(Kalos, beautiful, idios, a form, and σκοπεῖν, I see), an optical instrument, which, by means of two equal plane mirrors inclined to each other at a certain angle, and placed in a particular manner relative to the eye and object, is used, as its name imports, to produce and to exhibit beautiful forms. It was invented in 1814 by Sir David Brewster while experimenting on the polarization of light; and ere the inventor had time to secure it by patent unprincipled opticians made kaleidoscopes by thousands, and sent them to all parts of the world. Sir David Brewster states that no fewer than 200,000 of these instruments were sold in London and Paris in the space of three months; and yet, he says, that out of this immense number, there are, perhaps, not one thousand constructed upon scientific principles, or capable of giving anything like a correct idea of the power of the kaleidoscope; and of the millions who have witnessed its effects, there are perhaps not one hundred who have any idea of the principles upon which it is constructed, and of the mode in which its effects are produced.

In order to produce its effects, the instrument may be said to depend on the principle of a repetition of the reflections of an object situated between two plane mirrors inclined to each other at a certain angle; or, more particularly, if two reflecting planes form a section with each other, then the reflections of an object between the planes will all be found in the circumference of a circle, the centre of which is the projection of the intersection of the planes, and the number of images will be such as will exactly complete the circle. This will be more easily understood from fig. 1, where AC BC, are the orthogonal projections of two plane mirrors, C the projection of their line of junction, and P' the position of a luminous point or object within the angle ABC, made by the reflecting planes; then from centre C and radius equal to CP', describe a circle AB. It is clear that we shall have two series of virtual images which will be all arranged round the circumference of the circle AB; for the rays of light, and, therefore, a perpendicular ray from P, regarded as a luminous point, will have a virtual image P₁, an image of itself on the other side of the plane BC, and as far distant from that mirror as P is. But the bright image P₁, letting a perpendicular ray fall on the mirror AC, has a virtual image P₂ as far distant from AC as P₁ is; P₂ is also a luminous point, and has its image at P₃ in the mirror BC produced, and at the same distance from it as is its focus P₂; the last repeated reflection of P is caused by the bright point P₂ being seen at P₃, its virtual image behind and as far from the mirror AC produced as P₂. If we make a similar construction for a ray of light emanating from the focus P upon the mirror AC, the virtual image of P will be Q₁, which will also produce Q₂ as its image, and so on, till at last we arrive at Q₄. Now, since the bright images P₁ and Q₁ are at the back of both reflecting planes produced, they can suffer no reflection; therefore, the repeated reflections of P in the two mirrors are P₁, P₂, P₃, P₄, and Q₁, Q₂, Q₃, Q₄, and they are, by Euclid 3, III., points in the circumference. Now, since these points are the respective foci of these perpendicular rays, they will also be the foci of all the rays diverging from their respective points, and, therefore, will form perfect images of the object between the mirrors.

Suppose, now, that instead of having the mirrors perpendicular to the plane of the paper (fig. 2) they have an inclination to each other, and have on the inner edges of AC, BC, one or both, small bits of vari-coloured glass; and if the system of mirrors be inclosed in a case blackened on the inside, then an eye placed at e will see a gorgeous and symmetrical pattern or picture. If the instrument be turned to different parts of the room, the pieces of glass remaining as before, the light will fall on the other portions of the coloured glass, and consequently produce a different pattern. This was the first kind of kaleidoscope which Sir D. Brewster made. It occurred to him some time afterwards, that the pattern might be varied by a motion or change of position in the objects reflected by the mirrors; the coloured glass or other objects were therefore placed between two plates of very thin glass, which formed, as it were, an object-glass; and being held in the hand, could be moved about at pleasure. The kaleidoscope was still further improved by making the object-plates circular, while a motion took place round the axis of the tube, or by sliding the object-plate in a groove, the object being placed in a cell of the reflectors.

