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In conclusion, then, crystals considered with reference to the effects of heat on them, may be thus arranged :

THERMOTIC CLASSIFICATION OF CRYSTALS.

CLASS 1.

Equiexpanding crystals (single refractors, equiaxed).

CLASS 2.

Unequiexpanding

crystals

(double refractors, unequiaxed)

*

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Order 1. Di-unequiexpanding (one optic axis, di-unequiaxed).

Order 2. Tri-unequiexpanding(two optic axes,tri-unequiaxed).

4. Atoms or Molecules. It has been correctly stated by Dr. Brewster, that the polarizing or doubly refracting structure of crystals must depend on the form of their integrant molecules, and the variation in their density." A few observations on the atoms or molecules of crystals, will not, therefore, be out of place on the present occasion.

Like all other aggregates, crystals are made up of certain small parts conventionally called atoms or molecules. It is unnecessary to discuss the question of their finite or infinite divisibility; and to obviate the necessity of this, I shall assume with Dumas,† that an atom is the smallest particle of a body, which by mere juxtaposition with the particles of other bodies, gives rise to a combination. Hence, therefore, the small parts of any one body which combine chemically with certain small parts of another body, without suffering further division, are what we understand by the terms atoms or molecules.

As these small parts or atoms are invisible, even when we aid the eye by the most powerful microscope, it is obvious that all observations on their size and shape must be speculative. Two opinions, however, have prevailed with respect to their form, Haüy and others have adopted the notion of their angular shape, while Hooke, Wollaston, and other more recent writers, assume them to be rounded. If we were to deduce the form of the molecules from that of their aggregates, we should adopt the angular hypothesis; for the most minute fragment of a crystal which we can procure and see, is angular. On the other hand, the spheroidal form of the planetary bodies, the tendency which liquids manifest to assume the spherical shape, and the mechanical facilities which the hypothesis of rounded atoms offers in the grouping of the atoms, have led later writers to adopt almost exclusively the views of Hooke and Wollaston.

But it may be asked, Is the shape of an atom constant? or can it suffer change? May not the atoms of liquids be spherical or ellipsoidal and those of crystals angular? Ellipsoidal forms become angular by mutual compression; and hence may not the ellipsoidal atoms of a liquid become angular in the act of crystallization? The idea has not, to my knowledge, oc

* Phil. Trans. for 1818, p. 264. + Traité de Chimie, t. 1, p. 33, 1828.

curred to crystallographers, but it appears to me that the subject well deserves consideration.

A spheroid is said to be oblate, when, as in the case of the earth, the shortest diameter is its axis of revolution, but it is prolate or oblong, when the longer diameter is its axis of revolution. Now the shorter diameter may be regarded as the direction of the greatest attraction, or of compression, while the longer diameter is the direction of least attraction or of dilatation. In the case of the earth it is well known that gravity is greater at the poles than at the equator, a body weighing about th more at the former than at the latter. It might, therefore, be supposed that crystals with one positive or attractive axis of double refraction would be formed of oblate spheroids, while those with one negative or repulsive axis, would be made up of prolate spheroids.

But an objection exists to this hypothesis. According to it, obtuse rhombohedra ought to have one positive axis, while acute rhombohedra should have one negative axis of double refraction. Now the crystalline form of Iceland spar is an obtuse rhombohedron, but the optic axis of this substance is negative, so that its crystalline form is that which is produced by an oblate spheroid, while its optical property is that of a prolate spheroid. To obviate this objection, Dr. Brewster* suggests that the molecules have the form of oblate spheroids, whose polar is to their equatorial axis as 1 to 2.8204, and that they were originally more oblate, but have been rendered less so by the force of aggregation, which dilated them in the direction of the smaller axis.

In point of fact, however, this assumption does not entirely obviate the difficulty, as the spheroids are still supposed to be oblate, though their axis is a negative one; and it appears probable, that the same force which would render the axis negative, should change the shape of the spheroid from the oblate to the prolate. Moreover, Dr. Brewster's explanation involves the improbable supposition that the original very oblate spheroids if "placed together without any forces which would alter their form," would" compose a rhombohedron with a greater angle, and having no double refraction."

On the assumption that the axes of the atoms of crystals bear the same relations to each other that the axes of the systems of crystals themselves do, I have drawn up the following table of the supposed shapes of the atoms:

Ellipsoids.

TABLE OF THE SHAPES OF THE ATOMS OF CRYSTALS.

CLASS 1. Equiaxed (spheres).......

CLASS 2. Unequiaxed

..............

Systems of Crystals. .................................. 1. Cubic

Order 1. Two equal axes (spheroids) {2. Rhombohedric

Order 2. Three unequal axes......

3. Square Prismatic
4. Right Prismatic
5. Oblique Prismatic
6. Doubly Oblique

* Phil. Trans., 1830.

The doubly refracting structure is not inherent in the molecules themselves. Quartz or crystallized silica doubly refracts; but tabasheer, opal, and melted quartz, all siliceous substances, do not. Ice doubly refracts, while water singly refracts. What is the reason of this?

It will be generally admitted, I presume, that the double refraction of ice is a molecular property, and is associated with the shape of the atom; and hence, if the atoms of water have the same form as those of ice, they ought also to possess the doubly refracting property of the latter. Now, the advocates for the hypothesis of the unchangeability of atomic forms contend, that in ice the atoms are symmetrically and regularly arranged, with their axes pointing in the same direction; while in water they are unsymmetrically or irregularly arranged or jumbled together in such a manner that their axes have every possible direction, so as to create a general equilibrium of the polarizing forces. But, if this were the case, two specimens of water would scarcely ever present the same optical properties. If, by any accident, the axes of a large majority of the molecules should happen to be arranged in the same direction, the liquid would then possess a doubly refracting property. Now, it appears to me, that no hypothesis can be correct which ascribes to accident or chance a constant and invariable property of a body; for I hold, that, except when approaching the freezing point, liquid water is invariably a single refractor.

But on the assumption that the shapes of atoms are, to a certain extent, capable of change, the difficulty is easily obviated. Suppose the atoms of liquid water to be spheres, and that in the act of freezing they become spheroids, the expansion of water in the act of freezing, the doubly refracting property, and the crystalline form of ice would then be readily explicable.

A consistent explanation of Dimorphism can scarcely be offered except on the assumption of the changeability of the shapes of the atoms. Carbonate of lime, for example, crystallizes in two distinct and incompatible forms, the one belonging to the rhombohedric, the other to the right prismatic system. In the first case, we call it Iceland-spar; in the other, arragonite. Iceland-spar has one negative optic axis, arragonite has two negative optic axes. The shapes of the atoms of these bodies must, therefore, be different. Admit that, under certain circumstances, the atom of carbonate of lime can change its shape, and all difficulty as to the production of these forms is at an end.

We suppose, therefore, that " when in the process of evaporation or cooling, any two molecules are brought together by the forces or polarities which produce a crystalline arrangement, and strongly adhere, they will mutually compress one another." If the compression in three rectangular directions be equal, the

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 attrac tion and repulsion, a third molecular force called polarity, which may 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.

It is

A crystal has length, breadth, and depth or thickness. 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.

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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 A A A or a a a are supposed to mutually repel each other, while Aa Aa Aa 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 BBB or bbb are supposed to mutually repel, while Bb Bb Bb mutually attract. These three rows of particles by 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 or ccc 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 oscillations 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 has disturbed it is withdrawn.

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