[22] See Appendix, p. 185. 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 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.[23] 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 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. [23] 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. APPENDIX.