Weighing water to find density

This lesson asks you to show how mass, volume and density are related, and to determine whether an object floats, given its density, in different fluids. The museum offers two medieval accounts of how weight and displaced water were used to compare materials; the calculations and the comparison of floating and sinking in several fluids are for the class to carry out. ¹

The expectations relate three quantities. For each device you read about, write down what it measures directly, what is worked out from it, and where the measurement could go wrong.

Robert Hall, whose account the museum's record follows, places the balance of wisdom at Merv under Sultan Sanjar and says it was built for the treasury ². He also passes on an older story: an earlier balance, made by al-Asfizari, was destroyed out of fear that it would expose fraud. The record treats this with care. It calls it a transmitted account, not a modern eyewitness finding ³. Afterwards al-Khazini described a similar, further refined instrument and left a substantial technical account of it ³.

The museum's records preserve no sentence in which al-Khazini says why he took up this work. They show three things. The balance was made for a ruler's treasury, to investigate metals and gems ⁴. His own preface, printed in Arabic and English, identifies Muhammad as his prophet ⁵. And his treatise traces a history that begins with Archimedes: he does not present himself as the first person to discover weighing, and he connects the accuracy of the balance to the contributions of those before him ³.

The balance of wisdom is sometimes presented as al-Khazini's invention from nothing. Hall credits al-Asfizari with the earlier movable pans and regards most of the fundamental theory as inherited; the museum classes al-Khazini's work as an improvement: a refined version and its calibration procedures ⁶. The same care applies to al-Biruni's vessel: the drawing that names it reached us through a nineteenth-century publication whose publisher acknowledges a deficient, erroneous manuscript ⁷.

The story of the destroyed balance is a transmitted account, and no one today can check it. Should a historian of science still tell it, and what would have to be found for you to treat it as a fact?

• The balance of wisdom: how five pans turn two weighings into a judgement about a material.
• al-Khazini: what is known of his life, and what is not.
• al-Biruni's displacement vessel: the drawing, the stray drops, and the damaged manuscript it comes from.

Read about the displacement vessel and the balance of wisdom. For each, list in your own words the two weights that are compared and what the comparison tells you about the material.