Mr. Harris repeats the same mistake in a more serious form, in his second Scholium, § 240, where he shows that the images are arranged in the circumference of a circle. The two images =D=, _d_, says he, coincide and make but one image. Mr. Wood has committed the very same mistake in his second Corollary to Prop. XIV., and his demonstration of that Corollary is decidedly erroneous. This Corollary is stated in the following manner:—“When _a_ (the angle of the mirrors) is a measure of 180° _two images coincide_,” and it is demonstrated, that _since two images of any object_ =X= (Fig. 2) _must be formed_, viz., one by each mirror, and since these two images must be formed at 180° from the object =X=, placed between the mirrors, that is, at the same point _x_, it follows that the two images must coincide. Now, it will appear from the simplest considerations, that the assumption, as well as the conclusion, is erroneous. The image _x_ is seen by the last reflexion from the mirror =B O E=, and another image _would be seen at x_, if the mirror =A O E= had extended as far as _x_; but as this is impossible, without covering the part of the mirror =B O E=, which gives the first image _x_, there can be only one image seen at _x_. When the object =X= is equidistant from =A= and =B=, then one-half of the last reflected image _x_ will be formed by the last reflexion from the mirror =B O=, and the other half by the last reflexion from the mirror =A O=, and these two half images will join each other, and form a whole image at _e_, as perfect as any of the rest. In this last case, when the angle =A O B= is a little different from an even aliquot part of 360°, the eye at =E= will perceive at _e_ an appearance of two incoincident images; but this arises from the pupil of the eye being partly on one side of =E= and partly on the other; and, therefore, the apparent duplication of the image is removed by looking through a very small aperture at =E=. As the preceding remarks are equally true, whatever be the inclination of the mirrors, provided it is an even aliquot part of a circle, it follows,— 1. That when =A O B= is ¼, ⅙, ⅛, ⅒, ¹/₁₂, etc., of a circle, the number of reflected images of any object =X=, is 4 - 1, 6 - 1, 8 - 1, 10 - 1, 12 - 1. 2. That when =X= is nearer one mirror than another, the number of images seen by reflexion from the mirror to which it is nearest will be ⁴/₂, ⁶/₂, ⁸/₂, ¹⁰/₂, ¹²/₂, while the number of images formed by the mirror from which =X= is most distant will be ⁴/₂ - 1, ⁶/₂ - 1, ⁸/₂ - 1, ¹⁰/₂ - 1; that is, an image more always reaches the eye from the mirror nearest =X=, than from the mirror farthest from it. 3. That when =X= is equidistant from =A O= and =B O=, the number of images which reaches the eye from each mirror is equal, and is always 4 - 1, 6 - 1, 8 - 1, 10 - 1, 12 - 1 ----- ----- ----- ------ ------ 2 2 2 2 2