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 right angles; “conjugate diameters” are such that each bisects chords parallel to the other. The diameter of a quadric surface is a line at the extremities of which the tangent planes are parallel. Newton defined the diameter of a curve of any order as the locus of the centres of the mean distances of the points of intersection of a system of parallel chords with the curve; this locus may be shown to be a straight line. The word is also used as a unit of linear measurement of the magnifying power of a lens or microscope.

In architecture, the term is used to express the measure of the lower part of the shaft of a column. It is employed by Vitruvius (iii. 2) to determine the height of a column, which should vary from eight to ten diameters according to the intercolumniation: and it is generally the custom to fix the lower diameter of the shaft by the height required and the Order employed. Thus the diameter of the Roman Doric should be about one-eighth of the height, that of the Ionic one-ninth, and of the Corinthian one-tenth (see ).

 DIAMOND, a mineral universally recognized as chief among precious stones; it is the hardest, the most imperishable, and also the most brilliant of minerals. These qualities alone have made it supreme as a jewel since early times, and yet the real brilliancy of the stone is not displayed until it has been faceted by the art of the (q.v.); and this was scarcely developed before the year 1746. The consummate hardness of the diamond, in spite of its high price, has made it most useful for purposes of grinding, polishing and drilling. Numerous attempts have been made to manufacture the diamond by artificial means, and these attempts have a high scientific interest on account of the mystery which surrounds the natural origin of this remarkable mineral. Its physical and chemical properties have been the subject of much study, and have a special interest in view of the extraordinary difference between the physical characters of the diamond and those of graphite (blacklead) or charcoal, with which it is chemically identical, and into which it can be converted by the action of heat or electricity. Again, on account of the great value of the diamond, much of the romance of precious stones has centred round this mineral; and the history of some of the great diamonds of historic times has been traced through many extraordinary vicissitudes.

The name , “the invincible,” was probably applied by the Greeks to hard metals, and thence to corundum (emery) and other hard stones. According to Charles William King, the first undoubted application of the name to the diamond is found in Manilius ( 16),—Sic Adamas, punctum lapidis, pretiosior auro,—and Pliny ( 100) speaks of the rarity of the stone, “the most valuable of gems, known only to kings.” Pliny described six varieties, among which the Indian, having six pointed angles, and also resembling two pyramids (turbines, whip-tops) placed base to base, may probably be identified as the ordinary octahedral crystal (fig. 1). The “diamond” (Yahalom) in the breastplate of the high priest (Ex. xxxix. 11) was certainly some other stone, for it bore the name of a tribe, and methods of engraving the true diamond cannot have been known so early. The stone can hardly have become familiar to the Romans until introduced from India, where it was probably mined at a very early period. But one or other of the remaining varieties mentioned by Pliny (the Macedonian, the Arabian, the Cyprian, &c.) may be the true diamond, which was in great request for the tool of the gem-engraver. Later Roman authors mentioned various rivers in India as yielding the Adamas among their sands. The name Adamas became corrupted into the forms adamant, diamaunt, diamant, diamond; but the same word, owing to a medieval misinterpretation which derived it from adamare (compare the French word aimant), was also applied to the lodestone.

Like all the precious stones, the diamond was credited with many marvellous virtues; among others the power of averting insanity, and of rendering poison harmless; and in the middle ages it was known as the “pietra della reconciliazione,” as the peacemaker between husband and wife.

Scientific Characters.—The majority of minerals are found most commonly in masses which can with difficulty be recognized as aggregates of crystalline grains, and occur comparatively seldom as distinct crystals; but the diamond is almost always found in single crystals, which show no signs of previous attachment to any matrix; the stones were, until the discovery of the South African mines, almost entirely derived from sands or gravels, but owing to the hardness of the mineral it is rarely, if ever, water-worn, and the crystals are often very perfect. The crystals belong to the cubic system, generally assuming the form of the octahedron (fig. 1), but they may, in accordance with the principles of crystallography, also occur in other forms symmetrically derived from the octahedron,—for example, the cube, the 12-faced figure known as the rhombic dodecahedron (fig. 2), or the 48-faced figure known as the hexakis-octahedron (fig. 3), or in combinations of these. The octahedron faces are usually smooth; most of the other faces are rounded (fig. 4). The cube faces are rough with protruding points. The cube is sometimes found in Brazil, but is very rare among the S. African stones; and the dodecahedron is perhaps more common in Brazil than elsewhere. There is often a furrow running along the edges of the octahedron, or across the edges of the cube, and this indicates that the apparently simple crystal may really consist of eight individuals meeting at the centre; or, what comes to the same thing, of two individuals interpenetrating and projecting through each other. If this be so the form of the diamond is really the tetrahedron (and the various figures derived symmetrically from it) and not the octahedron. Fig. 5 shows how the octahedron with furrowed edge may be constructed from two interpenetrating tetrahedra (shown in dotted lines). If the grooves be left out of account, the large faces which have replaced each tetrahedron corner then make up a figure which has the aspect of a simple octahedron. Such regular interpenetrations are known in crystallography as “twins.” There are also twins of diamond in which two octahedra (fig. 6) are united by contact along a surface parallel to an octahedron face without interpenetration. On account of their resemblance to the twins of the mineral spinel (which crystallizes in octahedra) these are known as “spinel twins.” They are generally flattened along the plane of union. The crystals often display triangular markings, either elevations or pits, upon the octahedron faces; the latter are particularly well defined and have the form of equilateral triangles (fig. 7). They are similar to the “etched figures” produced by moistening an octahedron of alum, and have probably been produced, like them, by the action of some solvent. Similar, but somewhat different markings are produced by the combustion of diamond in oxygen, unaccompanied by any rounding of the edges.

Diamond possesses a brilliant “adamantine” lustre, but this tends to be greasy on the surface of the natural stones and gives 