Traité de l'equilibre et du mouvement des fluides, pour servir de suite au Traité de dynamique

ALEMBERT, Jean le Rond d

Editore: David l’ainé, Paris, 1744

D ALEMBERT S PRINCIPLE APPLIED TO HYDRODYNAMICS . First edition of this continuation of d Alembert s classic Traité de dynamique published in the previous year. "The Treatise on Dynamics was d Alembert s first major book and it is a landmark in the history of mechanics. It reduces the laws of the motion of bodies to a law of equilibrium. Its statement that the internal forces of inertia must be equal and opposite to the forces that produce the acceleration is still known as d Alembert s principle . This principle is applied to many phenomena and, in particular, to the theory of the motion of fluids" (PMM 195). D Alembert had applied his principle to fluid mechanics in a brief section at the end of the Traité de dynamique, but in the present work he gives a far more detailed treatment."In 1744 d Alembert published a companion volume to his first work, the Traité de l équilibre et du mouvement des fluides. In this work d Alembert used his principle to describe fluid motion, treating the major problems of fluid mechanics that were current. The sources of his interest in fluids were many. First, Newton had attempted a treatment of fluid motion in his Principia, primarily to refute Descartes s tourbillon theory of planetary motion. Second, there was a lively interest in fluids by the experimental physicists in the eighteenth century, for fluids were most frequently invoked to give physical explanations for a variety of phenomena, such as electricity, magnetism, and heat. There was also the problem of the shape of the earth: What shape would it be expected to take if it were thought of as a rotating fluid body? Clairaut published a work in 1744 which treated the earth as such, a treatise that was a landmark in fluid mechanics. Furthermore, the vis viva controversy was often centered on fluid flow, since the quantity of vis viva was used almost exclusively by the Bernoullis in their work on such problems. Finally, of course, there was the inherent interest in fluids themselves. D Alembert s first treatise had been devoted to the study of rigid bodies; now he was giving attention to the other class of matter, the fluids. He was actually giving an alternative treatment to one already published by Daniel Bernoulli [Hydrodynamica, 1738], and he commented that both he and Bernoulli usually arrived at the same conclusions. He felt that his own method was superior. Bernoulli did not agree" (DSB). D Alembert himself gives an account of the Traité des fluides in the article Hydrodynamique in the Encyclopédie. "My object in this book has been to reduce the laws of fluid equilibrium and motion to the least possible number and to determine by an extremely simple general principle, everything that is concerned with the motion of fluid bodies. I have examined the theories given by M. Bernoulli and M. Maclaurin and I believe that I have revealed the difficulties as well as confusion. I also believe that on certain occasions M. Daniel Bernoulli has used the principle of live forces in cases where he should not have done so. I must add that this great geometer has used this principle without having proved it, or rather that the proof that he has provided is unsatisfactory. However this should not stop from providing this work with the merit that other scientists as well as I should give to this work. I deal as well in this work on the resistance of fluids to bodily motion, of refraction or the motion of a body as it enters into a fluid and finally concerning laws of motion governing fluids which move in vortices" (The Encyclopedia of Diderot and d Alembert Collaborative Translation Project). The Traité des fluides is based on the principle set forth in the Traité de dynamique. In the first part of the earlier work, "d Alembert developed his own three laws of motion. It should be remembered that Newton had stated his laws verbally in the Principia, and that expressing them in algebraic form was a task taken up by the mathematicians of the eig. Codice articolo 5320

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Titolo: Traité de l'equilibre et du mouvement des ...
Casa editrice: David l ainé, Paris
Data di pubblicazione: 1744
Edizione: First edition.