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to those of nitre, and like the latter, the red ends of the rings are inwards, the blue ends outwards.

Arragonite forms an interesting polariscope object. It is identical iu chemical composition with calcareous or Iceland spar, but differs in crystalline form: calcareous spar belonging to the rhombohedric, arragonite to the right prismatic, system. According to Gustav Rose, both these forms of carbonate of lime may be artificially produced in the humid way, but calcareous spar at a lower, arragonite at a higher, temperature. In the dry way, however, calcareous spar alone can be formed.

The inclination of the optic axes of arragonite being small (about 18°) we can easily see, at the same time, the two negative systems of rings surrounding their two poles, but considerably more separated than in the case of nitre. For this purpose, a plate of the crystal is to be cut perpendicularly to the prismatic axis, that is, equally inclined (at about 9°) on each of the optic axes. If we rotate the plate of arragonite on its axis in the polariscope, the tourmaline plates being crossed and unmoved, the two sets of rings appear to revolve around each other. By superposing two plates of arragonite, we obtain four systems of rings.

In Rochelle salt (tartrate of potash and soda) the optic axes of the differently refrangible or coloured rays are considerably separated. If a plate of this crystal, cut perpendicularly to the prismatic axis, be inclined first on one side and then on the other, both the systems of rings may be successively perceived. But to observe the separation of the axes for differently coloured rays, Sir J. Herschel directs the plate to be cut perpendicularly to one of its optic axes. If we view the rings with homogeneous light they appear to have a perfect regularity of form, and to be remarkably well defined. With differently coloured lights, however, they not only differ in size but in position. If the light be "alternately altered from red to violet, and back again, the pole, with the rings about it, will also move backwards and forwards, vibrating, as it were, over a considerable space. If homogeneous rays of two colours be thrown at once on the lens, two sets of rings will be seen, having their centres more or less distant, and their magnitudes more or less different, according to the difference of refrangibility of the two species of light employed."

Topaz (a fluosilicate of alumina) belongs to this system. As the inclination of its optic axes is great (about 50°), we can see at once only one of its two system of rings. It slits with facility in planes perpendicular to its prismatic axis, and equally inclined to its two optic axes. If we take a plate cut perpendicularly to



the prismatic axis, and incline it first on one side and then on the other, we shall see successively two systems of oval rings, which have been very elaborately described by Dr. Brewster.

The plates of topaz sold in the opticians' shops, for polariscope purposes, have been obtained by cutting the crystal perpendicularly to one of the optic axes; that is, at an angle of about 25° to the prismatic axis. With these we only see one system of nearly circular rings traversed by a bar or arm of the cross. We observe also, that the optic axes for different colours are somewhat separated; for the red ends of the rings are inwards, or within the resultant axes, while the blue ends are outwards.

The topazes, which are cut for optical purposes, come from Australia, and are technically known as Nova Minas. They are colourless and remarkably free from flaws and macles.

Exceptions.—In this system, as in the others, we meet with exceptions to some of the statements above made.

1. Macled crystals, especially of Nitre and Arragonite, are very common. Occasionally idiocyclophanous crystals of nitre are met with. These will be noticed subsequently.

2. Sulphate of potash is a tesselated or composite crystal, and as such will be described hereafter.

3. Some specimens of Brazilian topaz are tesselated.



Synonymes.—The two- and one-memberedsystem, the hemiorthotype system, the monoklinohedric system, or the hemihedricrhombic system.

Forms.—To this system belong the oblique octohedron with a rectangular base, the oblique rectangular prism, the oblique octohedron with or rhombic base, and the oblique rhombic prism. Mr. Brooke's right oblique-angled prism is referred to this system.

Rose makes no distinction between the homohedral and hemihedral forms in this system; but enumerates the following as the forms of the system:

1. Forms whose faces are inclined to all the three axes (Octohedra).

2. Forms whose faces are inclined to two^axes, and are parallel to the third axis (Prisms).

3. Forms of which the faces are inclined towards one axis and parallel to the two others.

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Oblique Rectangular Prism, Oblique Rhombic Prism, Oblique Rectangular Octohedron, and Oblique Rhombic Octohedron.

a a. Principal axis. bb,cc. Secondary axes.

Crystals.—To this system belong the crystals of sulphur, when obtained by slow cooling; realgar (red sulphuret of arsenic), and red antimony (native Kermes).

A considerable number of salts belong here also: as the sulphates of soda, lime (selenite), and iron; carbonate and sesguicarbonate (trona) of soda, bicarbonate of potash, chlorate of potash, phosphate of soda, borax (tincal), the acetates'of soda, copper, zinc, and lead, binacetate of copper, binoxalate of potash, glauberite (sulphate of lime and soda), and chromate of lead.

To this system are also referred oblique prismatic mica (one of the kinds of diaxial mica described by Count de Bournon), tartaric and oxalic acids, sugar candy, and the crystals from oil ofcubebs.

