Robert Routledge

The foregoing pages have been devoted to the description of inventions or operations in which mechanical actions are the most obvious features. Some of the contrivances described have for their end and object the communication of motion to certain bodies, others the arrangement of materials in some definite form, and all are essentially associated with the idea of what is called matter. But we are now about to enter on another region—a region of marvels where all is enchanted ground—a region in which we seem to leave far behind us our grosser conceptions of matter, and to attain to a sphere of more refined and subtile existence. For we are about to show some results of those beautiful investigations in which modern science has penetrated the secrets of Nature by unfolding the laws of light—

“Light

Ethereal, first of things, quintessence pure.”

The diversity and magnificence of the spectacles which, by day as well as by night, are revealed to us by the agency of light, have been the theme of the poet in every age and in every country. It cannot fail to arrest the attention to find Science declaring that all the loveliness of the landscape, the fresh green tints of early summer and the golden glow of autumn, the brilliant dyes of flowers, of insects, of birds, the soft blue of the cloudless sky, the rosy hues of sunset and of dawn, the chromatic splendour of rubies, emeralds, and other gems, the beauties of the million-coloured rainbow,—are all due to light—to light alone, and are not qualities of the bodies themselves, which merely seem to possess the colours. The following quaint stanzas, in which a poet of the seventeenth century addresses “Light” have a literal correspondence with scientific truth:

“All the world’s bravery, that delights our eyes,

Is but thy several liveries;

Thou the rich dye on them bestowest,

Thy nimble pencil paints this landscape as thou goest.

“A crimson garment in the rose thou wearest:;

A crown of studded gold thou bearest;

The virgin lilies, in their white,

Are clad but with the lawn of almost naked light.

“The violet, Spring’s little infant, stands

Girt in thy purple swaddling-bands;

On the fair tulip thou dost dote;

Thou clothest it in a gay and parti-coloured coat.”

All these beauties are indeed derived from the imponderable and invisible agent, light; and the variety and changefulness of the effects we may constantly observe show that light possesses the power of impressing our visual organs in a thousand different ways, modified by the surrounding circumstances, as witness that ever-shifting transformation scene—the sky. In the skies of such a climate as that of England there are ceaseless changes and ever-beautiful effects, producing everywhere more perfect and diversified pictures than the richest galleries can show. In the night how changed is the spectacle, when the sun’s more powerful rays are succeeded by the soft light of the moon, sailing through the azure star-bestudded vault! What limitless scope for the artist is afforded by these innumerable modifications of a single subtile agent, in light and shade, brightness and obscurity, in the contrasts and harmonies of colours, and in the countless hues resulting from their mixtures and blendings!

It will be necessary, before attempting to explain the discoveries and inventions which prove how successfully science, aided by the powerful mathematical analysis of modern times, has acquired a knowledge of the ways of light, to discuss such of the ordinary phenomena as have a direct bearing upon the subjects to be considered.

Fig. 189.—Rays.

SOME PHENOMENA OF LIGHT.

It may be considered as a matter of common experience that light is able to pass through certain bodies, such as air and gases, pure water, glass, and a number of other liquids and solids, which, by virtue of this passage of light, we term transparent, in opposition to another class of bodies, called opaque, through which light does not pass. That light traverses a vacuum may be held as proved by the light of the sun and stars reaching us across the interplanetary spaces; but it may also be made the subject of direct experiment by an apparatus described below, Fig. 190. Another fact, very obvious from common observation, is that light usually travels in straight lines. Some familiar experiences may be appealed to for establishing this fact. For example, every one has observed that the beams of sunlight which penetrate an apartment through any small opening pursue their course in perfectly straight lines across the atmosphere, in which their path is rendered visible by the floating particles of dust. It is by reason of the straightness with which rays of light pursue their course that the joiner, by looking along the edge of a plank, can judge of its truth, and that the engineer or surveyor is able by his theodolite and staff to set out the work for rectilinear roads or railways. On a grander scale than in the sunbeam traversing a room, we witness the same fact in the effect represented in Fig. 189, where the sun, concealed from direct observation, is seen to send through openings in the clouds, beams that reveal their paths by lighting up the particles of haze or mist contained in the atmosphere. It is not the air itself which is rendered visible; but whenever a beam of sunlight, or of any other brilliant light, is allowed to pass through an apartment which is otherwise kept dark, the track of the beam is always distinctly visible, and, especially if the light be concentrated by a lens or concave mirror, the fact is revealed that the air, which under ordinary circumstances appears so pure and transparent, is in reality loaded with floating particles, requiring only to be properly lighted up to show themselves.

Fig. 190.

Professor Tyndall, in the course of some remarkable researches on the decomposition of vapours by light, wished to have such a glass tube as that represented in Fig. 190, filled with air perfectly free from these floating particles. When the beam of the electric lamp passed through the exhausted tube, no trace of the existence of anything within the tube was revealed, for it appeared merely like a black gap cut out of the visible rays that traversed the air; thus proving that light, although the agent which makes all things become visible, is itself invisible—that, in fact, we see not light, but only illuminated substances. When, however, air was admitted to the tube, even after passing through sulphuric acid, the beam of the light became clearly revealed within the tube, and it was only by allowing the air to stream very slowly into the exhausted glass tube through platinum pipes, packed with platinum gauze and intensely heated, that Professor Tyndall succeeded in obtaining air “optically empty,” that is, air in which no floating particles revealed the track of the beams. The destruction of the floating matter by the incandescent metal proves the particles to be organic; but a more convenient method of obtaining air free from all suspended matter was found by Professor Tyndall to be the passing of the air through a filter of cotton wool. It must not be supposed that it is only occasionally, or in dusty rooms, laboratories, or lecture-halls, that the air is charged with organic and other particles—

“As thick as motes in the sunbeams.”

“The air of our London rooms,” says Tyndall, “is loaded with this organic dust, nor is the country air free from its pollution. However ordinary daylight may permit it to disguise itself, a sufficiently powerful beam causes the air in which the dust is suspended to appear as a semi-solid, rather than as a gas. Nobody could, in the first instance, without repugnance, place the mouth at the illuminated focus of the electric beam and inhale the dust revealed there. Nor is this disgust abolished by the reflection that, although we do not see the nastiness, we are drawing it in our lungs every hour and minute of our lives. There is no respite to this contact with dirt; and the wonder is, not that we should from time to time suffer from its presence, but that so small a portion of it would appear to be deadly to man.” The Professor then goes on to develop a very remarkable theory, which attributes such diseases as cholera, scarlet fever, small pox, and the like, to the inhalation of organic germs which may form part of the floating particles. But we must return to our immediate subject by a few words on the

VELOCITY OF LIGHT.

Fig. 191.—Telescopic appearance of Jupiter and Satellites.

It may be stated at once, that this velocity has the amazing magnitude of 185,000 miles in one second of time, and that the fact of light requiring time to travel was first discovered, and the speed with which it does travel was first estimated, about 200 years ago, by a Danish astronomer, named Roemer, by observations on the eclipses of the satellites of Jupiter. The satellites of Jupiter are four in number, and as they revolve nearly in plane of the planet’s orbit, they are subject to frequent eclipses by entering the shadow cast by the planet; in fact, the three inner satellites at every revolution. Fig. 191 represents the telescopic appearance of the planet, from a drawing by Mr. De La Rue, and in this we see the well-known “belts,” and two of the satellites, one of which is passing across the face of the planet, on which its shadow falls, and is distinctly seen as a round black spot, while the other may be noticed at the lower right-hand corner of the cut. The satellite next the planet (Io) revolves round its primary in about 42½ hours, and consequently it is eclipsed by plunging into the shadow of Jupiter at intervals of 42½ hours, an occurrence which must take place with the greatest regularity as regards the duration of the intervals, and which can be calculated by known laws when the distance of the satellite from the planet has been determined. Nevertheless, Roemer observed that the actual intervals between the successive immersions of Io in the shadow of Jupiter did not agree with the calculated period of rotation when the distance between Jupiter and the earth was changing, in consequence chiefly of the movement of the latter (for Jupiter requires nearly twelve years to complete his revolution, and may, therefore, be regarded as stationary as compared for a short time with the earth). Roemer saw also, that when this distance was increasing, the observed intervals between the successive eclipses were a little greater, and that when the distance was decreasing they were a little less, than the calculated period. And he found that, supposing the earth, being at the point of its orbit nearest to Jupiter, to recede from that planet, the sum of all the retardations of the eclipses which occur while the earth is travelling to the farthest point of its orbit, amounts to 16½ minutes, as does also the sum of the deficiencies in the period when the earth, approaching Jupiter, is passing from the farthest to the nearest point of her orbit. While, however, the earth is near the points in her orbit farthest from, or nearest to Jupiter, the distance between the two planets is not materially changing between successive eclipses, and then the observed intervals of the eclipses coincide, with the period of the satellite’s rotation. The reader will, after a little reflection, have no difficulty in perceiving that the 16½ minutes represent the time which is required by the light to traverse the diameter of the earth’s orbit; or, if he should have any difficulty, it may be removed by comparing the case with the following.

