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GONIOMETER (from Gr. ytavia, angle, a...
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See also:GONIOMETER (from Gr. ytavia, See also:angle, and d rpov, measure) , an See also:instrument for measuring the angles of crystals; there are two kinds—the contact goniometer and the reflecting goniometer. Nicolaus Stena in 1669 determined the interfacial angles of See also:quartz crystals by cutting sections perpendicular to the edges, the See also:plane angles of the sections being then the angles between the faces which are perpendicular to the sections. The earliest instrument was the contact goniometer devised by Carangeot in 1783. The Contact Goniometer (or See also:Hand-Goniometer).—This consists of two See also:metal rules pivoted together at the centre of a graduated semi-circle (fig. I). The instrument is placed with its plane perpendicular to an edge between two faces of the crystal to be measured, and the rules are brought into contact with the faces; this is best done by holding the crystal up against the See also:light with the edge in the See also:line of sight. The angle between the rules, as read on the graduated semi-circle, then gives, the angle between the two faces. The rules are slotted, so that they may be shortened and their tips applied to a crystal partly embedded in its See also:matrix. The instrument represented in fig. 1 is practically the same in all its details as that made for Carangeot, and it is employed at the See also:present See also:day for the approximate measurement of large crystals with dull and rough faces. S. L. Penfiekl (1900) has devised some cheap and See also:simple forms of contact goniometer, consisting of jointed arms and protractors made of cardboard or cellulsid. The Reflecting Goniometer.—This is an instrument of far greater precision, and is always used for the accurate measurement of the angles when small crystals with See also:bright faces are available. As a See also:rule, the smaller the crystal the more even are its faces, and when these are smooth and bright they reflect sharply defined images of a bright See also:object. By turning the crystal about an See also:axis parallel to the edge between two faces, the See also:image reflected from a second See also:face may be brought into the same position as that formerly occupied by the image reflected from the first face; the angle through which the crystal has been rotated, as determined by a graduated circle to which the crystal is fixed, is the angle between the normals to the two faces. Several forms of See also:instruments depending on this principle have been devised, the earliest being the See also:vertical-circle goniometer of W. H. See also:Wollaston, made in 1809. This consists of a circle m (fig. 2), graduated to degrees of arc and See also:reading with the See also:vernier h to minutes, which turns with the milled See also:head t about a See also:horizontal axis. The crystal is attached with See also:wax (a mixture of bees- FIG. 2.—Vertical-Circle Goniometer. wax and See also:pitch) to the holder q, and by means of the pivoted arcs it may be adjusted so that the edge between two faces (a See also:zone-axis) is parallel to, and coincident with, the axis of the instrument. The crystal-holder and See also:adjustment-arcs, together with the milled head s, are carried on an axis which passes through the hollow axis of the graduated circle, and may thus be rotated independently of the circle. In use, the goniometer is placed directly opposite to a window, with its axis parallel to the horizontal window-bars, and as far distant as possible. The See also:eye is placed quite See also:close to the crystal, and the image of an upper window-See also:bar (or better still a slit in a dark See also:screen) as seen in the crystal-face is made to coincide with a See also:lower window-bar (or See also:chalk See also:mark on the See also:floor) as seen directly: this is done by turning the milled head s, the reading of the graduated circle having previously been observed. Without moving the eye, the milled head t, together with the crystal, is then rotated until the image from a second face is brought into the same position; the difference between the first and second readings of the graduated circle will then give the angle between the normals of the two faces. Several improvements have been made on Wollaston's goniometer. The adjustment-arcs have been modified; a See also:mirror of See also:black See also:glass fixed to the stand beneath the crystal gives a reflected image of the See also:signal, with which the reflec- C tion from the crystal can be more conveniently made to coincide; a See also:telescope provided with See also:cross-wires gives greater precision to the direction of the reflected rays of light; and with the telescope a collimator has sometimes been used. A still greater improvement was effected by placing the graduated circle in a horizontal position, as in the instruments of E. L. See also:Malus (181o), F. C. von Riese (1829) and J. Babinet (1839). Many forms• of the horizontal-circle goniometer have been constructed; they are provided with a telescope and collimator, and in construction are essentially the same as a spectrometer, with the addition of arrangements for