Over and undershot waterwheels in the 18th century. Science and technology controversy

The present paper concerns the development of theory and experiments on water wheels in the 18th cen- tury. At that time, as a result of a growing demand for energy, a better understanding of the functioning of watermills, even at the theoretical level, was required in order to improve their efficiency. A hint about the evolution of the theory of wheels in the 19th century is reported also. We have tried to clarify the role played by some protagonists as Antoine Parent, Jean-Charles de Borda and John Smeaton. Their role has not been fully recognised even in contemporary studies. Then some considerations are developed on the relationships between science and technology on this particular subject, concluding that it was a happy and well-balanced marriage.