as clerk to the Court of Quarter Sessions. The jurisdiction of the Court of Quarter Sessions is confined to criminal business, and is very important. It includes all criminal offences whatever, except the highest classes; thus, it has no jurisdiction to try for treason, murder, or capital felony, or blasphemy, perjury, forgery, arson, bigamy, abduction of women or girls, concealment of birth, offences against the Queen's title or the bankrupt laws, bribery, blasphemous, seditious, or defamatory libels, unlawful combinations or conspiracies, stealing or destroying wills or records. Besides its jurisdiction in criminal offences, there are numerous miscellaneous matters of which the Court has cognizance, including appeals from petty

The quartermaster is an officer on the staff of each regiment, in which he holds the relative rank of lieutenant. His duties are to superintend, assign to their respective occupants, and have charge of, quarters, barracks, tents, &c. used by the regiment. He is also regimental storekeeper. He rises, with scarcely an exception, from the ranks, the experience of an old sergeant being considered highly useful in the office. The quartermaster has no further promotion to look forward to; but after 30 years' service in all-sessions, and from justices in special sessions, on a including 10 as an officer-he may retire with the honorary rank of captain. The quartermaster-sergeant is a non-commissioned officer appointed to assist the quartermaster in his various duties.

In the Navy, the quartermasters are certain petty officers appointed in each ship by the captain to have charge of the stowage of ballast and provisions, of

368

great variety of subjects, as to convictions of vagrants, stopping up highways, removal of paupers, &c. The justices who do the work of Quarter Sessions are all unpaid. and thus save the country much expense. They generally choose a chairman of their own body to preside regularly at these courts, which office is considered a great honour,

49

QUARTER-STAFF-QUASSIA.

and is generally given to an able practical man, well versed in business.

This plan, however, of unpaid judges has been found inexpedient in boroughs and large towns, where the justices of the peace, being appointed chiefly from successful tradesmen, are not possessed of the necessary education to secure the efficient performance of like duties. There is therefore appointed for every borough in England a Recorder, who is a barrister, appointed by the Home Secretary, and is paid by salary out of the borough fund-a salary, however, very trifling in amount. His duty is confined to trying prisoners and other judicial business, and he is in fact, in his own person, the Court of Quarter Sessions for boroughs. There is also an exception to unpaid judges of Quarter Sessions in the county of Middlesex, where a barrister is appointed to act in the trial of prisoners, and called the assistant judge, being the official chairman of the Middlesex Sessions. The routine of business at Quarter Sessions consists of the trial of offenders, the trial of appeals, and the hearing of motions upon different subjects. Sometimes a second court sits, consisting of some of the justices appointed by the whole court, whenever the business is unusually heavy. In Scotland, there is also a Court of Quarter Sessions of the peace, held four times a year at the county town-viz., on the first Tuesdays in May, August, and March, and the last Tuesday in October. At these courts, the justices have power to review the sentences of special and petty sessions. But these courts are of a trifling description compared to the courts of the same name in England. In Scotland, the judicial business which in England devolves on Courts of Quarter Sessions, is chiefly disposed of by the sheriff of the county.

QUARTER-STAFF, formerly a favourite weapon with the English for hand-to-hand encounters, was a stout pole of heavy wood, about 6 feet long, shod with iron at both ends. It was grasped in the middle by one hand, and the attack was made by giving it a rapid circular motion, which brought the loaded ends on the adversary at unexpected points. QUARTETT, a piece of music arranged for four voices or instruments, in which all the parts are obligati, i. e., no one can be omitted without injuring the proper effect of the composition. Vocal quartetts are generally accompanied by instruments to sustain the voices. A mere interchange of melody, by which the parts become in turn principal and subordinate, without any interweaving of them, does not constitute a quartett. Quartetts for stringed instruments are generally arranged for two violins, a tenor violin, and violoncello. The most important quartetts have been composed by Haydn, Mozart, Beethoven, Spohr, and Onslow.

QUARTILE. See ASPECTS.

QUA'RTO-DE'CIMANS, those who, after the final decision of the Council of Nicæa, continued to

hold that it was obligatory on Christians to celebrate Easter on the 14th day of the first lunar month near the vernal equinox, whether that 14th day fell on Sunday or not, or who, even before the Council of Nicæa, held the observance of the Jewish Passover to be of obligation. The controversies as to the celebration of Easter have been briefly described under the head EASTER (q. v.).

