As the axis of motion in the preceding construction is necessarily the axis of the cones and rings, the diameter of these cones and rings must everywhere be double the breadth of the reflectors. From this cause, the tube, and consequently the object-box, are wide, and the instrument is, to a certain degree, not very portable. This defect is completely avoided in another Polyangular Kaleidoscope constructed by Mr. Bate, upon entirely different principles, which we shall now proceed to describe. _Bate’s Polyangular Kaleidoscope with Glass Reflectors._ [Illustration: FIG. 33.] [Illustration: FIG. 34.] [Illustration: FIG. 35.] [Illustration: FIG. 36.] A section of the whole of this instrument, in the direction of its length, is shown in Fig. 33. A section through =M N= or =O P=, near the eye-end, is shown in Fig. 35, Fig. 34 representing the mode of supporting the fixed reflector, and Fig. 36 the mode of supporting the movable reflector. The tube of the Kaleidoscope, in Fig. 33, is represented by _b c d e f g h_, and consists of two parts, _b c g h_, and _c d e f g_. The first of these parts unscrews from the second, and the second contains all the apparatus for holding and moving the reflectors. At the parts =M N O P=, of the tube, are inserted a short tube, a section of which is shown in Fig. 34. The object of these tubes is to support the fixed mirror =A O=, which rests with its lower end =O= upon the piece of brass _t_. It is kept from falling forwards by the tongue _r_, connected with the upper part _s s_, and from falling backward by the piece of cork =Q=, which may be removed at any time, for the purpose of taking out and cleaning the reflectors. This little tube is fixed to the outer tube by the screws _s_, _s_. The contrivance for supporting and moving the second reflector =B O=, is shown in Fig. 36, in section; and a longitudinal view of it is given in Fig. 33. The mirror =B O= lies in an opening, cut into two pieces of brass, =_v_ B _p_=, one of which is placed at =M N=, and the other at =O P=. These two pieces of brass are connected by a rod _m n_, Fig. 33; and in the middle of this rod there is inserted a screw _k_, which passes through the main tube _c d e f g_, into a broad milled ring _w w_, which revolves upon the tube. As the screw _k_, therefore, fastens the ring _w w_ to the rod _m n_, the reflector =B O= will be supported in the tube by the ring _w w_. The lower part of the mirror =B O=, or rather of the brass piece =_v_ B _p_=, rests at _y_, upon the piece of watch-spring _x y z_, fastened to the main tube at _z_. This spring presses the face of the reflector =B O= against the ground and straight edge of the other reflector =A O=, so as always to effect a perfect junction in every part of their length:—The apparatus for both reflectors is shown in Fig. 35. An arch of about 45° is cut out of the main tube, so as to permit the screw _k_ to move along it; and