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polarizing plate, we observe, by means of the analyzer, four spirals (proceeding from a black cross in the centre) which cut a series of circles at every quadrant. At some distance from the centre the black brushes are seen. If the right-handed slice be nearer the polarizing plate, the spirals are turned in the opposite directions.

8. Mr. Earnshawinferred, theoretically,from Fresuel's formulae, that if right-handed circularly-polarized light be incident nearly perpendicularly upon a plane surface of glass, the reflected light will be left-handed circularly-polarized, and vice versa. The Rev. Professor Powell has subsequently verified experimentally Mr. Earnshaw's theoretical deduction.

Airy's analyzer for Circularly-Polarized Light.— I have already stated and described two kinds of circularly-polarized light; theonecalled right-handed, the other left-handed. Todistinguish them, Mr. Airy contrived an analyzer which suppresses one and transmits the other. "It is well known," he observes, " that if circularly-polarized light is incident on Fresnel's rhomb, it emerges plane-polarized, and the position of the plane of polarization at emergence makes an angle of +45°, or —45° with the plane of reflection, according as the incident light was righthanded or left-handed. Let the light emerging from the rhomb be received on an unsilvered glass at the polarizing angle, whose plane of reflection makes the angle +45° with that of the rhomb. Now it is plain that if the light incident on the rhomb was righthanded, it becomes plane-polarized in the plane of reflection of the glass, and, therefore, is wholly reflected; if it was lefthanded, it becomes plane-polarized in the plane perpendicular'to the plane of reflection of the glass, and, therefore, is wholly suppressed." It is then obvious, that this combination of Fresnel's rhomb and on unsilvered glass at +4/5°, or —45°, would form an analyzer for circularly-polarized light. But as Fresnel's rhomb is inconvenient, on account of its length, Mr. Airy has substituted " a plate of mica of such a thickness that the ray polarized in the plane of one of its principal sections is retarded either .Jth, -Jths, or -|ths of a wave (according to the convenience of splitting) more than that polarized in the plane of the other. The mica being attached to the unsilvered glass, so that its principal section makes an angle of 45° with the plane of reflection, an analyzer is produced, which answers the same purposes, in general, as that described above."


Time will permit to say a few words only respecting elliptically polarized light.

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If two systems of waves of equal intensity, polarized rectangularly to each other, differ in their progress a fractional number of J undulation, the vibratory movements of the ethereal molecules will be neither rectilinear nor circular, but elliptical. The waves formed by such vibrations will be elliptical, and may be compared to an elliptical helix (that is, to a helix traced round an elliptical cylinder), right-handed or left-handed, as the case may be.

Powell's machine gives a very good idea of elliptical vibrations and elliptical waves.

The manner in which two rectangularly polarized waves interfere and produce elliptical waves, is shown by Wheatstone's apparatus.

There are several modes of effecting the elliptical polarization of light. If in the experiments with Fresnel's rhomb (see Circular Polarization) the planes of polarization and incidence be at any other angle than 45° the emergent ray will be elliptically polarized.

Airy's mode of producing circular polarization may be used to obtain elliptical light; but the mica plate, through which the ray is perpendicularly transmitted, must be placed at an azimuth between that which yields circularly polarized, and that which admits plane polarized light.

Compressed, or unannealed glass, also yields elliptically polarized light, under conditions which I have explained when describing Dove's method of circular polarization.

Quartz also produces elliptical polarization when the direction of the incident ray is inclined to the axis.

By reflection from metallic surfaces light becomes elliptically polarized. The elliptical light reflected from silver is nearly circular, while that from galena is almost plane: that is, the ellipsis in the one case is nearly a circle, in the other nearly a straight line.

Elliptically polarized light is not distinguishable, by the eye, from other kinds of light. If it be analyzed by a Nichol's prism, an unsilvered glass mirror, or a plate of tourmaline, it never vanishes during the revolution of the analyzer. By this it may be known from rectilinearly polarized light. But at different azimuths of the analyzer the intensity of the light varies; and by this it may be known from both unpolarized and circularly polarized light. If it be analyzed by a rhombohedron of calc spar, it gives two images in all positions of the analyzer. In this respect it differs from plane polarized light. But one of the images exhibits a defalcation of light, showing that the incident light is not common or unpolarized. If elliptically polarized light be transmitted through an uniaxial crystal (as Iceland spar) cut perpendicularly to its axis, and the emergent light be afterwards analyzed, it presents a system of rings and cross different to those obtained from either plane or circularly polarized light.

The preceding are some only of the peculiarities which distinguish this from other kinds of light; and in conclusion, I may observe, that elliptical polarization forms a connecting link between plane and circular polarization.