The principal parts of the kaleidoscope, then, are the two mirrors (fig. 2) ACe₁, BCe₂; which should be from 6 to 10 inches in length, and from 1 to 1½ inches broad at the end ABC, but about half this breadth at the end abe₁. These mirrors are kept apart at their upper, and united along their lower edges Cc₁, so as to form the solid angle ACo₁b₁, which must be some measure of 4 right angles, or 180°. The planes, which must always be free from dust, are placed in a tube, as in fig. 3; but the end ab₁ is covered, and a small eye-piece affixed, so that the eye may take in the field of view ACB. It is of importance to have the angle of the mirrors as accurate as possible, for any deviation from the even angle will be immediately perceived by the eye. If the angle be a little larger than it should be, the image is deficient, and in some parts irregular or non-symmetrical; if the angle be a little smaller than it should be, the image is redundant, from a reduplication of one part. Sometimes portions of the images overlap and interfere with each other; but on the angle of the mirrors being rectified, these double images coalesce and form one image perfectly symmetrical in all its parts. The angles, therefore, which the mirrors of a kaleidoscope must make with each other are such as the following:—1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, &c., of 180°; or 90°, 60°, 45°, 36°, 30°, 18°, 15°, 12°, 10°, 9°, &c. Whatever part, therefore, the angle ACB is of 180°, the same will be the number of times the image is reflected or repeated in the mirrors. If, in fig. 1, ACB were an aliquot part of 180°, then the images P₁, Q₁ would form a single image; but when this is not the case, a want of symmetry will be perceived. It is important also that the line of junction c₁ of the mirrors (fig. 2) be of the finest possible kind and free from chips, for otherwise, an imperfection will take place in the image. The planes, which have been previously blackened on the back, may be kept together at the proper angle by means of a piece of cloth glued on to their non-reflecting surface, so that they may fold in and out like the leaves of a book. By this contrivance the mirrors may be adjusted to the proper inclination, but chiefly by directing them to any line, or the straight edge of any object in contact with the broad ends, and very obliquely situate with respect to the edge of either of the mirrors; then looking through the instrument at one end, if the image be symmetrical with respect to its pattern, we may be sure that the planes are accurately inclined. The mirrors are now to be carefully set in the hollow tube which is to receive them; and the arrangement of a piece of cork or wood (e.g.) at the back of the mirrors must be such that the angle of inclination will remain unaltered. The remaining side AB₁a₁ of the hollow prism made by the planes (fig. 2) may be effectually closed up by a piece of black velvet glued to the back part of the mirrors. The object-case of the instrument at the farther end from the eye is made up of two pieces of thin glass, kept separate by a brass rim about ¼th or ⅛th of an inch broad; the intervening hollow part contains the objects which are to be reflected. This case is seen in fig. 3, and at the wide end of the mirrors to which it is to be affixed. The end ABC of the planes (fig. 2) is in fig. 3 represented by abed₁; mn is a brass ring, which moves easily upon the tube, and rests steadily in its place; MN is a brass cell, slipping tightly on the moveable ring mn. The objects are placed in a case, one of the glasses of which is transparent, and the other ground; the brass rim separating them should consist of two pieces, the one screwing into the other, so that the objects in the case might be unscrewed and changed at pleasure. The object-box is placed at the bottom of the cell MN, as at OP; and the depth of the cell is such as to allow the side O to touch the end of the mirrors when the cell is slipped upon the ring mn. It is an essential condition that the objects be as near as possible to the plane ABC of the mirrors. The objects employed for reflection are various; but generally small pieces of transparent coloured glass, occupying a certain portion of the interval between the mirrors, produce at times the most splendid patterns. Wires of glass also, both spun and twisted, different in colour and form, may be intermixed with larger masses of coloured glass, beads, bugles, fine needles, metallic wires, lace, seaweed, looped figures and letters (as S and S), circles, ovals, spirals, triangular lines, varnish, indurated Canada balsam, &c.; the case, however, must not be too crowded with objects, so as to interfere with each other's motion.

The patterns produced are of the most gorgeous description, and sometimes defy imitation; the pictures of the images are best comprehended by looking into the instrument itself. When objects are to be looked at which are not in the case, they must be held as near as possible to the object end; such objects are generally viewed as through a microscope, the light falling very strongly upon the object.

The simple kaleidoscope has, as we have seen, two mirrors, but on the same principles as above, we may construct one with 3, 4, 5, &c., or any number of reflecting planes, and which will repeat images in endless succession on every side. Such optical instruments are termed Polycentral Kaleidoscopes. But where symmetry and regularity of form are required, the polycentral kaleidoscope is confined within narrow bounds; for the angles of the several reflecting planes with each other must be an aliquot part of $180^\circ$. Thus, if the kaleidoscope have three mirrors, the angles, in order that a perfect image may be produced by each angle of the prism, must be $60^\circ$, $60^\circ$, $60^\circ$; or $45^\circ$, $45^\circ$, $90^\circ$; or $30^\circ$, $60^\circ$, $90^\circ$. When the reflecting planes are equilateral, and, therefore, have each side making an angle of $60^\circ$ with each other, the instrument is termed the Trioscope, from the triangular symmetry which the images present, the images of each plane being combined in groups of three together in every part of the pattern. When we have an isosceles right angled triangular prism, and, consequently, with angles of $45^\circ$, $45^\circ$, $90^\circ$, the pattern produced is regularly divided into square compartments, and therefore this disposition of the mirrors has received the name of Tetroscope. When the polycentral kaleidoscope has its angles of $30^\circ$, $60^\circ$, $90^\circ$, the pattern produced is hexagonal, and the symmetry is very conspicuous, especially with reference to that centre round which are congregated the greatest number of repetitions caused by the angle of $30^\circ$. This disposition of the reflecting mirrors is termed a Hexoscope. Of these the last two kaleidoscopes are of use to the draughtsman, in affording him the best material for his designs.

