Mathematics and hydraulics between Turin and Ferrara in the 18th century: the works by F. D. Michelotti and T. Bonati

During the 18th century mathematical studies devoted to hydraulic and hydrodynamics applications become relevant. The importance of such kind of studies both from a theoretical and a practical point of view is well documented by a remarkable increase of papers about the motion of waters. A lot of mathematicians were involved in this research field. They were asked to describe the motion of waters by means of mathematical formulas. Unfortunately, the motion of water can’t be described by Euler’s equations. That’s why in this period many practical experiments were conducted in order to find the better description of the motion of waters in rivers and streams. After a brief overview of the condition of the Italian studies about hydraulics and hydrodynamics in the 17th century, we will focus on the case studies of Turin and Ferrara. In 1763 the King Carlo Emanuele III of Savoy financially supported the construction of a laboratory for hydraulic experiments in Turin and appointed Francesco Domenico Michelotti (1710-1787), professor of hydraulics at the university of Turin, with these experiments. In the same period another mathematician from Ferrara, Teodoro Bonati (1726-1820), is involved in similar studies and experiments on behalf of the Papal State. The scientific relationship between Michelotti and Bonati will be presented in this article, starting from the exam of the correspondence between the two mathematicians in the period 1768-1772, soon after the publication of the first volume of the Sperimenti idraulici by Michelotti.