Properties.—The forms of this system have three axes, all of which are unequal. Two of them cut one another obliquely, and are perpendicular to the third. From the forms of the preceding system they are distinguished by this obliquity of two of their axes. As the three axes are unequal, it is indifferent which we take for the principal axis; but one of the inclined axes is usually selected, because, in general, the crystals are extended in the direction of one of these, so that in most cases the faces which are parallel to this axis greatly predominate. This axis, therefore, corresponds with that which Mr. Brooke calls the prismatic axis. The other two axes are called secondary axes. the one whicli is oblique being termed the first secondary axis; the other, which is perpendicular to it, being denominated the second secondary axis.

The crystals of this system are doubly refracting with two optic axes. They are tri-unequiexpanding, and tri-uneqtiiaxed. On the ellipsoidal hypothesis their atoms are assumed to be ellipsoids with three unequal axes.

G 2

In the opticians' shops, plates, cut from several crystals of the this system, are sold for showing:, in the polariscope, the systems of lemniscates. They are usually cut perpendicularly to one of the optic axes; and, therefore, show but one system of rings traversed by a bar. Of these I shall notice three.

Borax deserves especial notice on account of its optic axes for the different homogeneous colours lying in different planes, a fact for the knowledge of which we are indebted to Sir John Herschel. As in other biaxial crystals it will be observed that the rings, or lemniscates, are traversed by only one bar or arm of the cross. In the next place it will be perceived, that the axes for red light make a greater angle with each other than the axes for blue or purple; hence, unlike nitre and carbonate of lead, the red ends of the rings are outwards, while the blue ends are inwards. This fact, however, only proves that the axes for different colours do not coincide: it does not show that they lie in different planes. But if, the tourmaline plates being crossed, the plate of borax be placed at such an azimuth that the bar or arm of the black cross distinctly traverses the centre of the system of lemniscates and leaves an interval perfectly obscure, we shall then see that the arm of the cross is not straight, as in nitre (fig. 40), but has a hyperbolic form. The reason of this difference is obvious: in nitre all the axes lie in the same straight line or plane, while in borax they are disposed obliquely, or in different planes.

Selenite is sometimes cut to show one of its two systems of rings. I have already described this crystal, and demonstrated the uniform tints produced by films of selenite of equal thickness. To show the rings the crystal must be cut at right angles to one of its optic axes.

Sugar Candy makes an interesting polariscope object. This crystal is also cut perpendicular to one of its optic axes, and, therefore, shows only one of its two systems of rings.

Exceptions.—Owing to irregularities of crystallization, the rings of some of the crystals of this system are often seen more or less distorted. Macled selenite is very common, as I have before mentioned. Sir John Herschel states, that idiocyclophonous crystals of bicarbonate of potash are frequent. 1 shall hereafter notice them.



Synonymes.—The one- and one-membered, the anorthotype, the triklinohedric, or the tetartohedric-rhombic system.

Forms.—To this system belong the doubly oblique octohedron and the doubly oblique prism. Rose makes no distinction of homohedral and hemihedral forms; but arranges the forms of this system as follows:

1. Forms whose faces are inclined to all the three axes. (Octohedra.)

2. Forms whose faces are inclined to two axes, and are parallel to the third. (Prisms.)

3. Forms which have their faces inclined towards one axis only. These forms are the faces of truncation of the three kinds of angles of the octahedron.



Two Doubly Oblique Prisms, and two Doubly Oblique Octohedra.
a a. The Principal Axis, bb, cc. The Secondary axes.

Crystals —The most important substances, whose crystalline forms are referable to this system, are boracic acid, sulphate of copper*, nitrate of bismuth, sulphate of cinchonia, quadroxalate of potash, and gallic acid.

Properties.—The forms belonging to this system have three axes all unequal and oblique-angular to one another; they are doubly refracting, with two optic axes; and they are tri-unequiexpanding. Consequently they have three unequal elasticities.

Of the three axes just referred to, one is taken for the principal axis, the other two for the secondary axes; but geometrically considered the selection is altogether arbitrary. The principal axis coincides with Mr. Brooke's prismatic axis.

"The forms of this system," says G. Rose, " have not symmetrical faces. All the faces are unique, so that this system is the one which differs the most from the regular or cubic system, in which we find the greatest symmetry on account of the equality and perpendicularity of the axes." It is sometimes exceedingly difficult to distinguish the forms of this system. "The doubly oblique prism," observes Mr. Brooke, " will be found the most

* Mr. Brooke (art. Mineralogy, in the Encyclopaedia Metropolitana), says, that the primary form of Sulphate of Copper is an oblique rhombic prism, and Mr. E. Phillips (Translation of the Pharmacopoeia, p. 237, 4th edit., 1841) has adopted Mr. Brooke's statement If this be correct, sulphate of copper of course belongs to the oblique prismatic system, and not to the doubly oblique prismatic system. I have, however, referred it to the latter system on the authority of Gustav Rose, and most of the other eminent German crystallograpbers.

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