Miscellaneous optical illusions—Conversion of cameos into intaglios, or elevations into depressions, and the reverse—Explanation of this class of deceptions—Singular effects of illumination with light of one simple colour—Lamps for producing homogeneous yellow light—Methods of increasing the effect of this exhibition—Method of reading the inscription of coins in the dark—Art of deciphering the effaced inscription of coins—Explanation of these singular effects—Apparent motion of the eyes in portraits—Remarkable examples of this—Apparent motion of the features of a portrait, when the eyes are made to move—Remarkable experiment of breathing light and darkness.

In the preceding letter I have given an account of the most important instruments of Natural Magic which depend on optical principles: but there still remain several miscellaneous phenomena on which the stamp of the marvellous is deeply impressed, and the study of which is pregnant with instruction and amusement.

One of the most curious of these is that false perception in vision by which we conceive depressions to be elevations, and elevations depressions, or by which intaglios are converted into cameos, and cameos into intaglios. This curious fact seems to have been first observed at one of the early meetings of the Royal Society of London, when one of the members, in looking at a guinea through a compound microscope of new construction, was surprised to see the head upon the coin depressed, while other members could only see it embossed as it really was.

While using telescopes and compound microscopes, Dr. Gmelin of Wurtemburg observed the same fact. The protuberant parts of objects appeared to him depressed, and the depressed parts protuberant: but what perplexed him extremely, this illusion took place at some times and not at others, in some experiments and not in others, and appeared to some eyes and not to others.

After making a great number of experiments, Dr. Gmelin is said to have constantly observed the following effects: Whenever he viewed any object rising upon a plane of any colour whatever, provided it was neither white nor shining, and provided the eye and the optical tube were directly opposite to it, the elevated parts appeared depressed, and the depressed parts elevated. This happened when he was viewing a seal, and as often as he held the tube of the telescope perpendicularly, and applied it in such a manner that its whole surface almost covered the last glass of the tube. The same effect was produced when a compound microscope was used. When the object hung perpendicularly, from a plane, and the tube was supported horizontally and directly opposite to it, the illusion also took place, and the appearance was not altered when the object hung obliquely and even horizontally. Dr. Gmelin is said to have at last discovered a method of preventing this illusion, which was by looking, not towards the centre of the convexity, but at first to the edges of it only, and then gradually taking in the whole. “But why these things should so happen, he did not pretend to determine.”

The best method of observing this deception is to view the engraved seal of a watch with the eyepiece of an achromatic telescope, or with a compound microscope, or any combination of lenses which inverts the objects that are viewed through it.11 The depression in the seal will immediately appear an elevation, like the wax impression which is taken from it; and though we know it to be hollow, and feel its concavity with the point of our finger, the illusion is so strong that it continues to appear a protuberance. The cause of this will be understood from Fig. 14, where S is the window of the apartment, or the light which illuminates the hollow seal LR, whose shaded side is of course on the same side L with the light. If we now invert the seal, with one or more lenses, so that it may look in the opposite direction, it will appear to the eye as in Fig. 15, with the shaded side L farthest from the window. But as we know that the window is still on our left hand, and that the light falls in the direction RL, and as everybody with its shaded side farthest from the light must necessarily be convex or protuberant, we immediately believe that the hollow seal is now a cameo or bas-relief. The proof which the eye thus receives of the seal being raised, overcomes the evidence of its being hollow, derived from our actual knowledge, and from the sense of touch. In this experiment the deception takes place from our knowing the real direction of the light which falls upon the seal; for if the place of the window, with respect to the seal, had been inverted as well as the seal itself, the illusion could not have taken place.

In order to explain this better, let us suppose the seal LR, Fig. 14, to be illuminated with a candle S, the place of which we can change at pleasure. If we invert LR, it will rise into a cameo, as in Fig. 15; and if we then place another candle S on the other side of it, as in Fig. 16, the hollow seal will be equally illuminated on all sides, and it will sink down into a cavity or intaglio. If the two candles do not illuminate the seal equally, or if any accidental circumstance produces a belief that the light is wholly or principally on one side, the mind will entertain a corresponding opinion respecting the state of the seal, regarding it as a hollow if it believes the light to come wholly or principally from the right hand, and as a cameo if it believes the light to come from the left hand.

