When a mineral is broken under the blow of a hammer, instead of yielding an irregular fracture, like that of glass, it generally tends to part along one or more directions so as to leave plane surfaces. This property of _cleavage_ is strikingly illustrated for a single direction in the mineral mica, for two directions in feldspar, and for three directions in calcite or Iceland spar. Other properties of minerals, such as hardness, specific gravity, luster, color, fusibility, etc., are all made use of in rough determinations of the minerals. Far more delicate methods depend upon the behavior of minerals when observed in polarized light, and such behavior is the basis of those branches of geological science known as optical mineralogy and as microscopical petrography. An outline description of some of the common minerals and the means for identifying them will be found in appendix A. =The alterations of minerals.=—By far the larger number of minerals have been formed in the cooling and consequent consolidation of molten rock material such as during a volcanic eruption reaches the earth’s surface as lava. Beginning their growth at many points within the viscous mass, the individual crystals eventually may grow together and so prevent a development of their crystal faces. Another class of minerals are deposited from solution in water within the cavities and fissures of the rocks; and if this process ceases before the cavities have been completely closed, the minerals are found projecting from the walls in a beautiful lining of crystal—the _Krystallkeller_ or “crystal cellar.” It is from such pockets or veins within the rocks that the valuable ores are obtained, as are the crystals which are displayed in our mineral cabinets. [Illustration: FIG. 13.—Crystal of garnet developed in a schist with grains of quartz included because not assimilated.] There is, however, a third process by which minerals are formed, and minerals of this class are produced within the solid rock as a product of the alteration of preëxisting minerals. Under the enormous pressures of the rocks deep below the earth’s surface, they are as permeable to the percolating waters as is a sponge at the surface. Under these conditions certain minerals are dissolved and their material redeposited after traveling in the solution, or solution and redeposition of mineral matter may go on together within the mass of the same rock. One new mineral may have been produced from the dissolved materials of a number of earlier species, or several new minerals may be the result of the alteration of a preëxisting mineral with a more complex chemical structure. Where the new mineral has been formed “in place”, it has sometimes been able to utilize the materials of all the minerals which before existed there, or it may have been obliged to inclose within itself those earlier constituents which it could not assimilate in its own structure (Fig. 13). [Illustration: