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Example I: Take

Take a solid body, the specific gravity of which is less than that of water, deal, 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 wholesomest 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 crown, or half a crown, 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 which 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.