If we use a small telescope to invert the seal, and if we cover up all the candle but the flame, and arrange the experiment so that the candle may be inverted along with the image, the seal will still retain its concavity, because the shadow is still on the same side with the illuminating body.

If we make the same experiments with the raised impression of the seal taken upon wax, we shall observe the very same phenomena, the seal being depressed when it alone is inverted, and retaining its convexity when the light is inverted along with it.

The illusion, therefore, under our consideration is the result of an operation of our own minds, whereby we judge of the forms of bodies by the knowledge we have acquired of light and shadow. Hence the illusion depends on the accuracy and extent of our knowledge on this subject; and while some persons are under its influence, others are entirely insensible to it. When the seal or hollow cavity is not polished, but ground, and the surface round it of uniform colour and smoothness, almost every person, whether young or old, learned or ignorant, will be subject to the illusion; because the youngest and the most careless observers cannot but know that the shadow of a hollow is always on the side next the light, and the shadow of a protuberance on the side opposite to the light; but if the object is the raised impression of a seal upon wax, I have found that, when inverted, it still seemed raised to the three youngest of six persons, while the three eldest were subject to the deception.

This illusion may be dissipated by a process of reasoning arising from the introduction of a new circumstance in the experiment. Thus, let RL, Fig. 17, be the inverted seal, which consequently appears raised, and let an opaque and unpolished pin, A, be placed on one side of the seal. Its shadow will be of course opposite the candle as at B. In this case the seal, which had become a cameo by its inversion, will now sink down into a cavity by the introduction of the pin and its shadow; for as the pin and its shadow are inverted, as shown in Fig. 18, while the candle retains its place, the shadow of the pin falling in the direction AB is a stronger proof to the eye that the light is coming from the right hand, than the actual knowledge of the candle being on the left hand, and therefore the cameo necessarily sinks into a cavity, or the shadow is now on the same side as the light. This experiment will explain to us why on some occasions an acute observer will elude the deception, while every other person is subject to it. Let us suppose that a particle of dust, or a little bit of wax, capable of giving a shadow, is adhering to the surface of the seal, an ordinary observer will take no notice of this, or if he does, he will probably not make it a subject of consideration, and will therefore see the head on the seal raised into a cameo; but the attentive observer, noticing the little protuberance, and observing that its shadow lies to the left of it, will instantly infer that the light comes in that direction, and will still see the seal hollow.

I have already mentioned that in some cases even the sense of touch does not correct the erroneous perception. We of course feel that the part of the hollow on which the finger is placed is actually hollow; but if we look at the other part of the hollow it will still appear raised.

By using two candles yielding different degrees of light, and thus giving an uncertainty to the direction of the light, we may weaken the illusion in any degree we choose, so as to overpower it by touch, or by a process of reasoning.

I have had occasion to observe a series of analogous phenomena arising from the same cause, but produced without any instrument for inverting the object. If AB, for example, is a plate of mother-of-pearl, and LR a circular or any other cavity (Fig. 19) ground or turned in it, then if this cavity is illuminated by a candle or a window at S, in place of there being a shadow of the margin L of the hollow next the light, as there would have been had the body been opaque, a quantity of bright refracted light will appear where there would have been a shadow, and the rest of the cavity will be comparatively obscure, as if it were in shade. The necessary consequence of this is, that the cavity will appear as an elevation when seen only by the naked eye, as it is only an elevated surface that could have its most luminous side at L.

Similar illusions take place in certain pieces of polished wood, chalcedony, and mother-of-pearl, where the surface is perfectly smooth. This arises from there being at that place a knot or growth, or nodule, of different transparency from the surrounding mass, and the cause of it will be understood from Fig. 20. Let m o be the surface of a mahogany table, m A o B a section of the table, and m n o a section of a knot more transparent than the rest of the mass. Owing to the transparency of the thin edge at o, opposite to the candle S, the side o is illuminated, while the rest of the knot is comparatively dark, so that, on the principles already explained, the spot m n o appears to be a hollow in the table. From this cause arises the appearance of dimples in certain plates of chalcedony, called hammered chalcedony, owing to its having the look of being dimpled with a hammer. The surface on which these cavities are seen is a section of small spherical aggregations of siliceous matter, which exhibit the same phenomena as the cavities in wood. Mother-of-pearl presents the very same phenomena, and it is indeed so common in this substance, that it is nearly impossible to find a mother-of-pearl button or counter which seems to have its surface flat, although they are perfectly so when examined by the touch. Owing to the different refraction of the incident light by the different growths of the shell cut in different directions by the artificial surface, like the annual growth of wood in a dressed plank, the surface has necessarily an unequal and undulating appearance.