Let us suppose that from a railway terminus trains are dispatched every quarter of an hour, and that the trains proceed with a common and uniform velocity of, say, one mile per minute. Now, a person who remains stationary, at any point on the railway, observes the trains passing at regular intervals of fifteen minutes, no matter at what part of the line he may be placed. But now, let us imagine that a train having that very instant passed him, he begins to walk along the line towards the place from which the trains are dispatched: it is plain that he will meet the next train before fifteen minutes—he would, in fact, meet it a mile higher up the line than the point from which he began his walk fourteen minutes before; but the train, taking a minute to pass over this mile, would pass his point of departure just fifteen minutes after its predecessor. And our imaginary pedestrian, supposing him to continue his journey at the same rate, would meet train after train at intervals of fourteen minutes. Similarly, if he walked away from the approaching trains, they would overtake him at intervals of sixteen minutes. And again, it would be easy for him to calculate the speed of the trains, knowing that they passed over each point of the line every fifteen minutes. Thus, suppose him to pass down the line a distance known to be, say, a quarter of a mile; suppose he leaves his station at noon, the moment a train has passed, and that he takes, say an hour, to arrive at his new station a quarter of a mile lower; here, observing a train to pass at fifteen seconds after one o’clock, and knowing that it passed his original station at one, he has a direct measure of the speed of the trains. Here we have been explaining a discovery two centuries old; but our purpose is to prepare the reader for an account of how the velocity of light has been recently measured in a direct manner, and it certainly appears a marvellous achievement that means have been found to measure a velocity so astounding, not in the spaces of the solar system, or along the diameter of the earth’s orbit, but within the narrow limits of an ordinary room! The reliance with which the results of these direct measures will be received, will be greatly increased by the knowledge of the astronomical facts with which they show an entire concordance. In taking leave of Roemer, we may mention that his discovery, like many others, and like some inventions which have been described in this book, did not for some time find favour with even the scientific world, nor was the truth generally accepted, until Bradley’s discovery of the aberration of light completely confirmed it.

Fig. 192.

To two gifted and ingenious Frenchmen we are indebted for independent measurements of the velocity of light by two different methods. The general arrangement of M. Fizeau’s method is represented in Fig. 192, in which the rays from a lamp, L, after passing through a system of lenses, fall upon a small mirror, M N, formed of unsilvered plate-glass inclined at an angle of 45° to the direction of the rays; from this they are reflected along the axis of a telescope, T, by the lens of which being rendered parallel, they become a cylindrical beam, B, which passes in a straight line to a station, D, at a distance of some miles (in the actual experiment the lamp was at Suresnes and the other station at Montmartre, 5½ miles distant) whence the beam is reflected along the same path, and returns to the little plate of glass at M N, passing through which it reaches the eye of the observer at E. At W is a toothed wheel, the teeth of which pass through the point F, where the rays from the lamp come to a focus; and as each tooth passes, the light is stopped from issuing to the distant station. This wheel is capable of receiving a regular and very rapid rotation from clockwork in the case, C, provided with a register for recording the number of its revolutions. If the wheel turns with such a speed that the light permitted to pass through one of the spaces travels to the mirror and back in exactly the same time that the wheel moves and brings the next space into the tube, or the second space, or the third, or any space, the reflected light will reach the spectator’s eye just as if the wheel were stationary; but if the speed be such that a tooth is in the centre of the tube when the light returns from the mirror, then it will be prevented from reaching the spectator’s eye at all, so long as this particular speed is maintained, but either a decrease or an increase of velocity would cause the luminous image to reappear. Speeds between those by which the light is seen, and those by which it entirely disappears, cause it to appear with merely diminished brilliancy. It is only necessary to observe the speed of the wheel when the light is at its brightest, and when it suffers complete eclipse, for then the time is known which is required for space and tooth respectively to take the place of another space—and hence the time required for the light to pass to the mirror and back is found.

M. Foucault’s method is similar in principle to that used by Wheatstone in the measurement of the velocity of electricity. He used a mirror which was made to revolve at the rate of 700 or 800 turns per second, and the arrangement of the apparatus was such as to admit of the measurement of the time taken by light to pass over the short space of about four yards! More recently, however, he has modified and improved his apparatus by adopting a most ingenious plan of maintaining the speed of the mirror at a determined rate, which he now prefers should be 400 turns per second, while the light is reflected backwards and forwards several times, so that it traverses a path of above 20 yards in length. The time taken by the light to travel this short distance is, of course, extremely small, but it is accurately measured by the clockwork mechanism, and found to be about the 1
150000000th of a second! The results of these experiments of Foucault’s make the velocity of light several thousand miles per second less than that deduced from the astronomical observation of Roemer and Bradley, in which the distance of the earth from the sun formed the basis of the calculations; and hence arose a surmise that this distance had been over-estimated. That such had, indeed, been the case was confirmed almost immediately afterwards by a discussion among the astronomers as to the correctness of the accepted distance, the result of which has been that the mean distance, which was formerly estimated at 95 millions of miles, has, by careful astronomical observations and strict deductions, been now estimated at between 91 and 92 millions of miles. The famous transit of Venus December 9th, 1873–-to observe which the Governments of all the chief nations of the world sent out expeditions—derived its astronomical and scientific importance from its furnishing the means of calculating, with greater correctness than had yet been attained, the distance of the earth from the sun.

Fig. 193.

Fig. 194.

Fig. 195.

REFLECTION OF LIGHT.

Long before plate glass backed by brilliant quicksilver ever reflected the luxurious appointments of a drawing-room; long before looking-glass ever formed the mediÆval image of “ladye fair”; long before the haughty dames of imperial Rome were aided in their toilettes by specula; long before the dark-browed beauties of Egypt peered into their brazen mirrors; long, in fact, before men knew how to make glass or to polish metals, their attention and admiration must have often been riveted by those perfect and inverted pictures of the landscape, with its rocks, trees, and skies, which every quiet lake and every silent pool presents. Enjoyment of the spectacle probably prompted its imitation by the formation artificially of smooth flat reflecting surfaces; and no doubt great skill in the production of these, and their application to purposes of utility, coquetry, and luxury, preceded by many ages any attempt to discover the laws by which light is reflected. The most fundamental of these laws are very simple, and for the purpose we have in view, it is necessary that they should be borne in mind. Let A B, Fig. 193, be a plane reflecting surface, such as the surface of pure quicksilver or still water, or a polished surface of glass or metal, and let a ray of light fall upon it in the direction, I O, meeting the surface at O, it will be reflected along a line, O R,—such that if at the point O we draw a line, O P, perpendicular to the surface, the incident ray, I O, and the reflected ray, O R, will form equal angles with the perpendicular—in other words, the angle of incidence will be equal to the angle of reflection, and the perpendicular, the incident ray, and the reflected ray, will all be in one plane perpendicular to the reflecting plane. It would be quite easy to prove from this law that the luminous rays from any object falling on a plane reflecting surface are thrown back just as if they came from an object placed behind the reflecting surface symmetrically to the real object. The diagrams in Figs. 194 and 195 will render this clear. In the second diagram, Fig. 195, it will be noticed that only the portion of the mirror between Q and P takes any part in the action, and therefore it is not necessary, in order to see objects in a plane mirror, that the mirror should be exactly opposite to them; thus the portion O Q might be removed without the eye losing any part of the image of the object A B.

