Théorie mathématique de la chaleur

POISSON, Siméon-Denis

Published by Bachelier, Paris, 1835

About this Item

POISSON'S MOLECULAR MODEL OF HEAT CONDUCTION. First edition, presentation copy inscribed by Poisson to Marie Jean Pierre Flourens, of this classic work on the mathematical theory of heat conduction. "Poisson scored a point in this work by demonstrating how the conductibility of heat in the interior of bodies, far from being contained in the notion of flux as Fourier had held, must be derived from an absorption coefficient that restores a neglected functional dimension. It was in this area that . Poisson's mechanical model for conduction of heat was the most fruitful. That conception enabled Poisson to understand on the molecular scale the complete and correct equation for radiation of heat" (DSB). "The year . 1835 saw the appearance of the next installment of Poisson's 'treatise of mathematical physics': his Théorie mathématique de la Chaleur, a 532-page volume put out by Bachelier in 1,000 copies. The introduction included his history of heat theory, and was followed by accounts of, in order: physical parameters, and some aspects of radiant heat; general theory of radiant heat; principles of heat diffusion; interior diffusion in solids and liquids (including the constants defined as cumulative integrals; surface diffusion; solutions to the diffusion equation, especially Laplace's integral form but also Fourier series and surface harmonics; and the cooling of a bar of varying section and of a sphere . Poisson also laid especial emphasis on terrestrial heat distribution in two of the chapters on spheres . After reporting data from Arago and others on temperatures measured in various situations below ground, he challenged the belief of Laplace and Fourier that the heat of the earth was largely conserved internally from its creation on the grounds that the temperatures in the earth's core would be too high: he wondered if the temperature of the universe varied in the different parts of the earth's course, and he also considered solar, stellar and atmospheric heat" (Grattan-Guinness). Provenance: Marie Jean Pierre Flourens (13 April 1794 - 6 December 1867) was a French physician, famous for various significant discoveries relating to the nervous system, cerebral localisation and brain functions. He was known for his studies on brain physiology. He was one of the pioneers in the usage of experimental methods in neuroanatomy. The first significant mathematical theory of heat conduction was read to the Institut de France by Jean-Baptiste-Joseph Fourier (1772-1837) in December 1807. It was not favoured with a report, and it was only through Poisson's efforts that it was published (three months later, in abridged form). Fourier's work excited controversy on two counts. Neither Joseph-Louis Lagrange (1736-1813), nor Pierre-Simon Laplace (1749-1827), nor Poisson, considered his solutions in trigonometric series, rather than power series, to be rigorously founded. "Fourier's method of obtaining the partial differential equation of heat conduction excited equal controversy, for he very nearly wrote it down as a direct expression of experimental results. To the prevailing orthodoxy, rigour in physique mathématique meant rigorous deduction of observable consequences from a detailed microscopic model of atoms or molecules and their interactions. Conceptually, the net action of a system at any point in space derived from a sum (or less rigorously an integral) over the independent actions of all the discrete sources in the system. Rigour therefore required one to begin with an integral conception, then carefully to convert it to the more manageable form of a partial differential equation, and finally to find a power-series solution. Fourier violated every step in the process, beginning with his appeal directly to experimental laws . "Notwithstanding the 'splendour and poetry' that William Thomson [Lord Kelvin] would see in Fourier's treatise, his Laplacian contemporaries did not see its beauty. After more than twenty-five years of controversy, Seller Inventory # 5242

Bibliographic Details

Title: Théorie mathématique de la chaleur

Publisher: Bachelier, Paris

Publication Date: 1835