160 Q U A Q U A brought in accordance with either the Act giving the appeal or the Summary Jurisdiction Act. There is no appeal from quarter sessions on the facts, but their decision may be reviewed by the High Court of Justice by means of ccrtiorari, mandamus, prohibition, or a case stated under 12 & 13 Viet. c. 45, 11. A case may be stated for the opinion of the court of criminal appeal under 11 & 12 Viet. c. 78, 1. Ireland. In Ireland the chairman of quarter sessions is a salaried professional lawyer, and has important civil jurisdiction corresponding very much to that of a county court judge in Eng- land. His jurisdiction depends chiefly upon 14 & 15 Viet. c. 57. The recorders of Dublin and Cork are judges of the civil bill courts in those cities. Scotland. In Scotland quarter sessions were established by the Act 1661, c. 338, under which justices were to meet on the first Tuesday of March, May, and August, and the last Tuesday of October to "administrate justice to the people in things that are within their jurisdiction and punish the guilty for faults and crimes done and committed in the preceding quarter." The jurisdiction of quarter sessions in Scotland is more limited than in England, much of what would be quarter-sessions work in Eng- land being done by the sheriff or the commissioners of supply. Quarter sessions have appellate jurisdiction in poaching, revenue, and licensing cases, and under the Pawnbrokers and other Acts. All appeals from proceedings under the Summary Jurisdiction Acts are taken to the High Court of Justiciary at Edinburgh or on circuit (44 & 45 Viet. c. 33). The original jurisdiction of quarter sessions is very limited, and almost entirely civil. Thus they have power to divide a county and to make rules for carrying into effect the provisions of the Small Debts Act, 6 Geo. IV. c. 48. The decision of quarter sessions may be reviewed by advocation, suspension, or appeal. United States. In the United States courts of quarter sessions exist in many of the States ; their jurisdiction is determined by State legislation, and extends as a rule only to the less grave crimes. They are in some States constituted of professional judges. QUARTZ, the name of a mineralogical species which includes nearly all the native forms of silica. It thus embraces a great number of distinct minerals, several of which are cut as ornamental stones or otherwise used in the arts. For a general description of the species, see MINERALOGY, vol. xvi. p. 389 ; and for its chief varieties, see AGATE, vol. i. p. 277 ; AMETHYST, vol. i. p. 736 ; FLINT, vol. ix. p. 325 ; and JASPER, vol. xiii. p. 596. The crystallography of quartz has been fully investigated by Des Cloizeaux in his classical Memoire sur la cristal- lisation et la structure interieure du Quartz, Paris, 1855. QUASSIA, the generic name given by Linnaeus to a small tree of Surinam in honour of the negro Quassi or Coissi, who employed the intensely bitter bark of the tree as a remedy for fever. This bark was introduced into European medicine about the middle of the last century, and was officially recognized in the London Pharmacopoeia of 1788. In 1809 it was replaced by the bitter wood or bitter ash of Jamaica, Picrsena excelsa, Lindl., which was found to possess similar properties and could be obtained in pieces of much larger size. Since that date this wood has continued in use in Britain under the name of quassia to the exclusion of the Surinam quassia, which, however, is still employed in France and Germany. Picr&na ex- celsa, Lindl. (Quassia excelsa, Swartz) is a tree 50 to 60 feet in height, and resembles the common ash in appear- ance. It has imparipinnate leaves composed of four or five pairs of short-stalked, oblong, blunt, leathery leaflets, and inconspicuous green flowers. The fruit consists of shining drupes about the size of a pea. It is found also in Antigua and St Vincent. Quassia amara, L., is a shrub or small tree belonging to the same natural order as Picrxna, viz., Simarubacex, but is readily distinguished by its large handsome red flowers arranged in terminal clusters. It is a native of Panama, Venezuela, Guiana, and northern Brazil Jamaica quassia is imported into England in logs several feet in length and often nearly one foot in thickness, consisting of pieces of the trunk and larger branches. The thin greyish bark is usually removed. The wood is nearly white, or of a yellowish tint, but sometimes exhibits blackish markings due to the mycelium of a fungus. The wood has a pure bitter taste, and is without odour or aroma. It is usually to be met with in the form of turnings or raspings, the former being obtained in the manufacture of the " bitter cups " which are made of this wood. The medicinal properties are due to the presence of quassiin (first obtained by Winckler in 1835), which exists in the wood to the extent of T jth P er cent. It is a neutral crystalline substance, soluble in hot dilute alcohol and chloroform and in 200 parts of water. It is also readily soluble in alkalies, and is reprecipitated by acids. It is almost insoluble in ether, and forms an insoluble compound with tannin. Quassia is used in medicine in the form of infusion and tincture as a pure bitter tonic and febrifuge, and in consequence of contain- ing no tannin is often prescribed in combination with iron. An infusion of the wood sweetened with sugar is also used as a fly poison, and forms an effectual injection for destroying thread worms. Quassia also forms a principal ingredient of several " hop substitutes," for which use it was employed as long ago as 1791, when John Lindsay, a medical practitioner in Jamaica, wrote that the bark was exported to England ' ' in considerable quantities for the purposes of brewers of ale and porter." QUATERNIONS. The word quaternion properly means "a set of four." In employing such a word to denote a new mathematical method, Sir W. R. HAMILTON (q.v.) was probably influenced by the recollection of its Greek equivalent, the Pythagorean Tetractys, the mystic source of all things. Quaternions (as a mathematical method) is an exten- sion, or improvement, of Cartesian geometry, in which the artifices of coordinate axes, &c., are got rid of, all directions in space being treated on precisely the same terms. It is therefore, except in some of its degraded forms, possessed of the perfect isotropy of Euclidian space. From the purely geometrical point of view, a quater- nion may be regarded as the quotient of two directed lines in space or, what comes to the same thing, as the factor, or operator, which changes one directed line into another. Its analytical definition cannot be given for the moment ; it will appear in the course of the article. History of the Method. The evolution of quaternions belongs in part to each of two weighty branches of mathe- matical history the interpretation of the imaginary (or impossible) quantity of common algebra, and the Cartesian application of algebra to geometry. Sir W. R. Hamilton was led to his great invention by keeping geometrical applications constantly before him while he endeavoured to give a real significance to ^/ - 1. We will therefore confine ourselves, so far as his predecessors are concerned, to attempts at interpretation which had geometrical appli- cations in view. One geometrical interpretation of the negative sign of algebra was early seen to be mere reversal of direction along a line. Thus, when an image is formed by a plane mirror, the distance of any point in it from the mirror is simply the negative of that of the corresponding point of the object. Or if motion in one direction along a line be treated as positive, motion in the opposite direction along the same -line is negative. In the case of time, measured from the Christian era, this distinction is at once given by the letters A.D. or B.C., prefixed to the date. And to find the position, in time, of one event relatively to another, we have only to subtract the date of the second (taking account of its sign) from that of the first. Thus to find the interval between the battles of Marathon (490 B.C.) and Waterloo (1815 A.D.) we have + 1815 - ( - 490) - 2305 years. And it is obvious that the same process applies in all cases in which we deal with quantities which may be regarded as of one directed dimension only, such as dis- tances along a line, rotations about an axis, &c. But it
