ON THE CHANGES PRODUCED BY THE KALEIDOSCOPE. The property of the Kaleidoscope, which has excited more wonder, and therefore more controversy than any other, is the number of combinations or changes which it is capable of producing from a small number of objects. Many persons, entirely ignorant of the nature of the instrument, have calculated the number of forms which may be created from a certain number of pieces of glass, upon the ordinary principles of combination. In this way it follows, that twenty-four pieces of glass may be combined 1,391,724,288,887,252,999,425,128,493,402,200 times—an operation, the performance of which would require hundreds of thousands of millions of years, even upon the supposition that twenty of them were performed every minute. This calculation, surprising as it appears, is quite false, not from being exaggerated, but from being far inferior to the reality. It proceeds upon the supposition that _one_ piece of glass can exhibit only _one_ figure, and that _two_ pieces can exhibit only _two_ figures, whereas it is obvious that the two pieces, though they can only be combined in two ways, _in the same straight line_, yet the one can be put _above_ and _below_ the other, as well as upon its right side and its left side, and may be joined, so that the line connecting their centres may have an infinite number of positions with respect to a horizontal line. It follows, indeed, from the principles of the Kaleidoscope, that _if only one object is used, and if that object is a mathematical line without breadth, the instrument will form an infinite number of figures from this single line_. The line may be placed at an infinite number of distances from the centre of the aperture, and equally inclined to the extremities of the reflectors. It may be inclined at an infinite variety of angles to the radii of the circular field, and it may be placed in an infinite variety of positions parallel to any radius. In all these cases, the Kaleidoscope will form a figure differing in character and in magnitude. In the first case, all the figures are polygons of the same character, but of different sizes. In the second case, they are stars, differing from each other in the magnitude of their salient and re-entering angles; and in the third case, they form imperfect figures, in which the lines unite at one extremity and are open at the other.