It is one of the most interesting and remarkable features connected with crystallization that the composition and the physical characters—for instance, the refractive indices and specific gravity—may, without any serious disturbance of the molecular arrangement, vary considerably owing to the more or less complete replacement of one element by another closely allied to it. That is the cause of the range of the physical characters which has been observed in such species as tourmaline, peridot, spinel, etc. The principal replacements in the case of the gem-stones are ferric oxide, Fe_{2}O_{3}, by alumina, Al_{2}O_{3}, and ferrous oxide, FeO, by magnesia, MgO. A list of the principal gem-stones, arranged by their chemical composition, is given in Table I at the end of the book. CHAPTER III REFLECTION, REFRACTION, AND DISPERSION It is obvious that, since a stone suitable for ornamental use must appeal to the eye, its most important characters are those which depend upon light; indeed, the whole art of the lapidary consists in shaping it in such a way as to show these qualities to the best advantage. To understand why certain forms are given to a cut stone, it is essential for us to ascertain what becomes of the light which falls upon the surface of the stone; further, we shall find that the action of a stone upon light is of very great help in distinguishing the different species of gem-stones. The phenomena displayed by light which impinges upon the surface separating two media[1] are very similar in character, whatever be the nature of the media. Ordinary experience with a plane mirror tells us that, when light is returned, or reflected, as it is usually termed, from a plane or flat surface, there is no alteration in the size of objects viewed in this way, but that the right and the left hands are interchanged: our right hand becomes the left hand in our reflection in the mirror. We notice, further, that our reflection is apparently just as far distant from the mirror on the farther side as we are on this side. In Fig. 13 _MM´_ is a section of the mirror, and _O´_ is the image of the hand _O_ as seen in the mirror. Light from _O_ reaches the eye _E_ by way of _m_, but it appears to come from _O´_. Since _OO´_ is perpendicular to the mirror, and _O_ and _O´_ lie at equal distances from it, it follows from elementary geometry that the angle _i´_, which the reflected ray makes with _mn_, the normal to the mirror, is equal to _i_, the angle which the incident ray makes with the same direction. [Illustration: FIG. 13.—Reflection at a Plane Mirror.]