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to the principal axis, be placed in the polariscope, it presents a system of circular rings, with a cross, which is either black or white, according to the relative positions of the polarizer and analyzer.

Ferrocyanide of potassium (commonly called prussiate of potash) may be conveniently used to show these effects. As found in commerce it usually occurs in the form of truncated octohedrons having a square base. It should be split with a lancet in the direction of its lamina, that is, perpendicularly to its principal axis. Plates, of about a quarter of an inch or more in thickness, serve for the polariscope. They present a cross, and a negative system of circular rings; but the yellow colour of the crystal affects the brilliancy of the tints.

Zircon (a compound of silica and zirconia) is valuable for optical purposes, on account of its being a positive uniaxial crystal. Hence if a plate of it, which gives a system of rings of the very same size as that produced by a plate of Iceland spar (a negative uniaxial crystal) be superposed over the latter plate, the one system of rings is completely obliterated by the other; and the combined system exhibits neither double refraction nor polarization.

I shall defer all explanation respecting the rings and cross of this system, until I speak of Iceland spar (a crystal of the rhombohedric system).

Exceptions.-Some exceptions to the above mentioned properties of the crystals of this system exist, and require to be noticed.

1. Ferrocyanide of potassium is subject to irregularities of crystallization; and certain specimens present a double system of rings, or, in other words, are biaxial. Certain uniaxial specimens give a positive system of rings.

2. Apophyllite or Fisheye-stone (a compound of silica, lime, potash, and water) possesses some remarkable properties. In the most common variety, that from Cipit in the Tyrol, the diameters of the rings are nearly alike for all colours those of the green rings being a little less. Some specimens of apophyllite, called by Dr. Brewster tesselated apophyllite, present, in the polariscope, a tesselated or composite structure, instead of the ordinary cross and circular rings. They will be described hereafter among the tesselated or intersected crystals.



Synonymes.-The three- and one-axed, the klinohedric, the hexagonal, or the trimetric system.

Forms.-The forms of this system are either homohedral or hemihedral.

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Three forms of the Rhombohedric System; viz., the Hexagonal Prism, the Scalene Dodecahedron and the Rhombohedron.

a a. The principal axis. bb, cc, dd. The secondary axes.

Crystals. To this system belong some bodies supposed to be simple or elementary; viz., antimony, arsenicum, and tellurium.* Plumbago or graphite and the native alloy of iridium and osmium also belong to this system.

Ice, magnetic iron pyrites, cinnabar, chloride of calcium, Iceland spar, carbonates of iron and zinc, dolomite (magnesian carbonate of lime), nitrate of soda, hydrate of magnesia, tourmaline, talc, beryl, chabusite, quartz, and one-axed mica belong to this system. And here it may be necessary to remark, that the substance known to mineralogists by the name of mica, and which, in trade, is usually but improperly termed talet, varies in its crystalline forms and optical properties. One kind crystallizes. in regular hexagonal prisms, which cleave with extreme facility in one direction, viz., perpendicularly to their axis. This has only one axis of [no] double refraction, and consequently when a lamina of it is placed in the polariscope it presents only one system of circular rings traversed by a cross. This is the kind called rhombohedral or uniaxial mica, the majority of specimens of which have a negative or repulsive axis, though some have a positive or attractive one. But there is another kind of mica, of more frequent occurrence in the shops, and which is called by mineralogists prismatic or diaxial mica. It has two

* Rose inserts "Palladium (?)" among rhombohedric crystals. Talc is readily distinguished from mica by its greasy or unctuous feel. The most familiar kind of talc is that sold in the shops under the name of French chalk. It is talc in an indurated earthy form.

axes of double refraction, and consequently when a plate of it is placed in the polariscope, two systems of coloured rings are perceived. This kind of mica exists in two forms; one is crystallized in right prisms, the other in oblique prisms. Hence I shall distinguish the one as right prismatic mica, the other as oblique prismatic mica. They will be described hereafter. In conclusion, then, the kinds of mica may be thus arranged:

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With a negative axis, or

Rhombohedric or Uniaxial {With a positive axis.

Prismatic or Diaxial {Bight Prismatic.

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Oblique Prismatic.

The principal constituents of mica are silica and alumina. But it also contains potash and sesquioxide of iron.