Fig. 196.

There are many very interesting and important scientific instruments in which the laws of reflection from plane surfaces are made use of—such, for example, as the sextant and the goniometer; but passing over all these, we may say a word about the formation of several images from one object by using two mirrors. It has already been explained that the action of a plane mirror is equivalent to the placing of objects behind it symmetrically disposed to the real object. The reflections, or virtual images in the mirror, behave optically exactly as if they were themselves real objects, and are reflected by other mirrors in precisely the same manner. From this it follows that two planes inclined to each other at an angle of 90° give three images of an object placed between them, the images and the object apparently placed at the four angles of a rectangle. When the mirrors are inclined to each other at an angle of 60°, five images are produced, which, with the original object, show an hexagonal arrangement. The formation of these by the principle of symmetry is indicated in Fig. 196. It was these symmetrically disposed images which suggested to Sir David Brewster the construction of the instrument so well known as the kaleidoscope, in which two—or, still better, three—mirrors of black glass, or of glass blackened on one side, are placed in a pasteboard tube inclined to each other at 60°: one end of the tube is closed by two parallel plates of glass; the outer one ground, but the inner transparent, leaving between them an interval, in which are placed fragments of variously-coloured glass, which every movement of the instrument arranges in new combinations. At the other end of the tube is a small opening—on applying the eye to which one sees directly the fragments of glass, with their images so reflected that beautifully symmetrical patterns are produced; and this with endless variety. When this instrument was first made in the cheap form in which it is now so familiarly known, it obtained a popularity which has perhaps never been equalled by any scientific toy, for it is said that no fewer than 200,000 kaleidoscopes were sold in London and Paris in one month.

Fig. 197.—Polemoscope.

By way of contrast to the mirrors of the kaleidoscope harmlessly producing beautiful designs, by symmetrical images of fragments of coloured glass, we show the reader, in Fig. 197, mirrors which are reflecting quite other scenes, for here is seen the manner in which even the plane mirror has been pressed into the service of the stern art of war. The mirrors are employed, not like those of Archimedes, to send back the sunbeams from every side, and by their concentration at one spot to set on fire the enemy’s works, but to enable the artillerymen in a battery to observe the effect of their shot, and the movement of their adversaries, without exposing themselves to fire by looking over the parapet of their works. The contrivance has received the appropriate name of Polemoscope (p??e??, war, and s??pe?, to view), and it consists simply, as shown in the figure, of two plane mirrors so inclined and directed, that in the lower one is seen by reflection the localities which it is desired to observe.

Fig. 198.—Apparatus for Ghost Illusion.

We return once more to the arts of peace, in noticing the advantage which has been lately taken of plane mirrors for the production of spectral and other illusions, in exhibitions and theatrical entertainments, the improvement in the manufacture of plate-glass having permitted the production of enormous sheets of that substance. Among the most popular exhibitions of this class was that known as “Pepper’s Ghost,” the arrangement of the mirrors having been the subject of a patent taken out by Mr. Pepper and Mr. Dircks jointly. The principle on which the production of the illusion depends, may be explained by the familiar experience of everybody who has noticed that, in the twilight, the glass of a window presents to a person inside of a room the images of the light or bright objects in the apartment, while the objects outside are also visible through the glass. As, by night coming on, the reflections increase in brilliancy, the darkness outside is almost equivalent to a coat of black paint on the exterior surface of the glass; but, on the contrary, in the daylight no reflection of the interior of the room is visible to the spectator inside, on looking towards the window. The reflections are present, nevertheless, in the day-time as well as at night, only they are overpowered and lost when the rays which reach the eye through the glass are relatively much more powerful. Even in the day-time the image of a lighted candle is usually visible, in the absence of direct sunshine, against a dark portion of the exterior objects as a back-ground. The visibility, or otherwise, of the internal objects by reflection, and of the external objects seen through the glass, depends entirely on the relative intensities of the illumination, for the more illuminated side overpowers and conceals the other, just as the rising sun causes the stars “to pale their ineffectual fires.” Hence, on looking through the window on a dark night, we cannot see objects out of doors unless we screen off the reflection of the illuminated objects in the room. If the rays transmitted through the glass, and those which are reflected, have intensities not very different, we see then the reflected images mixed up in the most curious manner with the real objects. It is exactly in this way that the ghosts are made to appear in the illusion of which we are speaking. The real actors are seen through a large plate of colourless and transparent glass, and from the front surface of this glass rays are reflected which apparently proceed from a phantom taking a part in the scene among the real actors. The arrangement is shown in Fig. 198, where E G is the stage, separated from the auditorium, h, by a large plate of transparent glass, E F, placed in an inclined position, and not visible to the spectators, for the lights in front are turned down, and the stage is also kept comparatively dark. Parallel to the large plate of glass is a silvered mirror, C D, placed out of the spectators’ sight, and receiving the rays from a person at A, also out of sight of the spectators, and strongly illuminated by an oxy-hydrogen lime-light at B. The manner in which the rays are reflected from the silvered mirror to the plate-glass, and hence reflected so as to reach the spectators and give them the impression of a figure standing on the stage at G, is sufficiently indicated by the lines drawn in the diagram. The apparitional and unsubstantial character of the image is derived from its seeming transparency, and from the manner in which it may be made to melt away, by diminishing the brightness of the light which falls on the real person. The introduction of the second mirror was a great improvement, for by this the phantom is made to appear erect, while its original stands in a natural attitude. Whereas, with only the plate-glass, E F, the ghost could not be made to appear upright, unless, indeed, as was sometimes done, the plate was inclined at an angle of 45°, and the actor of the ghost lay horizontally beneath it. A scene of the kind produced by the improved apparatus, is represented in Fig. 198a.

Fig. 198a.—The Ghost Illusion.

Another illusion is produced by the help of a large silvered mirror, placed at an inclination of 45°, sloping backwards from the floor, and, in consequence, presenting to the spectators the image of the ceiling, which appears to them the back of the scene. The mirror is perforated near the centre by an opening, through which a person passes his head, and, all his body being concealed by the mirror, the effect produced is that of a head floating in the air. Means are provided of withdrawing the mirror, when necessary, while the curtain is down, and then the real back of the scene appears, which, of course, is exactly similar to the false one painted on the ceiling. Fig. 199 represents a scene produced at the Polytechnic by a somewhat similar arrangement of mirrors, under the management of Mr. Pepper. Plane mirrors were employed in another piece of natural magic which this gentleman exhibited to the public, who were shown a kind of large box, or cabinet, raised from the floor, and placed in the middle of the stage, so that the spectators might see under it and all round it. Inside of the box were two silvered mirrors the full height of it, and these were hinged to the farther angles, so that each one being folded with its face against a side of the box, their backs formed the apparent sides, and were painted exactly the same as the real interior of the box. When the performer enters the box, the door is closed for an instant, while he, stepping to the back, turns the mirrors on their hinges until their front edges meet, where an upright post in the middle of the box conceals their line of junction. The performer thus places himself behind the mirrors in the triangular space between them and the back of the box, while the mirrors, now inclined at angles of 45° to the sides, reflect images of these to the spectators when the door is opened, and the spectators see then the box apparently empty, for the reflection of the sides appears to them as the back of the cabinet. The entertainment was sometimes varied by a skeleton appearing, on the door being opened, in the place of the person who entered the cabinet. It is hardly necessary to say that the skeleton was previously placed in the angle between the mirrors where the performer conceals himself.

Fig. 199.—Illusion produced by Mirrors.

Fig. 200.—A Stage Illusion.

To the same inventive gentleman, whose ingenious use of plane mirrors has thus largely increased the resources of the public entertainer, is due another stage illusion, the effect of which is represented in Fig. 200; and, although it does not depend on reflection, it may be introduced here as showing how the perfection of the manufacture of plate-glass, which makes it available for the ghost exhibition, can be applied in another way in dramatic spectacles. The female form, here supposed to be seen in a dream by the sleeper, is not a reflection, although she appears floating in mid-air, strangely detached from all supports, but the real actress. This is accomplished by making use of the transparency of plate-glass, a material strong enough to afford the necessary support, and yet invisible under the circumstances of the exhibition.

