heating and cooling they improve to assume the crystalline condition. This is still better seen where the particles of bodies are thrown into motion by blows and vibration. Metals, by hammering, lose their ductility and tenacity, and become brittle and crystalline. Coppersmiths, when hammering their vessels, frequently anneal them, to prevent their flying to pieces; that is, they heat them, and then allow them to slowly cool. Thus also bells, long rung, change their tone; cannon, after frequent firing, lose their strength, and are rejected; and so the perpetual jar and vibration of railroad-axles and the shafts of machinery gradually change the tough, fibrous wrought-iron into the crystalline state, weakening them and increasing their liability to fracture.

58. Crystals by Decomposition.-It is also possible, by the decomposition or other chemical change wrought in various bodies, to obtain substances not before present in the shape of crystals. Thus, many compound gases, when passed through red-hot tubes, deposit crystals, and solutions of metallic salts are decomposed by the galvanic current, with the separation of the metals in the crystalline form.

59. Phenomena attending Crystallization.-This change of state is usually attended by change of bulk. Water in freezing expands to a considerable degree, and with great power; 1,000 parts of water are dilated to 1,063 parts of ice; and the force exerted by the particles in changing positions is so enormous as to burst the strongest iron vessels. Heat is always manifested when crystals are formed, in proportion to the rapidity of the change from the liquid to the solid state. Light has also occasionally been noticed to accompany the process, but its cause is not explained. Muddy and impure solutions often yield the largest crystals, and the presence of foreign bodies which do not themselves crystallize may thus modify the form which the crystal assumes. For example, common salt usually crystallizes in the form of a cube (Fig. 27), but, if urine be present in the

solution, it takes the form of the octahedron. When a crystal is broken, there is a tendency to repair it; it continues to increase in every direction, but the growth is most active upon the fractured surface, so that the proper outline of the figure is restored in a few hours.

60. Favorable and Unfavorable Conditions.-Vibration may so disturb the process as to check the growth of those which have commenced, and start a second crop upon them. Crystals are seldom found perfect, being generally irregular,

disguised, and distorted.

Masses of Imperfect Alum-Crystals.

Perfect alum-crystals, for example, are regular octahedrons (Fig. 19), but Fig. 20 shows how they appear in the large vat of the manufacturer. Sometimes the attractions are so balanced that a jar or agitation is needed to start the action. In a perfectly still atmosphere, water may be cooled eight or ten degrees below the freezing-point without congealing, but the vibration of the vessel produces a sudden crystallization of part of the liquid into ice. Any solid body intruded into the liquid, by adhesion, may destroy the equilibrium and begin the play of the crystallizing attractions. Thus, threads are stretched across vessels containing solutions of sugar, and form a nucleus around which rock-candy is crystallized.

61. Forms of Crystals.-Leaving disturbing influences out of view, all liquids tend to assume the spherical shape of drops. We might, therefore, anticipate that, in returning to the solid state, their molecules would still group themselves round centres into spheres. But, although something of this kind may take place with amorphous bodies, the forms produced in the solidification of crystallizable substances are angular, and bounded on all sides by plane surfaces symmetrically arranged.

62. Elements of Crystalline Form.-Although there is an almost endless diversity in the forms which substances take when crystallizing, crystals are built up in obedience to universal geometrical laws, and present in the most varied forms certain constant elements of construction. All crystals are solids of the class known to geometry as polyhedrons; they are bounded by plane surfaces, or faces, which meet by twos in stright lines, or edges, inclosing between them interfacial angles. The faces, polygons in shape, present three or more plane angles, and three or more of these, having a common apex, inclose a solid angle.

63. Axes of Crystals.-Single crystals often present a large number of faces, but the position of all of these bears a fixed mathematical relation to that of the faces of simpler forms, so that the former may be calculated when the latter are known. These simple shapes, from which the others are said to be derived by modification, are termed primary forms. The primary forms, as usually assumed, are solids bounded by six quadrilateral faces meeting in twelve edges and eight solid angles. Every one of the faces will be opposite and parallel to another; therefore, when their centres are connected by straight lines, these must be three in number, and intersect each other in the centre of the primary. In some cases it has been found more convenient to assume four. They are termed the axes of the crystal, and it is known that all the faces observed in any crystal,

when extended to meet them, will always do so at distances from the centre, bearing a very simple numerical relation to the distances at which they are met by the faces of the primary form. The different geometrical elements of crystalline form are thus mutually dependent; hence, when a certain number of these are known, the rest may be computed. Accordingly, when it is desired to determine the position of all the faces, the length of the axes, etc., of any crystal, all that is required is the measurement of some of the interfacial angles, an operation performed by the aid of certain instruments called goniometers.

64. Systems of Crystallization.-All the different crystalline forms which have been observed have been classified and arranged in a number of groups termed systems of crystallization. There are six of these systems, and the forms belonging to each of these differ from the forms belonging to the other systems, either in the number or the relative length of the axes, or in regard to the angles which the axes form at their intersection in the centre of the crystal.

65. Monometric or Regular System. In the forms of this system (Fig. 21) the axes are three in number, of equal length, and intersect

FIG. 21.

Regular System.

each other at right angles. Crystals of this system expand equally in all directions by heat, and refract light

FIG. 22.

in the ordinary manner. Common salt and iron pyrites are examples.

66. Dimetric, Quadratic, or Square Prismatic System. In this system there are three axes intersecting each other at right angles. Two are equal, the third is of a different length. Its forms expand by heat equally in two directions only, and split

Square Prismatic System.

the ray of light passing through them (double refraction), as do also the forms of the four systems remaining to be noticed. Examples: stannous oxide and mercuric cyanide. 67 Trimetric, Rhombic, or Right Prismatic System.-In

FIG. 23.

the forms of this system, the three axes are also at right angles to each other, but all three of unequal length. Crystals of this system (Fig. 23) expand unequally in the three directions of the axes. Nitre and topaz may be taken as examples.

68. Oblique Rhombic or Oblique Prismatic System.-The forms of this system have three axes, which may be unequal (Fig. 24). Two are placed at right angles to each other, and the third is oblique to one and perpendicular to the other. Sodic sulphate and borax are common examples.

69. Oblique Rhomboidal or Doubly Oblique Prismatic System.-In this there are three axes, which may be all unequal and all oblique (Fig.

Doubly Oblique Prismatic System. 25). Examples: cupric sulphate

FIG. 26.

Rhombohedral System.

and bismuthous nitrate.

70. Rhombohedral or Hexagonal System. The forms of this system (Fig. 26) differ from those of the others in having four axes, three of which are equal, in the same plane,

and inclined at angles of 60°, while the fourth is of different length and perpendicular to the other three. Examples: quartz, Iceland spar, and ice.

71. Axial Polarity. The axes of crystals are not mere imaginary lines. The force which builds the crystal works