Romans were gone; to the physician he gave his hand to be dressed, which was swelled by the blow he had given his slave. This being an intimation that he intended to live, gave great joy to his family. Butas soon returned, and brought word that they were all gone except Crassus, who had laid upon some business, but was just ready to depart. He added, that the wind was high, and the sea rough. These words drew a sigh from Cato. He sent Butas again to the port, to know whether there might not be some one, who, in the hurry of embarkation, had forgot some necessary provisions, and had been obliged to put back to Utica. It was now break of day, and Cato slept yet a little more, till Butas returned to tell him, that all was perfectly quiet. He then ordered him to shut his door; and he flung himself upon his bed, as if he meant to finish his night's rest; but immediately he took his sword, and stabbed himself a little below his chest; yet not being able to use his hand so well by reason of the swelling, the blow did not kill him. It threw him into a convulsion, in which he fell from his bed, and overturned a table near it. The noise gave

CATOPTRICS is that part of optics which explains the properties of reflected light, and particularly that which is reflected from mirrors.

As this and the other branches of Optics are fully treated under the collective word, we shall, in the present article, 1st, just give a summary of the principles of the branch, in a few plain aphorisms, with some preliminary definitions; and, 2ndly, insert a set of entertaining experiments founded upon them.

Sect. I. Definitions.

Definitions.

1. Every polished body that reflects the rays of light is called a mirror, whether its surface be plane, spherical, conical, cylindric, or of any other form whatever.

Plate CXXVIII. Of mirrors there are three principally used in optical experiments: The plane mirror, GHI, (fig. 1); the spherical convex mirror, GHI, (fig. 2); and the spherical concave mirror, GHI, (fig. 3).

3. The point K, (fig. 2, 3,) round which the reflecting surface of a spherical mirror is described, is called its centre. The line KH, drawn from its centre perpendicular to its two surfaces, is the axis of the mirror; and the point H, to which that line is drawn, is its vertex.

4. The distance between the lines AG and BG, (fig. 1,) is called the angle of incidence, and the distance between BG and CG is the angle of reflection.

Sect. II. Aphorisms.

1. In a plain mirror.

1. The image DF, (fig. 1,) will appear as far behind the mirror, as the object AC is before it.

2. The image will appear of the same size, and in the same position as the object.

3. Every such mirror will reflect the image of an object of twice its own length and breadth.

4. If the object be an opaque body, and its rays fall on the mirror nearly in direct lines, there will be only one image visible, which will be reflected by the inner surface of the glass. But,

5. If the object be a luminous body, and its rays fall very obliquely on the mirror, there will appear, to an eye placed in a proper position, several images; the first of which, reflected from the outer surface of the glass, will not be so bright as the second, reflected from the inner surface. The following images, that are produced by the repeated reflections of the rays between the two surfaces of the glass, will be in proportion less vivid, to the eighth or tenth, which will be scarce visible.

1. The image DF, (fig. 2,) will always appear behind it.

2. The image will be in the same position as the object.

3. It will be less than the object.

4. It will be curved, but not, as the mirror, spherical.

5. Parallel rays falling on this mirror will have the focus or image at half the distance of the centre K, from the mirror.

6. In converging rays, the distance of the object must be equal to half the distance of the centre, to make the image appear behind the mirror.

7. Diverging rays will have their image at less than half the distance of the centre. If the object be placed in the centre of the mirror, its image will appear at one-eighth of that distance behind it.

1. That point where the image appears of the same dimensions as the object, is the centre of that mirror.

2. Parallel rays will have their focus at one half the distance of the centre.

3. Converging rays will form an image before the mirror.

4. In diverging rays, if the object be at less than one half the distance of the centre, the image will be behind the mirror, erect, curved, and magnified, as K k z DEF. DEF, (fig. 3.) but if the distance of the object be greater, the image will be before the mirror, inverted and diminished, as DEF, (fig. 4.)

