Let =A C B D=, Fig. 37, be two plane mirrors, and let their inclination be measured by the angle =A O B=; then, if the eye is placed between =C= and =D=, it will observe the reflected images of the objects which are placed before the aperture =A C B D=, arranged, in the annular segment =M A B N=, round =O=, as a centre. The effect is exactly the same as if the reflectors had been continued to =O=, with this difference only, that the annular segment can never be complete. This defect in the segment arises from two causes: When the centre =O= is near =C D=, the defect is occasioned by the want of a reflecting surface to complete the ring, and not from any want of light in the reflected images; but when the centre =O= is remote from =C D=, the defect arises from the want of light in the last reflexions, as well as from the want of a reflecting surface. The theory of the Annular Kaleidoscope is exactly the same as that of the common instrument; and therefore all the contrivances for producing symmetrical pictures, from near and distant objects, are applicable to this instrument. As the picture, however, never can return into itself, it is of no importance that the angle =A O B= be the aliquot part of a circle, the picture being equally complete at all angles. In order to have the most perfect symmetry with this Kaleidoscope, the eye should be placed at =E=, between the nearest ends of the reflectors, as it will there be nearer the plane of both reflectors than in any other position. If the two mirrors are brought nearer each other, so that their surfaces always pass through the point O, the deviation from perfect symmetry will diminish as the eye becomes more and more in the plane of both; and for the same reason the light of the field will be more brilliant. When the point =O= is infinitely distant, the two reflectors become parallel to each other, as in Fig. 38, and the series of reflected images extends in a straight line, forming beautiful rectilineal patterns for borders, &c. In this position of the reflectors the eye should be placed in the centre at =E=, and the symmetry of the picture and the light of the field will increase as the distance of the reflectors diminishes, or as their length is increased. [Illustration: FIG. 38.] Two different kinds of instruments have been constructed on the preceding principles, the one by Mr. Dollond, and the other by Mr. John Ruthven, both of which possess very valuable properties. _Mr. Dollond’s Universal Kaleidoscope._ [Illustration: FIG. 39.] [Illustration: FIG. 40.]