Among the wonders of science there are perhaps none more surprising than the effects produced upon coloured objects by illuminating them with homogeneous light, or light of one colour. The light which emanates from the sun, and by which all the objects of the material world are exhibited to us, is composed of three different colours, red, yellow, and blue, by the mixture of which in different proportions all the various hues of nature may be produced. These three colours, when mixed in the proportion in which they occur in the sun’s rays, compose a purely white light; but if any body on which this white light falls shall absorb, or stop, or detain within its substance any part of any one or more of these simple colours, it will appear to the eye of that colour which arises from the mixture of all the rays which it does not absorb, or of that colour which white light would have if deprived of the colours which are absorbed. Scarlet cloth, for example, absorbs most of the blue rays and many of the yellow, and hence appears red. Yellow cloth absorbs most of the blue and many of the red rays, and therefore appears yellow; and blue cloth absorbs most of the yellow and red rays. If we were to illuminate the scarlet cloth with pure and unmixed yellow light, it would appear yellow, because the scarlet cloth does not absorb all the yellow rays, but reflects some of them; and if we illuminate blue cloth with yellow light, it will appear nearly black, because it absorbs all the yellow light, and reflects almost none of it. But whatever be the nature and colour of the bodies on which the yellow light falls, the light which it reflects must be yellow, for no other light falls upon them, and those which are not capable of reflecting yellow light must appear absolutely black, however brilliant be their colour in the light of day.

As the methods now discovered of producing yellow light in abundance were not known to the ancient conjurors, nor even to those of later times, they have never availed themselves of this valuable resource. It has been long known that salt thrown into the wick of a flame produces yellow light, but this light is mixed with blue and green rays, and is, besides, so small in quantity, that it illuminates objects only that are in the immediate vicinity of the flame. A method which I have found capable of producing it in abundance is shown in Fig. 21, where AB is a lamp, containing at A a large quantity of alcohol and water, or ardent spirits, which gradually descends into a platina or metallic cup D. This cup is strongly heated by a spirit-lamp L, inclosed in a dark lantern, and when the diluted alcohol in D is inflamed, it will burn with a fierce and powerful yellow flame. If the flame should not be perfectly yellow, owing to an excess of alcohol, a proportion of salt thrown into the cup will answer the same purpose as a further dilution of the alcohol.12

A monochromatic lamp for producing yellow light may be constructed most effectually, by employing a portable gas lamp, containing compressed oil gas. If we allow the gas to escape in a copious stream, and set it on fire, it will form an explosive mixture with the atmospheric air, and will no longer burn with a white flame, but will emit a bluish and reddish light. The force of the issuing gas, or any accidental current of air, is capable of blowing out this flame, so that it is necessary to have a contrivance for sustaining it. The method which I used for this purpose is shown in Fig. 22. A small gas tube a b c, arising from the main burner MN of the gas lamp PQ, terminates above the burner, and has a short tube d e, moveable up and down within it, so as to be gas-tight. This tube d e, closed at e, communicates with the hollow ring f g, in the inside of which four apertures are perforated in such a manner as to throw their jets of gas to the apex of a cone, of which f g is the base. When we cause the gas to flow from the burner M, by opening the main cock A, it will rush into the tube a b c d, and issue in small flames at the four holes in the ring f g. The size of these flames is regulated by the cock b. The inflammation, therefore, of the ignited gas will be sustained by these four subsidiary flames through which it passes, independent of any agitation of the air, or of the force with which it issues from the burner. On a projecting arm e h, carrying a ring h, I fixed a broad collar, made of coarse cotton wick, which had been previously soaked in a saturated solution of common salt. When the gas was allowed to escape at M, with such force as to produce a long and broad column of an explosive mixture of gas and atmospheric air, the bluish flame occasioned by the explosion passes through the salted collar, and is converted by it into a mass of homogeneous yellow light. This collar will last a long time without any fresh supply of salt, so that the gas lamp will yield a permanent monochromatic yellow flame, which will last as long as there is gas in the reservoir. In place of a collar of cotton wick, a hollow cylinder of sponge, with numerous projecting tufts, may be used, or a collar may be similarly constructed with asbestos cloth, and, if thought necessary, it might be supplied with a saline solution from a capillary fountain.

