"Suppose... in the second solid, the permanent temperature a^\prime ...is that of boiling water, 1... b^\prime is that of melting ice, 0... distance e^\prime is the unit of measure... [Then \frac{a^\prime - b^\prime}{e^\prime} = \frac{1-0}{1} = 1.] [D]enote by K the constant flow of heat which, during unit of time... would cross unit of surface in this [second] solid, if it were formed of a given substance; K expressing a certain number of units of heat, that~is to say a certain... [multiple] of the heat necessary to convert a kilogramme of ice into water... [T]o determine the constant flow F, in a solid... of the same substance, the \frac{F}{K} = \frac{a - b}{e} \div 1 or F = K \frac{a - b}{e}. ... F denotes the quantity of heat which, during the unit of time, passes across a unit of area of the surface taken on a section parallel to the base."
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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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