I have now arrived at the last part of my subject, viz., the consideration of the optical properties of those remarkable crystalline structures commonly known by the name of macles, a term introduced into mineralogy by Rome de Lisle. Sometimes these structures appear to consist of one crystal, whose parts are transposed, dislocated, or displaced. When one-half of the crystal appears to have been turned partly round on an imaginary axis, passing through the centreof the crystal, and perpendicularly to the plane of section, and to have been united to the other half in this position, the body thus produced has been called the hemitrope (from fiftt half and rptVa / turn). Of this arrowheaded selenite is a familiar example. Sometimes two or more crystals are found intersecting each other, and are then called intersecting crystals. When two crystals are joined, they form the structure called a twin or double crystal.

Many or most of the forms I have now referred to are irregular, and might appear to be accidental. But there are some others which have great regularity, and cannot be ascribed to accident. Such are some specimens of apophyllite and sulphate of potash. They constitute what Dr. Brewster has termed tesselated or composite crystals; the real structure of many of which is only discoverable by the aid of polarized light; they consist of several crystals, or portions of crystals, juxtaposed, or united so as to form a compound crystal, the figure of which is very different from that of the crystals composing it.

Macled crystals of nitre and arragonite are very common, and frequently their precise structure is undiscoverable by the naked eye.

In quartz we often find right and left-handed crystals intersecting each other.

Amethyst (by many mineralogists considered to be a variety of quartz), is a remarkable example of a combination of right and left-handed varieties of quartz. If a plate of amethyst, cut perpendicularly to the principal axis of the crystal, be examined by the polariscope, it presents a striped or fringed appearance, variegated with the most gorgeous and brilliant tints. This is owing to its being composed of alternate minute strata of right and left-handed quartz, whose planes of polarization are parallel to the principal axis of the prism.

Topaz sometimes presents a remarkably composite structure. It belongs to the right rhombic system, and presents, when regularly formed, two systems of rings. Cut at right angles to the axis it often presents a central rhomb, "surrounded by a horder in which the optic meridians of the alternate sides are inclined at a quarter of a right angle to that of the central compartment, and half of a right angle to each other. In consequence, when such a rhombic plate is held with its long diagonal in the plane of primitive polarization, two opposite sides^of the border appear bright, the other two black, and the central compartment of intermediate brightness. Such specimens often present the phenomena of dichroism in the central compartment, while the border is colourless in all positions'."

Sulphate of potash is composed of six crystals belonging to the right prismatic system, joined so as to form a single or double six-sided pyramid, and simulating the crystals of the rhombohedric system. When, therefore, we put a slice of it, cut at right angles, to the axis of the pyramid, in the polariscope, we observe not a circular cross and rings, but a tesselated structure.

One variety of apophyllite, called tesselite, presents a remarkable structure of the same kind; but its phenomena are still more extraordinary. Apophyllite is composed principally of silicate of lime, with a little silicate of potash. It crystallizes in right square prisms. Plates cut transversely to the axis, and examined by polarized light, appear to consist of nine crystals contained within a number of parallel veins or plates. The central crystal has only one axis of no double refraction, the others two. (See p. 68).

Analcime or Cubizite is another remarkable crystal. It consists principally of silicate of alumina with silicate of soda. It crystallizes in the form of the cube, or some form allied to this, as the icosatetrahedron. Instead of being without double refraction, as cubical crystals usually are, it presents a number of planes of no double refraction. It is, therefore, a compound crystal, that is, is composed of a number of crystalline parts disposed symmetrically. (See p. 66).

And here also may be noticed what has been called interrupted Iceland spar. Some specimens of Iceland spar give four or even more images, which sometimes exhibit complementary tints. They owe this property to the presence of one or more intersecting

* Herschel, Eneycl Metrop.

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or interrupting films or strata of the same substance, placed perpendicularly to the short diagonal of the faces of the crystal. This film acts like the depolarizing plate in the polariscope, while the two portions of the crystal between which it is placed, act, the one as the polarizer, the other as the analyzer of the polariscope. Crystals like these, which thus exhibit their colours and rings per se, that is without the polariscope, have been called by Sir John Herschel, idiocyclophanous (from Ibios proper, Kvkxos a circle, and 'f,alva I appear). Similar phenomena are sometimes exhibited by crystals of nitre, and still more frequently by bicarbonate of potash.

Conclusion.—The lateness of the hour compels me to avoid any lengthened peroration. I shall, therefore, content myself with thanking my auditors for the great attention which they have manifested during the entire course.



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