But it is not behind the turned-down footlights, or in the exhibitions of the showman, that we find the most beautiful illustrations of the laws of reflection. In the quiet mountain mere, amid the sweet freshness of nature, we may often see tree, and crag, and cliff, so faithfully reproduced, that it needs an effort of the understanding to determine where substance leaves off and shadow begins, a condition of the liquid surface indicated in two lines by Wordsworth:

“The swan, on still St. Mary’s Lake,

Floats double, swan and shadow.”

The landscape painter is always gratified if he can introduce into his picture some piece of water, and it can hardly be doubted that much of the charm of lakes and rivers is due to their power of reflecting. Look on Fig. 201, a view of some buildings at Venice; and, in order to see how much of its beauty is owing to the quivering reflections, imagine the impression it would produce were the place of the water occupied by asphalte pavement, or a grass lawn. The condition of the reflections here represented is perhaps even more pleasing than that produced by perfect repose: they are in movement, and yet not broken and confused:

“In bright uncertainty they lie,

Like future joys to Fancy’s eye.”

Fig. 201.—View of Venice—Reflections.

REFRACTION.

That light moves in straight lines is a statement which is true only when the media through which it passes are uniform; for it is easily proved that when light passes from one medium to another, a change of direction takes place at the common surface of the media in all rays that meet this surface otherwise than perpendicularly. As a consequence of this, it really is possible to see round a corner, as the reader may convince himself by performing the following easy experiment. Having procured a cup or basin, Fig. 202, let him, by means of a little bees’-wax or tallow, attach to the bottom of the vessel, at R, a small coin. If he now places the cup so that its edge just conceals the coin from view, and maintains his eye steadily in the same position as at I, he will, when water is poured into the cup, perceive the coin apparently above the edge of the vessel in the direction I R´, that is, the bottom of the cup will appear to have risen higher. Since it is known that in each medium the rays pass in straight lines, the bending which renders the coin visible can therefore only take place at the common junction of the media, or, in other words, the ray, R O, passing from the object in a straight line through the water, is bent abruptly aside as it passes out at the surface of the water, A B, and enters the air, in which it again pursues a straight course, reaching the eye at I, where it gives the spectator an impression of an object at R´. This experiment is also an illustration of the cause of the well-known tendency we have to under-estimate the depth of water when we can see the bottom. The broken appearance presented by an oar plunged into clear water is due to precisely the same cause. The curious exaggerated sizes and distorted shapes of the gold-fish seen in a transparent globe have their origin in the same bending aside of the rays. This deviation which light undergoes in passing obliquely from one medium into another is known by the name of refraction, and it is essential for the understanding of the sequel that the reader should be acquainted with some of the laws of this phenomenon, although their discovery by Snell dates two centuries and a half anterior to the present time. Let T O, Fig. 203, be a ray of light which falls obliquely upon a plane surface, A B, common to two different media, one of which is represented by the shaded portion of the figure, A B C D, of which C D represents another plane surface, parallel to the former. If the ray, T O, suffered no refraction, it would pursue its course in a straight line to R´; but as a matter of fact it is found that such a ray is always bent aside at O, if the medium A B C D is more or less dense than the other. If, for example, A B C D is water, and the medium above it glass, then the ray entering at O will take the course O R; but if A B C D is a plate of glass with water above and below it, the ray will take the course T O, O R, R B, suffering refraction on entering the glass, and again on leaving it, so that R B will emerge from the glass parallel to its original direction at T O. If through the point of incidence, O, we suppose a line, O P, to be drawn perpendicular to the surface, A B, then we may say that the ray in passing from the rarer medium (water, air, &c.) into the denser medium (glass, &c.) is bent towards the perpendicular, or normal, as at O; but that on leaving the denser to enter the rarer medium, as at R, it is bent away from the perpendicular. In other words, the angle b O a is less than the angle m O T, and O R forms a less angle with R P´ than R B´ does. It is also a law of ordinary refraction that the normal, O P, at the point of incidence, the incident ray, T O, and the refracted ray, O R, are all in the same plane. Besides, there is the important and interesting law discovered by Snell and by Descartes, which may thus be explained with reference to Fig. 203. On the incident and refracted rays, T O and O R, let us suppose that any equal distances, O d and O b, are measured off from O, and that from each of the points a and b, perpendiculars, a m and b n, are drawn to the normal, P P, which passes through O; then it is found that, whatever may be the angle of incidence, T O P, or however it is made to vary, the length of the line a m bears always the same proportion to the line b n for the same two media. Thus, if A B C D be water, and T O enters it out of the air, the length of the line a m divided by the length of the line a b will always (whatever slope T O may have) give the quotient 1·33. This number is, therefore, a constant quantity for air and water, and is called the index of refraction for air into water. The law just explained is expressed by the language of mathematics thus: For two given media the ratio of the sines of the angles of incidence and of refraction is constant.

Fig. 202.

Fig. 203.

It is an axiom in optical science that a ray of light when sent in the opposite direction will pursue the same path. Thus in Fig. 203 the direction of the light is represented as from T towards B´; but if we suppose B´ R to be an incident ray, it would pursue the path B´ R, R O, O T, and in passing out of the denser medium, A B C D at O, its direction is farther from the normal, P P, or O T, as the law of sines, a m will be always longer than n b, and will bear a constant ratio to it. Suppose the angle R O P to increase, then P O B will become a right angle; that is, the emergent ray, O T, will just graze the surface, A B, when the angle R O P has some definite value. If this last angle be further increased, no light at all will pass out of the medium A B C D, but the ray R O will be totally reflected at O back into the medium, A B C D, according to the laws of reflection. The angle which R O forms with O P when O T just skims the surface, A B, is termed the limiting angle, or the critical angle, and its value varies with the media. The reader may easily see the total reflection in an aquarium, or even in a tumbler of water, when he looks up through the glass at the surface of the water, which has then all the properties of a perfect mirror.

The power of lenses to form images of objects is entirely due to these laws of refraction. The ordinary double-convex lens, for example, having its surfaces formed of portions of spheres, refracts the rays so that all the rays which from one luminous point fall upon the lens, meet together again at a point on the other side, the said point being termed their focus. It is thus that images of luminous bodies are formed by lenses. An explanation of the construction and theory of lenses cannot, however, be entered into in this place.

One important remark remains to be made—namely, that in the above statement of the laws of reflection and refraction, certain limitations and conditions under which they are true and perfectly general have not been expressed; for the mention of a number of particulars, which the reader would probably not be in a condition to understand, would only tend to confuse, and the explanation of them would lead us beyond our limits. Some of these conditions belong to the phenomena we have to describe, and are named in connection with them, and others, which are not in immediate relation to our subject, we leave the reader to find for himself in any good treatise on optics.

DOUBLE REFRACTION AND POLARIZATION.

About two hundred years ago, a traveller, returning from Iceland, brought to Copenhagen some crystals, which he had obtained from the Bay of RoËrford, in that island. These crystals, which are remarkable for their size and transparency, were sent by the traveller to his friend, Erasmus Bartholinus, a medical man of great learning, who examined them with great interest, and was much surprised by finding that all objects viewed through them appeared double. He published an account of this singular circumstance in 1669, and by the discovery of this property of Iceland spar, it became evident that the theory of refraction, the laws of which had been studied by Snell and by Huyghens a few years before, required some modification, for these laws required only one refracted ray, and Iceland spar gave two. Huyghens studied the subject afresh, and was able, by a geometrical conception, to bring the new phenomena within the general theory of light. Iceland spar is chemically carbonate of lime (calcium carbonate), and hence is also called calc spar, and, from the shape of the crystals, it has also been termed rhombohedral spar. The form in which the crystals actually present themselves is seen in Fig. 204, which also represents the phenomenon of double refraction. Iceland spar splits up very readily, but only along certain definite directions, and from such a piece as that represented in Fig. 204 a perfect rhombohedron, such as that shown in Fig. 206, is readily obtained by cleavage; and then we have a solid having six lozenge-shaped sides, each lozenge or side having two obtuse angles of 101° 55´, and two acute angles of 78° 5´. Of the eight solid corners, such as A B C, &c., six are produced by the meeting of one obtuse and two acute angles, and the remaining two solid corners are formed by the meeting of three obtuse angles. Let us imagine that a line is drawn from one of these angles to the other: the diagonal so drawn forms the optic axis of the crystal, and a plane passing through the optic axis, A B, Fig. 205, and through the bisectors of the angles, E A D and F B G, marks a certain definite direction in the crystal, to which also belong all planes parallel to that just indicated. Any one of such planes forms what is termed a “principal section,” to which we shall presently refer.