adjusting and centring the crystal. The instrument shown in fig. 3 is made by R. Fuess of See also:Berlin. It has four concentric axes, which enable the crystal-holder A, together with the adjustment-arcs B and centring-slides D, to be raised or lowered, or to be rotated independently of the circle H; further, either the crystal-holder or the telescope T may be rotated with the circle, while the other With a one-circle goniometer, such as is described above, it is necessary to See also:mount and re-adjust the crystal afresh for the measurement of each zone of faces (i.e. each set of faces intersecting in parallel edges) ; with very small crystals this operation takes a considerable See also:time, and the See also:minute faces are not readily identified again. Further, in certain cases, it is not possible to measure the angles between zones, nor to determine the position of small faces which do not See also:lie in prominent zones on the crystal. These difficulties have been overcome by the use of a two-circle goniometer or See also:theodolite-goniometer, which as a See also:combination of a vertical-circle goniometer and one with a horizontal-circle was first employed by W. H. See also:Miller in 1874. See also:Special forms have been designed by E. S. Fedorov (1889), V. See also:Goldschmidt (1893), S. Czapski (1893) and F. Stoeber (1898), which differ mainly in the arrangement of the See also:optical parts. In these instruments the crystal is set up and adjusted once for all, with the axis of a prominent zone parallel to the axis of either the horizontal or the vertical circle. As a rule, only in this zone can the angles between the faces be measured directly; the positions of all the other faces, which need be observed only once, are fixed by the simultaneous readings of the two circles. These readings, corresponding to the polar distance and See also:azimuth, or See also:latitude and See also:longitude readings of astronomical telescopes, must be plotted on a See also:projection before the symmetry of the crystal is apparent; and laborious calculations are necessary in See also:order to determine the indices of the faces and the angles between them, and the other.constants of.the crystal, or to test whether any three faces are accurately in a zone.
These disadvantages are overcome by adding still another graduated circle to the instrument, with its axis perpendicular to the axis of the vertical circle, thus forming a three-circle goniometer. With such an instrument measurements may be made in any zone or between any two faces without re-adjusting the crystal; further the troublesome calculations are avoided, and, indeed, the instrument may be used for solving spherical triangles. Different forms of three-circle goniometers have been designed by G. F. H. See also: F. C. See also:Klein (1900). Besides being used as a one-, two-, or three-circle goniometer for the measurement of the interfacial angles of crystals, and as a refractometer for determining refractive indices by the prismatic method or by See also:total reflection, Klein's instrument, which is called a polymeter, is fitted with See also:accessory optical apparatus which enables it to be used for examining a crystal in parallel or convergent polarized light and for measuring the optic axial angle. Goniometers of special construction have been devised for certain purposes; for instance, the inverted horizontal-circle goniometer of H. A. Miers (1903) for measuring crystals during their growth in the See also:mother-liquid. A. E. Tutton (1894) has combined a goniometer with lapidaries' appliances for cutting See also:section-plates and prisms from crystals accurately in any desired direction. The instrument commonly employed for measuring the optic axial angle of biaxial crystals is really a combination of a goniometer with a polariscope. For the optical investigation of minute crystals under the See also:microscope, various forms of See also:stage-goniometer with one, two or three graduated circles have been constructed. An See also:ordinary microscope fitted with cross-wires and a rotating graduated stage serves the purpose of a goniometer for measuring the plane angles of a crystal face or section, being the same in principle as the contact goniometer.
For See also:fuller descriptions of goniometers reference may be made to the See also:text-books of See also:Crystallography and See also:Mineralogy, especially to P. H. See also:Groth, Physikalische Krystallographie (4th ed., See also:Leipzig, 1905). See also C. Leiss, See also:Die optischen Instrumente der Firma R. See also:mess, deren Beschreibung, Justierung and Anwendung (Leipzig, 1899). (L. J. S.)
(1773—18J7), was See also:born in See also:Paris on the 3rd of See also:August 1773, daughter of Augustin See also:Francois, See also:comte de Montaut-Navailles, who had been See also:governor of See also: Madame de Gontaut became See also:lady-in-waiting to See also:Caroline, duchess of See also:Berry, and, on the See also:birth of the princess See also:Louise (Mlle d'See also:Artois, afterwards duchess of See also:Parma), governess to the children of France. Next See also:year the birth of See also: Additional information and CommentsThere are no comments yet for this article.
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