In place of logarithm-tables we may make use of the diagram on Plate II. The radial lines correspond to the angles of minimum deviation and the skew lines to the prism angles, and the distance along the radial lines gives the refractive index. We run our eye along the line for the observed angle of minimum deviation and note where it meets the curve for the observed prism angle; the refractive index corresponding to the point of intersection is at once read off. This method has several obvious disadvantages: it requires the use of an expensive and elaborate instrument, an observation takes considerable time, and the values of the principal refractive indices cannot in general be immediately determined. Table III at the end of the book gives the refractive indices of the gem-stones. [Illustration: _PLATE II_ REFRACTIVE INDEX DIAGRAM] CHAPTER V LUSTRE AND SHEEN It has been already stated that whenever light in one medium falls upon the surface separating it from another medium some of the light is reflected within the first, while the remainder passes out into the second medium, except when the first is of lower refractivity than the second and light falls at an angle greater than that of total-reflection. Similarly, when light impinges upon a cut stone some of it is reflected and the remainder passes into the stone. What is the relative amount of reflected light depends upon the nature of the stone—its refractivity and hardness—and determines its lustre; the greater the amount the more lustrous will the stone appear. There are different kinds of lustre, and the intensity of each depends on the polish of the surface. From a dull, _i.e._ an uneven, surface the reflected light is scattered, and there are no brilliant reflections. All gem-stones take a good polish, and have therefore, so long as the surface retains its polish, considerable brilliancy; turquoise, on account of its softness, is always comparatively dull. The different kinds of lustre are— (1) Adamantine, characteristic of diamond. (2) Vitreous, as seen on the surface of fractured glass. (3) Resinous, as shown by resins. Zircon and demantoid, the green garnet called by jewellers “olivine,” alone among gem-stones have a lustre approaching that of diamond. The remainder all have a vitreous lustre, though varying in degree, the harder and the more refractive species being on the whole the more lustrous. Some stones—for instance, a cinnamon garnet—appear to have a certain greasiness in the lustre, which is caused by stray reflections from inclusions or other breaks in the homogeneity of the interior. A pearly lustre, which arises from cleavage cracks and is typically displayed by the cleavage face of topaz, would be seen in a cut stone only when flawed.