The factors that govern the properties of a brilliant-cut stone are large colour-dispersion, high refraction, and freedom from any trace of intrinsic colour. The only gem-stone that can vie with diamond in these respects is zircon. Although it is rare to find a zircon naturally without colour, yet many kinds are easily deprived of their tint by the application of heat. A brilliant-cut zircon is, indeed, far from readily distinguished by eye from diamond, and has probably often passed as one, but it may easily be identified by its large double refraction (cf. p. 41) and inferior hardness. The remaining colourless stones, such as white sapphire, topaz, and quartz (rock-crystal), have insufficient refractivity to give total-reflection at the base, and, moreover, they are comparatively deficient in ‘fire.’ [Illustration: FIG. 51.—Step- or Trap-Cut (top view).] [Illustration: FIG. 52.—Step- or Trap-Cut (side view).] A popular style of cutting which is much in vogue for coloured stones is the step- or trap-cut, consisting of a table and a series of facets with parallel horizontal edges (Figs. 51-52) above and below the girdle; in recent jewellery, however, the top of the stone is often brilliant-cut. The contour may be oblong, square, lozenge, or heart-shaped, or have less regular forms. The table is sometimes slightly rounded. Since the object of this style is primarily to display the intrinsic colour of the stone and not so much a brilliant play of light from the interior, no attempt is made to secure total-reflection at the lower facets. The stone therefore varies in depth according to its tint; if dark, it is cut shallow, lest light be wholly absorbed within, and the stone appear practically opaque, but if light, it is cut deep, in order to secure fullness of tint. Much precision in shape and disposition of the facets is not demanded, and the stones are usually cut in such a way that, provided the desired effect is obtained, the weight is kept as great as possible; we may recall that stones are sold by weight. In considering what will be the optical effect of any particular shape, regard must be had to the effective colour of the transmitted light. For instance, although sapphire and ruby belong to the same species and have the same refractive indices, yet, since the former transmits mainly blue and the latter red light, they have for practical purposes appreciably different indices, and lapidaries find it therefore possible to cut the base of ruby thicker than that of sapphire, and thus keep the weight greater. It is instructive too what can be done with the most unpromising material by the exercise of a little ingenuity. Thus Ceylon sapphires are often so irregularly coloured that considerable skill is called for in cutting them. A stone may, for instance, be almost colourless except for a single spot of blue; yet, if the stone be cut steeply and the spot be brought to the base, the effect will be