The object of the disposition of the facets on a brilliant is to assure that all the light that enters the stone, principally by way of the table, is wholly reflected from the base and emerges through the crown, preferably by way of the inclined facets. A brilliant-cut diamond, if viewed with the table between the observer and the light, appears quite dark except for the small amount of light escaping through the culet. Light should therefore fall on the lower facets at angles greater than the critical angle of total-reflection, which for diamond is 24° 26´. The pavilions should be inclined properly at double this angle, or 48° 52´, to the culet; but a ray that emerges at a pavilion in the actual arrangement entered the table at nearly grazing incidence, and the amount of light entering this facet at such acute perspective is negligible. On the other hand, after reflection at the base light must, in order to emerge, fall on the crown at less than the critical angle of total-reflection. In Fig. 50 are shown diagrammatically the paths of rays that entered the table in divers ways. The ray emerging again at the table suffers little or no dispersion and is almost white, but those coming out through the inclined facets are split up into the rainbow effect, known as ‘fire,’ for which diamond is so famous. It is in order that so much of the light entering by the table may emerge through the inclined facets of the crown that the pavilions are inclined at not much more than 40° to the culet. It might be suggested that instead of being faceted the stone should be conically shaped, truncated above and nearly complete below. The result would no doubt be steadier, but, on the other hand, far less pleasing. It is the ever-changing nuance that chiefly attracts the eye; now a brilliant flash of purest white, anon a gleam of cerulean blue, waxing to richest orange and dying in a crimson glow, all intermingled with the manifold glitter from the surface of the stone. Absolute cleanliness is essential if the full beauty of any stone is to be realized, but this is particularly true of diamond. If the back of the stone be clogged with grease and dirt, as so often happens in claw-set rings, light is no longer wholly reflected from the base; much of it escapes, and the amount of ‘fire’ is seriously diminished. [Illustration: FIG. 50.—Course of the Rays of Light passing through a Brilliant.] Needless to state, lapidaries make no careful angular measurements when cutting stones, but judge of the position of the facets entirely by eye. It sometimes therefore happens that the permissible limits are overstepped, in which event the stone is dead and may resist all efforts to vivify it short of the heroic course of re-cutting it, too expensive a treatment in the case of small stones.