5. The sun's rays falling on a concave mirror, and being parallel, will be collected in a focus at half the distance of its centre, where their heat will be augmented in proportion of the surface of the mirror to that of the focal spot.

6. If a luminous body be placed in the focus of a concave mirror, its rays being reflected in parallel lines will strongly enlighten a space of the same dimension with the mirror, at a great distance. If the luminous object be placed nearer than the focus, its rays will diverge, and consequently enlighten a larger space. It is on this principle that reverberators are constructed.

IV. In all plane and spherical mirrors the angle of incidence is equal to the angle of reflection.

Sect. III. Entertaining Experiments.

I. Of all our senses the sight is certainly subject to the greatest illusion. The various writers on optics have described a great number of instances in which it deceives us, and have constantly endeavoured to investigate the causes, to explain their effects, and to reconcile appearance with reality. We every day discover new phenomena, and doubts many more are reserved for posterity. It frequently happens, moreover, that a discovery which at first seemed of little consequence, has led to matters of the highest importance.

Take a glass bottle A (fig. 14.) and fill it with water to the point B; leave the upper part BC empty, and cork it in the common manner. Place this bottle opposite a concave mirror, and beyond its focus, that it may appear reversed, and before the mirror (see sect. ii. aphor. 4. of a sphere, concave mirror,) place yourself still further distant from the bottle, and it will appear to you in the situation, a, b, c, (fig. 15.)

Now it is remarkable in this apparent bottle, that the water, which, according to all the laws of catoptrics, and all the experiments made on other objects, should appear at a b, appears on the contrary at b c, and consequently the part a b appears empty.

If the bottle be inverted and placed before the mirror (as in fig. 16.), its image will appear in its natural, erect position; and the water, which is in reality at BC, will appear at a b.

If while the bottle is inverted it be uncorked, and the water run gently out, it will appear, that while the part BC is emptying, that of a b in the image is filling; and what is likewise very remarkable, as soon as the bottle is empty the illusion ceases, the image also appearing entirely empty. If the bottle likewise be quite full there is no illusion.

If while the bottle is held inverted, and partly empty, some drops of water fall from the bottom A towards BC, it seems in the image as if there were formed at the bottom of the part a b, bubbles of air that rose from a to b; which is the part that seems full of water. All these phenomena constantly appear.

The remarkable circumstances in this experiment, are, first, not only to see an object where it is not, but also where its image is not; and secondly, that of two objects which are really in the same place, as the surface of the bottle and the water it contains, the one is seen at one place, and the other at another; and to see the bottle in the place of its image, and the water where neither it nor its image are.

II. Construct a box AB, of about a foot long, eight inches wide, and fix high; or what other dimensions of a you shall think fit, provided it does not greatly vary from these proportions.

On the inside of this box, and against each of its opposite ends A and B, place a mirror of the same size. Take off the quicksilver from the mirror that you place at B, for about an inch and an half, at the part C, where you are to make a hole in the box of the same size, by which you may easily view its inside. Cover the top of the box with a frame, in which must be placed a transparent glass, covered with gauze, on the side next the inner part of the box. Let there be two grooves at the parts E and F to receive the two painted scenes hereafter mentioned. On two pieces of cut pasteboard let there be skilfully painted on both sides (see fig. 6. and 7.) any subject you think proper; as woods, gardens, bowers, colonnades, &c. and on two other pasteboards, the same subjects on one side only; observing that there ought to be on one of them some object relative to the subject placed at A, that the mirror placed at D may not reflect the hole at C on the opposite side.

Place the two boards painted on both sides in the grooves E and F; and those that are painted on one side only, against the opposite mirrors C and D; and then cover the box with its transparent top. This box should be placed in a strong light to have a good effect.

When the eye is placed at C, and views the objects on the inside of the box, of which some, as we have said, are painted on both sides, they are successively reflected from one mirror to the other; and if, for example, the painting consists of trees, they will appear like a very long vista, of which the eye cannot discern the end: for each of the mirrors repeating the objects, continually more faintly, contribute greatly to augment the illusion.

