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