On the six-sided plane A B C D E F, Fig. 21, draw six semi-diameters; and on each of these place perpendicularly two plane mirrors, which must join exactly at the centre, and which, placed back to back, must be as thin as possible. Decorate the exterior boundary of this piece, (which is at the extremity of the angles of the hexagon,) with six columns, that at the same time serve to support the mirrors by grooves formed on their inner sides. Add to these columns their entablatures, and cover the edifice in whatever manner you please. In each one of these six triangular spaces, contained between two mirrors, place little figures of pasteboard, in relief, representing such subjects, as, when seen in an hexagonal form, will produce an agreeable effect. To these add small figures of enamel, and take particular care to conceal by some object that has no relation to the subject, the place where the mirrors join, which, as before observed, all meet in the common centre. [Illustration: Fig. 21.] When you look into any one of the six openings of this palace, the objects there contained, being reflected six times, will seem entirely to fill up the whole of the building. This illusion will appear very remarkable, especially if the objects chosen are properly adapted to the effect which the mirrors are intended to produce. If you place between two of these mirrors part of a fortification, as a curtain, and two demi-bastions, you will see an entire citadel with six bastions; or if you place part of a ball-room, ornamented with chandeliers and figures, all these objects being here multiplied, will afford a very pleasing prospect. _Opaque Bodies seemingly Transparent._ Within the case A B C D, place four mirrors O P Q R, Fig. 22, so disposed, that they may each make an angle of 45 degrees, that is, that they may be half-way inclined from the perpendicular, as in the figure. In each of the two extremities A B, make a circular overture; in one of which fix the tube G L, in the other the tube M F, and observe, that in each of these is to be inserted another tube, as H and I. [_Observe._ These four tubes must terminate in the substance of the case, and not enter the inside, that they may not hinder the effect of the mirrors. The four-fold reflection of the rays of light from the mirrors, darkens in some degree the brightness of the object; some light is also lost by the magnifying power of the perspective. If, therefore, instead of the object-glass at G, and concave eye-glass at F, plain glasses were substituted, the magnifying power of the perspective will be taken away, and the object appear brighter.] [Illustration: Fig. 22.]