THE FIRST USE OF PARTIAL DIFFERENTIAL EQUATIONS IN MATHEMATICAL PHYSICS

D'ALEMBERT, (JEAN le ROND).

Reflexions sur la Cause Generale des Vents. Piece qui a remporté le Prix proposé par l'Academie Royale des Sciences de Berlin, pour l'année 1746. 2 Parts (French and Latin). (Latin title: Meditationes de Generali Ventorum Causa...).

Paris, David l'aine, 1747. 4to. Cont. full calf, raised bands. Rebacked in old style. Inner hinges strenghtened. Corners restored. Engraved title-vignette and 1 large engraved vignette in the text. (8),XXVIII,194,138 pp. and 2 engraved folded plates (all). First 4 and last 6 leaves waterstained in margins. Occational marginal dampstaining.

First edition, issued in the same year in both Paris and Berlin, but only the Paris-edition also has the Latin text, which was translated into French by d'Alembert himself.

The work is highly important, as it is the first work at all in which the general use of partial differential equations in mathematical physics appeared. D'Alembert discusses the mathematical theory of vibrations of cords and hereby he was led to partial differential equations which he applied to the "Theory of Winds" and laid the base of a scientific meteorology. He rejected the conception of Edmund Halley that the general circulation of the atmosphere is significantly controlled by the distribution of solar heating, and applies a mathematical theory, based on Newton's law of gravitation, thus explaining the winds by means of the gravitational forces from the sun and moon. - D'Alembert's name survives in the mathematics of today, the "Dalabertian" for wave equation, D'alembert's paradox in hydrodynamics etc.

Order-nr.: 31091