QUARTZ, a mineral, which is essentially Silicic Acid, or Oxide of Silicon (see SILICON), although it is often combined or mixed with other substances. It is a very abundant and widely-diffused mineral. It is almost the sole constituent of quartz rock, in which gold is far more frequently found than in any other matrix; and it is a principal constituent

of granite, syenite, protogine, eurite, pegmatite, granulite, elvanite, all the different kinds of sandstone, and many other rocks. It is also a common mineral in trap-rocks, limestone, &c., and the sands of the sea-shore and of deserts are chiefly formed of it. It is found both massive and crystallised; the primary form of the crystals is a rhomboid, but it far more frequently occurs in six-sided prisms, terminated by six-sided pyramids; or in six-sided pyramids; or sometimes in dodecahedrons, formed by sixsided pyramids base to base. It is hard enough to scratch glass easily, and it gives fire with steel. It becomes positively electrical by friction; and two pieces, rubbed together, give light in the dark. When pure, it is quite colourless; but, owing to the presence of foreign substances, it often exhibits great variety of colours; and many minerals, known by different names, and consisting chiefly of quartz, have little or nothing to distinguish them but their colour. Thus Rock Crystal, Chalcedony, Carnelian, Cairngorm, Agate, Amethyst, Prase, Chrysoprase, Jasper, &c., are mere varieties of quartz. Opal (q. v.) is very nearly allied to it.

Quartz Rock, or Quartzite, is a sedimentary sandstone, converted into a very hard, compact rock by metamorphic action. It is distinctly granular; the grains, however, seem to melt into each other, or to be enveloped in a homogeneous silicious paste. It is frequently brittle, and in weathering, it breaks up into small irregular cubes.

Quartz Veins occur in metamorphic rocks. The structure of the veins is compact and homogeneous, and very different from that of quartzite. Veins not only differ in width, but the same vein is very variable throughout its course, sometimes thinning to a very fine film, and then swelling out to great thicknesses. Quartz veins are more metalliferous than the mass of the rocks in which they occur. They are the principal natural repositories of gold, for though the precious metal is chiefly obtained from alluvial sands and gravels, these are the weathered and abraded fragments of the under-lying, or neighbouring Paleozoic rocks. Small quantities of gold have been found in the quartz veins traversing the Silurian and Cambrian rocks of Wales and Scotland; and in Victoria, the great veins are so highly auriferous, that they are mined for the precious metal.

Wherever the Lower Silurian

rocks make their appearance on the surface throughout the colony, they are everywhere intersected by enormous numbers of quartz veins, which often reach a thickness of 10 to 15 feet. As yet, only a very small proportion of these have been explored; but the results have been so remunerative, that mining in the solid rock for gold is extensively pursued. One mine has been driven to a depth of 400 feet, and, contrary to the generally-received opinion, the vein at this depth continued to be auriferous.

QUASIMODO SUNDAY, called also DOMINICA The IN ALBIS, the first Sunday after Easter. Introit (1 Peter, ii. 2) of the mass of the day. The name Q. S. is taken from the first words of the name Dominica in Albis is derived from the custom had been baptised at Easter appearing in white which was formerly observed of the neophytes who garments in the church.

It is

QUASS, a sort of weak beer produced in Russia by fermenting rye-meal in warm water. usually bottled in stone bottles, and is a favourite beverage with the people generally. becomes too sour, it is used as vinegar.

When it

QUA'SSIA, a genus of trees and shrubs of the natural order Simarubaceæ (q. v.); having hermaphrodite flowers, with five petals combined into a

QUATERNARY-QUATERNIONS.

tube, and much longer than the small calyx, ten stamens, five germens, and only one style; the fruit composed of five drupes. Q. amara is a native of the tropical parts of America, and of some of the West India Islands. It is a shrub of 10-15 feet high, with racemes of bright-red flowers, and large pinnate leaves, the stalks of which are remarkably winged and jointed. The wood, and particularly that of the root, has a very strong bitter taste, and was at one time much used in medicine under the names of Q.-wood, Bitterwood, &c. The flowers were valued in Surinam for their stomachic properties, as early as the beginning of the 18th c.; the wood of the root began to be known in Europe before the middle of that century, and was more fully brought into notice about 1756, by Rolander, a Swede, who had visited Surinam, and had learned its value from a negro, called Quassi, or Quasha. This negro had employed it with great success as a remedy for fevers, and although, as Rolander says, a very simple man, had acquired a great reputation by his use of it. Linnæus published a dissertation on it in 1763, and it was he who gave to the genus the name Quassia, from the name of the slave by whom its medicinal qualities had been made known. The true Q. is now, however, little used; its name having been transferred to the Bitterwood (q. v.) of the West Indies, Picrana (or Simaruba) excelsa, a lofty tree, the wood of which possesses the same properties, although in an inferior degree; but this inferiority is compensated by the greater facility with which any requisite supply is obtained. It is the wood of this tree which is now sold as Q.-wood, or Q.-chips, in the shops. It is used to a considerable extent instead of hops for making beer, although the use of it is illegal in Britain, and beer made with it is said to become muddy and flat, and not to keep. Q.-wood is narcotic, and a decoction of it is used for killing flies. Cabinet-work made of it is safe from all attacks of insects. In medicine, it is a valuable tonic; but in fevers, it is not to be compared with Peruvian bark and its alkaloids. Its properties depend chiefly on a bitter principle, called Quassite or Quassin.

