majority, are doubly refractive. A bright spot of light, say a small candle-flame, when viewed through a single refracting stone appears single; through a doubly refracting stone, double. The stone should be moved from the eye until, even when at a considerable distance, the flame seen through it appears single or double, as the case may be. All crystals belonging to the cubical system, such as diamond, spinel, and garnet, are, like glass and strass, simply refracting; ruby, beryl, topaz, and quartz are all doubly refracting. There are very precise and beautiful methods for ascertaining this quality in transparent crystals, but they are not applicable generally to cut and polished gem-stones. The results of some of these accurate measurements of the indices of refraction of transparent minerals will be found in chapter vii.; that they differ much in different species may be seen from this brief list of indices for the yellow ray:—
| Diamond | 2·417 | Tourmaline | 1·642 | |
| Zircon | 1·950 | Heavy flint glass | 1·619 | |
| Almandine | 1·810 | Beryl | 1·575 | |
| Ruby | 1·779 | Rock crystal | 1·549 | |
| Pyrope | 1·750 | Iolite | 1·540 | |
| Chrysoberyl | 1·748 | Crown glass | 1·524 | |
| Peridot | 1·659 | Water | 1·336 |
Although this series of refractive indices may be accepted as containing numbers near the truth it must be remarked that every doubly refracting substance has two indices of refraction for each ray, although the difference between these indices rarely, if ever, exceeds five units in the second decimal place, and generally amounts to no more than one unit. And it should be mentioned that the same species of stone, even in its apparently purest condition, does not present, in all specimens, precisely the same optical features; there are differences due in part to chemical, in part to molecular causes. Thus there have been observed in fine diamonds variations of refractive index amounting to several units
