of thin glass is used, for polarization from a single surface is incomplete.

nomena.

On the undulatory theory we can give a very clear account of all these pheCommon light originates in vibratory movements taking place in the ether; but it differs from the vibrations in the air which constitute sound in this essential particular-that while in the waves of sound the movements of the vibrating particles lie in the course of the ray, in the case of light they are transverse to it. This may be made plain by considering the wavelike motions into which a cord may be thrown by shaking it at one end, the movement being in the up-and-down, or in the lateral direction, while the wave runs straight onward. The ethereal particles, therefore, vibrate transversely to the course of the ray. But then there are an infinite number of directions in which these transverse vibrations may be made: a cord may be shaken vertically or laterally, or in an infinite number of intermediate angular positions, all of which are transverse to its length.

d

Common light, therefore, arises in ethereal vibrations taking place in every possible direction transverse to the path of the ray; but in polarized light the vibrations are all in one plane. Thus, in the case of tourmaline, when a ray passes through it all vibrations are taking place in one direction, and therefore the ray can pass through a second plate placed symmetrically with the first; but if the second be turned a quarter

a

7

round the vibrations
can no longer pass in
the same way as a Fig. 257.
sheet of paper, cd, Fig. 257, may be slipped
through a grating, a b, while its plane
coincides with the length of the bars; but
can no longer go through when it is turned
as at ef, a quarter round.

Again, in the case of polarization by reflection, let AB, Fig. 258, be the mirror on which a ray of common light, ab, falls Dat the proper angle of polarization, and is reflected in a polarized condition along b c. CD will be the plane in which the ethereal particles vibrate after reflection, and the curve line drawn on it may represent the intensities of their vibrations.

Fig. 258.

So, too, in Fig. 259, we have an illustration of polarization by refraction. Let A B be a bundle of glass plates, a b the incident, and c d the polarized

B

Fig. 259.

ray; the plane C D at right angles to the plates is the plane of polarization, and the curve drawn on it represents the intensities with which the polarized particles move.

In every instance the plane of polarization is perpendicular to the planes of reflexion and refraction.

The polariscope is an instrument for exhibiting the properties of polarized light. There are many different forms of it: Fig. 260 represents one of them. It consists of a mirror of black glass, a, which can be set at

any suitable angle to the brass tube, A B, by means of a graduated arc, e; it can also be rotated on the axis of the tube, B A, and the amount of that rotation read off on the graduated circle, b. At the other end of the tube

B

A

C

a

there is a second mirror of black glass, d, which, like a, can be arranged at any required angle, and likewise turn round on the axis of the brass tube, A B, the amount of its rotation being ascertained by the divided circle, c. Sometimes, instead of this mirror of black glass, a bundle of glass plates in a suitable frame is used. The instrument is supported on a pillar, C.

The fundamental property of light polarized by reflection may be exhibited by this instrument as follows:-Set its two mirrors, a and d, Fig. 260. so as to receive the light which falls on them at an angle of 56°. Then, when the first, a, makes its reflection in a vertical plane, the light can be reflected by d, also in a vertical plane, upward or downward. But if d be turned round 90°, so as to attempt to reflect the ray to the right or left in a horizontal plane, it will be found to be impossible, the light becoming extinct and in intermediate positions. As the mirror revolves the light is of intermediate intensity.

CHAPTER XLIII.

ON DOUBLE REFRACTION AND THE PRODUCTION OF COLOURS IN

POLARIZED LIGHT.

Double Refraction of Iceland Spar-Axis of the Crystals-Crystal with two Axes-Production of Colours in Polarized Light-Complementary Colours produced-Colours depend on the Thickness of the Film-Symmetrical Rings and Crosses-Colours produced by Heat and Pressure-Circular and Elliptical Polarization.

By double refraction we mean a property possessed by certain crystals, such as Iceland spar, of dividing an incident ray into two emergent ones. Let

Rr, Fig. 261, be a ray of light falling on a rhomboid of Iceland spar, ABC X, in the point r; it will be divided during its passage through the crystals into two rays, r E, r O, the latter of which follows the ordinary law of refraction, and therefore takes the name of the ordinary ray; the former follows a different law, and is spoken of as the extraordinary ray.

Objects through such a crystal appear double. A line, M N, on a piece

of paper, viewed through it, is exhibited as two lines, M N, mn, the amount of separation depending on the thickness of the crystal. The emergent rays, E e, O o, are parallel after they leave the surface, X.

A line drawn through the crystal from one of its obtuse angles to the other is called the axis of the crystal, and if artificial planes be ground and polished, as n m, op, perpendicular to this axis, a b, Fig. 262, rays of light falling upon this axis, or parallel to it, do not undergo double refraction.

Or if new faces, op, n m, Fig. 263, be ground and polished parallel to the axis, a b, a ray falling in the direction dƒ also remains single.

m

Fig. 263.

But if the refracting faces are neither at right angles nor parallel

Fig. 262.

to the axis, double refraction always ensues.

While Iceland spar has only one axis of double refraction, there are other crystals, such as mica, topaz, gypsum, &c., that have two. In crystals that have but one axis there are differences. In some the extraordinary ray is inclined from the axi; in others towards it, when compared with the ordinary ray. The former are called negative crystals, the latter positive.

