A difficulty now presents itself in accounting for the formation of the last or sixth sector, =α O β=. Mr. Harris, in the XVIIth Prop. of his Optics, has evaded this difficulty, and given a false demonstration of the proposition. He remarks, that the last sector, =α O β= is produced “by the reflexion of the rays forming either of the two last images” (namely, =_b_ O β= and =_a_ O α=); but this is clearly absurd, for the sector =α O β= would thus be formed of two images lying above each other, which is impossible. In order to understand the true cause of the formation of the sector =α O β=, we must recollect that the line =O E= is the line of junction of the mirrors, and that the eye is placed any where in the plane passing through =O E= and bisecting =A O B=. Now, if the mirror, =B O=, had extended as far as =O β=, the sector =α O β= would have been the image of the sector =_b_ O β=, reflected from =B O=; and in like manner, if the mirror =A O= had extended as far as =O α=, the sector =α O β= would have been the image of the sector =_a_ O α= reflected from =A O=; but as this overlapping or extension of the mirrors is impossible, and as they must necessarily join at the line =O E=, it follows, that an image =α O _e_=, of only half the sector =_b_ O β=, viz., =_b_ O _r_=, can be seen by reflexion from the mirror =B O=; and that an image =β O _e_=, of only half the sector =_a_ O α=, viz., =_a_ O _s_=, can be seen by reflexion from the mirror =A O=. Hence it is manifest, that the last sector, =α O β=, is not, as Mr. Harris supposes, _a reflexion from either of the two last images_, =_b o_ β=, =_a o_ α=, but is composed of the images of two half sectors, one of which is formed by the mirror =A O=, and the other by the mirror =B O=.