Under the general belief that the harder the gem the higher its refractive powers would be, it has been maintained that the brilliancy of the diamond arose from the simple property of its excessive hardness. Investigation, however, does not sustain this widespread view. Hardness, indeed, may have considerable relation with the arrangement and form of the molecules composing the gem, for in the same crystal it is not uniform,--some faces and angles being harder than others,--but it does not determine the degree of brilliancy. To strengthen this statement we will take for instances the soft minerals, crocroisite, the chromate of lead; the Greenockite, the sulphuret of cadmium; and the octahedrite, the oxide of titanium, which exceed even the diamond in brilliancy. There are also other decided examples among the transparent minerals to sustain this view; the most remarkable of which perhaps may be found in the zircon, a gem which is soft as quartz; yet it ranks next to the diamond in brightness, and far surpasses in eclat every other gem, even the sapphire, which is next to the diamond in hardness. Density does not seem to have anything to do with the determination of the refractive power of gems, for the garnet, spinel, sapphire, and zircon are much heavier than the diamond, and are yet far inferior in brilliancy. The topaz is exactly of the same specific gravity as the diamond (3.55), but nevertheless its refractive powers have but little more than one half the energy of the diamond. The relative brilliancy of the diamond to that of the purest limpid quartz is 8 to 3; but the relative density is only as 4 to 3. All diamonds do not exhibit the same degree of brilliancy, because they do not possess alike the same quality of purity or perfection of crystallization.