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LEFT AVONDALE 363 AXIS AVONDALE, a parish of Scotland, in the county Lanark, At the battle of Drumclog, fought near this place June 1, 1679, Grahame of Claverhouse, the famous Viscount Dundee, was defeated by the forces of the Scottish Covenant. A graphic description of this battle is found in Sir Walter Scott's "Old Mor- tality." AWE, LOCH, a lake of Scotland, in Argyleshire, 18 miles N. W. of Inverary. It is 23 miles long, by 3 broad. On one of its many islands stand the magnificent ruins of Kilchurn Castle, for centuries the baronial fortress of the Campbells, Earls of Breadalbane. This lake re- ceives the river Urchan; and at its N. W. extremity rises the great mountain of Ben Cruachan, 3,670 feet in height. AX, or AXE, an instrument for cutting or chopping timber or smaller pieces of wood. As a rule, it is used with both hands, while a hatchet, which is smaller, is intended for one. AXIL, in botany, the angle between the upper side of a leaf and the stem or branch from which it grows. Buds usually grow out from the stem in axils of leaves, and this position is naturally termed axillary. In anatomical termi- nology, the axilla is the armpit. AXIM, an important station and port on the African Gold Coast, a little to the E. of the mouth of th_e Ancobrah river. AXINITE, a triclinic mineral, called also yanolit and thumite. The crystals are broad with their edges sharp. It is found, both in its normal state and al- tered, in Europe and in the United States. AXIOM, a Greek word meaning a de- cision or assumption, is commonly used to signify a general proposition which the understanding recognizes as true, as soon as the import of the words convey- ing it is apprehended. Such a proposi- tion is, therefore, known directly, and does not need to be deduced from any other. Mathematicians used the word axiom to denote those propositions which they must assume as known from some other source than deductive reasoning, and employ in proving all the other truths of the science. The rigor of method requires that no more be as- sumed than are absolutely necessary. Every self-evident proposition, therefore, is not an axiom in this sense, though, of course, it is desirable that every axiom be self-evident; thus, Euclid rests the whole of geometry on 15 assumptions, but he proves propositions that are at least as self-evident as some that he takes for granted. Euclid's assumptions are divided into three postulates, or de- mands, and 12 common notions ; the term axiom is of later introduction. The dis- tinction between axioms and postulates is usually stated in this way: an axiom is "a theorem granted without demon- stration;" a postulate is "a problem granted without construction" — as, to draw a straight line between two given points. AXIS, a straight line, real or imagi- nary, passing through a body, and around which that body revolves, or at least may revolve; also, the imaginary line con- necting the poles of a planet, and around which the planet rotates. In geometry, an imaginary line drawn through a plane figure, and about which the plane figure is supposed to revolve, with the result of defining the limits of a solid. In astronomy the axis of the earth or the axis of rotation of the earth, is that diameter about which it revolves. It is the one which has for its extremities the North and South Poles. The term is similarly used of the sun, the moon, and the planets. The axis of the celestial sphere is the imaginary line around which the heavens appear to revolve. The axis of an orbit is the major axis of the orbit of a planet, the line joining the aphelion and perihelion points. The minor axis is the line perpendicular to the former, and passing through the center of the ellipse. In mechanics, the axis of suspension of a pendulum is the point from which it is suspended, and, consequently, around which it turns. In optics, the axis of a lens is a line passing through the center of its curved, and perpendicular to its plane, surface. In architecture, a spiral axis is the axis of a spirally twisted column. The axis of an Ionic capital is a line passing perpendicularly through the middle of the eye of the volute. In geology an axis is an imaginary line on the opposite sides of -^hich the strata dip in different directions. If the angle formed at their point of junction be a salient one, they form an anticlinal axis, or anticlinal; but, if it is a re- entering one, then they constitute a synclinal axis, or synclinal. In botany, the axis is that part of a plant around which the organs are ssmi- metrically arranged. The ascending axis means the stem. The descending axis is the root, Recessory axes are axes in addition to the main one, found in the stems of calycanthus, chiraonanthus, and some other plants. The appendages of