"[D]uring... cooling... heat escapes, at each instant, through the external surface, and passes into the medium... [and] this quantity is not constant; it is greatest at the beginning of... cooling. If... we consider the variable state of the internal spherical surface... [at] radius... x... there must be at each instant a... quantity of heat which traverses that surface, and passes through that part... more distant from the centre. This continuous flow of heat is variable like that through the external surface, and both are quantities comparable with each other; their ratios are numbers whose varying values are functions of the distance x, and of the time t... elapsed. It is required to determine these functions."
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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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