Fraudulent balance

84 x 55
Steel and brass

INDEX 1788 : C.II.108

Bilanx quaedam dolosa, composita ex jugo brachiis longitudine inaequalibus constructo.

Balance with two pans, fraudulent, which includes a beam composed of two arms of unequal lengths.

This balance has two arms of different lengths: one is 21 cm in length, the other measures 17.5 cm. In the Index Instrumentorum, dalla Bella refers to it as a fraudulent balance. This is basically a trick balance, and was used in Instrumental Physics lessons to illustrate what used to happen at times in the market, sometimes purposefully, sometimes accidentally.

This balance has the distinctive feature that, in addition to having unequal arms, it also have pans of unequal weights, so that when the dishes are empty the balance remains in equilibrium. This may suggest, incorrectly, that it is an ordinary equal arm balance.

To check that a balance is not fraudulent, place an object in each pan and proceed to level the balance. When equilibrium has been achieved, the same two objects must be exchanged to the opposite pans. If the balance remains levelled it may then be concluded that the length of the arms are equal, if not, it is a fraudulent balance.

In spite of this balance's unique characteristic feature, it is possible to achieve a correct weighing. To do this the object to be weighed is placed in one of the pans. Next, level the balance off, placing weights of a known weight in the other pan, calling them P1. Afterwards, proceed in levelling the balance with the object in the opposite pan. Under the same conditions, find an equilibrium again with other known weights, whose value shall be called P2. The weight, P, of the object will be determined by: P=.

This scale is mounted on a universal stand (instrument 24).

From Colégio dos Nobres, catalogue n.º 100.

Musschenbroek, Peter Van, Introductio ad Philosophiam Naturalem, Leiden, 1762, Vol. I, § 403, Tab.IV, Fig 7.
's Gravesande, Willem Jacob, Physices Elementa, Leiden, 1742, Vol. I, § 96, Tab VI, Fig 5.

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