We come now to consider the method of applying the mirrors to the object shown in Fig. 55, which is an exact, but reduced copy of Bradley’s figure. Because the angles of this figure are 90°, he directs that the mirrors “be opened and fixed to an exact square; and that the edge of one of the mirrors must always be placed so as to coincide exactly with one of the sides of the rectangle, and carefully kept in this line when the position of the mirrors is changed.” Hence it is manifest, that Bradley was entirely ignorant of the fundamental principle of the Kaleidoscope, namely, that if the inclination of the mirrors is an even aliquot part of a circle, and if they are _set in any position upon any object or set of objects, however confused, or distorted, or irregular, they will create the most perfect and symmetrical designs_. But even if Bradley had been aware of this principle in theory, neither he nor any other person was acquainted with the mode of constructing and fitting up the reflectors, in order to render them capable of producing the effect. The position of the eye, for symmetry of light, and for symmetry of form;—the position of the mirrors, to produce a perfect junction of the last sectors;—the position of the object necessary to produce an equality and perfect junction between the object and the reflected images;—and the method of accomplishing this for objects at all distances, were fundamental points, in the combination of plane mirrors, which, so far as I know, have never been investigated by any author. But even though a knowledge of these theoretical points had been obtained, numerous difficulties in the practical construction of the instrument remained to be surmounted; and it required no slight degree of labour and attention to enable the instrument to develop, in the most simple and efficacious manner, the various effects which, in theory, it was found susceptible of producing. As the combination of mirrors, described by Kircher and Bradley, had been long known to opticians, and had excited so little attention that they had even ceased to be noticed in works on optical instruments, it became necessary to discover some other origin for the Kaleidoscope. The thirteenth and fourteenth Propositions of Wood’s _Optics_, and some analogous propositions in Harris’s _Optics_, were therefore presumed to be an anticipation of the invention. Professor Wood gives a mathematical investigation of the number and arrangement of the images formed by two reflectors, either inclined or parallel to each other. These theorems assign no position to the eye, or to the object, and do not include the principle of inversion, which is absolutely necessary to the production of symmetrical forms. The theorems, indeed, which have no connexion whatever with any instrument, are true, whatever be the position of the eye or the object; and Mr. Wood has frankly acknowledged, “that the effects produced by the Kaleidoscope were never in his contemplation.”[22]