III. Take a square box ABCD, of about six inches long, and twelve high; cover the inside of it with fortification four plain mirrors, which must be placed perpendicular to the bottom of the box CHFD.

Place certain objects in relief on the bottom of this box; suppose, for example, a piece of fortification, (as fig. 9.) with tents, soldiers, &c. or any other subject that you judge will produce an agreeable effect by its disposition when repeatedly reflected by the mirrors.

On the top of this box place a frame of glass, in form of the bottom part of a pyramid, whose base AGEB is equal to the size of the box: its top ILN, must form a square of six inches, and should not be more than four or five inches higher than the box. Cover the four sides of this frame with a gauze, that the inside may not be visible but at the top ILN, which should be covered with a transparent glass.

When you look into this box through the glass ILN, the mirrors that are diametrically opposite each other, mutually reflecting the figures inclosed, the eye beholds a boundless extent, completely covered with the these objects; and if they are properly disposed, the illusion will occasion no small surprize, and afford great entertainment.

Note, The nearer the opening LN is to the top of the box, the greater will be the apparent extent of the subject. The same will happen if the four mirrors placed on the sides of the box be more elevated. The objects, by either of these dispositions will appear to be repeated nine, twenty-five, forty-nine times, &c. by taking always the square of the odd numbers of the arithmetical progression 3, 5, 7, 9, &c., as is very easy to conceive; if we remember that the subject enclosed in the box is always in the centre of a square, composed of several others, equal to that which forms the bottom of the box.

Other pieces of the same kind (that is viewed from above) may be contrived, in which mirrors may be placed perpendicular on a triangular, pentagon, or hexagon, (that is, a three, five, or six-sided) plane. All these different dispositions, properly directed, as well with regard to the choice as position of the objects, will constantly produce very remarkable and pleasing illusions.

If instead of placing the mirrors perpendicular, they were to incline equally, so as to form part of a reversed pyramid, the subject placed in the box would then have the appearance of a very extensive globular or many-sided figure.

IV. On the hexagonal or six-sided plane ABCDEF draw six semi-diameters GA, GB, GC, GD, GE, GF; and on each of these place perpendicularly two plane mirrors, which must join exactly at the centre G, and which placed back to back must be as thin as possible. Decorate the exterior boundary of this piece (which is at the extremity of the angles of the hexagon) with six columns, that at the same time serve to support the mirrors, by grooves formed on their inner sides. (See the profile H). Add to these columns their entablatures, and cover the edifice in such manner as you shall think proper.

In each one of these six triangular spaces, contained between two mirrors, place little figures of pasteboard, in relief, representing such objects as when seen in an hexagonal form will produce an agreeable effect. To these add small figures of enamel; and take particular care to conceal, by some object that has relation to the subject, the place where the mirrors join, which, as we have said before, all meet in the common centre G.

When you look into any one of the six openings of this palace, the objects there contained being repeated six times, will seem entirely to fill up the whole of the building. This illusion will appear very remarkable; especially if the objects made choice of are properly adapted to the effect that is to be produced by the mirrors.

Note, if you place between two of these mirrors part of a fortification, as a curtain and two demi-bastions, you will see an entire citadel, with its six bastions. Or if you place part of a ball-room, ornamented with chandeliers and figures in enamel, all those objects being here multiplied, will afford a very pleasing prospect.

V. Within the case ABCD, place four mirrors, V. Opaque O, P, Q, R, so disposed that they may each of them bodies make an angle of forty-five degrees, that is, that they may be half way inclined from the perpendicular, as transparent, in the figure. In each of the two extremities AB, fig. 11, make a circular overture, in one of which fix the tube GL, in the other the tube MF, and observe that in each of these is to be inserted another tube, as H and I (A).

