In order to convey to the reader some idea of the effect produced by the Kaleidoscope in grouping figures, we have given in Fig. 51 a design created by the instrument. The inclination of the mirrors by which the figures were arranged is 36°, or ⅒th of a circle; and therefore the object is multiplied _ten_ times, so as to give _five_ pair of direct and inverted images. 3. _Designs for Carpets._ There is none of the useful arts to which the creations of the Kaleidoscope are more directly applicable than the manufacture of carpets. In this case, the manufacturer requires not merely the outline of a design, but a design filled up with the most brilliant colours; and upon the nature of the figure which he selects, and the tints with which he enriches it, will depend the beauty of the effect which is produced. A carpet, indeed, is in general covered with a number of Kaleidoscope designs, arranged in lines parallel to the sides of the apartment; and while this instrument creates an individual pattern, it may also be employed, by the assistance of the lens, in exhibiting the effect or arranging or grouping these individual patterns, according to the form of the apartment, and other circumstances which should invariably be attended to. When a plasterer ornaments the ceiling of a room, the figure which he chooses is always related to the shape of the ceiling, and varies according as it is circular, elliptical, square, or rectangular. In like manner, a carpet should always have a relation to the form of the apartment, not only in the shape and character of the individual designs, but in the mode in which they are combined into a whole. Although the designs given by the Kaleidoscope are in general circular, yet, when they are once drawn, their outline may be made either triangular, square, rectangular, elliptical, or of any other form that we please, without destroying their beauty. The outline of the pattern may be varied in the instrument, by varying the shape of the part of the tube or aperture which bounds the field of view at the widest end of the angular aperture; but it is only at certain inclinations of the reflectors that any of the regular figures can be produced in this way. If the bounding line is circular, the field of view will be a circle; if the bounding line is rectilineal, and equally inclined to the reflectors, the field of view will be a regular polygon, of as many sides as the number of times that the angle of the reflectors is contained in 360°; if the bounding line is rectilineal, but placed at right angles to one of the reflectors, the figure will still be a regular polygon, but its number of sides will be equal to _half_ the number of times that the angle of the reflectors is contained in 360°. Hence it follows, that a square field may be obtained in two ways, either by placing the mirrors at an angle of 45°, and making the bounding line perpendicular to one of the reflectors; or by inclining