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rliombic face of Iceland spar(fig. 23, D), it will be found that while the obtuse angles (a a') are contained within the circle, the acute ones (b b') project beyond it. Now, under the influence of heat, this face expands in the direction of the shortest axis, but contracts in that of the longest axis, by which the rhomb approaches to the square, the obtuse angles becoming more acute, the acute ones more obtuse (fig. 23, E).

These illustrations will serve to give some general notions ofthe relations which exist between the forms and expansibilities of crystals.

The di-unequiaxed crystals — that is, the doubly-refracting crystals, which have only one axis of [no] double refraction— expand equally in the direction of the equal crystallographical axes, but differently in that of the remaining one; and we may, therefore, denominate them di-unequiexpanding crystals. If, for example, a rhombohedron of Iceland spar be subjected to heat, it expands in the direction of its shortest axis, but contracts in all directions perpendicular to this, and in an intermediate direction it neither dilates nor contracts. Thus, according to Mitscherlich and Dulong, when heated from 32° to 212° Fahr, it actually expands, in the direction of the shorter axis, 0.00286, and contracts in a direction perpendicular to this 0.00056; so that its apparent or relative expansion in this axis is 0.00342 (that is 0.00286 + 0.00056). Now a necessary consequence of this unequal expansion is an alteration in the angles of the crystal: the obtuse ones become more acute, the acute ones more obtuse. In other words, the rhombohedron approximates to the cube; and in proportion to this change of form is the diminution of doubly refracting energy. Mitscherlich had conjectured that the latter effect would take place, and Rudberg has verified the conjecture. The last mentioned philosopher found, that while the ordinary refraction of Iceland spar underwent little or no change, the extraordinary refraction was considerably diminished by an augmentation of temperature. The tri-unequiaxed crystals expand when heated, unequally in the direction of all their axes, and, therefore, they may be denominated triunequiexpanding crystals. When the temperature of selenite is augmented, the inclinations of all its faces suffer changes. Thus according to Mitscherlich by heating it from 32° to 212°, the inclination of the faces cc was altered 10'50", that of the faces a a 8'25", and that of the edges b b' only 7'26". I have already explained what is meant by the terms positive or attractive, and repulsive or negative axes. They refer to optical differences in crystals, for which we find no corresponding

FlO. 24.


geometric or crystallographical differences. Now there have been observed, in the effects of heat on crystals, differences analogous to the optical ones just referred to. Thus, in crystals with a repulsive or negative axis, as Iceland spar, expansion is greatest in the d i rection of the shortest axis, showing that the molecular attraction in this direction is the weakest; whereas in positive or attractive crystals, as selenite, heat produces less dilatation in a direction parallel to the axis than in a direction perpendicular to it.

"The inclination of the optic axes, in biaxial crystals," says Mr. Lloyd, "is a simple function of the elasticities of the vibrating medium in the direction of three rectangular axes, and the plane of the optic axes is that of the greatest and least elasticities. If, then, these three principal elasticities be altered by heat in different proportions, the inclination of the axes will likewise vary; and if, in the course of this change, the difference between the greatest elasticity and the mean, or between the mean and the least, should vanish and afterwards change sign, the two axes will collapse into one, and finally open out in a plane perpendicular to their former plane. All these variations have been actually observed. Professor Mitscherlich found, that in sulphate of lime the angle between the axes (which is about 60° at the ordinary temperature) diminishes on the application of heat; that, as the temperature increases, these axes approach until they unite; and that, on a still further augmentation of heat, they again separate, and open out in a perpendicular plane. The primitive form of the crystal undergoes a corresponding change, the dilatation being greater in one direction than in another at right angles to it. Sir David Brewster has observed an analogous and even yet more remarkable property in glauberite. At the freezing temperature, this crystal has two axes for all the rays of the spectrum, the inclination of the axes being greatest in red light and least in violet. As the temperature rises, the two axes approach, and those of different colours unite in succession; and at the ordinary temperature of the atmosphere, the crystal possesses the singular property of being uniaxial for violet light, and biaxial for red. When the heat is further increased, the axes which have united open out in order, and in a plane at right angles to that in which they formerly lay, and at a temperature much below that of boiling water, the planes of the axes for all colours are perpendicular to their first position.* The inclination of the optic axes in topaz, on the other hand, augments with the increase of temperature, and the variation M. Marx has observed, is much greater in the coloured than in the colourless varieties of this mineralf."

* Edin. Trans., vol. xi.; and Phil. Mag., 3d series, vol. i, 417. t Jahrb. der Chemie, vol. ix.

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

Class 1.
Equicxpandiog crystals (tingle refractors, equiaxed).
Class 2. -1

Order 1. Di-onequiexpaoding (one optic axis, di-untquiaxed).



(double refractors,


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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,f 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, Haiiy 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 Iran*, for 1818, p. 264. t TraiUde 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 -f^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:


Systems of Crystals.

. ('class 1. Equiaxed (spheres) ). Cubic

| I rar*r i. Two equal -iwmw {J ESSwSSll.

o.; Class 2. Unequiaxed^ f 4. Right Prismatic

3 1 | Orders, Three unequal axes < 5. Oblique Prismatic

* L * 16. Doubly Oblique

Phil. Trant., 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 1 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

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