6.1 Hydrostatic balance

The "Eureka" story about Archimedes and the bath tub was as well known in Galileo's day as it is in ours. Galileo,who was a great admirer of Archimedes and adopted many of his methods, probably read it in one of the editions of Vitruvius's The Ten Books on Architecture ,

Weighing precious metals in air and then in water was presumably a practice that was common amongjewelers in Europe. Galileo had some ideas for refining the practice and, at the age of 22, he wrote a little tract about it,which he entitled La Bilancetta , or "The Little Balance." What Galileo described was an accurate balance forweighing things in air and water, in which the part of the arm on which the counter weight was hung was wrapped with metal wire. Theamount by which the counterweight had to be moved when weighing in water could then be determined very accurately by counting thenumber of turns of the wire, and the proportion of, say, gold to silver in the object could be read off directly.

This little tract illustrates the mixture of the theoretical and practical that marks Galileo's science in contrastto that of most of his contemporaries.