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."1

The propositions in Harris's Optics relate, like Professor Wood's, merely to the multiplication and circular arrangement of the apertures or sectors formed by the inclined mirrors, and to the progress of a ray of light reflected between two inclined or parallel mirrors; and no allusion

1 See Appendix, p. 185.

whatever is made, in the propositions themselves, to any instrument. In the propositions respecting the multiplication of the sectors, the eye of the observer is never once mentioned; and the proposition is true, if the eye has an infinite number of positions; whereas, in the Kaleidoscope, the eye can only have one position. In the other proposition (Prop. XVII.) respecting the progress of the rays, the eye and the object are actually stated to be placed between the reflectors; and even if the eye had been placed without the reflectors, as in the Kaleidoscope, the position assigned it, at a great distance from the angular point, is a demonstration that Harris was entirely ignorant of the positions of symmetry, either for the object or the eye, and could not have combined two reflectors so as to form a Kaleidoscope for producing beautiful or symmetrical forms.1 It is important also to remark, that all Harris's propositions relate either to sectors or to small circular objects; and that he supposes the very same effects to be produced when the inclination of the mirrors is an odd, as when it is an even, aliquot part of a circle. It is clear, therefore, that he was neither acquainted with the fundamental point in the theory of the Kaleidoscope, nor with any of its practical effects. The only practical part of Harris's propositions is the fifth and sixth scholia to Prop. XVII. In the fifth scholium he proposes a sort of catoptric box, or cistula, known long before his time, composed of four mirrors, arranged in a most unscientific manner, and containing opaque objects between the speculums. "Whatever they are," says he, when speaking of the objects, "the upright

1 See Chap. I. pp. 11, 12, where we have shown that Harris was not even acquainted with the way in which the last sector is formed by reflexion.

figures between the speculums should be slender, and not too many in number, otherwise they will too much obstruct the reflected rays from coming to the eye." This shows, in a most decisive manner, that Harris knew nothing of the Kaleidoscope, and that he has not even improved the common catoptric cistula, which had been known long before. The principle of inversion, and the positions of symmetry, were entirely unknown to him. In the sixth scholium, he speaks of rooms lined with looking-glasses, and of luminous amphitheatres, which were known even to the ancients, and have been described and figured by all the old writers on optics.

APPENDIX.

ALTHOUGH I have no doubt that the observations contained in the preceding Chapters are sufficient to satisfy every candid and intelligent person respecting the true nature of all the combinations of plane mirrors that preceded the invention of the Kaleidoscope, yet as there are many who are incapable, from want of optical knowledge, to understand the comparison which has been made between them, I shall here present the opinions of four of the most eminent mathematicians and natural philosophers.

The first of these is contained in a note from the late Professor Wood, Master of St. John's College, Cambridge, written in reply to a letter, in which I requested him to say, if he had any idea of the effects of the Kaleidoscope when he wrote the thirteenth and fourteenth Propositions of his works on Optics.

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ST. JOHN'S, May 19, 1818. "SIR, The propositions I have given relating to the number of images formed by plane reflectors, inclined to each other, contain merely the mathematical calculation of their number and arrangement. The effects produced by the Kaleidoscope were never in my contemplation. My attention has for some years been turned to other subjects,