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The Mécanique Physique of Siméon Denis Poisson: The evolution and isolation in France of his approach to physical theory (1800-1840). I-X. (English) Zbl 0548.01015

This suite of articles is the virtually unchanged text of the author’s dissertation defended at the University of Toronto in 1978. For some reason it has been broken up into papers submitted at various dates, and published in non-consecutive order across two of its issues.
Chapter headings: I: Physics in France after the revolution (Vol. 28, pp. 243-266); II: The Laplacian program (pp. 267-287); III: Poisson: mathematician or physicist? (pp. 289-297); IV: Disquiet with respect to Fourier’s treatment of heat (pp. 299-320); V: Fresnel and the circular screen (pp. 321-342); VI: Elasticity: The crystallization of Poisson’s views on the nature of matter (pp. 343-367); VII: Mécanique Physique (Vol. 29, pp. 37-51); VIII: Applications of the Mécanique Physique (pp. 53-72); IX: Poisson’s closing synthesis: Traité de physique mathématique (pp. 73-94); X: Some perspective on Poisson’s contributions to the emergence of mathematical physics (pp. 287-307).
The author’s purpose is to outline Poisson’s approach to mathematical physics, and its growing isolation from concurrent developments of the subject. Starting in the 1800s to develop the research program of mathematised models of inter-molecular forces acting under some unknown law of attraction, a program often called ’Laplacian physics’ by historians today, Poisson tried to extend it to cover, at least in principle, the whole empire of mathematical physics, including heat diffusion and magnetism as well as the ”classical” areas of elasticity and fluid dynamics. The most useful parts of this account occur in parts 6 and 7, where it is shown how his developing ideas on the constitution of (”all”) matter caused him to replace integrals by sums when expressing the cumulative inter-molecular action across a finite (part of a) body. For the purpose he enlisted the Euler-Maclaurin summation formula, of which he studied the convergence (Part 8). While the topic is certainly worthy of lengthy study, the account here cannot be recommended as authoritative for several reasons: indiscriminate use of secondary literature, causing some of the many errors of detail in biography and relationship; failure to draw on, and enrich, the text by insights provided in various overlooked secondary sources; omission of several key papers by Poisson, on sound, elasticity, magnetism, Fourier series, numerical integration, and Taylorian expansions.
Reviewer: I.Grattan-Guinness

MSC:

01A55 History of mathematics in the 19th century
70-03 History of mechanics of particles and systems

Biographic References:

Poisson, Siméon Denis
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