Fig. 204.

It will be observed that in Fig. 204 the white circle on a black ground seen through the crystal is doubled; but that, instead of being white as the circle really is, the images appear grey, except where they overlap, and there the full whiteness is seen. If we place the crystal upon a dot made on a sheet of paper, or having made a small hole with a pin in a piece of cardboard, hold this up to the light, and place the crystal against it, we see apparently two dots or two holes. The two images will, if the dot or hole be sufficiently small, appear entirely detached from each other. Now, if, keeping the face of the crystal against the cardboard or paper, the observer turn the crystal round, he will see one of the images revolve in a circle round the other, which remains stationary. The latter is called the ordinary image, and the former the extraordinary image. Let us place the crystal upon a straight black line ruled on a horizontal sheet of paper, Fig. 205, and let us suppose, in order to better define the appearance, that we place it so that the optic axis, A B, is in a plane perpendicular to the paper, A being one of the two corners where the three obtuse angles meet, and B the other, and the face, A B C D, parallel to E G H B, which touches the paper. Then, according to the laws of ordinary refraction, if we look straight down upon the crystal, we should see through it the line I K, unchanged in position—that is, the ray would pass perpendicularly through the crystal as shown by L M—and, in fact, a part of the ray does this, and gives us the ordinary image, O O´; but another part of the ray departs from the laws of Snell and Descartes, and, following the course L N Y´, enters the eye in the direction N Y´, producing the impression of another line at L´, which is the extraordinary ray, E E´. If the crystal be turned round on the paper, E E´ will gradually approach O O´, and the two images will coincide when the principal section is parallel to the line I K; but the coincidence is only apparent, and results from the superposition of the two images—for a mark placed on the line drawn on the paper will show two images, one of which will follow the rotation of the crystal, and show itself to the right or left of the ordinary image, according as C is to the right or left of A. So that there are really in every portion of the crystal two images on the line, one of which turns round the other, and the coalescence of the two images twice in each revolution is only apparent, for the different parts of the lengths of the images do not coincide. On continuing the revolution of the crystal after they apparently coincide, the images are again seen to separate, the extraordinary one being now displaced on the other side, or always towards the point, C. Thus, then, the ray, on entering the crystal, bifurcates, one branch passing through the crystal and out of it in the same straight line, just as it would in passing through a piece of glass, while the other is refracted at its entrance into the crystal, although falling perpendicularly upon its face, and again at its exit. And again, when a beam of light, R r, Fig. 206, falls obliquely on a crystal of Iceland spar, it divides at the face of the crystal into two rays, R O, and r E; the former, which is the ordinary ray, follows the laws of ordinary refraction—it lies in the plane of incidence, and obeys the law of sines, just as if it passed through a piece of plate-glass. The extraordinary ray, on the other hand, departs from the plane of incidence, except when the latter is parallel to the principal section, and the ratio of the sines of the angles of incidence and refraction varies with the incidence. The reader who is desirous of studying these curious phenomena of double refraction, and those of polarization, is strongly recommended to procure some fragments of Iceland spar, which he can very easily cleave into rhombohedra, and with these, which need not exceed half an inch square, or cost more than a few pence, he can demonstrate for himself the phenomena, and become familiar with their laws. He will find very convenient the simple plan recommended by the Rev. Baden Powell, of fixing one of the crystals to the inside of the lid of a pill-box, through which a small hole has been made, and through the hole and the crystal view a pin-hole in the bottom of the box, turning the lid, and the crystal with it, to observe the rotation of the image. The same arrangement will serve, by merely attaching another rhomb of spar within the box, to study the very interesting facts of the polarization to which we are about to claim the reader’s attention.

The curious phenomena which have just been described, although in themselves by no means recent discoveries, have led to some of the most interesting and beautiful results in the whole range of physical science. The examination and discussion of them by such able investigators as Huyghens, Descartes, Newton, Fresnel, Malus, and Hamilton, have largely conduced to the establishment of the undulatory hypothesis—that comprehensive theory of light, which brings the whole subject within the reach of a few simple mechanical conceptions.

It was at first supposed that it was only one of the rays which are produced in double refraction that departed from the ordinary laws, and Iceland spar was almost the only crystal known to have the property in question. At the present day, however, the substances which are known to produce double refraction are far more numerous than those which do not possess this property, for, by a more refined mode of examination than the production of double images, Arago has been able to infer the existence of a similar effect on light in a vast number of bodies. Crystals have also been found which split up a ray of light entering them into two rays, neither of which obeys the laws of Descartes. It may, in fact, be said that, with the exception of water, and most other liquids, of gelatine and other colloidal substances, and of well-annealed glass, there are few bodies which do not exercise similar power on light.

On examining the two rays which emerge from a rhomb of Iceland spar, on which only one ray of ordinary light has been allowed to fall, we find that these emergent rays have acquired new and striking properties, of which the incident ray afforded no trace; for, if we allow the two rays emerging from a rhomb of the spar to fall upon a second rhomb, we shall find, on viewing the images produced, that their intensity varies with the position into which its second crystal is turned. Thus, if we place a rhomb of the spar upon a dot made on a sheet of white paper, we shall have, as already pointed out, two images of equal darkness. But, in placing a second rhomb of the spar upon the first, in such a manner that their principal sections coincide, and the faces of one rhomb are also parallel to the faces of the other, we shall still see two equally intense images of the dot, only the images will be more widely separated than before, and no difference will be produced by separating the crystals if the parallelism of the planes of their respective principal sections be preserved. Here, then, is at once a notable difference between a ray of ordinary light and one that emerges from a rhomb of Iceland spar; for, in the case of rays of ordinary light, we have seen that the second rhomb would divide each ray into two, whereas it is incapable (in the position of crystals under consideration) of dividing either the ordinary or the extraordinary ray which emerges from the first rhomb. If, still keeping the second rhomb above the other, we make the former rotate in a horizontal plane, we may observe that, as we turn the upper crystal so that the planes of the principal sections form a small angle with each, each image will be doubled, and, as the upper crystal is turned, each pair of images exhibits a varying difference of intensity. The ordinary ray in entering the second crystal is divided by it into a second ordinary ray and a second extraordinary ray, the intensities of which vary according to the angle between the principal sections. When the two principal sections are parallel to one plane, that is, when the angle between them is either 0° or 180°, the extraordinary image disappears, and only the ordinary one is seen, and with its greatest intensity. When the two principal sections are perpendicular to each other, that is, when the second crystal has been turned through either 90° or 270°, the extraordinary has, on the contrary, its greatest intensity, and the ordinary one disappears. When the principal section of the second crystal has been turned into any intermediate position, such as through 45° and 135°, or any odd multiple of 45°, both images are visible and have equal intensities. This experiment shows that the two rays which emerge from the first crystal have acquired new properties, that each is affected differently by the second crystal, according as the crystal is presented to it in different directions round the ray as an axis. The ray of light is no longer uniform in its properties all round, but appears to have acquired different sides, as it were, in passing through the rhomb of Iceland spar. This condition is indicated by saying that the ray is polarized, and the first rhomb of spar is termed the polarizer, while the second rhomb, by which we recognize the fact that both the ordinary and the extraordinary rays emerge having different sides, has received the name of analyser. But, in order to study conveniently all the phenomena in Iceland spar, we should have crystals of a considerable size, otherwise the two rays do not become sufficiently separated so as to make it an easy matter to intercept one of them while we examine the other. A very ingenious mode of getting rid of one of the rays was devised by Nicol, and as his apparatus is much used for experiments on polarized light, we shall state the mode of constructing Nicol’s Prism. It is made from a rhomb of Iceland spar, Fig. 207, in which a and b are the corners where the three obtuse angles meet, all equal. If we draw through a and b lines bisecting the angles d a c and f h g, and join a b, these lines will all be in one plane, which is a principal section of the crystal, and contains the axis, a b. Now suppose another plane, passing through a b, to be turned so that it is at right angles to the plane containing a b and the bisectors: this plane would cut the sides of the crystal in the lines a i, i h, b k, k a; and in making the Nicol prism, the crystal is cut into two along this plane, and the two pieces are then cemented together by Canada balsam. A ray of light, R, entering the prism, undergoes double refraction; but the ordinary ray, meeting the surface of the Canada balsam at a certain angle greater than the limiting angle, is totally reflected, and passes out of the crystal at O; while the extraordinary ray, meeting the layer of balsam at a less angle than its limiting angle, does not undergo total reflection, but passes through the balsam, and emerges in the direction of E, completely polarized, so that the ray is unable to penetrate another Nicol’s prism of which the principal section is placed at right angles to that of the first.