QUATERNARY, a term employed by some French and English geologists to characterise the Post-tertiary strata, which they group together into an epoch of equal value with the three great divisions of Primary, Secondary, and Tertiary. The deposits included under the name will be found described under the Pleistocene and Recent strata, to which we refer the reader.

QUATE'RNIONS, the name given by its inventor, Sir W. R. Hamilton (q. v.), to one of the most remarkable of the mathematical methods or calculi, which have so enormously extended the range of analysis, while simplifying its application to the most formidable problems in geometry and physics.

It would be inconsistent with our plan to give even a complete though elementary analytical view of this calculus; but it is possible, by means of elementary geometry and algebra alone, to give the reader a notion of its nature and value.

For this purpose, it will be necessary to consider some very simple, but important, ideas with reference to the relative position of points in space. Suppose A and B to be any two stations, one, for instance, at the top of a mountain, the other at the bottom of a coal-pit. Upon how many distinct numbers does their relative position depend? This can be easily answered thus: B is so many degrees of longitude to the east or west of A, so many degrees of latitude to the north or south of A, and so many feet above or below the level of A. THREE

numbers suffice, according to this mode of viewing the question, to determine the position of B when that of A is given. Looking at it from another point of view, suppose A to be the earth, B a fixed star. To point a telescope at B, we require to know its altitude and azimuth, its latitude and longitude, or its right ascension and declination. Any of these pairs of numbers will give us the direction of the line AB, but to determine absolutely the position of B, we require a third number-viz., the length of AB. Hence, it appears that any given line AB, of definite length and direction, is completely determined by three numbers. Also, if the line ab be parallel and equal to AB, it evidently depends on the same three numbers. Hence, if we take the expression (AB) to denote (not, as in geometry, the length of AB merely, but) the length and direction of AB; we see that there will be no error introduced, if we use it in the following sense: A + (AB) B;

i. e., if, beginning with A, we take the step repre-
sented by (AB), we shall find ourselves at B. From
this it follows at once that, if C be any third point,
A + (AB) + (BC) C ;

i. e., beginning at A, and taking the successive steps
(AB) and (BC), we are finally brought to C. But
we have also
*A + (AC) C,

by taking the step from A to C at once. Hence,
with the present signification of (AB) &c., we see
(AB) + (BC) = (AC),

that

and therefore (AC)

- (CA),

(CA), or the sign (only) of a vector is changed if its direction be reversed. The rules for the addition, and therefore for the subtraction, of vectors are thus extremely simple; and, without any further preface, we are in a position to solve a great many geometrical problems, some of which are of no common difficulty. A comparatively simple one must suffice; let us prove Euclid I., 33; i. e., if AB be parallel and equal to CD, AC is parallel and equal to BD. In vectors, given (AB) (CD), prove (AC) (BD). We have by the course A, B, D, C at once, by going directly from A to C, and then

(AC) = (AB) + (BD) + (DC).

But (AB) (CD) (DC) by what we have just proved. Hence the first and third terms of the expression for (AC) are equal and of opposite signs,

and therefore

(AC) (BD).

This example has been chosen from its simplicity, and gives an extremely inadequate idea of the grasp which vectors take in common geometry.

So far, we have not advanced much beyond common geometrical methods; but we now come to the step in which quaternions proper are introduced, a vector being merely a degraded species

of

QUATERNIONS-QUATRE-BRAS.

quaternion. This new step contains Hamilton's
answer to the question, answered over and over
again during the last fifty years in forms of the
most uncouth complexity, How to express the pro-
duct, or the quotient, of two vectors, or directed lines.'
In other words, keeping to one part of the question
only, what is the nature of the factor q in the
equation
(AC) = q(AB),

where A, B, C are any three points?