Furnish the first of these tubes with an object-glass at G, and a concave eye-glass at F. You are to observe, that in regulating the focus of these glasses, with regard to the length of the tube, you are to suppose it equal to the line G, or visual pointed ray, which entering at the overture G, is reflected by the four mirrors, and goes out at the other overture F, where the ocular glass is placed. Put any glass you will into the two ends of the moveable tubes H and I; and lastly place the machine on a stand E, moveable at the point S, that it may be elevated or depressed at pleasure.

When the eye is placed at F, and you look through the tube, the rays of light that proceed from the object T, passing through the glass G, are successively reflected by the mirrors, O, P, Q, and R, to the eye at F, and there paint the object T, in its proper situation, and these rays appear to proceed directly from that object.

The two moveable tubes H and I, at the extremities of each of which a glass is placed, serve only the more to disguise the illusion, for they have no communication with the interior part of the machine. This instrument being moveable on the stand E, may be directed to any object; and if furnished with proper glasses will answer the purpose of a common perspective.

The two moveable tubes H and I being brought together, the machine is directed toward any object, and desiring a person to look in at the end F, you ask him if he see distinctly that object. You then separate the two moveable tubes, and leaving a space between them sufficient to place your hand, or any other solid body, you tell him that the machine has the power of making objects visible through the most opaque body; and as a proof you desire him then to look at the same object, when, to his great surprize, he will see it as distinct as when there was no solid body placed between the tubes.

Note, This experiment is the more extraordinary, as it is very difficult to conceive how the effect is produced. The two arms of the case appearing to be made to support the perspective glasses; and to whatever object it is directed, the effect is still the same.

(A) These four tubes must terminate in the substance of the case, and not enter the inside, that they may not hinder the effect of the mirrors. The fourfold reflection of the rays of light from the mirrors, darkens in some degree the brightness of the object; some light is also lost by the magnifying power of the perspective: If, therefore, instead of the object-glass at G, and concave eye-glass at F, plain glasses were substituted; the magnifying power of the perspective will be taken away, and the object will appear brighter. VI. In the partition AB, make two overtures, CD, and EF, of a fort high, and ten inches wide, and about a foot distant from each other. Let them be at the common height of a man's head; and in each of them place a transparent glass, surrounded with a frame, like a common mirror.

Behind this partition place two mirrors H and I, inclined to it in an angle of forty-five degrees: that is, half-way between a line drawn perpendicular to the ground and its surface: let them be both 18 inches square: let all the space between them be inclosed by boards or pateboard painted black, and well closed, that no light may enter: let there be also two curtains to cover them, which may be drawn aside at pleasure.

When a person looks into one of these supposed mirrors, instead of seeing his own face, he will perceive the object that is in front of the other: so that if two persons present themselves at the same time before these mirrors, instead of each one seeing himself, they will reciprocally see each other.

Note, There should be a fence with a candle placed on each side of the two glasses in the wainscot, to enlighten the faces of the persons who look in them, otherwise this experiment will have no remarkable effect.

This experiment may be considerably improved by placing the two glasses in the partition in adjoining rooms, and a number of persons being previously placed in one room, when a stranger enters the other, you may tell him his face is dirty; and desire him to look in the glass, which he will naturally do; and on seeing a strange face he will draw back: but returning to it, and seeing another, another, and another, like the phantom kings in Macbeth, what his surprize will be is more easy to conceive than express. After this, a real mirror may be privately let down on the back of the glass; and if he can be prevailed to look in it once more, he will then, to his further astonishment, see his own face; and may be told, perhaps persuaded, that all he thought he saw before was mere imagination.

How many tricks, less artful than this, have passed in former times for sorcery; and pass at this time, in some countries, for apparitions?