Having thus obtained the means of illuminating any apartment with yellow light, let the exhibition be made in a room with furniture of various bright colours, with oil or water-coloured paintings on the wall. The party which is to witness the experiment should be dressed in a diversity of the gayest colours; and the brightest-coloured flowers and highly-coloured drawings should be placed on the tables. The room being at first lighted with ordinary lights, the bright and gay colours of everything that it contains will be finely displayed. If the white lights are now suddenly extinguished, and the yellow lamps lighted, the most appalling metamorphosis will be exhibited. The astonished individuals will no longer be able to recognize each other. All the furniture in the room, and all the objects which it contains, will exhibit only one colour. The flowers will lose their hues. The paintings and drawings will appear as if they were executed in China ink; and the gayest dresses, the brightest scarlets, the purest lilacs, the richest blues, and the most vivid greens, will all be converted into one monotonous yellow. The complexions of the parties, too, will suffer a corresponding change. One pallid, death-like yellow,

will envelope the young and the old, and the sallow faces will alone escape from the metamorphosis. Each individual derives merriment from the cadaverous appearance of his neighbour, without being sensible that he is himself one of the ghostly assemblage.

If, in the midst of the astonishment which is thus created, the white lights are restored at one end of the room, while the yellow lights are taken to the other end, one side of the dress of every person, namely, that next the white light, will be restored to its original colours, while the other side will retain its yellow hue. One cheek will appear in a state of health and colour, while the other retains the paleness of death; and, as the individuals change their position, they will exhibit the most extraordinary transformations of colour.

If, when all the lights are yellow, beams of white light are transmitted through a number of holes, like those in a sieve, each luminous spot will restore the colour of the dress or furniture upon which it falls, and the nankeen family will appear all mottled over with every variety of tint. If a magic lantern is employed to throw upon the walls or upon the dresses of the company luminous figures of flowers or animals, the dresses will be painted with these figures in the real colour of the dress itself. Those alone who appeared in yellow, and with yellow complexions, will, to a great degree, escape all these singular changes.

If red and blue light could be produced with the same facility and in the same abundance as yellow light, the illumination of the apartment with these lights in succession would add to the variety and wonder of the exhibition. The red light might perhaps be procured in sufficient quantity from the nitrate and other salts of strontian; but it would be difficult to obtain a blue flame of sufficient intensity for the suitable illumination of a large room. Brilliant white lights, however, might be used, having for screens glass troughs containing a mass one or two inches thick of a solution of the ammoniacal carbonate of copper. This solution absorbs all the rays of the spectrum but the blue, and the intensity of the blue light thus produced would increase in the same proportion as the white light employed.

Amongst the numerous experiments with which science astonishes and sometimes even strikes terror into the ignorant, there is none more calculated to produce this effect than that of displaying to the eye in absolute darkness the legend or inscription upon a coin. To do this, take a silver coin (I have always used an old one), and after polishing the surface as much as possible, make the parts of it which are raised rough by the action of an acid, the parts not raised, or those which are to be rendered darkest, retaining their polish. If the coin thus prepared is placed upon a mass of red-hot iron, and removed into a dark room, the inscription upon it will become less luminous than the rest, so that it may be distinctly read by the spectator. The mass of red-hot iron should be concealed from the observer’s eye, both for the purpose of rendering the eye fitter for observing the effect, and of removing all doubt that the inscription is really read in the dark, that is, without receiving any light, direct or reflected, from any other body. If, in place of polishing the depressed parts and roughening its raised parts, we make the raised parts polished and roughen the depressed parts, the inscription will now be less luminous than the depressed parts, and we shall still be able to read it, from its being as it were written in black letters on a white ground. The first time I made this experiment, without being aware of what would be the result, I used a French shilling of Louis XV., and I was not a little surprised to observe upon its surface, in black letters, the inscription BENEDICTUM SIT NOMEN DEI.

