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—

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 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.

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.

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—

“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.

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.

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.

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.

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.

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 (πολεμος, war, and σκοπεω, 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.

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.

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.

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 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:

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.

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.

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.