If the plates of glass have been skilfully cut with the diamond, so as to have their edges perfectly straight, and free from chips, two of the edges may be placed together, as in Fig. 17 (p. 49), or one edge of one plate may be placed against the surface of the other plate, as shown in the section of Mr. Bates’s Kaleidoscope. But if the edges are rough and uneven, one of them may be made quite straight, and freed from all imperfections, by grinding it upon a flat surface, with very fine emery, or with the powder scraped from a hone. When the two plates are laid together, so as to form a perfect junction, they are then to be placed in a brass or any other tube, so as to form an angle of 45°, 36°, 30°, or any even aliquot part of a circle. In order to do this with perfect accuracy, direct the tube containing the reflectors to any line, such as _m n_, Fig. 2, placed very obliquely to one of the reflectors =A O=, and open or shut the plates till the figure of a star is formed, composed of 8, 10, or 12 sectors, or with 4, 5, or 6 points, corresponding to angles of 45°, 36°, and 30°. When all the points of the star are equally perfect, and none of the lines which form the salient and re-entering angles disunited, the reflectors must be fixed in that position by small arches of brass or wood =A B=, =_a b_=, Fig. 21, filed down till they exactly fit the space between the open ends of the plates. The plates must then be kept in this position by pieces or wedges of cork or wood, or any other substance pushed between them and the tube. The greatest care, however, must be taken that these wedges press lightly upon the reflectors, for a very slight force is capable of bending and altering the figure even of very thick plates of glass. When the reflectors are thus placed in the tube, as in Fig. 21, their extremities =_a_ E=, =_b_ E=, next the eye, must reach to the very end of the tube, as it is of the greatest importance that the eye get as near as possible to the reflectors. The other ends of the reflectors =A O=, =B O=, must also extend to the other extremity of the tube, in order that they may be brought into contact with the objects which are to be applied to the instrument. In using transparent objects the cell or box which contains them may be screwed into the end of the tube, so as to reach the ends of the reflectors, if they happen to terminate within the tube; but an instrument thus constructed is incapable of being applied to opaque objects, or to transparent objects seen by reflected light. [Illustration: FIG. 21.]