Among other crystals which possess the property of doubly refracting, and therefore of polarizing, is the mineral called tourmaline, which is a semi-transparent substance, different specimens having different tints. In Fig. 208, A, B, represent the prismatic crystals of tourmaline, and C shows a crystal which has been cut, by means of a lapidary’s wheel, into four pieces, the planes of division being parallel to the axis of the prism. The two inner portions form slices, having a uniform thickness of about 1
20 in., and when the faces of these have been polished, the plates form a convenient polarizer and analyser. Let us imagine one of the plates placed perpendicularly between the eye and a lighted candle. The light will be seen distinctly through it, partaking, however, of the colour of the tourmaline; and if the plate be turned round so that the direction of the axis of the crystal takes all possible positions with regard to the horizon, while the plane of the plate is always perpendicular to the line between the eye and the candle, no change whatever will be seen in the appearance of the flame. But if we fix the plate of crystal in a given position, let us say with the axial direction vertical, and place between it and the eye the second plate of tourmaline, the appearances become very curious indeed, and the candle is visible or invisible according to the position of this second plate. When the axis of the second is, like that of the first, vertical, the candle is distinctly seen; but when the axis of the second plate is horizontal, no rays from the candle can reach the eye. If the second plate be slowly turned in its own plane, the candle becomes visible or invisible at each quarter of a revolution, the image passing through all degrees of brightness. Thus the luminous rays which pass through the first plate are polarized like those which emerge from a crystal of Iceland spar. It is not necessary that the plates used should be cut from the same crystal of tourmaline, for any two plates will answer equally well which have been cut parallel to the axes of the crystals which furnished them. In the case of tourmaline the extraordinary ray possesses the power of penetrating the substance of the crystal much more freely than the ordinary ray, which a small thickness suffices to absorb altogether. It may be noted that in the simple experiment we have just described, the plate of tourmaline next the candle forms the polarizer, and that next the eye the analyser; and that until the latter was employed, the eye was quite incapable of detecting the change which the light had undergone in passing through the first plate, for the unassisted eye had no means of recognizing that the rays emerged with sides. The usual manner of examining light, to find whether it is polarized, is to look through a plate of tourmaline or a Nicol’s prism, and observe whether any change in brightness takes place as the prism or plate is rotated. Now, it so happened that in 1808 a very eminent French man of science, named Malus, was looking through a crystal of Iceland spar, and seeing in the glass panes of the windows of the Luxembourg Palace, which was opposite his house, the image of the setting sun, he turned the crystal towards the windows, and instead of the two bright images he expected to see, he perceived only one; and on turning the crystal a quarter of a revolution, this one vanished as the other image appeared. It was, indeed, by a careful analysis of this phenomenon that Malus founded a new branch of science, namely, that which treats of polarized light; and his views soon led to other discoveries, which, with their theoretical investigations, constitute one of the most interesting departments of optical science, as remarkable for the grasp it gives of the theory of light as for the number of practical applications to which it has led.

The accidental observation of Malus led to the discovery that when a ray of ordinary light falls obliquely on a mirror—not of metal, but of any other polished surface, such as glass, wood, ivory, marble, or leather—it acquires by reflection at the surface the same properties that it would acquire by passing through a Nicol’s prism or a plate of tourmaline: in a word, it is polarized. Thus, if a ray of light is allowed to fall upon a mirror of black glass at an angle of incidence of 54° 35´, the reflected ray will be found to be polarized in the plane of reflection—that is, it will pass freely through a Nicol’s prism when the principal section is parallel to the plane of reflection; but when it is at right angles to the latter, the reflected ray will be completely extinguished by the prism—that is, it is completely polarized. If the angle of the incident ray is different from 54° 35´, then the reflected ray is not completely intercepted by the prism—it is not completely but only partially polarized. The angle at which maximum polarization takes place varies with the reflecting substance; thus, for water it is 53°, for diamond 68°, for air 45°. A simple law was discovered by Sir David Brewster by which the polarizing angle of every substance is connected with its refractive index, so that when one is known, the other may be deduced. It may be expressed by saying that the polarizing angle is that angle of incidence which makes the reflected and the refracted rays perpendicular to each other. The refracted rays are also found to be polarized in a plane perpendicular to that of reflection.

Instruments of various forms have been devised for examining the phenomena of polarized light. They all consist essentially of a polarizer and an analyser, which may be two mirrors of black glass placed at the polarizing angle, or two bundles of thin glass plates, or two Nicol’s prisms, or two plates of tourmaline, or any pair formed by two of these. Fig. 209 represents a polariscope, this instrument being designed to permit any desired combination of polarizer and analyser, and having graduations for measuring the angles, and a stage upon which may be placed various substances in order to observe the effects of polarized light when transmitted through them. It is found that thin slices of crystals placed between the polarizer and analyser exhibit varied and beautiful effects of colour, and by such effects the doubly refracting power of substances can be recognized, where the observation of the production of double images would, on account of their small separation, be impossible. And the polariscope is of great service in revealing structures in bodies which with ordinary light appear entirely devoid of it—such, for example, as quill, horn, whalebone, &c. Except liquids, well-annealed glass, and gelatinous substances, there are, in fact, few bodies in which polarized light does not show us the existence of some kind of structure. A very interesting experiment can be made by placing in the apparatus, shown in Fig. 210, a square bar of well-annealed glass; on examining it by polarized light, it will be found that before any pressure from the screw C is applied to the glass, it allows the light to pass equally through every part of it; but when by turning the screw the particles have been thrown into a state of strain, as shown in the figure, distinct bands will make their appearance, arranged somewhat in the manner represented; but the shapes of the figures thus produced vary with every change in the strain and in the mode of applying the pressure.

CAUSE OF LIGHT AND COLOUR.

