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 impregnated by quartz, chalcedony and opal, derived from the silica set free by decomposition (kaolinization) of the original felspar. This re-deposited silica forms veins and patches of indefinite shape or may bodily replace a considerable area of the rock by meta somatic substitution. The opal is amorphous, the chalcedony finely crystalline and often arranged in spherulitic growths which yield an excellent black cross in polarized light. The microcrystalline ground-masses are those which can be resolved into their component minerals in thin slices by use of the microscope. They prove to consist essentially of quartz and felspars, which are often in grains of quite irregular shape (microgranitic). In other cases these two minerals are in graphic inter growth, often forming radiate growths of spherulites consisting of fibres of extreme tenuity; this type is known as granophyric. There is another group in which the matrix contains small rounded or shapeless patches of quartz in which many rectangular felspars are embedded; this structure is called micropoikilitic, and though often primary is sometimes developed by secondary changes which involve the deposit of new quartz in the ground-mass. As a whole those quartz-porphyries which have microcrystalline ground-masses are rocks of intrusive origin, Elvan is a name given locally to the quartz-porphyries which occur as dikes in Cornwall; in many of them the matrix contains scales of colourless muscovite or minute needles of blue tourmaline. Fluorite and kaolin appear also in these rocks, and the whole of these minerals are due to pneumatolytic action by vapours permeating the porphyry after it had consolidated but probably before it had entirely cooled.

Many ancient rhyolitic quartz-porphyries show on their weathered surfaces numerous globular projections. They may be several inches in diameter, and vary from this size down to a minute fraction of an inch. When struck with a hammer they may detach readily from the matrix as if their margins were defined by a fissure. If they are broken across their inner portions are often seen to be filled with secondary quartz, chalcedony or agate: some of them have a central cavity, often with deposits of quartz crystals; they also frequently exhibit a succession of rounded cracks or dark lines occupied by secondary products. Rocks having these structures are common in N. Wales and Cumberland; they occur also in jersey, the Vosges and Hungary. It has been proposed to call them pyromérides. Much discussion has taken place regarding the origin of these spheroids, but it is generally admitted that most of them were originally spherulites, and that they have suffered extensive changes through decomposition and silicification.

Many of the older quartz-porphyries which occur in Palaeozoic and Pre-Cambrian rocks have been affected by earth movements and have experienced crushing and shearing. In this way they become schistose, and from their felspar minute plates of sericitic white mica are developed, giving the rock in some cases very much of the appearance of mica-schists. If there have been no phenocrysts in the original rock, very perfect mica-schists may be produced, which can hardly be distinguished from sedimentary schists, though chemically somewhat different on account of the larger amounts of alkalis which igneous rocks contain. When phenocrysts were present they often remain, though rounded and dragged apart while the matrix flows around them. The glassy or felsitic enclosures in the quartz are then very suggestive of an igneous origin for the rock. Such porphyry-schists have been called porphyroids or porphyroid-schists, and in America the name aporhyolite has been used for them. They are well known in some parts of the Alps, Westphalia, Charnwood (England), and Pennsylvania. The hälleflintas of Sweden are also in part acid igneous rocks with a well-banded schistose or granulitic texture.

The quartz-porphyries are distinguished from the rhyolites by being either intrusive rocks or Palaeozoic lavas. All Tertiary acid lavas are included under rhyolites. The intrusive quartz-porphyries are equally well described as granite-porphyries. The palaeozoic effusive quartz-porphyries (or acid lavas) would be called rhyolites by many English petrologists, who regard geological age as of no importance in petrological classifications. But the name quartz-porphyry, though somewhat ambiguous, is so expressive and so firmly established by long-continued use that it cannot be discarded, especially as a descriptive name for the use of field geologists.

 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 (Quassia amara) as a remedy for fever. The original quassia was officially recognized in the London Pharmacopoeia of 1788. In 1809 it was replaced by the bitter wood or bitter ash of Jamaica, Picraena excelsa, 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. Picraena excelsa is a tree 50 to 60 ft. in height, and resembles the common ash in appearance. It has large compound leaves composed of four or five pairs, with a terminal odd one, of short-stalked, oblong, blunt, leathery leaflets, and inconspicuous green flowers. The fruit consists of black shining drupes about the size of a pea. It is found also in other West Indian islands, as Antigua and St Vincent. Quassia amara is a shrub or small tree belonging to the same natural order as Picraena, viz. Simarubaceae, 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 chief constituent is a bitter neutral principle known as quassin. It exists in the wood to the extent of about %. It forms crystalline needles soluble in alkalis, chloroform and zoo parts of water. There is also present a volatile oil. The wood contains no tannin, and for this reason quassia, like chiretta and calumba, may be preserved with iron. The infusion is useful as a bitter tonic—a group of substances of which calumba is the type—and is also a very efficient anthelmintic for the thread worm (Oxyuris vermicularis). It is used by brewers as a substitute for hops.

QUATERNARY, in geology, the time-division which embraces the Pleistocene and Holocene epochs, i.e. the later portion of the Cainozoic era, equivalent to the "Post-Pliocene" or “Post-Tertiary” of certain writers. The term was proposed by J. Desnoyers in 1829 to cover those formations which were formed just anterior to the present. There are other ways of regarding the Quaternary time. Sir A. Geikie (Text Book of Geology, 4th ed., 1903) divides it into an upper, post-glacial or Human period, and a lower, Pleistocene or Glacial period; but he subdivides the former into a Historic and a Prehistoric epoch, a scheme presenting difficulties, for the Palaeolithic or lower stage of prehistoric time cannot really be separated from the (q.v.). E. Kayser Formationskunde, 3rd. ed., 1906), who is in agreement with the definition accepted above, employs a nomenclature which is rarely adopted by British geologists; he divides the Quartarformation (Quartär) into a younger, modern epoch, the Alluvium, and an older epoch, the Pleistocene or Diluvium (＝Glacial). A. de Lapparent, on the other hand (Traité de géologie', 5th ed., 1906), treats the Era moderne or Quaternaire as a great time division equivalent in value to the Tertiary, Secondary, &c., which is so far represented only by a first epoch, the Pleistocene.

QUATERNIONS, in mathematics. The word “quaternion” properly means “ a set of four.” In employing such a word to denote a new mathematical method, Sir W. R. Hamilton was probably influenced by the recollection of its Greek equivalent, the Pythagorean Tetractys (, the number four), the mystic source of all things. Quaternions (as a mathematical method) is an extension, or improvement, of Cartesian geometry, in which the artifices of co-ordinate 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 quaternion 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 will appear later.

History.—The evolution of quaternions belongs in part to each of two weighty branches of mathematical 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