Properties. The forms of this system possess four axes+; viz., three equal ones, called the secondary axes, placed in one plane, and crossing in the centre at an angle of 60°; and a fourth, termed the principal axis, or the axis of symmetry, or the crystallographical axis, perpendicular to the others, from which it differs in length. They are double refractors, with one optic axis coincident with the principal axis. They are di-unequiexpanding bodies, the expansion being different (greater or less) in the principal axis from that in the secondary ones. They are di-unequielastic; the elasticity in the principal axis being either more or less than that in the secondary axes. With regard to the atoms, we may assume their shape to be spheroids. Iceland spar (Ca O. CO2) may be conveniently used to illustrate the optical properties of the crystals of this system. It occurs in rhomboidal masses, which by cleavage yield obtuse rhombohedra. The line which joins the two obtuse suminits of one of these rhombohedra, is called the shortest or principal axis, the crystallographical axis, the axis of the rhomboid, or simply the axis. A plane drawn through this axis, perpendicularly to a face of the crystal, is called the principal section. This section belongs rather to a face than to the entire crystal, for each face has its own. Now when the incident rays are perpendicular to the face of the crystal, both the ordinary and extraordinary rays are always found in the same plane, so that the deviation of the extraordinary pencil takes place in the plane of the principal section. Every plane in the interior of the crystal, which is perpendicular to the axis, is called a section perpendicular to the axis, or the equator of double refraction. In this plane the

†The description adopted in the lectures is that of Weiss and Rose; some other writers admit only three axes. Thus, Turner (Elements of Chemistry 7th ed., p. 588) describes three equal but not rectangular axes; while Griffin (System of Crystallography, pp. 151 and 258) admits three rectangular but unequal axes. Neither of these modes of descriptions appear to me so completely to connect the form with the optical and other properties of the crystals, as Weiss and Rose's method.

doubly refracting force is at a maximum, and when a ray is incident in this plane, the resulting extraordinary and ordinary rays are both in the same plane.

If a plate of Iceland spar, cut perpendicularly to the principal or shortest axis, be placed in the polariscope, the polarizing and analyzing plates being crossed, we observe coloured curves or concentric rings intersected by a rectangular black cross, the arms of which meet at the centre of the rings (fig. 32).

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The coloured curves or rings are called the lines of equal tint, or isochromatic lines (from îoos equal and xpaparikòs coloured). In this and other uniaxial crystals, they are disposed in concentric circles, and are similar to Newton's rings seen by reflection.

If we revolve the plate of Iceland spar on its axis, the rings and cross preserve the same position; but if either the polarizing or analyzing plate be rotated, some remarkable changes occur.

Suppose the analyzing plate to be turned 450 round the incident ray in a left-handed direction, we observe that the original or primary coloured rings grow fainter or more dilute, and the cross seems to shift its position to the left, while its blackness lessens and is replaced by another set of rings, which alternate with, and are complementary to, the original curves (fig. 33).

If the analyzing plate be rotated 45° further in the same direction, that is 90° to the first or original position, the black cross is replaced by a white one, and the original set of coloured rings is succeeded by a second or complementary set, the rings of which are intermediate to the original ones, and are similar to Newton's rings seen by transmission (fig. 34).

If the system of rings with a black cross (fig. 32) were superposed in the system with the white cross (fig. 34) white light would be reproduced.

If the incident polarized light be white, the rings consist of compound tints produced by the superposition on each other of rings formed by each of the homogeneous rays composing white light.

Of course, if the rings of all the colours were of the same size, the resulting system would consist of black and white rings; but being of different dimensions, we obtain a system of different colours. In this case, the cross is either black or white, not coloured.

If the incident polarized light be homogeneous the rings consist of rings of the colour of the light employed separated by black rings. Thus, suppose red light to be used, the rings will be alternately red and black; whereas if blue light be employed, they will be alternately blue and black. Their size varies with the colour of the light red produces the largest, violet the smallest system of rings. In all cases in which homogeneous light is employed the cross is either a black or a coloured one.

The radii of the bright rings are as the square roots of the odd numbers, 1, 3, 5, 7, &c.; while those of the dark rings are as the square roots of the even numbers, 2, 4, 6, 8, &c. In other, words, the squares of the diameters of the bright rings are as the odd numbers, 1, 3, 5, 7, &c.; while the squares of the diameters of the dark rings are as the even numbers, 2, 4, 6, 8, &c.

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The actual diameter and breadth of the rings are increased by diminishing the thickness of the crystalline plate. To speak more precisely, the radii of the rings are inversely as the square root of the thickness of the plate; and, therefore, the rings are smaller with a thick plate than with a thin one. Thus while a plate of a given thickness will produce a system of rings, the whole of which can be seen at once, a plate considerably thinner will give rings of so much larger diameter and greater breadth, that the whole system cannot be taken in at once by the eye. It is obvious, therefore, that the comparative doubly refracting power of two uniaxial crystals may be ascertained by observing the size of the rings produced by plates of equal thickness: with a powerful doubly refracting crystal the rings are less than with a crystal possessing this property in a weaker degree. In fact, the radii of the rings are inversely as the doubly refracting power of the crystal.

Let us now endeavour to explain generally the origin of the coloured rings and of the cross, according to the undulatory hypothesis; and, for precision and brevity of description, I shall suppose that tourmaline plates are used in the polariscope both for polarizing and analyzing.

The first tourmaline plate polarizes the light which is then incident on the Iceland spar. In their progress through the latter, some of the polarized rays suffer double refraction, others are transmitted without undergoing this change. For there are

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