The most surprising form of this experiment is when we use a coin from which the inscription has been either wholly obliterated, or obliterated in such a degree as to be illegible. When such a coin is laid upon the red-hot iron, the letters and figures become oxidated, and the film of oxide radiating more powerfully than the rest of the coin, the illegible inscription may be now distinctly read, to the great surprise of the observer, who had examined the blank surface of the coin previous to its being placed upon the hot iron. The different appearances of the same coin, according as the raised parts are polished or roughened, are shown in Fig. 23 and 24.

In order to explain the cause of these remarkable effects, we must notice a method which has been long known, though never explained, of deciphering the inscriptions on worn-out coins. This is done by merely placing the coin upon a hot iron; an oxidation takes place over the whole surface of the coin, the film of oxide changing its tint with the intensity or continuance of the heat. The parts, however, where the letters of the inscription had existed, oxidate at a different rate from the surrounding parts, so that these letters exhibit their shape, and become legible in consequence of the film of oxide which covers them having a different thickness, and therefore reflecting a different tint from that of the adjacent parts. The tints thus developed sometimes pass through many orders of brilliant colours, particularly pink and green, and settle in a bronze, and sometimes a black tint, resting upon the inscription alone. In some cases the tint left on the trace of the letters is so very faint that it can just be seen, and may be entirely removed by a slight rub of the finger.

When the experiment is often repeated with the same coin, and the oxidations successively removed after each experiment, the film of oxide continues to diminish, and at last ceases to make its appearance. It recovers the property, however, in the course of time. When the coin is put upon the hot iron, and consequently when the oxidation is the greatest, a considerable smoke arises from the coin, and this diminishes like the film of oxide by frequent repetition. A coin which had ceased to emit this smoke, smoked slightly after having been exposed twelve hours to the air. I have found, from numerous trials, that it is always the raised parts of the coin, and in modern coins the elevated ledge round the inscription, that become first oxidated. In an English shilling of 1816, this ledge exhibited a brilliant yellow tint before it appeared on any other part of the coin.

If we use a uniform and homogeneous disc of silver that has never been hammered or compressed, its surface will oxidate equally, provided all its parts are equally heated. In the process of converting this disc into a coin, the sunk parts have obviously been most compressed by the prominent parts of the die, and the elevated parts least compressed, the metal being in the latter left as it were in its natural state. The raised letters and figures on a coin have therefore less density than the other parts, and these parts oxidate sooner or at a lower temperature. When the letters of the legend are worn off by friction, the parts immediately below them have also less density than the surrounding metal, and the site as it were of the letters therefore receives from heat a degree of oxidation, and a colour different from that of the surrounding surface. Hence we obtain an explanation of the revival of the invisible letters by oxidation.

The same influence of difference of density may be observed in the beautiful oxidations which are produced on the surface of highly-polished steel, heated in contact with air, at temperatures between 430° and 630° of Fahrenheit.13 When the steel has hard portions called pins by the workmen, the uniform tint of the film of oxide stops near these hard portions, which always exhibit colours different from those of the rest of the mass. These parts, on account of their increased density, absorb the oxygen of atmospheric air less copiously than the surrounding portions. Hence we see the cause why steel expanded by heat absorbs oxygen, which when united with the metal, forms the coloured superficial film. As the heat increases, a greater quantity of oxygen is absorbed, and the film increases in thickness.

These observations enable us to explain the legibility of inscriptions in the dark, whether the coin is in a perfect state, or the letters of it worn off. All black or rough surfaces radiate light more copiously than polished or smooth surfaces, and hence the inscription is luminous when it is rough, and obscure when it is polished, and the letters covered with black oxide are more luminous than the adjacent parts, on account of the superior radiation of light by the black oxide which covers them.

By the means now described, invisible writing might be conveyed by impressing it upon a metallic surface, and afterwards erasing it by grinding and polishing that surface perfectly smooth. When exposed to a proper degree of heat, the secret would display itself written in oxidated letters. Many amusing experiments might be made upon the same principle.

A series of curious and sometimes alarming deceptions, arises from the representation of objects in perspective upon a plane surface. One of the most interesting of these depends on the principles which regulate the apparent direction of the eyes in a portrait. Dr. Wollaston has thought this subject of sufficient importance to be treated at some length in the Philosophical Transactions. When we look at any person we direct to them both our face and our eyes, and in this position the circular iris will be in the middle of the white of the eye ball, or, what is the same thing, there will be the same quantity of white on each side of the iris. If the eyes are now moved to either side, while the head remains fixed, we shall readily judge of the change of their direction by the greater or less quantity of white on each side of the iris. This test, however, accurate as it is, enables us only to estimate the extent to which the eyes deviate in direction from the direction of the face to which they belong. But their direction in reference to the person who views them is entirely a different matter; and Dr. Wollaston is of opinion, that we are not guided by the eyes alone, but are unconsciously aided by the concurrent position of the entire face.

