What 1586 tract by Galileo described a balance for weighing objects in air or water?

Galileo's 1586 tract describing a balance for weighing objects in air or water was The Little Balance, or La Bilancetta.

Galileo wrote the tract at about age 22, while studying the problem of determining the composition of precious-metal objects. Its subject connects directly to the ancient story of Archimedes and the crown of Hiero, but Galileo proposed a more precise practical method than the familiar water-displacement version.

The instrument was a hydrostatic balance. An object could be weighed in air and then in water; the difference revealed information about its specific weight and therefore about the proportions of metals such as gold and silver. Galileo improved precision by using a fine wire on the arm, allowing the counterweight's position to be measured by counting turns.

The work is often confused with Galileo's later writings on motion and mechanics, including On Motion and Mechanics. Those works addressed dynamics, whereas The Little Balance focused on measurement, buoyancy, and the analysis of alloys. The tract was written in 1586 but was not published during Galileo's lifetime.