"7th. ...[E]ach of these solutions gives the equation proper to the phenomenon, since it represents it distinctly throughout the... extent of its course, and... determine[s] with facility all its results numerically. The functions... obtained by these solutions are then composed of a multitude of terms... finite or infinitely small: but the form of these expressions is... [not] arbitrary; it is determined by the physical character of the phenomenon. For this reason, when the value of the function is expressed by a series into which exponentials relative to the time enter, it is of necessity... since the natural effect whose laws we seek, is... decomposed into distinct parts, corresponding to the... terms of the series. The parts express so many simple movements compatible with the special conditions; for each one of these movements, all the temperatures decrease, preserving their primitive ratios. In this composition we ought not to see a result of analysis due to the linear form of the differential equations, but an actual effect which becomes sensible in experiments. It appears also in dynamical problems in which we consider the causes which destroy motion; but it belongs necessarily to all problems of the theory of heat, and determines the nature of the method which we have followed for the solution..."