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must have reference to certain directions transverse to that of the ray is equally established as a consequence of phenomena and these two principles must form the basis of any explanation which can be attempted."

In order to understand transversal vibrations, let us first consider how waves of water, and of other liquids, are formed. If a stone be thrown into a pond, there is formed a system or group of waves, which commences at the spot where the stone impinges, and gradually extends outwards in the form of concentric circles. The aqueous particles in the centre are forced down, and the surrounding ones thereby urged upwards above the normal level of the water. In this way the central depression, and the first or innermost circular heap, are formed. But gravity soon causes this heap to subside, and fill up the central depression, while by its downward progress it acquires momentum, and thereby descends below its normal level, thus not only giving rise to a circular depression, but causing the formation of another and outer circular heap by the elevation of the neighbouring particles. In this way the waves gradually extend outwards. It is obvious, then, that in waves of liquids, the directions of vibration of the molecules is vertical, or nearly so, while the propagation of the waves is horizontal.

In a vibrating cord, the vibrations are rectangular to the propagation of the undulations along the cord.

In luminous waves, the direction of vibration is supposed by Fresnel to be transverse to the direction of propagation; and the more recent researches of Cauchy seem to have established the doctrine of transversal vibrations; but he assumes a third vibration, namely, one parallel to the ray, so that, according to him, the motions of the molecules take place in three rectangular axes. The necessity for this third axis of vibration, parallel to the ray, seems to be derived from the phenomena of dispersion.

Now, polarized light, on the wave hypothesis, is light which has only one plane of vibration; whereas common or unpolarized light consists of light having two or more planes of vibrations, of which two must be rectangular-that is, after the molecules have vibrated in one plane, they change their vibration to another plane. So that common light consists in a rapid succession of waves in which the vibrations take place in different planes. It does not, however, appear that the planes of vibration are continually changing; but that in each system of waves, there are probably several hundred successive vibrations, which are all performed in the same plane; although the vibrations. of one system bear no relation to those of another. Thus, then, we call that light polarized, in which all the vibrations take place in one plane; but when vibrations are succeeded rapidly

by other vibrations in an opposite plane, the two waves though separately called polarized, are together, termed unpolarized or common light; so that, as Fresnel has observed, common light is merely polarized light, having two planes of polarization at right angles to each other.

Thus, then, I have now replied theoretically, as well as practically, to the question, "What is polarized light?"

Partially polarized light consists, according to Sir John Herschel, of two unequally intense portions; one completely polarized, the other not at all. Sir David Brewster, however, regards it as light whose planes of polarization are inclined at angles less than 90°. But to the latter view some objections have been raised by Mr. Lloyd.

In the following diagram, let the straight lines represent the directions in which the ethereal molecules are supposed to vibrate. Then A B and CD will represent the direction of vibration of the ethereal molecules of two oppositely polarized rays; A B' C'D' the two rectangular directions of vibration of a ray mon or unpolarized light ; and A" B" C" D" a ray of partially polarized light, according to Sir D. Brewster's hypothesis.

FIG. 10.

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"The difference between a polarized and an ordinary ray of light," says Sir John Herschel, "can hardly be more readily conceived than by assimilating the latter to a cylindrical, and the former to a four-sided prismatic rod, such as a lath or a ruler, or other long, flat, straight stick."

In order to illustrate Fresnel's notion of transversal vibrations, and of the hypothetical difference between common and polarized light, painted card models are very convenient. A piece of cardboard is cut out in a waved or undulated form, so that the curves of the upper and lower edges accord. Then, midway between these edges, a row of circular black spots is painted on the card these are to represent the ethereal molecules, while the card-board represents the plane of vibration. A single card thus cut and painted serves to illustrate a ray of plane-polarized light (Fig 4): two of them placed side by side, with their planes at right angles to each other, B, represent the two oppositely-polarized rays produced by a double refracting prism, while two so placed that they mutually cross, represent common light, C.

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We are now prepared to understand how common light becomes polarized. In the case of the doubly refracting bodies the two planes separate, for reasons that will be explained in the next lecture; and as the two waves have the planes of their vibrations at right angles to each other, we see now how the rays are said to be oppositely polarized. As these two waves are propagated with different velocities, they in consequence follow different paths. The tourmaline likewise separates the two planes; but it gradually extinguishes the one, by offering such an impediment to its progress that its vibrations are destroyed. The agency of the reflecting plate in polarizing light may also be readily accounted for. When a ray of common light falls on a transparent surface, at a certain angle, its planes of vibration are resolved into two, one of which is transmitted, the other reflected; both are polarized, but oppositely.

