Page:The New International Encyclopædia 1st ed. v. 02.djvu/384

AXINITE. Europe, notably Dauphiné, France, and Scopi, Switzerland, where the crystals are cut into beautiful brown gems. It has been found in the United States near Bethlehem, Pa., and in Maine, but in crystals that are too small for cutting.

AXIN'OMAN'CY (Gk. ἀξίνη, axinē, axe + μαντεία, manteia, divination). A kind of divination practiced in ancient times by means of an axe. The ancients tell us nothing with regard to its method or its use. See.

AX'IOM (Gk. ἀξίωμα, axiōma, that which is thought worthy, fit, self-evident). A general statement, the truth of which is accepted without proof. Plato probably limited it to geometric propositions, but Aristotle applied it to statements of a more general nature. Euclid followed Aristotle's use of the term, regarding axioms as 'common notions' not limited to geometry, and applying the term postulate to a premise specifically geometric in character. The early English translators of Euclid failed to consult the most trustworthy sources, and hence the terms axiom and postulate have come to be confused. Heiberg, the latest and best editor of the Elements, has made clear the distinction which Euclid recognized, and has shown that he gave five axioms and five postulates. Euclid regarded as an axiom that, "If equals be added to equals, the sums are equal;" as a postulate that (stated in simpler language than his), "Through a given point only one line can be drawn parallel to a given line." The first statement is general, the second is specifically geometric. Mathematicians formerly sought to limit the list of axioms and postulates to the smallest number upon which the subject in question, as geometry, could be built; the modern tendency is rather to seek a list, however extended, of the really independent properties of space. To the followers of Kant seems due the common definition of axiom as 'a self-evident truth,' a definition no longer recognized as valid. See and.

AX'IS (Lat. axis, axle). In mathematics, a line of reference called by various names, according to its different uses. In geometry, a line which bisects at right angles the lines joining corresponding points in symmetric systems is called an axis of symmetry; e.g. the altitude of an isosceles triangle. An axis of a geometric solid is a diameter about which the points of the solid are symmetrically distributed; e.g. the diameters of spheres and ellipsoids. Axes of coördinates are the lines of reference from which the coördinates are measured. (See .) The radical axis of two circles is the line joining their points of intersection; the line is real, even when the circles cut in imaginary points. The transverse axis of a conic is the diameter which passes through the foci. The conjuqate axis is the line through the origin perpendicular to the transverse axis.

In physics, the optic axis of a lens is the straight line passing through its optical centre and perpendicular to its surfaces. The axis of a telescope is the straight line joining the centres of its lenses (objective and ocular). The axis of rotation is a straight line which remains at rest while a body rotates around it, as the line joining the poles of the earth.

AXIS (Lat., of unknown origin). A species of deer (Cervus axis) abundant throughout India and in many islands of the Eastern Archipelago. One of its Indian names is chittra, and by British sportsmen in India it is generally called the spotted hog-deer. It was known to the ancients as axis. The axis resembles in size and color the European fallow-deer; it is generally of a rich fawn color, beautifully spotted with white, nearly black along the back, the under parts snow-white. The horns are slender, sharp-pointed, little branched, and not at all palmated. The female has no horns. The axis frequents thick jungles in the vicinity of water, and feeds during the night. It is commonly found in herds of 15 or 20, of which three or four are males. Its sense of smell is remarkably acute, and it is generally very shy and timid, so that sportsmen find it difficult to get within shot. The male, however, sometimes exhibits great courage in defense of the young. It is very easily domesticated, is gentle in its manners, and breeds freely in captivity, so that it is commonly seen in zoölogical parks. See colored plate of.

In architecture, axis is either the temporary central line used in making drawings or the imaginary central line of a building. Sometimes buildings have a curved axis, sometimes several have a common axis. The relation of the axis of neighboring monumental structures has always been a matter of careful study in architectural history.

AXIS. See.

AX'LE (Ger. Achse[l], dim. of form found in Lat. axis). The bar of metal or wood which carries the wheel or wheels of vehicles or of machinery, and around which the wheel or wheels revolve, sometimes with the axle and sometimes upon it. Axles for wagons are made of iron or wood and are fixed, the wheels revolving around them. Axles of Railway cars have the wheels keyed to them and revolve with the wheels, the ends of the axle projecting outside of the wheels, and turning in journal-boxes on which the body of the car rests. Railway axles are forged from steel of high quality and have the wheels forced upon a taper wheel-fit by hydraulic pressure. The projecting ends or journals are turned and finished smooth. Standard dimensions of axles for cars of different weights have been adopted in the United States by the American Master Car Builders' Association. See.

AX'MINSTER (AS. Axan Mynster, minster of the [river] Axe). A market-town in Devonshire, England, on the Axe, 24 miles east-northeast of Exeter. Axminster was once famous for the manufacture of a superior grade of carpets (Map: England, D 6). Population, in 1891, 4000: in 1901, 4100.

AXOLOTL, aks'61ot'l (Mex.). Any of several species of larval salamanders of the genus Amblystoma. They inhabit certain lakes of Mexico and the Rocky Mountain region of the United States. Its eggs resemble frogs' eggs, being laid in strings formed by a viscous covering, and attached to water-plants. They hatch in from two to three weeks. The young axolotl has external bushy gills, much like those that are retained throughout life by the mud-puppy (q.v.). It may become sexually mature while still bearing the external gills, and before its life-history was known it had been given the name Siredon lichenoides. The passage of the axolotl into an Amblystoma first became known to science in 1865,