Archimedes Texts

It is also asked why the large balances are more accurate and of more precision than the small balances. The principle of the answer regarding this cause is to ask why, in the case of a line that departs from the center of a circle and is long, and therefore the distance of its end from the center is a greater distance, the motion of its end is faster when both ends are moved by the same force. The faster of two mobiles is the one that travels over a greater distance in the same time. And the farther from the center travels over a greater distance along its circumference, and the nearer a smaller distance. It is evident from this reasoning that the suspension of the balance is a center, since it is fixed, and because the two sides of the beam, which are on either side of the suspension, stand for the lines departing from the center. If the beam is longer, the motion of its end, as it is caused by the same weight, will be stronger than the motion it would have if it were shorter. Hence, when some weights are put on small balances, they do not produce any inclination toward their side, because of their smallness and the shortness of the beam. But if they are put on a large balance, an evident inclination results, because of the length of the needle and of the beam.