"Between 1807 and 1811... Fourier... developed a mathematical theory of heat conduction... independent of the caloric hypothesis, but... was not published until 1822... as Théorie analytique de la chaleur... Fourier set the study of the theory of heat in the tradition of rational mechanics, basing it on differential equations... The heat transmitted between... molecules was proportional to the difference in their temperature and a function of the distance between them... [and] varied with the nature of the... substance. ...Fourier did not rely upon... speculation about the nature of heat. ...[W]hat was important was not what heat was, but what it did, in a given experimental setting."
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Diane Greco, "Fourier and the theory of heat" (Nov 16, 2020)
https://en.wikiquote.org/wiki/The_Analytic_Theory_of_Heat
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The Analytic Theory of Heat
The Analytic Theory of Heat (1878) is a translation by Alexander Freeman, M.A., with notes, of Joseph Fourier's Théorie Analytique de la Chaleur (1822). Fourier based his reasoning on : the flow of heat between two adjacent molecules is proportional to the extremely small difference of their temperatures. In this work Fourier claims that any function of a variable, can be expanded in a series of sines of multiples of the variable. Though not correct without additional conditions, Fourier's obser
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