We have hitherto limited ourselves to a description of some of the phenomena of light, without entering into any explanation of their presumed causes, or without making any statements concerning the nature of the agent which produces the phenomena. Whatever this cause or agent may be, we know already that light requires time for its propagation, and two principal theories have been proposed to explain and connect the facts. The first supposes light to consist of very subtile matter shot off from luminous bodies with the observed velocity of light; and the second theory, which has received its great development during the present century, regards luminous effects as being due to movements of the particles of a subtile fluid to which the name of “ether” has been given. Of the existence of this ether there is no proof: it is imagined; and properties are assigned to it for no other reason than that if it did exist and possess these properties, most of the phenomena of light could be easily explained. This theory requires us to suppose that a subtile imponderable fluid pervades all space, and even interpenetrates bodies—gaseous, liquid, and solid; that this fluid is enormously elastic, for that it resists compression with a force almost beyond calculation. The particles of luminous bodies, themselves in rapid vibratory motion, are supposed to communicate movement to the particles of the ether, which are displaced from a position of equilibrium, to which they return, executing backwards and forwards movements, like the stalks of corn in a field over which a gust of wind passes. While an ethereal particle is performing a complete oscillation, a series of others, to which it has communicated its motion, are also performing oscillations in various phases—the adjacent particle being a little behind the first, the next a little behind the second, and so on, until, in the file of particles, we come to one which is in the same phase of its oscillation as the first one. The distance of this from the first is called the “length of the luminous wave.” But the ether particles do not, like the ears of corn, sway backwards and forwards merely in the direction in which the wave itself advances: they perform their movements in a direction perpendicular to that in which the wave moves. This kind of movement may be exemplified by the undulation into which a long cord laid on the ground may be thrown when one end is violently jerked up and down, when a wave will be seen to travel along the cord, but each part of the latter only moves perpendicularly to the length. The same kind of undulation is produced on the surface of water when a stone is thrown into a quiet pool. In each of these cases the parts of the rope or of the water do not travel along with the wave, but each particle oscillates up and down. Now, it may sometimes be observed, when the waves are spreading out on the surface of a pool from the point where a stone has been dropped in, that another set of waves of equal height originating at another point may so meet the first set, that the crests of one set correspond with the hollows of the other, and thus strips of nearly smooth water are produced by the superposition of the two sets of waves. Let Fig. 212 represent two systems of such waves propagated from the two points A A, the lines representing the crests of the waves. Along the lines, b b, the crests of one set of waves are just over the hollows of the other set; so that along these lines the surface would be smooth, while along C C the crests would have double the height. Now, if light be due to undulation, it should be possible to obtain a similar effect—that is, to make two sets of luminous undulations destroy each other’s effects and produce darkness: in other words, we should be able, by adding light to light, to produce darkness! Now, this is precisely what is done in a celebrated experiment devised by Fresnel, which not only proves that darkness may be produced by the meeting of rays of light, but actually enables us to measure the lengths of the undulations which produce the rays.

In Fig. 213 is a diagram representing the experiment of the two mirrors, devised by Fresnel. We are supposed to be looking down upon the arrangement: the two plane mirrors, which are placed vertically, being seen edgeways, in the lines, M O, O N, and it will be observed that the mirrors are placed nearly in the same upright plane, or, in other words, they form an angle with each other, which is nearly 180°. At L is a very narrow upright slit, formed by metallic straight-edges, placed very close together, and allowing a direct beam of sunlight to pass into the apartment, this being the only light which is permitted to enter. From what has been already said on reflection from plane mirrors, it will readily be understood that these mirrors will reflect the beams from the slit in such a manner as to produce the same effect, in every way, as if there were a real slit placed behind each mirror in the symmetrical positions, A and B. Each virtual image of the slit may, therefore, be regarded as a real source of light at A and at B; thus, for example, it will be observed that the actual lengths of the paths traversed by the beams which enter at L, and are reflected from the mirrors, are precisely the same as if they came from A and B respectively. The virtual images may be made to approach as near to each other as may be required, by increasing the angle between the two mirrors, for, when this becomes 180°, that is, when the two mirrors are in one plane, the two images will coincide. If, now, a screen be placed as at F G, a very remarkable effect will be seen; for, instead of simply the images of the two slits, there will be visible a number of vertical coloured bands, like portions of very narrow rainbows, and these coloured bands are due to the two sources of light, A and B; for, if we cover or remove one of the mirrors, the bands will disappear and the simple image of the slit will be seen. If, however, we place in front of L a piece of coloured glass, say red, we shall no longer see rainbow-like bands on the screen, but in their place we shall find a number of strips of red light and dark spaces alternately, and, as before, these are found to depend upon the two luminous sources, A and B. We must, therefore, come to the conclusion that the two rays exercise a mutual effect, and that, by their superposition, they produce darkness at some points and light at others. These alternate dark and light bands are formed on the screen at all distances, and the spaces between them are greater as the two images, A and B, are nearer together. Further, with the same disposition of the apparatus, it is found that when yellow light is used instead of red, the bands are closer together; when green glass is substituted for yellow, blue for green, and violet for blue, that the bands become closer and closer with each colour successively. Hence, the effect of coloured bands, which is produced when pure sunlight is allowed to enter at L, is due to the superposition of the various coloured rays from the white light. Let us return to the case of the red glass, and suppose that the distance apart of the two images, A and B, has been measured, by observing the angle which they subtend at C, and by measuring the distance, C O D, or rather, the distance C O L. Now, the distances of A and B from the centre of each dark band, and of each light band, can easily be calculated, and it is found that the difference between the two distances is always the same for the same band, however the screen or the mirrors may be changed. On comparing the differences of the distances of A and B in case of bright bands, with those in the case of dark ones, it was found that the former could be expressed by the even multiples of a very small distance, which we will call d, thus:

while the differences for the dark bands followed the odd multiples of the same quantity, d, thus:

These results are perfectly explained on the supposition that light is a kind of wave motion, and that the distance, d, corresponds to half the length of a wave. We have the waves entering L, and pursuing different lengths of path to reach the screen at F G, and, if they arrive in opposite phases of undulation, the superposition of two will produce darkness. The undulations will plainly be in opposite phases when the lengths of paths differ by an odd number of half-wave lengths, but in the same phase when they differ by an even number. Hence, the length of the wave may be deduced from the measurement of the distances of A and B from each dark and light band, and it is found to differ with the colour of the light. It is also plain that, as we know the velocity of light, and also the length of the waves, we have only to divide the length that light passes over in one second, by the lengths of the waves, in order to find how many undulations must take place in one second. The following table gives the wave-lengths, and the number of undulations for each colour:

These are the results, then, of such experiments as that of Fresnel’s, and although such numbers as those given in the table above are apt to be considered as representing rather the exercise of scientific imagination than as real magnitudes actually measured, yet the reader need only go carefully over the account of the experiment, and over that of the measurement of the velocity of light, to become convinced that by these experiments something concerned in the phenomena of light has really been measured, and has the dimensions assigned to it, even if it be not actually the distance from crest to crest of ether waves—even, indeed, if the ether and its waves have no existence. But by picturing to ourselves light as produced by the swaying backwards and forwards of particles of ether, we are better able to think upon the subject, and we can represent to ourselves the whole of the phenomena by a few simple and comparatively familiar conceptions.

As an example of the facility with which the ether theory lends itself to aiding our notions of the phenomena of light, take the explanation of polarization. Let us suppose that we are looking at a ray of light along its direction, and that we can see the particles of ether. We should, in such a case, see them vibrating in planes having every direction, and their paths, as so seen, would be represented by an indefinite number of the diameters of a circle. Now, suppose we make the ray first pass through a rhomb of Iceland spar: we should, if we could see the vibrating particles in the emergent ordinary and extraordinary rays, perceive them swaying backwards and forwards across the direction of the rays in two planes only, as represented by the lines, B D and A C, in the two circles, O o and E e, Fig. 214–-that is, half the particles would be vibrating in the direction B D, and the other half in the direction A C; and further, the two directions would be at right angles to each other—the vibrations forming the extraordinary ray being performed in a plane at right angles to that in which the vibrations producing the ordinary ray take place. If—these planes being in the position indicated in 1, Fig. 214–-we turn the crystal round through 90°, they would rotate with it, and would come severally into the position shown in 2, Fig. 214.

