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two rectangular planes of polarization of the luminous rays in Iceland spar, one of the plane of polarization of the ordinary rays, the other of the extraordinary rays; and in those parts of the crystal in which the plane of polarization of the incident light coincides with either of the planes of polarization of the rays in the crystal, no double refraction occurs. On the other hand, in those parts of the crystal in which neither of its planes of polarization coincide with the plane of the incident polarized light, double refraction ensues.

FIG. 35.

a

All the ordinary rays which emerge from the crystal, are polarized in planes which pass through the principal axis of the crystal: while the extraordinary rays will be polarized in planes perpendicular to these. Let fig. 35 represent the crystalline plate cut perpendicularly to the axis e. The radiating white lines represent the planes of polarization for the ordinary rays, and the circular white lines the planes of polarization for the extraordinary rays.

The two sets of rays (that is, the ordinary and the extraordinary) form two cones of refracted rays, having a common axis coincident with the axis of the crystal. The summit, or apex of each cone, will be at the eye of the observer; and the diameter of the base of the cone will of course vary according to its distance from the eye. The different rays, of which each cone is made up, undergo different changes. Those which form the axis of the cone, traverse the plate at a perpendicular incidence, and, therefore, are not refracted; while those which pass through the plate obliquely, undergo double refraction.

The ordinary or the extraordinary rays forming the same cone have not all an equal intensity at different parts of its circumference. For if the plane of polarization of the incident light be identical with or parallel to a b, fig. 35, it is evident, that while the intensity of the ordinary rays will be at a maximum in the plane a b, and at a minimum or nil in a direction perpendicular to this c d, the intensity of the extraordinary rays will be at a maximum in the plane cd, and at a minimum or nil in a direction perpendicular to this, a b.

Hence those rays which are incident on the crystal in the plane a b, traverse the plate without having their plane of polarization charged, emerge as ordinary rays, and, by the subsequent action of the analyzing plate, form two arms of the rectangular cross, a b (fig. 36). Those rays which are incident on the crystal at any point of the line c d also traverse the crystal without having their plane of

[graphic]

FIG. 36.

polarization changed, but they emerge as extraordinary rays, and, by the subsequent action of the analyzer, form the remaining two arms of the rectangular cross c d (fig. 36). e Extraordinary rays. d The two sets of polarized incident rays which

- Ordinary rays.

thus traverse the crystal, without having their plane of polarization changed, and emerge, the one as the ordinary, the other as the extraordinary rays, form either a black or a white cross, according as they are either suppressed or transmitted by the second or analyzing tourmaline. If the two tourmalines be crossed the rays are suppressed-if they coincide the rays are transmitted. In the first case we perceive a black cross, in the second a white one.

FIG. 37.

a

d

Thus, then, all the rays which emerge from the second surface of the crystal, at any point of the two lines a b, c d (fig. 37), will not be divided into two, nor have their planes of polarization altered. But all the polarized rays which are incident. on the crystal in any direction intermediate between the positions a b and c d suffer double refraction, since their planes of polarization coincides neither with the plane of polarization of the ordinary, nor with that of the extraordinary rays; that is, the vibrations of the incident rays are resolved into two sets, one which forms the ordinary rays, and the other perpendicular to it, which forins the extraordinary rays. The two systems of waves, produced by these two sets of vibrations, proceed through the crystal with unequal velocities and describe different paths; consequently they emerge in different phases, that is, in a condition for suffering interference by the action of the analyzer. In my last lecture, however, I so fully explained the agency of the analyzer in giving rise to the phenomena of colour, that I need not now enter further into it. I shall, therefore, only add, that the coloured rings owe their origin to interference.

A circumstance which affects the formation of the rings, is the inclination of the polarized rays to the optic axis of the crystal. In the axis itself, where the arms of the cross pass athwart each other, no colour is produced, consequently there can be, in this position, no double refraction. But those rays which suffer double refraction and produce colour, traverse the crystal obliquely, and at an inclination to the optic axis, and the obliquity or inclination augments in proportion as we recede from the centre or axis. Now the effect of an increase in the inclination of the rays to the optic axis is equivalent to an increase of thickness in the crystal. Hence it is obvious why we have rings,

and not an uniform tint, as in the case of the thin films of selenite described in our last lecture. Moreover, it is obvious that at equal distances around the axis the inclinations will be the same, and consequently the similar tints will be found at equal distances from the axis; in other words, the lines of equal tint or isochromatic lines will be disposed in concentric circles.

That the tints of the system of rings accompanying the black cross should be complementary to those which accompany the white cross, will be readily understood from what was stated in the last lecture respecting the office of the analyzing plate.

The rings of the two systems do not occupy the same position, but are transposed; that is, the bright rings of the one system occupy the position of the dark rings of the other system. The cause of this is obvious—the rings of the two systems are produced by different rays. The two sets of rays which successively pass through the tourmaline analyzing plate in its two positions, would, if this plate were not interposed, pass simultaneously and produce an uniform tint of the same colour as that of the incident light. In other words, without the analyzer neither cross nor rings would be perceived.

But why, it may be asked, is the maximum brilliancy of the rings at the middle of the four quadrants; that is, in lines or directions which are equidistant from the two nearest arms of the cross? Because it may be replied, it is at these spots that the ordinary and extraordinary rays (produced by double refraction) are equal. On either side of these directions, the ordinary ray has either a greater or less intensity than the extraordinary one.

Iceland spar has, as I have already stated, a negative or repulsive axis; and I shall take this opportunity of explaining the method used by Dr. Brewster for distinguishing whether the axis of a crystal be positive or negative. Take a film of selenite (sulphate of lime), and mark on it the neutral axes; then, by a little wax, attach it to a plate of Iceland spar (cut so as to show the rings), and place them in the polariscope. If the film by itself produces the red of the second order, it will now, when combined with the Iceland spar, obliterate part of the red ring of the second order in two alternate and opposite quadrants (either a c and b d, or a d and bc, figs. 32 and 34). The line of the film which crosses these two quadrants at right angles to the rings is the principal axis of selenite, and should be marked as such. Then if we wish to examine whether any other system of rings is positive or negative, we have only to cross the rings with the principal axis "by interposing the film: and if it obliterates the red ring of the second order in the quadrant which it crosses, the system will be negative; but if it obliterates the same ring in the other two quadrants which it does not cross, then the system will be positive. It is of no consequence what colour the film polarizes, as it will always

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. I 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, c c, d d), placed in the same plane, and inclined to each other at an angle of 60°, while the fourth or principal axis (a a) is perpendicular to the other three.

FIG. 38.

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."

SYSTEM IV.

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 octohedron, the right rectangular prism, and the right rectangular octohedron. Rose enumerates the following forms as belonging to this system:

Homohedral.

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

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

3. Forms whose faces are inclined to one axis but are parallel to the two others (Single Planes).

Hemihedral.

Rhombic Tetrahedron.

FIG. 39.

Right Rectangular Prism.
Right Rhombic Prism.

Right Rectangular Octohedron.
Right Rhombic Octohedron.

a. Principal or prismatic axis. bb, c c. Secondary axes.

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