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 and so on. A symmetrical figure is constantly obtained, forming in one case a cross composed of four similar portions; in the other a triple star, the halves of each ray being similar. It is the symmetry of the figure that gives the pleasing effect. In the ordinary kaleidoscope the angle made by the reflecting surfaces is thirty degrees, and a star of six rays is formed, the halves of each ray being alike. The figures formed in the kaleidoscope are simply endless; and if the space between the glasses in the moveable cap be filled with bits of opaque as well as transparent substances, the varieties of light and shade may be added to those of colour. It was at one time the fashion to copy the images formed in the kaleidoscope as paterns for room papers, muslins, curtains, shawls, and other similar fabrics, but thanks to the spread of artistic taste in this country the decorative designer now relies more on his own talent than any aid he may receive from optical instruments.

Plane mirrors, as we have seen, reflect objects upright and symmetrical, reversing only the sides. Concave mirrors reverse them, and if they are not placed exactly in the proper focus, distort them by making one portion appear smaller than the other; while convex mirrors reflect them in an upright position, but also similarly slightly distorted. But when the mirror is not a portion of a sphere, like those whose properties we have been considering, the distortion is increased to so great an extent as to deform the object so that it is difficult to recognise its nature from its reflection. We all know the distortion that our face undergoes when reflected from the shining surface of a teapot or spoon, and the cylindrical mirrors that hang in the shop windows of many opticians are the source of much amusement to the passers by, whose physiognomies are shown to them either lengthened to many times their natural size, or widened to an extent that is ludicrously hide