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obliterate the tint of the same nature in the system of rings under examination."
Plates of tourmaline, obtained by cutting the crystals at right angles to the principal or prismatic axis, as described in my first lecture (fig. 6, p. 18), present circular rings and a cross when examined by the polariscope.
Ice belongs to the rhombohedric system. The beautiful and regular, though varied, crystalline forms of snow may be regarded as skeleton crystals of this system. 1 have here depicted (see fig. 38) a few forms taken from Captain Scoresby's work on the Arctic Regions ; and in them you may readily trace the three secondary axes (b b, cc, del), placed in the same plane, and inclined to each other at an angle of 60°, while the fourth or principal axis (o a) is perpendicular to the other three.
Crystals of Snow.
Now, if you take a sheet of clear ice, about an inch thick, and which has been slowly formed in still weather, and examine it by the polariscope, you will readily detect the circular rings and cross. The system of rings formed by ice is positive or attractive; and, therefore, is of an opposite kind to that of Iceland spar.
Exceptions.—To the general properties of crystals of the rhombohedric system some exceptions exist.
1. In Iceland spar, beryl, and other crystals of this system, the rings are not unfrequently distorted, owing to irregularities of crystalline structure.
2. Quartz belongs to this system, but its optical phenomena are very different to those of any other crystal, and will be described in my next Lecture, under the head of circular polarization.
3. Amethyst is another exception, which I shall hereafter describe.
4. Chabasite (a mineral compound of silica, alumina, lime water, and potash) is a rhombohedral crystal, sometimes endowed with remarkable optical properties. "In certain specimens of this mineral," says Dr. Brewster, "the molecules compose a regular central crystal, developing the phenomena of regular double refraction; but in consequence of some change in the state of the solution, the molecules not only begin to form a hemitrope crystal on all the sides of the central nucleus, but each successive stratum has an inferior doubly refracting force till it wholly disappears. Beyond this limit it appears with an opposite character, and gradually increases till the crystal is complete. In this case the relative intensities of the axes or poles from which the forces of aggregation emanate, have been gradually changed, probably by the introduction of some minute matter, which chemical analysis may be unable to detect. If we suppose these axes to be three, and the foreign particles to be introduced, so as to weaken the force of aggregation of the greater axis, then the doubly refracting force will gradually diminish with the intensity of this axis, till it disappears, when the three axes are reduced to equality. By continuing to diminish the force of the third axis, the doubly refracting force will reappear with an opposite character, exactly as it does in the chabasite under.consideration."
RIGHT PRISMATIC SYSTEM.
Synonymes. — The right rhombic prismatic, or right rectangular prismatic system, the prismatic system, the two- and two-membered or one- and one-axed system, the orthotype system, the rhombic or the holohedric-rhombic system.
Forms.—In this system are included the right rhombic prism, the right rhombic oclohedron, the right rectangular prism, and the right rectangular octohedron. Rose enumerates the following forms as belonging to this system:
1. Forms whose faces are inclined to
all three axes (Octohedra).
2. Forms whose faces are inclined to
two axes, but are parallel to
3. Forms whose faces are inclined
to one axis but are parallel to
Right Rectangular Priam. I Right Rectangular Octohedron.
Right Rhombic Prism. \ Right Rhombic Octohedron.
a. Principal or prismatic axis, b h,cc. Secondary axes.
Crystals.—The simple or elementary bodies which crystallize in forms belonging to this system are only three, namely, iodine, native sulphur, and selenium.
Among the binary compounds we have pyrolusite (binoxide of manganese), white antimony (sesquioxide of antimony), bichloride of mercury, chloride of barium, orpiment, and grey antimony (sesquisulphuret of antimony).
A considerable number of salts belong to this system, as the carbonates of lead, baryta, strontian, potash, and ammonia; the bicarbonate of ammonia, and that variety of carbonate of lime called arragonite; the nitrates, of potash, ammonia, and silver; the sulphates of magnesia, zinc, baryta, and strontian, ami bisulphate of potash; Rochelle salt (tartrate of potash and soda) and emetic tartar (tartrate of potash and antimony).
To the above must be added the following substances: topaz, dichroite, citric acid and morphia.
Properties.—The crystals of this system present the following properties: they have three rectangular axes all of different lengths: they are doubly refracting with two optic axes; and are tri-unequiexpanding. Consequently they have three rectangular unequal elasticities. On the ellipsoidal hypothesis, their atoms are ellipsoids, with three unequal axes.
