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.[5] [5] 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 KALEIDOSCOPES, 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°.