Note, When a man looks in a mirror that is placed perpendicular to another, his face will appear entirely deformed. If the mirror be a little inclined, so as to make an angle of 80 degrees (that is, one-ninth parts from the perpendicular), he will then see all the parts of his face, except the nose and forehead. If it be inclined to 60 degrees (that is, one-third part), he will appear with three noses and six eyes: in short, the apparent deformity will vary at each degree of inclination; and when the glass comes to 45 degrees (that is, half way down), the face will vanish. If, instead of placing the two mirrors in this situation, they are so disposed that their junction may be vertical, their different inclinations will produce other effects; as the situation of the object relative to these mirrors is quite different. The effects of these mirrors, though remarkable enough, occasions but little surprize, as there is no method of concealing the cause by which they are produced.

VII. Make a box of wood, of a cubical figure, ABCD, of about 15 inches every way. Let it be fixed on the pedestal E, at the usual height of a man's head. In each side of this box let there be an opening of an oval form, of ten inches high, and seven wide.

In this box place two mirrors A, D, with their backs against each other; let them cross the box in a diagonal line, and in a vertical position. Decorate the openings in the sides of this box with four oval frames and transparent glasses, and cover each of them with a curtain, so contrived that they may all draw up together.

Place four persons in front of the four sides, and at equal distances from the box, and then draw up the curtains that they may see themselves in the mirrors; when each of them, instead of his own figure, will see that of the person who is next him, and who, at the same time, will seem to him to be placed on the opposite side. Their confusion will be the greater, as it will be very difficult for them to discover the mirrors concealed in the box. The reason of this phenomenon is evident; for though the rays of light may be turned aside by a mirror, yet, as we have before said, they always appear to proceed in right lines.

VIII. Provide a box ABCD of about two feet long, VIII. The 15 inches wide, and 12 inches high. At the end perspective AC place a concave mirror, the focus of whose parallel rays is at 18 inches from the reflecting surface. At fig. 17, IL place a pateboard blacked, in which a hole is cut sufficiently large to see on the mirror H the object placed at BEFD.

Cover the top of the box, from A to I, close, that the mirror H may be entirely darkened. The other part IB, must be covered with a glass, under which is placed a gauze.

Make an aperture at G, near the top of the side EB; beneath which, on the inside, place, in succession, paintings of different subjects, as vistas, landscapes, &c., so that they may be in front of the mirror H. Let the box be so placed that the object may be strongly illuminated by the sun, or by wax lights placed under the enclosed part of the box AI.

By this simple construction the objects placed at GD will be thrown into their natural perspective; and if the subjects be properly chosen, the appearance will be altogether as pleasing as in optical machines of a much more complicated form.

Note, A glass mirror should be always here used, as those of metal do not represent the objects with equal vivacity, and are beside subject to tarnish. It is also necessary that the box be sufficiently large, that you may not be obliged to use a mirror whose focus is too short; for in that case, the right lines near the border of the picture will appear bent in the mirror, which will have a disagreeable effect, and cannot be avoided.

IX. The rays of a luminous body placed in the focus of a concave mirror being reflected in parallel lines, if a second mirror be placed diametrically opposite the first, it will, by collecting those rays in its focus, set fire to a combustible body.

Place two concave mirrors, A and B, at about 12 or 15 feet distance from each other, and let fig. 18, the axis of each of them be in the same line. In the focus C of one of them, place a live coal, and in the focus D of the other, some gun-powder. With a pair of double bellows, which make a continual blast, keep constantly blowing the coal, and notwithstanding the distance between them, the powder will presently take fire.

It is not necessary that these mirrors be of metal or brass, those made of wood or pasteboard, gilded, will produce the explosion, which has sometimes taken effect at the distance of 50 feet, when mirrors of 18 inches, or two feet diameter, have been used.

This experiment succeeds with more difficulty at great distances; which may proceed from the moisture in a large quantity of air. It would doubtless take effect more readily, if a tin tube, of an equal diameter with the mirrors, were to be placed between them.