The action of the analyzer or test may also be easily understood. Suppose the analyzer to be a reflecting plate: if this plate be at the same angle to the ray as the polarizing plate, the vibrations will be reflected when the planes of reflexion of the polarizing and analyzing plates coincide-but will be transmitted (that is not reflected) when the planes are at right angles to each other. Suppose the analyzer to be a tourmaline plate: in one position this plate permits the vibrations to be transmitted, but in a position perpendicular to this it destroys them. So that in these two rectangular directions, the crystal of tourmaline must possess unequal elasticities; for the motion or vibration is transmitted in the one, but stifled or destroyed in the other direction. Suppose the analyzer to be a rhombohedron of Iceland spar; in either of two rectangular directions the vibrations of the polarized incident ray are propagated unchanged, but at an angle of 45° to either of these positions, the plane of vibration of the incident ray is resolved into two rectangular planes, each of which forms an angle of 45° with the incident ray.

Interferences of Light.-It is a law in dynamics, that the velocity produced by two joint forces, when they act in the same direction, will be as the sum of the forces. Hence if two waves, all of whose parts respectively coincide, meet, it is evident that their velocities will be doubled. Whether the vibrating medium be water, air (sound), or ether (light), this statement holds good the intensity of the waves is doubled.

But the velocity of two joint forces, when they act in opposite directions, will be as their differences. Hence, if a wave (of water, air, or ether) be half an undulation behind another wave, the velocities of the two are mutually destroyed. When stones are thrown into a pond, and two groups of waves cross each other on its surface, there are points at which the water remains immoveable when the two systems are nearly of the same magnitude, while there are other places in which the force of the water is augmented by their concurrence. If two sonorous undulations differ a little from each other in frequency, they alternately tend to destroy each other, and to acquire a double, or, perhaps, a quadruple force; and the sound gradually increases and diminishes in continued succession at equal intervals. This alternate intension and remission is called a beat.

white.

FIG. 12.

In the same way, the waves of the luminiferous ether interfere, and, mutually destroying each other, cause darkness. This important fact, that under some circumstances, light added to light causes darkness—a fact apparently fatal to the projectile theory of light-was first established by Dr. Young. This distinguished philosopher-whose attainments and knowledge were insufficiently estimated while he was living-passed a sunbeam through a hole (O) made with a fine needle in thick paper, and brought into the diverging beam a slip of card (A B) one-thirtieth of an inch in breadth, and observed its shadow (EF) on a white screen, at different. distances. The

shadow was divided by parallel bands, but the central line (X) was always That these bands originated in the interference of the light passing on both sides of the card, Dr. Young demonstrated by simply intercepting the light on one side by a screen (CD), leaving the rays on the other side to pass freely. In this arrangement all the fringes which had before existed in the shadow immediately disappeared, although the light inflected on the edge

(A) was allowed to retain its course. The same result took place when the intercepting body was at C D, before the edge B of the body.

By a series of wooden sliders, originally contrived by Young*, but put into a very convenient form for use in the lecture-room, by my friend Mr. Woodward, the interference of waves may be neatly illustrated. By this apparatus it will be seen that when the difference amounts to 2, 4, 6, or other even number of half undulations, the waves coincide and mutually augment their intensities; while, when the difference amounts to 1, 3, 5, or other odd number of half undulations, there is discordance and mutual destruction. Now it will be perceived, that these numbers coincide with those referred to by Newton, as expressive of his fits of transmission and reflection.

If two waves of homogeneous or monochromatic light interfere, the result will be an augmentation or diminution of brilliancy, or complete destruction. The light is augmented when the waves accord-but is lessened or destroyed when they are mutually opposed. Hence Newton's rings, seen by homogeneous light, are merely dark and light bands of one and the same colour.

But if two waves of heterogeneous or white light interfere, the result will be the production of vivid coloured fringes. Certain colours are destroyed, while others remain, or have their brilliancy augmented.

It is a law in dynamics, that a body acted upon by two forces united, will describe the diagonal of a parallelogram in the same time in which it would have described its sides by the separate action of those forces+. Hence, if two waves, whose molecules are in the same phases of vibration, but whose planes of vibration are more or less angular, say rectangular, to each other, the only effect produced is an alteration of the plane of vibration.

This is an explanation of a fact discovered by Fresnel, and laid down by him as a law, that "two rays of light, polarized at right angles to each other, exhibit none of the phenomena of interference," that is, they produce no colours or fringes.

If both the forces act upon a body in such a manner as to move it uniformly, the diagonal described will be a straight line; but if one of the forces acts so as to make the body move faster and faster, then the line described will be a curve. Now this dynamical law explains how two plane luminous waves, whose molecules are vibrating in rectangular planes, by their mutual action, produce a circular or elliptical wave. For if two

* Lectures on Natural Philosophy, vol. i., p. 390, plate xxv., fig. 352 D. + This fact was demonstrated by a neat machine, invented by Mr. E. M. Clarke, of the Strand.

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