If a skilful painter draws a pair of eyes with great correctness directed to the spectator, and deviating from the general position of the face as much as is usual in good portraits, it is very difficult to determine their direction, and they will appear to have different directions to different persons. But what is very curious, Dr. Wollaston has shown that the same pair of eyes may be made to direct themselves either to or from the spectator by the addition of other features in which the position of the face is changed. Thus, in Fig. 25, the pair of eyes are looking intently at the spectator, and the face has a corresponding direction; but when we cover up the face in Fig. 25 with the face in Fig. 26, which looks to the right, the eyes change their direction, and look to the right also. In like manner, eyes drawn originally to look a little to the right or the left of the spectator, may be made to look directly at him by adding suitable features.

The nose is obviously the principal feature which produces this change of direction, as it is more subject to change of perspective than any of the other features; but Dr. Wollaston has shown by a very accurate experiment, that even a small portion of the nose introduced with the features will carry the eyes along with it. He obtained four exact copies of the same pair of eyes looking at the spectator, by transferring them upon copper from a steel plate, and having added to each of two pair of them a nose, in one case directed to the right, and in the other to the left, and to each of the other two pair a very small portion of the upper part of the nose, all the four pair of eyes lost their front direction, and looked to the right or to the left, according to the direction of the nose, or of the portion of it which was added.

But the effect thus produced is not limited, as Dr. Wollaston remarks, to the mere change in the direction of the eyes, “for a total difference of character may be given to the same eyes by a due representation of the other features. A lost look of devout abstraction in an uplifted countenance, may be exchanged for an appearance of inquisitive archness in the leer of a younger face turned downwards and obliquely towards the opposite side,” as in Fig. 27, 28. This, however, is perhaps not an exact expression of the fact. The new character which is said to be given to the eyes is given only to the eyes in combination with the new features, or, what is probably more correct, the inquisitive archness is in the other features, and the eye does not belie it.

Dr. Wollaston has not noticed the converse of these illusions, in which a change of direction is given to fixed features by a change in the direction of the eyes. This effect is finely seen in some magic lantern sliders, where a pair of eyes is made to move in the head of a figure, which invariably follows the motion of the eyeballs.

Having thus determined the influence which the general perspective of the face has upon the apparent direction of the eyes in a portrait, Dr. Wollaston applies it to the explanation of the well-known fact, that when the eyes of a portrait look at a spectator in front of it they will follow him, and appear to look at him in every other direction. This curious fact, which has received less consideration than it merits, has been often skilfully employed by the novelist, in alarming the fears or exciting the courage of his hero. On returning to the hall of his ancestors, his attention is powerfully fixed on the grim portraits which surround him. The parts which they have respectively performed in the family history rise to his mind: his own actions, whether good or evil, are called up in contrast, and as the preserver or the destroyer of his line, he stands, as it were, in judgment before them. His imagination, thus excited by conflicting feelings, transfers a sort of vitality to the canvas, and if the personages do not “start from their frames,” they will at least bend upon him their frowns or their approbation. It is in vain that he tries to evade their scrutiny. Wherever he goes their eyes eagerly pursue him; they will seem even to look at him over their shoulders, and he will find it impossible to shun their gaze but by quitting the apartment.

As the spectator in this case changes his position in a horizontal plane, the effect which we have described is accompanied by an apparent diminution in the breadth of the human face, from only seven or eight inches till it disappears at a great obliquity. In moving, therefore, from a front view to the most oblique view of the face, the change in its apparent breadth is so slow that the apparent motion of the head of the figure is scarcely recognized as it follows the spectator. But if the perspective figure has a great breadth in a horizontal plane, such as a soldier firing his musket, an artilleryman his piece of ordnance, a bowman drawing his bow, or a lancer pushing his spear, the apparent breadth of the figure will vary from five to six feet or upwards till it disappears, and therefore the change of apparent magnitude is sufficiently rapid to give the figure the dreaded appearance of turning round, and following the spectator. One of the best examples of this must have been often observed in the foreshortened figure of a dead body lying horizontally, which has the appearance of following the observer with great rapidity, and turning round upon the head as the centre of motion.