They present no crystallographieal character by which the principal axis can be distinguished from the others called secondary axes; so that in a geometrical point of view the choice of this axis is altogether arbitrary. But considered optically the principal axis is the middle point between the two nearest poles of no polarization. It corresponds with what is called by Mr. Brooke the prismatic axis; that is, the axis which passes through the centres of the terminal planes of the prism.
If you examine one of the simple or primary forms of this system—say this unmodified rectangular prism (the outer prism of figure 39), you observe there is no single line around which the figure is symmetrical; nor any square plane, or plane which can be inscribed within the circle. But let each of the two opposite terminal edges be replaced by a square plane, both equally inclined to the prismatic axis, and the line which passes through the centre of each of these planes will represent the direction of one of the optic axes.
As the crystals of this system have two optic axes, they present, when examined by the polariscope, a double system of rings. In nitre, carbonate of lead, and arragonite the inclination of these axes is small; and, therefore, both systems of rings may be seen at the same time.
In order to examine these by the polariscope, we must, in the case of the three crystals just mentioned, cut slices of them perpendicularly to the principal or prismatic axis. But in topaz, right prismatic mica, and Rochelle salt, the inclination of the optic axes is too great to permit both of them to be seen simultaneously; and, therefore, only one of them can be seen at a time. Consequently if we examine, by the polariscope, a plate of any of these crystals, cut at right angles to the prismatic axis, we must incline it first on one side and then on the other, to see successively the two systems of rings. To obviate this inconvenience, plates of these crystals should be prepared by grinding and polishing two parallel faces perpendicular to the axis of one system of rings.
Nitrate of potash, also called nitre or saltpetre, (N Os + K O) is a very instructive crystal for illustrating the double system of rings. It is usually met with in the form of a six-sided prism, with diedral summits.
For placing in the polariscope, we use plates of from -jijth to jJjth of an inch in thickness, cut perpendicular to the prismatic axis. If one of these be put in the polariscope in such a position that the plane passing through the optic axis is in the plane of primitive polarization, we shall then perceive a double system of coloured elliptical or oval rings, intersected by a cross, but the centre of the cross is equidistant from the centres of the two systems of rings, so that through the centre of each system passes one arm or bar of the cross, the other arm being at right angles to the former. When the polarizing and analyzing plates are crossed, we have a double system of coloured rings, with a black cross" (fig. 40); but when the polarizing and analyzing plates coincide, we have another double system of coloured rings, exactly complementary to the first, with a white cross (fig. 41).
If when the analyzing and polarizing tourmaline plates are crossed, we revolve the plate of nitre in its own plane (both the tourmaline plates remaining unmoved) the black cross opens into two black hyperbolic curves. When the angle of rotation is a quarter of a right angle, we have the appearance represented by (fig. 42); when it equals half of a right angle, the black arms have assumed the forms of fig. 43.
Here, then, is a remarkable distinction between biaxial and uniaxial crystals, for you will remember I demonstrated that when the uniaxial crystal was rotated in the polariscope, the black cross retained its position and shape.
The variation of form, as well as the general figure of the isochromatic lines, resembles the curve called by geometers the lemniscate. The inner rings encircle one pole only, but the outer ones surround both poles. The number of rings which surround both poles augments, as we diminish the thickness of the plate of nitre, until all the rings surround both poles, and the system thus greatly resembles, in appearance, the rings of an uniaxial crystal, from which, however, they are distinguished by their oval form.
I have already stated, that in biaxial crystals the optic axes for different colours do not coincide. In the case of nitre, the axes for red make with each other a smaller angle than the axes for blue. Hence the red ends of the rings are inward, that is, between or within the two optic axes, while the blue ends are outwards, or exterior to the two axes. But as the red rings are larger than the blue ones, it follows that there are points exterior to the axes where all the colours are mixed, or all are absent. At these spots, therefore, the rings are nearly white and black. Now if we trace the same rings to the positions between the axes, " the red rings will very much over-shoot the blue rings; and, therefore, the rings have the colour peculiar perhaps to a high order in Newton's scale *."
Native crystallized carbonate of lead constitutes a splendid polariscope object. It is to be cut like nitre; that is, perpendicularly to the prismatic axis. The optic axes are but slightly inclined (about 10^°) and, therefore, both of them may be simultaneously perceived. The systems of rings have a similar form
* Airy, Mathematical Tracts, p. 396, 2d ed. 1831.