In a trial for the infringement of a Patent several years ago, a distinguished judge (we believe it was Judge Alderson) stated it as a fact, that the Patent for the Kaleidoscope had been set aside in a Court of Law. The party whose case was prejudiced by this erroneous assertion, applied to me for an affidavit, by which he was enabled to contradict it in Court, and remove any unfavourable impression it might have made upon the jury. CHAPTER I. PRELIMINARY PRINCIPLES RESPECTING THE EFFECTS OF COMBINING TWO PLAIN MIRRORS. The principal parts of the Kaleidoscope are two reflecting planes, made of glass, or metal, or any other reflecting substance ground perfectly flat and highly polished. These reflectors, which are generally made of plate glass, either rough ground on their outer side, or covered with black varnish, may be of any size, but in general they should be from four or five to ten or twelve inches long; their greatest breadth being about an inch when the length is six inches, and increasing in proportion as the length increases. When these two plates are put together at an angle of 60°, or the sixth part of a circle, as shown in Fig. 1, and the eye placed at the narrow end =E=, it will observe the opening =A O B= multiplied six times, and arranged round the centre =O=, as shown in Fig. 2. [Illustration: FIG. 1.] [Illustration: FIG. 2.] In order to understand how this effect is produced, let us take a small sector of white paper of the shape =A O B=, Fig. 2, and having laid it on a black ground, let the extremity =A O= of one of the reflectors be placed upon the edge =A O= of the sector. It is then obvious that an image =A O _b_= of this white sector of paper will be formed behind the mirror =A O=, and will have the same magnitude and the same situation behind the mirror as the sector =A O B= had before it. In like manner, if we place the edge =B O= of the other reflector upon the other side =B O= of the paper sector, a similar image =B O _a_= will be formed behind it. The origin of three of the sectors seen round =O= is therefore explained: the first, =A O B=, is the white paper sector seen by direct vision; the second, =A O _b_=, is an image of the first formed by _one_ reflexion from the mirror =A O=; and the third is another image of the first formed by _one_ reflexion from the other mirror =B O=. But it is well known, that the reflected image of any object, when placed before another mirror, has an image of itself formed behind this mirror, in the very same manner as if it were a new object. Hence it follows, that the image =A O _b_= being, as it were, a new object placed before the mirror =B O=, will have an image =_a_ O α= of itself formed behind =B O=; and for the same reason the image =B O _a_= will have an image =_b_ O β= of itself, formed behind the mirror =A O=, and both these new images will occupy the same position behind the mirrors as the other images did before the mirrors.