The cause of this phenomenon is easily explained. Let us suppose a portrait with its face and its eyes directed straight in front, so as to look at the spectator. Let a straight line be drawn through the tip of the nose and half way between the eyes, which we shall call the middle line. On each side of this middle line there will be the same breadth of head, of cheek, of chin, and of neck, and each iris will be in the middle of the white of the eye. If we now go to one side, the apparent horizontal breadth of every part of the head and face will be diminished, but the parts on each side of the middle line will be diminished equally, and at any position, however oblique, there will be the same breadth of face on each side of the middle line, and the iris will be in the centre of the white of the eyeball, so that the portrait preserves all the characters of a figure looking at the spectator, and must necessarily do so wherever he stands.

This explanation might be illustrated by a picture which represents three artillerymen, each firing a piece of ordnance in parallel directions. Let the gun of the middle one be pointed accurately to the eye of the spectator, so that he sees neither its right side nor its left, nor its upper nor its under side, but directly down its muzzle, so that if there was an opening in the breech he would see through it. In like manner the spectator will see the left side of the gun on his left hand, and the right side of the gun on his right hand. If the spectator now changes his place, and takes ever such an oblique position, either laterally or vertically, he must still see the same thing; because nothing else is presented to his view. The gun of the middle soldier must always point to his eye, and the other guns to the right and left of him. They must therefore all three seem to move as he moves, and follow his eye in all its changes of place. The same observations are of course applicable to buildings and streets seen in perspective.

In common portraits the apparent motion of the head is generally rendered indistinct by the canvas being imperfectly stretched, as the slightest concavity or convexity entirely deforms the face when the obliquity is considerable. The deception is therefore best seen when the painting is executed on a very flat board, and in colours sufficiently vivid to represent every line in the face with tolerable distinctness at great obliquities. This distinctness of outline is indeed necessary to a satisfactory exhibition of this optical illusion. The most perfect exhibition, indeed, that I ever saw of it was in the case of a painting of a ship upon a sign-board executed in strongly gilt lines. It contained a view of the stern and side of a ship in the stocks, and, owing to the flatness of the board and the brightness of the lines, the gradual development of the figure, from the most violent foreshortening at great obliquities till it attained its perfect form, was an effect which surprised every person that saw it.

The only other optical illusion which our limits will permit us to explain, is the very remarkable experiment of what may be truly called breathing light or darkness. Let S be a candle whose light falls at an angle of 56° 45´ upon two glass plates A, B, placed close to each other, and let the reflected rays AC, BD, fall at the same angle upon two similar plates, C, D, but so placed that the plane of reflexion from the latter is at right angles to the plane of reflexion from the former. An eye placed at E, and looking at the same time into the two plates C and D, will see very faint images of the candle S, which by a slight adjustment of the plates, may be made to disappear almost wholly allowing the plate C to remain as it is, change the position of D, till its inclination to the ray BD is diminished about 3°, or made nearly 53° 11´. When this is done, the image that had disappeared on looking into D will be restored, so that the spectator at E, upon looking into the two mirrors C, D, will see no light in C, because the candle has nearly disappeared, while the candle is distinctly seen in D. If, while the spectator is looking into these two mirrors, either he or another person breathes upon them gently and quickly, the breath will revive the extinguished image in C, and will extinguish the visible image in D. The following is the cause of this singular result. The light AC, BD, is polarized by reflexion from the plates A, B, because it is incident at the polarizing angle of 56° 45´ for glass. When we breathe upon the plates C, D, we form upon their surface a thin film of water, whose polarizing angle is 53° 11´, so that if the polarized rays AC, BD, fell upon the plates C, D, at an angle of 53° 11´, the candle from which they proceeded would not be visible, or they would not suffer reflexion from the plates C, D. At all other angles the light would be reflected and the candles visible. Now the plate D is placed at an angle of 53° 11´ and C at an angle of 56° 45´, so that when a film of water is breathed upon them the light will be reflected from the latter, and none from the former; that is, the act of breathing upon the plates will restore the invisible and extinguish the visible image.