On the six-sided plane A B C D E F of the figure, draw six semi-diameters; and on each of these place perpendicularly two plane mirrors, which must join exactly at the center, and which, placed back to back, must be 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 center.
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.
TO KNOW WHICH OF TWO DIFFERENT WATERS IS THE LIGHTEST WITHOUT ANY SCALES.
Take a solid body, the specific gravity of which is less than that of water, pine, or fir wood, for instance, and put it into each of the two waters, and rest assured that it will sink deeper in the lighter than in the heavier water; and so by observing the difference of the sinking, you will know which is the lightest water, and consequently the most wholesome for drinking.
TO KNOW IF A SUSPICIOUS PIECE OF MONEY IS GOOD OR BAD.
If it be a piece of silver that is not very thick, as a dollar or a half dollar, the goodness of which you want to try, take another piece of good silver of equal balance with it, and tie both pieces with thread or horse-hair to the scales of an exact balance (to avoid the wetting of the scales themselves) and dip the two pieces thus tied in water; for then, if they are of equal goodness, that is, of equal purity, they will hang in equilibrio in the water as well as in the air; but if the piece in question is lighter in the water than the other, it is certainly false, that is, there is some other metal mixed with it that has less specific gravity than silver, such as copper. If it is heavier than the other, it is likewise bad, as being mixed with a metal of greater specific gravity than silver, such as lead.
If the piece proposed is very thick, such as that crown of gold that Hiero, king of Syracuse, sent to Archimedes to know if the goldsmith had put into it all the eighteen pounds of gold that he had given him for that end, take a piece of pure gold of equal weight with the crown proposed, viz., eighteen pounds, and without taking the trouble of weighing them in water, put them into a vessel full of water, one after another, and that which drives out most water must necessarily be mixed with another metal of less specific gravity than gold, as taking up more space, though of equal weight.
PYRAMID OF ALUM.