CHAPTER XIX.

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.

If, instead of supposing a mathematical line to be the object, we take a single piece of coloured glass, with an irregular outline, we shall have no difficulty in perceiving, from experiment, that an infinite variety of figures may be created from it alone. This system of endless changes is one of the most extraordinary properties of the Kaleidoscope. With a number of loose objects, it is impossible to reproduce any figure which we have admired. When it is once lost, centuries may elapse before the same combination returns. If the objects, however, are placed

in the cell, so as to have very little motion, the same figure, or one very near it, may, without difficulty, be recalled; and if they are absolutely fixed, the same pattern will recur in every revolution of the objectplate.

CHAPTER XX.

ON THE APPLICATION OF THE KALEIDOSCOPE TO THE

FINE AND USEFUL ARTS.

If we examine the various objects of art which have exercised the skill and ingenuity of man, we shall find that they derive all their beauty from the symmetry of their form, and that one work of art excels another in proportion as it exhibits a more perfect development of this principle of beauty. Even the forms of animal, vegetable, and mineral bodies, derive their beauty from the same source. The human figure consists of two halves, one of which is the reflected image of the other; and the same symmetry of form presents itself in the shapes of almost all the various tribes of animated beings. In the structure of vegetables, the principle of symmetry is less perfectly developed. From the extreme delicacy and elasticity of its parts, a plant, regularly constructed, would have lost all its symmetry from the influence of gravitation, or from the slightest breath of wind; and therefore a symmetrical combination of parts has been effected only in its leaves and flowers. When the laws of crystallization are allowed to perform their functions uncontrolled, the beautiful geometrical forms which they create are marked with the most perfect regularity. Even their physical properties are

symmetrically related to some axis or fixed line; and though all their functions are performed in utter silence and repose, yet their physiology, if we may apply that name to the actions of apparently dead matter, is not less wonderful than that which embraces the busy agencies of animal and vegetable bodies.

The irregular forms which are the foundation of picturesque beauty constitute a single exception to the general law, and therefore the landscape painter is the only artist who is not professionally led to the study of that species of beauty which arises from the inversion and multiplication of simple forms.

When we consider the immense variety of professions connected both with the fine and the useful arts, in which the creation of symmetrical ornaments forms a necessary part, we cannot fail to attach a high degree of utility to any instrument by which the operations of the artist may be facilitated and improved. We are disposed to imagine that no machine is really useful, unless it is directly employed in providing for our more urgent wants. This, however, is a vulgar error. An engine which forms the head of a pin, has, in reality, as much importance as an engine for raising water, or for manufacturing cloth; for in these cases the three machines have the same object, which is merely that of abridging manual labour. The water would still be raised, and the cloth and pins manufactured, if the machines did not exist; but the machinery insures us a more regular supply of these articles, and enables us to receive them at a cheaper rate.

The operations of machinery have, however, a still higher character in comparison with those of individual exertion,