It was at one time objected to the theory which represents light as due to wave-like movements that, just as the vibrations which constitute sound spread in all directions, and go round intercepting bodies, enabling us, for example, to hear the sound of a bell even when a building intervenes, so if vibrations really produce light, these would extend within the shadows, and we ought to perceive light within the shadows, bending, as it were, round the edge of the shadow-casting body. This objection, which at one time presented a great difficulty for the wave theory, was triumphantly removed by the discovery that the luminous vibrations do extend into the shadow, and that this is in reality never completely dark. It is true that, although we can hear round a corner, we are in general unable to see round it; but it should be noticed that in the case of hearing, the sound is much weakened by intervening objects, and that there are what may be termed sound shadows. A ray of light produces sensible effects only in the direction of its propagation; but it can be shown that the successive portions of the waves advancing along it are centres of lateral disturbances producing new or secondary waves in all directions, which, however, interfere with and destroy each other. When an opaque screen intercepts a portion of the principal wave, it also stops a number of oblique or secondary waves, which would interfere more or less with the rest. Under ordinary circumstances, the remaining oblique or secondary rays are quite insensible in the presence of the direct light. But, with an apparatus which will cost but the two or three minutes’ time required to construct it, the reader may see for himself that light is able to pass round an obstacle, and he may witness directly phenomena of the same order as those presented in the experiment of Fresnel’s mirrors, which require costly apparatus for their production. He has only to take two fragments of common window-glass, and having made a piece of tinfoil adhere to one surface of each piece of glass, cut, with a sharp penknife, the finest possible slit in each piece of tinfoil, making the slit from ½ in. to 1 in. in length. If he will then hold one piece of glass about 2 ft. from his eye, so that it may be in the line between his eye and the sun (or other luminous body), and hold the other piece close to his eye with its slit parallel to that in the first piece, he will see the latter not simply as a line of light, but parallel to it a number of brilliantly-coloured rainbow-like bands will be seen on either side. If, instead of receiving the light from the sun, or from a candle-flame, the light given off by a spirit-lamp, with a piece of salt on its wick, be used, bright yellow stripes will be seen with dark spaces between them. Or, if the piece of glass next the sun be red-coloured, instead of plain glass, no rainbow-like bands will be visible, but a number of bright red stripes alternating with dark bands will be seen. The reader will have probably now little difficulty in perceiving that these can be easily explained as the results of interferences of a kind quite analogous to those of the waves of water represented in the diagram, Fig. 212. The rainbow-like stripes are due to the different wave-lengths of the different colours, as a consequence of which the bright and dark bands would be formed at different positions. Our limits do not admit of a full explanation of these beautiful effects, but the reader requiring further information would peruse with the greatest advantage portions of Sir John Herschel’s “Familiar Lectures on Scientific Subjects.”

The undulatory theory gives also an easy explanation of colours; they being, according to the theory, only the effects, as already stated, of the different rates of vibrations of the ether. If the ether particles perform 514,000,000,000,000 oscillations in a second, we receive the impression we call red colour; if they execute 750,000,000,000,000 vibrations, the impression produced on our organ of sight is different—we call it violet; and so on. Thus science teaches us that visual impressions so different as red, green, blue, violet, and other distinct colours, are, in reality, all due to movements of one and the same——something; and that the different sensations of colour we experience, arise merely from different rates of recurrence in these movements. In the subsequent article we shall have occasion to show that ordinary light, such as that of the sun, or of a candle, contains rays of every imaginable colour, mixed together in such proportions, that when this light falls upon a piece of paper, or upon snow, we have, in looking at these objects, the sensation of whiteness. But, if the light falls upon any substance which is able, in some way, to absorb or destroy some of the vibrations, the admixture of which makes up “white light,” as it is called, then that object sending back to our eyes the rays formed of the remaining group of vibrations, gives us the sensation of colour. Suppose, for example, a substance to be so constituted that it is capable of absorbing, or quenching in some way, all the vibrations of the ether which occur at a quicker rate than 520,000,000,000,000 in a second: such a substance would send back to our eyes only the vibrations which constitute red light (see table, page 411), and we should say the substance in question had a red colour. Similarly, if the substance gave back only the vibrations which have the quickest rates, we should call the substance of a violet character. The agent which produces in our visual organs the impression of colour is, therefore, not in the objects, but in the light which falls upon them. The rose is red, not because it has redness in itself, but because the light which falls upon it contains some rays in which there are movements that occur just the number of times per second that gives us the impression we call redness; in short, the colour comes not from the flower but from the light. “But,” the reader might say, “the rose is always red by whatever light I see it, and therefore the colour must be in the flower. Whether I view it by sunlight, or moonlight, or candlelight, or gaslight, I invariably see that it is red.” Now, it is precisely this circumstance—the seemingly invariable association of the object with a certain impression—in this case, redness—that leads our judgment astray, and makes us believe that the colour is in the object. Most people live out their lives without anything occurring to them which would give them the least idea that the colours of the objects they see around them are not in these objects themselves, but are derived from the light that falls upon the objects. And it required the comparison of many observations and experiments, and some clear reasoning, to establish a truth so unlike the most settled convictions of ordinary minds.

The point in question is fortunately one extremely easy of experiment, since we have simple means of producing light in which the vibrations corresponding to only one colour are present. The reader is strongly recommended to try the following experiment for himself. Let him procure a spirit-lamp, and place on the wick a piece of common salt about as large as a pea. Let the lamp be lighted in a room from which all other light is completely excluded, and bring near the flame a red rose or a scarlet geranium. The flower will be seen with all its redness gone—it will appear of an ashy grey or leaden colour. A ball of bright scarlet wool, such as ladies use to work brilliant patterns for cushions, &c., held near this flame, is apparently transformed into a ball of the homely grey worsted with which, about a century ago, old ladies might be seen industriously darning stockings. The experiment is, perhaps, even more striking when, a little distance from the spirit-lamp, is placed a feeble light of the ordinary kind, a rushlight for example. The ball of wool, held near the latter, shows vivid scarlet, but, brought near the spirit-lamp with the salted wick, is pale, ashy grey. Moving thus the ball of worsted, first to one light then to the other, gives a most convincing and striking proof of the entire illusion we are under as to colour being an inherent quality of substances. Similar experiments may be multiplied indefinitely. A bouquet, viewed by the rushlight, shows the so-called natural colours of the flowers; viewed by the salted flame, roses, verbenas, violets, larkspurs, and leaves, all appear of the uniform ashy grey, and only yellow flowers come out in their natural colours. A picture, say a chromo-lithograph after one of the most gorgeous landscapes that Turner ever painted, appears a work in monochrome, and gives exactly the effect of a sepia or indian-ink drawing. The most blooming complexion vanishes, and the countenance assumes a cadaverous aspect very startling to persons of weak nerves; the lips especially, which might have rivalled pink coral by ordinary light, take a repulsive livid hue. All these effects may be seen to greater advantage by using the gas-flame of a Bunsen’s burner, having a lump of salt placed in the flame; or by means of a piece of fine wire gauze, about six inches square, supported about two or three inches above an ordinary gas-burner, from which the gas is allowed to issue without being lighted, but when to the top of the wire gauze, which is strewed with small fragments of salt, a light is applied, the gas will ignite only above the gauze, without the flame passing down to the burner below.

A fuller explanation of these strange appearances may be gathered from the subsequent article; but it may suffice now to state that spirit, or gas burned in the way we have indicated, gives off little or no light of any kind. If, however, common salt be introduced into the flame, then light—but light of only one particular colour—is given off, and that colour is yellow. There are no red, or green, or blue, or violet vibrations given off; and as the objects on which the light falls cannot supply these, it follows that with this light no impression corresponding to these colours can be produced on the eye, whatever may be the objects upon which it falls. Such experiments, not simply read about but actually performed, cannot fail to convince an intelligent person that the colours come from the light and not from the object. Of course, it is not denied that there is in each substance something that determines which are the rays absorbed, and which are the rays reflected to the eye—something that can destroy certain waves, but is powerless over others that rebound from the substance, and reaching the eye, there produce their characteristic impressions. And it is but this power of sending back only certain rays among the multitude which a sunbeam furnishes, that can be attributed to objects when we say that they have such or such a colour. In this sense, then, we may properly say that the rose is red, but it is also at the same time undeniably true that the redness is not in the rose.

Let it not be supposed that such scientific conclusions as those we have arrived at tend in any way to rob Nature of her beauty, or that our sense of the loveliness of colour is in any danger of being blunted by thus tracing out, as far as may be, the causes and sources of our sensations. The poets have occasionally said harsh things of science—indeed, one goes so far as to stigmatize the man of science as one who would “untwist the rainbow” and “botanize upon his mother’s grave;” and another thus laments dispelled illusions:

Now, in the case we have been considering, the scientific view is surely as beautiful as the ordinary one. We can, it is true, no longer regard the objects as having in themselves the colours which common observation attributes to them, but we look upon the material world as being, so to speak, the neutral canvas upon which Light, the great painter, spreads his varied tints, although, unlike the real canvas of an artist, which is not only neutral, but receives indifferently whatever hues are laid upon it, the objects around us exercise a selective effect—as if the picture of Nature were produced by each part of the canvas refusing all the tints save one, but itself supplying none. The tendency of the study of science to increase our interest in the great spectacle of Nature, and to enhance our appreciation of her charms, has been more justly indicated by another poet—thus: