Thus it is easy to perceive that an object, as at, on A 0, with its immediately reflected image at', will give rise to the appearances of similar figures at et ye, and an object, as N, on A 13, with its immediately reflected image will give rise to the appearances of similar figures at n re, a" n": also an object, as r, between A C and B C, will appear by reflection similarly situated iu all the other sectors.
1f the angle A c B be of four right angles, in which na is any term in the series of even numbers 4, 6, 8, 10, &c., the number of sectors will be ma, and each of them will be equal to A c B, while c ft, the appearance of the line in which the mirrors meet each other, will, as in the figure, bisect the angle which is opposite to A c n ; also if In be any term in the series of odd numbers 5, 7, 9, &c., the number of sectors will be an, and each of them will be equal to A 0 B, while a it will coincide with the line in which the two lowest sectors join one another. It may hence be easily understood that if a flat object placed in the sector A o B, with its plane perpendicular to the mirrors, have its bounding-lines similarly situated with respect to A c and B c, the reflected images will be similar and equal to the original object ; and the whole will constitute one symmetrical pattern, whether the value of an be odd or even : but if the bounding-lines are not similarly situated with respect to A c and B c, the reflected images will not, in the two lowest sectors, unite so as to correspond to the images in the other sectors, unless m be an even number. The second figure repre sents a pattern produced by the objects represented in the sector corresponding to A en in the first figure.
In order that the whole pattern in the field of view might possess perfect symmetry about the centre c, it would be necessary that the eye should be exactly in the direction of the line in which the glass plates meet one another ; but in such a situation the reflected images would not he visible: if the eye were far above the line of meeting, the visible field of view would be sensibly elliptical, and the brightness of the field would be diminished ; it follows, therefore, that the eye should be near the smaller ends of the mirrors, and very little above the line of their junction. Again, it may be readily understood that, in order to permit the reflected images of objects to be symmetrically disposed about the centre of the field of view, the object should be exactly in a plane contiguous to the mirrors at the extremities which are farthest from the eye; for the line in which the planes of glass meet each other appearing to pass through the common centre of the visible vectors, if the object were placed on that line of junction, and either between the eye and those extremities or beyond the latter, it is evident, the eye being above the line of meeting, that the appareut or projected place of the object would not coincide with that common centre, but in the former case would appear below, and in the latter above, that centre. The length of the mirrors should be such that the
object in the sector A o n may bo distinctly visible ; the eye may, how ever, if necessary , be assisted by a concave or a convex lens.
The first kaleidoscopes constructed by Sir David Brewster consisted simply of the two mirrors, which were fixed in a cylindrical tube ; the objects were pieces of variously coloured glass attached to the farther ends of the mirrors and projecting on the meetoml space n c B between then; • or the object. were plated between two plates of very thin and held by the hand or flied in a cell at the end of the tube. In sense came these plates were moved .crows the field of view, and in others they were made to turn round upon the axis of the tuba The pieces of eoloureal gig or other objects which were situated In the sector A CD were, by the different reflections, made to appear in all the other sectors; and thus the field of view presented the appearance of an entire object or pattern, all the parts of which were disposed with Gra wet symmetry. By moving the glass pietas between which tlesob*ta were contained, the pattern was made to vary in form ; ping variations In the tints were produced by moving the instrumest so that the light of the sky or of a Lamp might fall on the objects in direction.. When the objects in the sector A C s are CODADM near ite upper part, the Images evidently form an annular pattern ; and, on placing the two mirrors parallel to one another, the successive reflections of the object. produce one which is rectilinear.