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FIGURES OF CRYSTALS. 53 not quite so convenient in use, is free from some sources of inaccuracy to which a goniometer with a horizontal axis is subject. 280. When the points of p, q, at which the reflexions take place, are not equally distant from the axis of the circle, the angle through which the circle revolves between the two observations ■will differ slightly from the angle between the faces p, q. This error may be eliminated, when the signals a, b are nearly equi distant from the crystal, by turning the instrument half round m azimuth, and repeating the observations. A mean of the two results will be free from the error arising from the eccen tricity of the points at which the reflexions take place. When either of the faces is large, it should be blackened over, except at the point where it is intended the reflexion should take place. Any error that may arise from imperfect centring of the circle, will be eliminated, if the observations be repeated so that observations at a given face be made with zero ot the vernier at points of the graduated circle distant nearly 180 from each other. mim y crystals, not belonging to the cubic system, tscherlieh discovered that the angles between certain faces, vary slightly- with the temperature of the crystal; thus the l ections °f the cleavages of calcite, which, at the ordinary cmperature of the atmosphere, make angles of 76° 65' with each other, become more nearly right angled by 8''5, when the temperature of the crystal is increased 100° c. For the same increase of temperature a line perpendicular to the face ill expands 0'0028(l, and a line parallel to the face ill contracts 0 00050 of its length. The distance between the poles of the taces m, m,\ of a crystal of aragonite, is diminished 2’'8, and the distance between the poles of the faces k, k' is increased 5'-5 by increasing the temperature of the crystal 100° c. In a crystal °i gypsum, which belongs to the oblique system, the angle be tween the two axes, to which the third axis is perpendicular, and the ratios of the parameters, all vary with a change of tem perature. FIGURES OF CRYSTALS. 232. Tho drawing of a crystal is the projection, on a given plane, ot tho lines in which the faces of the crystal intersect each other. 1 Lenee, if lines bo drawn parallel to the projections ni the several edges, in the order in which they meet, the lines representing opposite edges being equidistant from the centre ot the drawing, the ligure of the crystal will bo obtained. When the inclination of the axes and tho ratios of the parameters are known, the direction of the projection of tho n 3