AXINITE

axinite, a mineral consisting of a complex aluminium and calcium boro-silicate with a small amount of basic hydrogen; the calcium is partly replaced in varying amounts by ferrous iron and manganese, and the aluminium by ferric iron: the formula is hca_3bal_2(sio_4)_4. the mineral was named (from [greek: axine], an axe) by r. j. hauy in 1799, on account of the characteristic thin wedge-like form of its anorthic crystals. the colour is usually clove-brown, but rarely it has a violet tinge (on this account the mineral was named yanolite, meaning violet stone, by j. c. delametherie in 1792). the best specimens are afforded by the beautifully developed transparent glassy crystals, found with albite, prehnite and quartz, in a zone of amphibolite and chlorite-schists at le bourg d'oisans in dauphine. it is found in the greenstone and hornblende-schists of batallack head near st just in cornwall, and in diabase in the harz; and small ones in maine and in northampton county, pennsylvania, u.s.a. large crystals have also been found in japan. in its occurrence in basic rather than in acid eruptive rocks, axinite differs from the boro-silicate tourmaline, which is usually found in granite. the specific gravity is 3.28. the hardness of 6 1/2-7, combined with the colour and transparency, renders axinite applicable for use as a gemstone, the dauphine crystals being occasionally cut for this purpose. (l. j. s.) axiom (gr. [greek: axioma]), a general proposition or principle accepted as self-evident, either absolutely or within a particular sphere of thought. each special science has its own axioms (cf. the aristotelian [greek: archai], "first principles") which, however, are sometimes susceptible of proof in another wider science. the greek word was probably confined by plato to mathematical axioms, but aristotle (_anal. post._ i. 2) gave it also the wider significance of the ultimate principles of thought which are behind all special sciences (_e.g._ the principle of contradiction). these are apprehended solely by the mind, which may, however, be led to them by an inductive process. after aristotle, the term was used by the stoics and the school of ramus for a proposition simply, and bacon (_nov. organ._ i. 7) used it of any general proposition. the word was reintroduced in modern philosophy probably by rene descartes (or by his followers) who, in the search for a definite self-evident principle as the basis of a new philosophy, naturally turned to the familiar science of mathematics. the axiom of cartesianism is, therefore, the _cogito ergo sum_. kant still further narrowed the meaning to include only self-evident (intuitive) synthetic propositions, _i.e._ of space and time. the nature of axiomatic certainty is part of the fundamental problem of logic and metaphysics. those who deny the possibility of all non-empirical knowledge naturally hold that every axiom is ultimately based on observation. for the euclidian axioms see geometry. axis (lat. for "axle"), a word having the same meaning as axle, and also used with many extensions of this primary meaning. it denotes the imaginary line about which a body or system of bodies rotates, or a line about which a body or action is symmetrically disposed. in geometry, and in geometrical crystallography, the term denotes a line which serves to aid the orientation of a figure. in anatomy, it is, among other uses, applied to the second cervical vertebra, and in botany it means the stem. axle (in mid. eng. _axel-tre_, from o. norweg. _oxull-tre_, cognate with the o. eng. _aexe_ or _eaxe_, and connected with sansk. _aksha_, gr. [greek: axon], and lat. _axis_), the pin or spindle on which a wheel turns. in carriages the axle-tree is the bar on which the wheels are mounted, the axles being strictly its thinner rounded prolongations on which they actually turn. the pins which pass through the ends of the axles and keep the wheels from slipping off are known as axle-pins or "linch-pins," "linch" being a corruption, due to confusion with "link," of the old english word for "axle," _lynis_, cf. ger. _luense_.