Consider next successive rays within a piece of glass or a stone which are about to emerge with different inclinations. (See Fig. 1.) As their course approaches more nearly to the surface, so will the emerging rays issue more nearly along the surface of the stone; but the obliquity of the emerging rays increases much more rapidly than that of the internal rays, until for one ray in the series the direction of the light (C in the figure) refracted out coincides with that surface. What, then, will happen to the light within the stone, which falls still more obliquely? It cannot be refracted out, and, as a fact, it is entirely reflected within the stone. Imagine, then, how much greater is the brilliancy of the beam of light, c, e, d, which is completely reflected, than that of the intermediate portion of the reflected light, a, b, c, which has lost a large part of its rays by refraction. The difference is easily seen by looking at a glass of water held above the head; the brilliant silvery appearance of the surface, when viewed obliquely, is due to total reflection. The light, c, d, e, is said to have been totally reflected; and half the angle between C and c is called the "angle of total reflection." This angle depends upon the refractive power of the stone.

The angle of total reflection for diamond is about 25°; in no other stone is the corresponding angle less than 30°; for most of them it is much greater; while for heavy glass it is about 40°. Light striking the internal surface more obliquely is reflected without losing any of its rays by refraction.

It is very clear, then, that of the light traveling in directions within a diamond, a far larger proportion is internally reflected than is the case with any other stone. We shall see presently that it is this property which gives the diamond its consummate brilliancy.

Another effect produced by refraction is, as every one knows, the separation of ordinary light into rays of different colors - it is seen in any prism of glass. This property is known as the "dispersion" of light; and a stone which possesses great dispersion will exhibit a beautiful play of spectral colors - will exhibit a high degree of what is called fire. In this respect again the diamond is pre-eminent; its dispersion is nearly twice as great as that of other stones.

All these optical properties are beautifully shown by those unworked jewels of which the smooth facets have been produced by nature; I mean the crystals of the various minerals. The beauty of natural crystals of transparent minerals is largely due to the optical effects which I have just been describing.

The beautiful specimens of rock crystal, calc spar, topaz, emerald, and other stones which adorn mineral collections are sufficient evidence of these properties. But it is very certain that natural crystals, although they possess a beauty of form which is all their own, are not by a long way so brilliant as the faceted stones which are cut from them by the art of the lapidary; that a natural diamond is not so lustrous as a faceted brilliant.

In fact, many of the finest gem stones present a very mean and sordid aspect before they have passed through the hands of the lapidary; one has only to compare the dull and unattractive appearance of a parcel of rough rubies, sapphires or rough diamonds with the finished jewels displayed in the jewelers' windows to see how much these owe to the lapidary's art.

In recutting the Koh-i-noor it was thought advisable to spend £8,000 on the process and to reduce its weight from 186 to 106 carats. When the great Pitt diamond was cut, its weight was reduced from 410 carats to 137; and the fragments and dust removed were valued at £8,000; but the extent to which the stone was improved is indicated in the fact that having been purchased for £20,000, it was after cutting sold for £135,000.

To understand how the cutting of a precious stone adds to its brilliancy, we have only to trace the course of the rays within the stone, and consider how it can best be faceted in order that the light which enters in various directions on the upper side, or crown, may be reflected internally from facet to facet on the under side of the stone with as little loss as possible, and may be thrown out from the front of the stone. For this purpose the facets must be so arranged that as much of the light as possible within the crystal shall meet the facets at an inclination exceeding the angle of total reflection. A brilliant with its 58 facets is one of the forms which experience has shown to be best adapted for the purpose. How little of the light gets through a stone so faceted, and, therefore, how much of it is totally reflected internally, is easily shown by holding the stone in a strong beam of light; first so that the light is so reflected, and then so that the light shall, if possible, be transmitted.

In the latter case, the stone merely throws a dark shadow, indicating that little light, if any, has passed through it.

A faceted stone is always cut from a single crystal, and not from an ordinary lump of the mineral, which is generally a mass of crystals. The chief reason why jewels are cut from natural crystals is that these, by virtue of their crystalline nature, are remarkably homogeneous, and therefore clear and limpid when free from cracks and flaws. A stone which is not homogeneous can never have the purity and limpid brilliancy of a single crystal, for at every point of contact of one part with another reflection takes place. Among minerals used as precious stones which are not crystals may be mentioned the opal. The opal probably owes its peculiar beauty to the very fact that it is filled with minute cracks or cavities, each of which contributes some tint of color by reason of its extreme thinness, just as the colors of the soap bubble are due to the thinness of its film.