The most difficult operations in connection with the investigation of the optical properties of the crystals of artificially-prepared substances, which are usually endowed with a much lower degree of hardness than the crystals of naturally-occurring minerals, are those which involve the preparation of the necessary section-plates and prisms. It is of primary importance that the plates should be truly parallel to the desired plane, or perpendicular to the desired direction in the crystal, and that they should possess plane surfaces truly parallel to each other. The prisms should likewise possess two plane surfaces, inclined to each other at an angle which may not usually exceed 70°, and whose edge of intersection is always required to be parallel to a given direction in the crystal; moreover, the two surfaces may with advantage be symmetrical to, or one of them parallel with, a given plane in the crystal. It is not too much to say that the accuracy of the determinations of the optical constants of crystals depends fundamentally upon the degree of precision with which these requirements are attained. The preparation of section-plates and prisms of these relatively soft and friable crystals, when, as happens in the large majority of cases, the crystals do not exhibit the desired planes, or do not present them sufficiently prominently developed to enable them to be utilised as plates and prisms, must of necessity be carried out by grinding. In very few cases, indeed, are the crystals of artificial preparations endowed with sufficient hardness to withstand a preliminary cutting, by means of an extremely fine fretsaw, or thin wire lubricated with oil or a solvent for the crystallised substance. The crystals usually require delicate handling, their relative softness or brittleness, together with the development of cleavage, rendering them particularly liable to fracture and splitting. Moreover, owing to their greater freedom from distortion, striation, and facial curvature, the smaller crystals are always to be preferred for the purposes of accurate investigations, and the preparation of sections and prisms from small crystals must necessarily be carried out entirely by grinding.