Let us first consider on how many independent numbers does it depend? It might at first sight appear to depend on six, for (AB) and (AC), as we have already seen, each contain three. But let us analyse the process of passing from the one vector to the other, much as we have already analysed the vector step of passing from one point to another. To simplify the idea of the process, let us suppose it to be effected by a species of rotation. First, ле

C

then, in order that
(AB) may be turned
so as to coincide in
direction with (AC),
it must be turned
about an axis per-
pendicular
the
to
plane of the triangle
ABC, and through an
angle BAC.
Now,

the direction of а

multiplier, changes one of these lines into the other. This result we must assume; as its proof, though not in any sense difficult, would require the free use of analytical symbols to condense it within our assigned limits. Hence, three vectors, each of unit length, and each perpendicular to the other two, have the property that the product of any two, taken in the proper order, is the third. For illus tration, suppose these to be drawn eastwards, northwards, and upwards, and let them be reprerespectively; we have the following equations sented (according to Hamilton's notation) by i, j, k

among them:

i.jk, j.ki, k.i=j;

where it is to be observed that the order of the alphabet is maintained throughout. Also, as before, we see that i'j' = k ·

1.

laid hold of to turn the whole system about one of
Considering them, for a moment, as handles to be
them, we see that i turns j into the position of k;
that is, the operation i may be effected by a left.
handed quadrantal rotation about the eastward
line i. What, then, is the result, upon the vector
i, of the rotation symbolised by j? Laying hold
of the northward line j, use it as
an axis of
left-handed quadrantal rotation, and the effect on
the system will be not only (as above, jk = i)
to make the upward line an eastward one, but
to make the eastward line a downward one; in
symbols,

line depends on two numbers, as we
we have seen
above; hence we have two for the direction of
the axis, and one for the angle through which AB
is turned. But AB and AŬ are not, in general, Comparing this with
of equal length; hence, after their directions
have by turning been made coincident, AB must
be compressed or stretched till its length is the
same as that of AC. Thus, a fourth number is
required for the complete description of the process,
and therefore 9 depends upon four independent
numerical quantities; hence its name, quaternion.
A similar investigation, but somewhat less elemen-
tary, shews that the product of two vectors also
depends on four distinct numbers. This will be
proved analytically further on in the article.

Now, suppose AB and AC to be equal to each other, and at right angles; and suppose

The particular quaternion, therefore, which turns a vector through 90° without altering its length, has its square equal to 1. Though, of course, they are essentially a real geometrical conception, this result shews how closely quaternions are connected with what are called Imaginary Quantities (q. v.) in analytical geometry and algebra.

Now, it is found, by a careful examination of all the consequences involved, that we are at liberty to represent by a vector of unit length, perpendicular to the plane of two equal lines at right angles to each other, the quaternion which, employed as a

j.ik.

i.j=k,

we see that in quaternions, the Commutative Law of Multiplication does not hold; i. e., that the product and algebra, but upon the order in which the mul depends not only on the factors, as in arithmetic tiplication is effected. This is, of course, a little perplexing to the beginner, but is easily got over; and the mere consideration of this fact is often sufficient for the proof of theorems regarded in general as of no ordinary difficulty.

reader to Sir W. R. Hamilton's Lectures on QuaterFor further information, we must refer the nions, and his Elements of Quaternions (1866). Some elementary information may also be derived from papers by Kelland and Tait in the Quarterly Messenger of Mathematics, and the Quarterly Mathematical Journal. The subject is yet in its infancy, but even now its power is herculean; and its extreme simplicity and generality recommend it to all who are desirous of extending the effective range of mathematical analysis.

QUA'TRAIN (Fr. quatre, four) is the name given (originally by the French) to a little poem of four verses (lines) rhyming alternately, or even sometimes to four verses of a longer poem, such as a sonnet, if they form a complete idea within themselves. Epigrams, epitaphs, proverbs, &c., are often expressed in quatrains.

QUATRE-BRAS (Four Arms), a village of Belgium, province of South Brabant, about ten miles south-south-east of Waterloo. It is situated at the intersection of the great roads from Brussels to Charleroi, and from Nivelles to Namur, whence its name. On the 16th of June 1815-two days before the battle of Waterloo, Q. was the scene of a desperate and sanguinary battle between the English under Wellington and the French under Ney. The honours of the field remained with the former; but the severe defeat of Blücher the same day at Ligny, rendered Wellington's hard won victory almost