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If by any force we approximate the particles of an elastic. body, we augment its elasticity, and vice versa. Now, as it is repulsion which opposes the approximation of particles, it appears that it is this force principally which confers on bodies the property called elasticity.

In some crystals their elasticity is equal in three rectangular directions. Such crystals may be denominated equielastic. Others, however, have unequal elasticities in different directions, and may be termed unequielastic. The first are single refractors, the latter are double refractors. Of the unequielastic crystals, some have two of their three elasticities equal, others have all three of their elasticities unequal: the first may be termed di-unequielastic-the second, tri-unequielastic.

The elasticity in the crystallographical axis may fall short of or exceed that in other directions: in the first case, crystals are said to have a negative or repulsive axis, or an axis of dilatation; in the latter case, they are said to have a positive or attractive axis, or an axis of compression.

By experiments made by Savart*, on the mode of sonorous vibration of crystalline substances, it has been shown, that the negative or repulsive axis is the axis of least elasticity, while the positive or attractive axis is the axis of greatest elasticity. "In carbonate of lime," he observes, "it is the small diagonal of the rhombohedron which is the axis of least elasticity, whilst it is that of greatest elasticity in quartz." To be convinced of the accuracy of this assertion, it is sufficient to cut, in a rhombohedron of carbonate of lime, a plate taken parallel to one of its natural faces, and to examine the arrangement of its two nodal systems, one of which consists of two lines crossed rectangularly, which are always placed on the diagonals of the lozenge, the primitive outline of the plate; and the other is formed of two hyperbolic branches, to which the preceding lines serve as axes, (fig. 27), but with this peculiarity, that it is the small diagonal

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which becomes the first axis of the hyperbola, whilst it is its second axis in the corresponding plate of rock crystal (fig. 28). The following table shows the relation between the elasticities and shapes of crystals:

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Conclusions. From the preceding remarks it will appear,

1. That singly refracting crystals are equiaxed, equiexpanding, equielastic, and, on the ellipsoidal hypothesis of molecules, may be assumed to be made up of spherical atoms.

2. That doubly refracting crystals are unequiaxed, unequiexpanding, unequielastic, and, on the ellipsoidal hypothesis of molecules, may be assumed to be made up of either spheroidal atoms or ellipsoids with three unequal axes.

3. That uniaxial crystals are di-unequiaxed, di-unequiexpanding, di-unequielastic, and, on the ellipsoidal hypothesis of molecules, may be assumed to be made up of spheroidal atoms.

4. That biaxial crystals are tri-unequiaxed, tri-unequiexpanding, tri-unequielastic; and, on the ellipsoidal hypothesis of mole cules, may be assumed to be made up of ellipsoids having three unequal axes.

5. That doubly refracting crystals, having a negative or repulsive axis, expand more, and have less elasticity in the direction of the axis than in directions perpendicular to this.

6. Lastly, that doubly refracting crystals, having a positive or attractive axis, expand less, and have more elasticity in the direction of the axis than in directions perpendicular to this.

I shall now go through the six systems of crystals, separately pointing out the most important of their optical and other properties.

SYSTEM I.

THE CUBIC OR OCTOHEDRAL SYSTEM.

Synonymes.-The regular, the tessular, the tesseral, or the isometric system.

Forms.-The forms of this system are either homohedral or whole forms, or hemihedral or half forms.

Homohedral Forms.

1. Regular Octohedron. 2. Cube or Hexahedron.

3. Rhombic Dodecahedron. 4. Icositetrahedron.

5. Triakisoctohedron.

6. Tetrakishexahedron.

Hemihedral Forms.

1. Tetrahedron or Hemioctohedron. 2. Hemicositetrahedron or Pyramidal Tetrahedron.

3. Hemitriakisoctohedron.

4. Hemihexakisoctohedron.

5. Hemitetrakishexahedron or Pentagonal Dodecahedron.

6. Hemioctakishexahedron.

7. Hexakisoctohedron.

FIG. 29.

Four forms of the Cubic System; viz., Cube, Regular Tetrahedron, Rhombic
Dodecahedron, and Regular Öctohedron.

aa, bb, c c. The three rectangular equal axes.

