The lower edge =O E= of the reflector =B O E= extends about the 15th of an inch below the axis of the cones, as represented by the dotted line in Fig. 30; but the lower edge =O E= of the other reflector =A O E=, which is finely ground to an acute angle, forming a perfectly straight and smooth line, is placed exactly in the axis of the cones, so as just to touch a line in the reflector =A O E=, which coincides with the axis of the cone, and to form a junction with that line in every part of the two meeting planes. The very nice adjustments which are necessary to produce so exact a motion are effected by the screws corresponding to =K= and =L=. If we now fix the outer ring _r r_ into the ring of a stand =S T=, so as to be held fast, and turn the cones with the hand, we shall give motion to the reflector =B O=, so as to place it at any angle we please, from 0° to 90°; and during its motion through this arch, the junction of the two reflectors must remain perfect, if the touching lines are adjusted, as we have described them, to the axis of motion, which must also be the axis of the cones and rings. If, on the contrary, we take away the stand, and, holding the instrument in the hand by either of the cones =M=, =N=, turn the ring =R R= with the other, we shall give motion to its reflector =A O=, and produce a variation in the angle in the same manner as before. The same effect may be produced by an endless screw working in teeth, cut upon the circumference of the outer ring _r r_. In order to enable the observer to set the reflectors at once to any even aliquot part of a circle, or so as to give any number of pairs of direct and inverted images, the most convenient of the even aliquot parts of the circle are engraven upon the ring _r r_; so that we have only to set the index to any of these parts, to the number 12, for example, and the reflectors will then be placed at an angle of 30° (12 × 30 = 360°), and will form a circular field with _twelve_ luminous sectors, or a star with _six_ points, and consequently a pattern composed of _six_ pairs of direct and inverted images.