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 B= produce a pattern =C D B I=, composed of eight triangles; the reflectors =B O=, =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 _a_=, from the mirror =B O=, and the other half a reflexion of half of =B 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 reflexion 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 =A O B=, as in the preceding combinations. The effect is, however, very pleasing, and all the reflected images included in the figure =C L G K= are sufficiently bright. 5. _On combinations of three reflectors at angles of 90°, 60°, and 30°._ [Illustration: FIG. 48.] 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 =D E H L M 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 B R C=, =R B K L M N=, every division of the hexagon consisting of two reflected images, and of two rhombs =C R N P=, =F B 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 =C R N 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 produced 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. CHAPTER XIV. ON KALEIDOSCOPES IN WHICH THE EFFECT IS PRODUCED BY TOTAL REFLEXION FROM THE INTERIOR SURFACES OF TRANSPARENT SOLIDS.