Crystals. Of the fifty-five or fifty-six simple or elementary bodies which have been hitherto discovered, the crystalline forms of not more than eighteen have been ascertained. Of this number, no less than thirteen are referable to the cubic system, namely bismuth, copper, silver, gold, platinum, iridium (?), iron, lead, titanium, mercury, sodium, phosphorus and diamond. Now it appears à priori probable that simple bodies would have spherical atoms, and, therefore, the fact that the above named substances crystallize in forms belonging to the cubic system, has been adduced as an additional evidence of their simple nature. A considerable number of binary compounds also belong to this system as the chlorides of sodium, potassium, and silver; sal ammoniac; the bromide and iodide of potassium; fluor-spar, and the sulphurets of zinc (blende), lead (galena), silver, and iron (pyrites).

Some substances, which contain more than two elements, also belong to this system, as alum and garnet.

Now, if the cubical form be an argument for the simple nature of the metals, why, it may be asked, do so many compound bodies present the same form? To this we can offer no satisfactory reply; and I think, therefore, we may conclude with Dr. Wollaston, "that any attempts to trace a general correspondence between the crystallographical and supposed chemical elements of nature, must, in the present state of the sciences, be premature."

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Properties.-The crystals of this system have the following properties they are equiaxed singly refracting, equiexpanding and equielastic. We assume their molecules to be spherical. When examined in the polariscope they present no traces of colour.

Exceptions.-A few exceptions exist to some of the preceding statements; but they are probably more apparent than real.

1. Several crystals of this system, as the diamond, fluor-spar, alum, and common salt, sometimes exhibit traces of a doubly refracting structure. But this is ascribable to irregularities of crystallization, or to the operation of compressing or dilating forces.

2. Boracite (a compound of boracic acid and magnesia) crystallizes in the general form of the cube; the edges of which are replaced, and the diagonally opposed solid angles dissimilarly modified. Instead, however, of being merely a single refractor, as its shape would lead us to expect, Dr. Brewster found that it was a double refractor, with one positive axis of double refraction in the direction of a line joining two opposite solid angles of the cube. So that, in point of fact, it possesses the properties of a rhombohedric crystal. We may, therefore, regard it as a rhombohedron, whose angles differ from a right angle by an infinitely small quantity.

3. Analcime or cubizite (hydrated silicate of alumina and soda) constitutes another remarkable exception to the general rule, that crystals of the cubic system are devoid of a doubly refracting structure. The most usual form of this crystal is the icositetrahedron. Now if we suppose, says Dr. Brewster, its contained cube" to be dissected by planes passing through all the twelve diagonals of its six faces, each of these planes will be found to be a plane of no double refraction or polarization." All intermediate portions doubly refract. From every other known doubly refracting crystal, analcime differs in the circumstance, that all its particles do not equally possess the property of double refraction, those in the planes above mentioned being devoid of this power, and the others possessing it in proportion to the squares of their distances from these planes. It differs from unannealed glass in the fact that a change in its external form does not give rise to a change in its polarizing power; but each fragment possesses the same optical property, when it is detached from the mass, that it had when naturally connected with its adjacent parts. Analcime, therefore, is a complete optical anomaly.

It has been suggested, that these curious optical properties may depend on the presence of both a doubly and a singly refracting mineral; and the fact, that the large opake crystals of analcime, found in the valley of Fassa in the Tyrol, are traversed by plates of apophyllite (a doubly refracting crystal), lends suport to this hypothesis.

SYSTEM II.

THE SQUARE PRISMATIC SYSTEM.

Synonymes.-The four-membered or two- and one-axed, the pyramidal, the tetragonal, or the monodimetric system. Forms.-The forms of this system are either homohedral or whole forms, or hemihedral or half forms.

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Four forms of the Square Prismatic System; viz., Two Square Prisms in different positions, and Two Octohedra with square bases.

aa. Principal axis. bb, c c. Secondary axes.

*

Crystals. Among the crystals of this system are chloride of mercury (calomel), bicyanide of mercury, ferrocyanide of potassium (yellow prussiate of potash), peroxide of tin, copper pyrites, zircon, and apophyllite.

Properties. The crystals of this system have the following properties: They are di-unequiaxed, doubly refracting with one optic axis, di-unequiexpanding, and di-unequielastic. We assume their molecules to be either prolate or oblate spheroids.

The two equal rectangular geometric axes of this system are called secondary axes; while the third or odd one, which may be greater or less than the others, is the principal or prismatic axis, or the crystallographical axis, or the axis of symmetry. The optical characters of this system are the following: The crystals are doubly refracting, with one optic axis which coincides with the principal axis.

If a thin slice of a crystal of this system, cut perpendicularly

* Sowerby (Ann. Phil. xvi. 223.) mentions crystals of Palladium in the form of octohedra with a square base and of symmetrical prisms.

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