The principal advantage which the polycentral has over the simple kaleidoscope is, that the former has a greater field of view than the latter. Were no loss of light to arise from repeated reflections, the field of view would be infinite; but since each reflected ray is not so intense as its corresponding incident one, a diminution of light takes place from repeated reflections. The effects of polarization also increase the loss, but more from this cause in the polycentral than in the simple kaleidoscope; hence metallic specula are preferred to the best of glass mirrors. The number of reflections required, in order to obtain any great extent of spectrum, that is, the whole appearance in the kaleidoscope, being greater than in the ordinary kinds of simple kaleidoscopes, the instrument must be of greater length comparatively with the breadth of the mirrors, as in this way the course of the rays will be more oblique with respect to the mirrors, and a larger portion of light will reach the eye. A greater obliquity is also obtained with the same proportion between the length and breadth of the mirrors, by making them taper at the end next the eye.

We may add, also, that of four-sided kaleidoscopes, those which can give perfectly symmetrical forms are the square and rectangle, where all the angles are right angles.

We may repeat here the conditions necessary for the kaleidoscope producing perfectly symmetrical images. 1st, The angle of inclination of the mirrors must be an even or odd aliquot part of $180^\circ$, or $360^\circ$, when the object is regular and similarly situate with respect to both of the mirrors; or an even aliquot part of $180^\circ$ or $360^\circ$, when the object is irregular. 2d, That out of an infinite number of positions for the object, both within and without the reflectors, there is only one position where perfect symmetry can be obtained, viz., by placing the object in contact with the ends of the reflectors, or between them. 3d, That out of an infinity of positions for the situation of the eye there is only one where the symmetry is perfect, viz., as near as possible to the angular point, so that the whole of the circular field can be distinctly seen; and this point is the only one at which the uniformity of the reflected light is the greatest. When these conditions are properly attended to, the pictures produced in the field of view are beautiful beyond description, and present an endless variety of symmetrical combinations, never recurring a second time when the objects have been displaced by a slight vibration, or by turning the instrument on its axis.

In order to extend the power of the instrument, and to introduce into symmetrical pictures external objects, whether animate or inanimate, Sir David Brewster very ingeniously substituted a double convex lens L (fig. 4), for the case of objects between the circular glass plates, by means of which the second condition for symmetry in kaleidoscopes can be fulfilled. This lens L formed at F between the mirrors an inverted image of the object R; and this image is multiplied by the reflecting planes, and forms a symmetrical spectrum precisely in the same way as if a real object of that size had occupied its place. The lens L may be placed in or at the mouth of one tube, while the reflecting planes are accurately placed in another, so that by pulling in or pushing out the tube next the eye, the images of objects at any distance can be formed at the place of symmetry. Thus may flowers, trees, animals, pictures, busts, &c., be introduced into symmetrical combinations. A blazing fire gives the appearance of beautiful fireworks. Such a disposition of the mirrors and the lens is a Telescopic, or Compound Kaleidoscope. If the distance of F from the eye-piece be less than that at which the eye sees objects distinctly, a convex lens must be placed before the eye, so as to give distinct vision of the objects in the picture.

The images produced by the kaleidoscope may be exhibited to an assembly of spectators at the same time by placing the flame of a lamp between a spherical reflector and a convex-plane lens, the latter of which concentrates the rays, and, being next the instrument, throws a flood of light upon the object-case; the picture is projected on the opposite wall through a double convex lens placed at the eye end. The lamp may be replaced by a jet of oxygen.

The beautiful designs produced by this simple instrument may be copied by means of the Camera obscura, but more successfully traced by using a Camera lucida.

Instead of employing reflecting surfaces, Sir David Brewster tried the effect of solid prisms of glass, and obtained in this way a total, instead of a partial, reflection of light. It is difficult, however, even to make these prisms free from veins or bubbles, and also to obtain a perfect junction of the planes.

Simple kaleidoscopes have been variously constructed, with reference to the angles of inclination of the mirrors, Brewster's Polyangular Kaleidoscopes are so constructed that the angle of the mirrors may be varied at pleasure, by allowing the reflecting surfaces to move on their connecting edges as on a hinge, and thus to open or close at pleasure by means of a screw. Others, again, admit of the mirrors entirely separating, so as gradually to become parallel to