Time measurement and uncertainty in Galileo’s inclined plane: From water clocks to electronic timing

A reconstruction of Galileo Galilei’s experimental apparatus used to investigate the dynamics of motion along an inclined plane is presented. The study not only replicates the measurements of distance and motion described in Galileo’s manuscripts, but also emphasizes the central role of time measurement in the formulation of the laws governing uniformly accelerated motion. The experiment is first reproduced using historically plausible instruments, including a reconstructed water clock, in order to assess the feasibility and precision of time measurements available in the seventeenth century. In addition, a comparative analysis is performed using modern measurement techniques: an electronic timing system based on LED–phototransistor pairs has been developed to acquire transit times with millisecond resolution. The comparison between historical and modern methods allows a quantitative evaluation of measurement uncertainty, and highlights the metrological limitations and capabilities of early experimental practices, while offering a contemporary verification of Galileo’s law of motion.