GONIOMETER. Strictly speaking this name is applicable to any instrument, such as a mural circle, a theodolite, and so on, used for measuring an angle ; it is in reality, however, applied exclusively to instruments used for measuring the angles between the faces of crystals. The oldest instrument of the kind was invented by Carangeot, and consisted simply of a pair of rulers jointed together and fitted with a graduated circle for measuring the angle between their edges. A carpenter uses a somewhat similar instrument, not, it is true, for measuring, but for transferring angles. The application of the principle of reflexion by-Wollaston in 1809 converted the goniometer into an instrument of precision. His form, with a vertical divided circle, is still much used. The principle of reflexion is briefly this. The crystal is mounted so that it can be rotated about au axis parallel to the edge in which its two faces meet. It is first placed so that a ray of light coining in some fixed direction (say, along the axis of a collimator), when reflected from one face, passes in another fixed direction (say, along the axis of a telescope). The crystal is then turned till the ray reflected from the other face passes in the same direction as before. The angle through which the crystal has been turned is either 180'+ 2A or 180' - 2A, where A is the angle between the faces. The introduction of the fixed mirror by Degen and Lang, and of the horizontal circle with collimators, brought the instrument into its most modern form. Babinet, Malus, Mitscherlich, Haidinger, Von Lang, and others have contributed towards perfecting the instrument. Recently Professor W. H, Miller (Mil. May., 1876) has described a new form of goniometer. In the paper quoted some useful details concerning the use of the instrument will be found. For further instructions how to use the goniometer the reader may refer to Phillips's Mineralogy, or Groth's Physikalische KrystallograpUe, Abth. iii. The modern goniometer has so much in common with the spectrometer that it is unnecessary to describe it in detail here. See SPECTROSCOPE.