4. On combinations of three reflectors at angles of 90°, 45°, and 45°. The effect produced by the combination of three reflectors at angles of 90°, 45°, and 45°, is shown in Fig. 47. The two reflectors a o, a в produce a pattern C D B I, composed of eight triangles; the reflectors B 0, B A, likewise give a pattern A F G H, composed of eight triangles; and the reflectors A O, O B, give a pattern A B H I, composed of four triangles. The triangle I H K is an image formed by three reflexions, one half of it being a reflexion of half of A I α, from the mirror B 0, and the other half a reflexion of half of в H b, from the mirror a o; and the triangle D E F consists of two half images, which are reflexions of the two half images in I O H. The remaining triangle D L F is a reflection of I K H, from the mirror A B, and is therefore formed by four reflexions. As the three mirrors are not symmetrically placed, with regard to each other, the equally luminous images are not arranged symmetrically round the open triangle ▲ O B, as in the preceding combinations. The effect is, however, very pleasing, and all the reflected images included in the figure CLG K are sufficiently bright. 5. On combinations of three reflectors at angles of The most complicated combinations of three reflectors is represented in Fig. 48. In the first combination, all the angles were equal; in the second, two of the angles only were equal; but in the present combination, none of them are equal. The field of view, represented in the figure by DEHLM P, is a truncated rhomb, consisting of no fewer than thirty-one images of the aperture A O B. The figure is composed of two hexagons D E F BRC, RBK L M N, every division of the hexagon consisting of two reflected images, and of two rhombs C R N P, FB K H, each of which is composed of four reflected images. In this combination, as in the last, the equally luminous sectors are not symmetrically arranged round the centre o of the figure. In the rhomb CRN P, for example, the four images are formed by three, four, and five reflexions; whereas in the corresponding rhomb F H K B, they are formed by two, three, and four reflexions. The effects pro duced by a Kaleidoscope constructed in this manner are very beautiful, particularly when the reflectors are metallic. In the four figures which represent the different combinations of the reflectors, the small figures indicate the number of reflexions by which each image is produced. H CHAPTER XIV. ON KALEIDOSCOPES IN WHICH THE EFFECT IS PRODUCED BY TOTAL REFLEXION FROM THE INTERIOR SURFACES OF TRANSPARENT SOLIDS. WHEN light is incident upon the most perfectly polished metals, a very considerable quantity of it is absorbed, and even when the reflexion is made at the greatest obliquities, there is a very manifest difference in the intensity of the direct and the reflected pencil. In the total reflexion of light from the second surfaces of transparent bodies, the loss of light is very inconsiderable, and the reflexion is made with a degree of brilliancy far surpassing that of the most resplendent metals. In constructing a Kaleidoscope upon this principle, we must procure a piece of glass entirely free from veins, and cut it into the form shown in Fig. 49.1 The two surfaces BOE, A O E, must be inclined at an angle which is the even 1 When this chapter was written (1818), it was very difficult to procure glass sufficiently homogeneous for this purpose: but it can now be procured from the Glass Works of Messrs. Chance & Co, at Sinethwick, near Birmingham. aliquot part of a circle. They must be ground perfectly flat and highly polished, and the junction o E must be made as fine as possible. The upper surface A B E should be rough-ground, and the side A B O, and the side at E, should be parallel and well polished. If the glass is colourless and good, the eye, when placed at E, will see the very same appearance as in the simple Kaleidoscope; and objects placed at ABO will be arranged into the same beautiful figures. The only defects attending this form of the Kaleidoscope, are the loss of light occasioned by its passing through a mass of solid glass, not perfectly transparent, and the difficulty of obtaining a perfect junction of the two reflecting planes. The first of these evils is, however, counterbalanced by the great intensity of the light which suffers total reflexion; and the second does not exist when the Kaleidoscope is intended to give rectilineal or annular patterns. In the construction of instruments of this kind, it is necessary to make the prism of glass longer than the distance at which the eye can see objects with perfect distinctness; that is, if the eye is capable of seeing objects distinctly at the distance of five inches, it will not perceive the same objects distinctly when they are placed at the end of a prism of glass five inches long. This singular effect arises from a property of plain lenses or pieces of plain glass, in consequence of which, they cause divergent rays to diverge from a point nearer the lens or plate, than that from which they radiated. It will therefore be more convenient, for many reasons, to make the glass prism only two or three inches long, and obtain distinct vision by means of a lens placed at the eye-end of it; but, for the |