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crystal will be a singly refracting one: if the compression in two directions be equal but different in the third, the crystal will be a doubly refracting one with one optic axis: and, lastly, if the compression be different in each of the three directions, the crystal will doubly refract, and have two optic axes.
5. Molecular Forces.—Between the molecules of crystals, as well as of other bodies, there exist attractive and repulsive forces, in virtue of which the molecules are retained, not in contact, but within certain distances of each other. These forces are antagonists, and, therefore, the molecules acting under their influence, take up a position of equilibrium, where the two opposing powers counterbalance each other.
But in crystals it is necessary to admit, besides ordinary attraction and repulsion, a third molecular force called polarity, which r.iay be regarded either as an original or a derivative property. Without this it is impossible to account for the regularity of crystalline forms. Under the influence of a mutually attractive force particles would adhere together and form masses; the shapes of which, however, would be subject to the greatest variety; and though occasionally they might happen to be regular, yet this could not constantly be the case.
The simplest conception we can form of polarity is that it depends on the unequal action of molecular attraction or repulsion in different directions. A molecule endowed with unequal attractive forces in different directions may be said to be possessed of polarity.
A crystal has length, breadth, and depth or thickness. It is composed of molecules accumulated in three different directions corresponding to these three measurements; and it is obvious, therefore, that to account for their cohesion we must suppose that they attract each other in three directions; moreover, as the relative intensity of their attraction in these directions is, in many cases, unequal, it might be even supposed that they are three different kinds of attractions. To render this subject intelligible I shall make use of some illustrations employed by Dr. Prout in one of the Bridgewater Treatises.
Suppose three molecules to adhere together to form a single row, line, or string of molecules, in virtue of an attractive force which I shall distinguish by the name of the length force. The points AAA or a a a are supposed to mutually repel each other, while AaAaAa mutually attract (fig. 24).
Let us further suppose that three such rows of particles cohere in virtue of an attractive force acting in a direction perpendicular to the first. We may distinguish this as the breadth force. The points B B B or b bb are supposed to mutually repel, while Bb Bb Bb mutually attract. These three rows of particles hy their cohesion form a plane (fig. 25).
Again let us assume, that three such planes cohere together, in virtue of an attractive force acting in a direction perpendicular to both the other forces. This force we may denominate the depth force. The points C C C otccc are assumed mutually to repel, while Cc Cc Cc mutually attract. These three planes by their union form a solid (fig. 26).
Thus, then, we suppose that the molecules of crystals have three rectangular axes of attraction, or " lines along which they are most powerfully attracted, and in the direction of which they cohere with different degrees of force."
Though for convenience and facility of explanation I have employed the terms length-force, breadth-force, and depth-force, I by no means wish you to suppose that I adopt the notion of the distinct nature of these forces. They may be, perhaps they are, one force acting in three directions.
These forces may be equal or unequal, and in the latter case two only, or all three, may be unequal. That is, in some crystals the length-force may be equal to the breadth-force, and this to the depth-force. Or two only of the forces may be equal, the third being unequal: or, lastly, all three may be unequal.
As I have already had frequent occasion to speak of the elasticity of crystals, and as I shall again have to refer to it, I think it proper to explain what is meant by it. I have stated that the molecules of bodies are not in actual contact, but are separated by greater or less intervals. They are kept from actual contact to which attraction urges them, by repulsion, while their further separation is opposed by attraction.
Now we may disturb their state of equilibrium. We may, for example, by some compressing force, compel the particles to approach nearer to each other; but when the disturbing cause ceases to act, the particles after a few oscillation* take up their original position. This then is what we mean by elasticity, which is obviously a consequence of attraction and repulsion. An elastic body is one which has the property of restoring itself to its former figure after any force which hug disturbed it is withdrawn.
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
Fio. 27. Fia. 28.
which hecomes the first axis of the hyperbola, whilst it is i(s second axis in the corresponding plate of rock crystal (fig. 28). The following table shows the relation between the elasticities and shapes of crystals:
TABLE OF THE ELASTICITIES OF CRYSTALS.
Class I. 1 Systems.
Equiclastic V 1. Cubic.
r Order I. r a. Rhombohcdric ...-).£ ji.«" f Ci.as« 2. Di-uncquielastic.. 13. Square Prismatic I vb H H a. Minusfnegative Uneqnielastic J ft. Right Prismatic.. 1-gq "J or repulsive) or crystals... I Orders. I 5. Oblique Prismatic [3 S"x!£ 1 5. Plus (positive iTri-uncquielastio. 1 6. Doubly Oblique I 8 "5" I or attractive) L Prismatic J5oo, L
Conclusions.—From the preceding remarks it will appear,
1. That singly refracting crystals are equiaxed, equiexpanding, cquielastic, and, on the ellipsoidal hypothesis of molecules, may be assumed to be made up of spherical atoms.
2. That doubly refracting crystuls 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-uncquiaxed, 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 molecules, 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.
G. 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.
THE CUBIC OR OCTOHEDRAL SYSTEM.
Synonymes.—The regular, the tessular, the tesserat, or the isometric system.
Forms.—The forms of this system are either homohedral or whole forms, or.hemihedral or half forms,
Four forms of the Cubic System; viz., Cube, Regular Tetrahedron, Rhombic
Dodecahedron, and Regulitr Octahedron,
a a, 0 b, 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 a 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."