The crystal on its adjusting apparatus can be raised or lowered to the proper height, level with the axes of the telescope and collimator, by means of a milled head at the base of the instrument, there being an inner crystal axis moving (vertically only) independently of the circle. Moreover, a second axis outside this enables the crystal to be rotated independently of the circle, the conical axis of which is outside this again. The two can be locked together when desired, however, by a clamping screw provided with a fine adjustment _q_. Freedom of movement of the crystal axis, unimpeded by the weight of the circle, is thus permitted for all adjusting purposes, the circle being only brought into play when measurement is actually to occur. With this instrument the most accurate work can be readily carried out, and for ease of manipulation and general convenience it is the best goniometer yet constructed. The idea of regarding the centre of the crystal as the centre of a sphere, within which the crystal is placed (Fig. 47, page 62), gives crystallographers a very convenient method of graphically representing a crystal on paper, by projecting the sphere on to the flat surface of the paper, the eye being supposed to be placed at either the north or south pole of the sphere, and the plane of projection to be that of the equatorial great circle. The faces in the upper hemisphere are represented by dots which are technically known as the “poles” of the faces, corresponding to the points where the needles normal to the faces emerge from the imaginary globe, and all these points or poles lie on a few arcs of great circles, which appear in the projection either also as circular arcs terminating at diametrically opposite points on the circumference of the equatorial circle, which forms the outer boundary of the figure and is termed the “primitive circle,” or else, when the planes of the great circles are at right angles to the equatorial primitive circle, they appear as diametral straight lines passing through the centre of the primitive circle. Such a stereographic projection offers a comprehensive plan of the whole of the crystal faces, which at once informs us of the symmetry in all cases other than very complicated ones. A typical one, that of the rhombic crystal of topaz shown in Fig. 22 (page 40), is given in Fig. 49.