The explanation which the undulatory theory gives of this phenomenon in crystals having a principal axis is, that the ether existing in the crystal is not equally elastic in every direction. Undulations are therefore propagated unequally, and a division of the ray takes place, those undulations which move quickest having the less index of refraction.

When the two rays emerging from a rhomb of Iceland spar are examined, they are both found to consist of light totally polarized, the one being polarized at right angles to the other. We have, therefore, several different ways in which light can be polarized-by reflection, refraction, absorption, and double refraction.

When a crystal of Iceland spar is ground to a prismatic shape, and then achromatized by a prism of glass, it forms one of the most valuable pieces of polarizing apparatus that we have. Such a prism may be used to very great vantage, instead of the mirror of the apparatus, Fig. 260.

E

If a ray of polarized light is passed through a thin plate of certain crystallized bodies, such as mica or gypsum, and the light then viewed through an achromatic prism, or by reflection from the second mirror of the polarizing machine, brilliant colours are at once developed. Thus, let R A, Fig. 264, be a ray of light incident on the first mirror of the polariscope, A C the resulting polarized ray, and D E F G be a thin plate of gypsum or mica. If, previously to the introduction of this

Fig. 264.

plate, the two mirrors A, and C, be crossed, or at right angles to one another, the eye placed at E will perceive no light; but, on the introduction of the crystal, its surface appears to be covered with brilliant colours, which change their tints according as it is inclined, or as the light passes through thicker or thinner places. On further examination it will be found that there are two lines, D E and F G, which, when either of them is parallel or perpendicular to

the plane of polarization, RA C, or A CE, no colours are produced. But if the plate be turned round in its own plane a single colour appears, which becomes most brilliant when either of the lines a b, c d, inclined 45° to the former ones, are brought into the plane of polarization. The former lines are called the neutral, and the latter the depolarizing axes of the film.

This is what takes place so long as we suppose the two mirrors, A C, fixed; but if we make the mirror nearest to the eye revolve while the film is stationary, the phenomena are different. Let the film be of such a thickness as to give a red tint, and be fixed in such a position as to give its maximum coloration, and the eye-mirror to revolve, it will be found that the brilliancy of the colour declines, and it disappears when a revolution of 45° has been accomplished; and now a pale green appears, which increases in brilliancy until 90° are reached, when it is at a maximum. Still continuing the revolution, it becomes paler, and at 135° it has ceased, and a red blush commences, which reaches its maximum at 180°; and the same system of changes is run through in passing from 180° to 360°; so that while the film revolves, only one colour is seen; but as the mirror revolves two appear.

If, instead of using a mirror, we use an achromatic prism, we have two images of the film at the same time, and we find that they exhibit comple

Fig. 265.

mentary colours that is, colours of such a tint that if they be mixed together they produce white light. This effect is represented in Fig. 265.

That the particular colours which appear, depend on the thickness of the films, is readily established by taking a thin wedge-shaped piece of sulphate of lime, and exposing it in the polariscope. All the different colours are then seen arranged in stripes according to the thickness of the film.

When a slice of an uniaxial crystal

cut at right angles to the axis is used, instead of the films in the foregoing experiment, very brilliant effects are produced, consisting of a series of

coloured rings, ar

ranged symmetrically, and marked in the middle by a cross, which may either be light or dark-Figs. 266, 267-light if the second mirror is in the proper position to reflect the light from the first, and dark if it be at right angles thereto.

In crystals having

two axes, a complicated

system of oval rings, originating round each axis, may be perceived, intersected by a cross. Figs. 268, 269, represent the appearance in a crystal of

nitrate of potash; and in the same way other figures arise with different crystals.

If transparent non-crystallized bodies are employed in these experiments, no colours whatever are perceived. Thus, a plate of glass, placed in the polariscope, gives rise to no such development; but if the structure of the glass be disturbed, either by warming it or cooling it unequally, or if it be subjected to unequal pressure from screws, then colours are at once developed : Figs. 270, 271. This property may, however, be rendered permanent in glass by heating until it becomes soft, and then cooling it with rapidity. All the phenomena here

described belong to the division of plane polarization; but there are other modifications which can be impressed on light, giving rise to very remarkable and intricate results; these are designated circular, elliptical, &c., polarization.

Fig. 270.

Fig. 271.

The mechanism of the motions impressed on the ether to produce these results is not difficult to comprehend; for common light, as has been stated, originates in vibrations taking place in every direction transverse to the ray; plane polarized light arises from vibrations in one direction only; and when the ethereal molecules move in circles they originate circularly polarized light, and if in ellipses, elliptical.

CHAPTER XLIV.

NATURAL OPTICAL PHENOMENA.

The Rainbow-Conditions of its Appearance-Formation of the Inner Bow -Formation of the Outer Bow-The Bows are Circular Arcs-Astronomical Refraction-Elevation of Objects-The Twilight-Reflection from the Air-Mirages and Spectral Apparitions, and Unusual Refraction.

THE rainbow, the most beautiful of meteorological phenomena, consists of one or more circular arcs of prismatic colours, seen when the back of the observer is turned to the sun, and rain is falling between him and a cloud,