For Example.
Let the number thought of be 5, which multiplied by itself gives 25; in the next place, 5 increased by 1 is 6, which multiplied by itself makes 36; and the difference between these two squares is 11, the least half of which is 5, the number thought of.
To make Alum Baskets.
Form a small basket, about the size of the hand, of iron wire; then take some worsted, and wind it round every part of it. Boil a pound of alum in a quart of water, let it boil well, stirring it all the time; when completely dissolved, pour it into a deep pan, and by a thread suspend the basket into it to a good depth, so as that no part shall touch the vessel; let it remain for one day, and when you take it out, the alum will be found crystallized all over the basket. The alum may be coloured pink, purple, or yellow, by boiling Brazil, logwood, or French berries with it.
Silver Tree on Glass.
Put a few drops of the solution of silver in aqua-fortis; on a piece of glass form a bit of copper or brass wire, to represent a tree with its branches, but flat, so as to lie upon the glass; lay it in the liquid, and let it remain for an hour or two. A beautiful vegetation will be perceived all round the wire, which will nearly be covered by it. This may be preserved by washing it very carefully with water, and putting another glass over it.
A person having written an odd number on one card, and an even on another, to tell which is the even and which is the odd.
Desire him to multiply the number in his right hand by 5 (or any odd number) and that in his left by 6, (or any even number) and tell you if the sum of the products added together be odd or even. If it be even, the even number is in the right; but if odd, the even number is in the left hand.
A Metal which bursts into flame when thrown upon cold water.
Place a piece of potassium, of about two grains weight, upon cold water in a bason, when it inflames, and exhibits a beautiful light of a violet red colour.