X. Behind the partition AB, place, in a position something oblique, the concave mirror EF, which must be at least ten inches in diameter, and its distance from the partition equal to three-fourths of the distance of its centre.

In the partition make an opening of seven or eight inches, either square or circular: it must face the mirror, and be of the same height with it. Behind this partition place a strong light, so disposed that it may not be seen at the opening, and may illumine an object placed at C, without throwing any light on the mirror.

Beneath the aperture in the partition place the object C, that you intend shall appear on the outside of the partition, in an inverted position; and which we will suppose to be a flower. Before the partition, and beneath the aperture, place a little flower-pot D, the top of which should be even with the bottom of the aperture, that the eye, placed at G, may see the flower in the same position as if its stalk came out of the pot.

Take care to paint the space between the back part of the partition and the mirror black, to prevent any reflections of light from being thrown on the mirror; in a word, so dispose the whole that it may be as little enlightened as possible.

When a person is placed at the point G, he will perceive the flower that is behind the partition, at the top of the pot at D, but on putting out his hand to pluck it, he will find that he attempts to grasp a shadow.

If in the opening of the partition a large double convex lens of a short focus be placed, or, which is not quite so well, a bottle of clear water, the image of the flower reflected thereon will appear much more vivid and distinct.

The phenomena that may be produced by means of concave mirrors are highly curious and astonishing. By their aid, spectres of various kinds may be exhibited. Suppose, for example, a person with a drawn sword places himself before a large concave mirror, but farther from it than its focus; he will then see an inverted image of himself in the air, between him and the mirror, of a less size than himself. If he steadily present the sword towards the centre of the mirror, an image of the sword will come out therefrom towards the sword in his hand, point to point, as it were to fence with him; and by his pushing the sword nearer, the image will appear to come nearer him, and almost to touch his breast, having a striking effect upon him. If the mirror be turned 45 degrees, or one eighth round, the reflected image will go out perpendicular to the direction of the sword presented, and apparently come to another person placed in the direction of the motion of the image. If that person is unacquainted with the experiment, and does not see the original sword, he will be much surprized and alarmed.—This experiment may be another way diversified, by telling any person, that at such an hour, and in such a place, he should see the apparition of an absent or deceased friend (of whose portrait you are in possession). In order to produce this phantom, instead of the hole in the partition AB in the last figure, there must be a door which opens into an apartment to which there is a considerable descent. Under that door you are to place the portrait, which must be inverted and strongly illuminated, that it may be lively reflected by the mirror, which must be large and well polished. Then having introduced the incredulous spectator at another door, and placed him in the proper point of view, you suddenly throw open the door at A.B., when, to his great astonishment, he will immediately see the apparition of his friend.

It will be objected, perhaps, that this is not a perfect apparition, because it is only visible at one point of view, and by one person. But it should be remembered, that it was an established maxim in the last centuries, that a spectre might be visible to one person and not to others. So Shakespeare makes both Hamlet and Macbeth see apparitions that were not visible to others, present at the same time. It is not unlikely, moreover, that this maxim took its rise from certain apparitions of this kind that were raised by the monks, to serve some purposes they called religious; as they alone were in possession of what little learning there then was in the world.

Opticians sometimes grind a glass mirror concave in one direction only, as it is said longitudinally; it is in fact a concave portion of a cylinder, the breadth of which may be considered that of the mirror. A person looking at his face in this mirror, in the direction of its concavity, will see it curiously distorted in a very lengthened appearance; and by turning the cylindrical mirror a quarter round, his visage will appear distorted another way, by an apparent increase in width only. Another curious and singular property attends this sort of mirrors: If in a very near situation before it, you put your finger on the right-hand side of your nose, it will appear the same in the mirror; but if in a distant situation, somewhat beyond the centre of concavity, you again look at your face in the mirror, your finger will appear to be removed to the other or left-hand side of your nose. This, though something extraordinary, will in its cause appear very evident from a small consideration of the properties of spherical concave mirrors.