1. _Composition._—This, according to the definition of a mineral, ought to be _definite_, and expressible by a chemical formula. When it is not so, we usually consider that the mineral is partially decomposed, or that we are dealing with a mixture of minerals. It is well to impress upon the mind of the pupil the important fact that the more fundamental properties of the elements, such as specific gravity and lustre, are not lost when they combine, but may be traced in the compounds. In other words, the properties of minerals are, in a very large degree, the average of the properties of the elements of which they are composed; minerals in which heavy metallic elements predominate being heavy and metallic, and _vice versa_. To fully appreciate this point it is only necessary to compare a mineral like galenite—a common ore of lead, and containing nearly 87 per cent. of that heavy metal; or hematite (specimen 13), containing 70 per cent. of another heavy metal, iron—with quartz (specimen 15), which is composed in nearly equal parts of oxygen and silicon, two typical non-metallic elements. Many minerals contain water, _i.e._, are hydrated. Now water, whether we consider the liquid or solid state, is one of the lightest and softest of mineral constituents; and it is a very important fact that hydrated minerals are invariably lighter and usually softer than anhydrous species of otherwise similar composition. Other striking illustrations of this principle will be pointed out in the descriptions of the minerals which follow. 2. _Crystalline form._—A crystal is bounded by plane surfaces symmetrically arranged with reference to certain imaginary lines passing through its centre and called axes. Crystals of the same species are always constant in the angles between like planes, while similar angles usually vary in different species; so that each species has its own peculiar form. “Besides external symmetry of form, crystallization produces also regularity of internal structure, and often of fracture. This regularity of fracture, or tendency to break or cleave along certain planes, is called cleavage. The surface afforded by cleavage is often smooth and brilliant (see specimens 17, 18, and 21), and is always parallel with some external plane of the crystal. It should be understood that the cleavage lamellæ are not in any sense present before they are made to appear by fracture.”—(Dana.) Crystals are arranged in six systems, based upon the number and relations of the axes, as follows:— Isometric System.—Three equal axes crossing at right angles. Example, cube. Tetragonal System.—Two axes equal, third unequal, all crossing at right angles. Example, square prism. Orthorhombic System.—Three unequal axes, but intersections all at right angles. Example, rhombic prism. Monoclinic System.—Three unequal axes, one intersection oblique. Example, oblique rhombic prism.