the angular aperture cannot be formed by successive reflexions into a continuous curve; and for the same reason, the upper sectors of the luminous field are larger than the lower ones, and consequently the centre of the pattern cannot coincide with that of the field. In order to avoid these defects, therefore, the diameter of the lens should be such, that when it is at its greatest distance from the reflectors, the field of view may be bounded by the arch A B, Fig. 13, and not by the brass rim which holds the lens. This may be readily known by removing the eyeglass, and applying the eye at E when the lens is at its greatest distance. If the eye cannot see the brass rim, then the lens is sufficiently large; but if the brass rim is visible, the lens is too small, and must be enlarged till it ceases to become visible. Sometimes the lens has been made so small that the brass rim is seen not only at A B, but appears also above the angular point o, and produces a dark spot in the centre of the picture. Instead of using two tubes, a lens is sometimes fitted into a tube about an inch longer than the focal length of the glass, and this tube is slipped upon the object end A B 0, Fig. 21. This mode of applying the lens is, however, inferior to the first method, as there is little room for adjusting it to different distances; whereas with the long tube all objects at a greater distance than four inches from the lens may be introduced into the picture a property which possesses very peculiar advantages. The extension of the instrument to distant objects is not the only advantage which is derived from the use of the lens. As the position for giving perfect symmetry is rather within the extremities of the reflectors than without them; and as it is impossible to place movable objects within the reflectors, we are compelled to admit a small error, arising principally from the thickness of the objects, and from the thickness of the plate of glass which is necessarily interposed between the objects and the reflectors. The compound Kaleidoscope, however, is entirely free from this defect. The image of a distant, or even of a near object, can be formed within the reflectors, and in the mathematical position of symmetry; while, at the same time, the substitution of the image for the object itself, enables us to produce all the changes in the picture which the motion of the object could have effected, merely by turning the instrument round its axis, or by moving it horizontally, or in any other direction across the object. This instrument may be advantageously placed upon a stand like a telescope, and may either have a partial motion of rotation by means of a ball and socket, as shown in the figure, or what is better, a complete motion of rotation round the axis of the tube C D, within a brass ring, occupying the place of the ball and socket.1 1 An instrument called The Improved Kaleidoscope has been recently brought out in Paris. It is merely the Telescopic Kaleidoscope deteriorated. It consists of a lens fixed at the distance of about two inches in front of the reflectors, and can therefore give symmetrical pictures of objects only at one distance, while it cannot be used as an ordinary Kaleidoscope. The instrument described in the preceding page, with a lens that can be slipped off, is a much better Kaleidoscope. CHAPTER XI. ON THE CONSTRUCTION AND USE OF POLYANGULAR KALEIDO SCOPES, IN WHICH THE REFLECTORS CAN BE FIXED AT ANY ANGLE. IN all the preceding instruments, the reflecting planes are fixed at an invariable angle, which is some even aliquot part of 360°; and therefore, though the forms or patterns which they create are literally infinite in number, yet they have all the same character, in so far as they are composed of as many pairs of direct and inverted images as half the number of times that the inclination of the reflectors is contained in 360°. It is therefore of the greatest importance, in the application of the Kaleidoscope to the arts, to have it constructed in such a manner, that patterns composed of any number of pairs of direct and inverted images may be created and drawn. With this view, the instrument may be fitted up in various ways, with paper, cloth, and metallic joints, by means of which the angle can be varied at pleasure; but the most convenient methods are shown in the Figures from Fig. 29 to 35, inclusive, which represent two different kinds of Polyangular Kaleidoscopes, as made by the late Mr. R. B. Bate, Optician, London, who had devoted much time and attention to the perfection of this species of Kaleidoscope. Bate's Polyangular Kaleidoscope with Metallic Reflectors. The three Figures, viz., 29, 30, and 31, represent the Polyangular Kaleidoscope with metallic reflectors, as made FIG. 29. D T by Mr. Bate. Fig. 29 shows the complete instrument, when mounted upon a stand; Fig. 30 is a section of it in the direction of its length; Fig. 31 is a transverse section of it through the line s T, Fig. 30, and Fig. 32 shows the lens of the eye-hole E. The tube of this instrument is composed of two cones, M M, N N, Fig. 30, connected together by a middle piece or ring, RR, into which they are both screwed. These two cones enclose two highly-polished metallic reflectors, A 0, B o, Fig. 31, only one of them, viz., BO E, being seen in Fig. 30. One of these reflectors, BO E, is fixed to the ring R R, by the inter- |