All the various forms which nature and art present to us, may be divided into two classes, namely, _simple_ or _irregular_ forms, and _compound_ or _regular_ forms. To the first class belong all those forms which are called picturesque, and which cannot be reduced to two forms similar, and similarly situated with regard to a given point; and to the second class belong the forms of animals, the forms of regular architectural buildings, the forms of most articles of furniture and ornament, the forms of many natural productions, and all forms, in short, which are composed of two forms, similar and similarly situated with regard to a given line or plane. Now, it is obvious that all compound forms of this kind are composed of a direct and an inverted image of a simple or an irregular form; and, therefore, every simple form can be converted into a compound or beautiful form, by skilfully combining it with an inverted image of itself, formed by reflexion. The image, however, must be formed by reflexion from the first surface of the mirror, in order that the direct and the reflected image may join, and constitute one united whole; for if the image is reflected from the posterior surface, as in the case of a looking-glass, the direct and the inverted image can never coalesce into one form, but must always be separated by a space equal to the thickness of the mirror-glass. If we arrange simple forms in the most perfect manner round a centre, it is impossible by any art to combine them into a symmetrical and beautiful picture. The regularity of their arrangement may give some satisfaction to the eye, but the adjacent forms can never join, and must therefore form a picture composed of disunited parts. The case, however, is quite different with compound forms. If we arrange a succession of similar forms of this class round a centre, it necessarily follows that they will all combine into one perfect whole, in which all the parts either are or may be united, and which will delight the eye by its symmetry and beauty. In order to illustrate the preceding observations, we have represented in Figs. 4 and 5 the effects produced by the multiplication of single and compound forms. The line _a b c d_, for example, Fig. 4, is a simple form, and is arranged round a centre in the same way as it would be done by a perfect multiplying glass, if such a thing could be made. The consecutive forms are all disunited, and do not compose a whole. Fig. 5 represents the very same simple form, _a b c d_, converted into a compound form, and then, as it were, multiplied and arranged round a centre. In this case every part of the figure is united, and forms a whole, in which there is nothing redundant and nothing deficient; and this is the precise effect which is produced by the application of the Kaleidoscope to the simple form _a b c_. [Illustration: FIG. 4.] [Illustration: FIG. 5.]