Theoretical Constructions (I): Clairaut and d'Alembert

Abstract

For a brief period in the middle of the eighteenth century, there was a moment of extraordinary brilliance in the development of fluid mechanics. Three men, Clairaut, d’Alembert, and Euler, raised the theory of fluid mechanics to the height where it remained almost unchanged for more than 50 years. The process began with Clairaut’s Théorie de la figure de la Terre, tirée des Principes de l’Hydrostatique (Theory of the shape of the Earth obtained from the Principles of Hydrostatics), which appeared in 1743, and continued with the Essai d’une nouvelle théorie de la résistance des fluides (Essay on a new theory of the resistance of fluids) of d’Alembert, which, though it published in 1752, had been presented in 1749. The process ended in 1755 with three monographs of Euler: ‘Principes généraux de l’état d’équilibre des fluides’ (‘General principles of the state of equilibrium of fluids’), ‘Principes généraux du mouvement des fluides’ (‘General principles of motion of fluids’) and ‘Continuation des recherches sur la théorie du mouvement des fluides’ sur la théorie du mouvement des fluids’ (‘Sequel to the researches on the theory of motion of fluids’). Less than 13 years had elapsed from the appearance of Clairaut’s work. That this brief period should produce such contributions is an indication that the time was ripe, and the theories were ready to bear fruit. This process must be explained as the result of a network of influences, as it is obvious that the key works are not isolated events, but form part of a linked chain. Very probably the distribution and dissemination of the work was accompanied by debates in the Academies and other forums, followed by letters and sundry documents circulating along all the highways and byways of European science. At the same time, this activity must be viewed as being framed by the development of mechanics, which in turn was promoting and making use of mathematical analysis. It is by chance that the three figures involved were great mathematicians.