5. _Distribution of Heat._ Lastly, to indicate another kind of questions, it is by similar steps that we are able, in the study of thermological phenomena, according to the happy conception of M. Fourier, to form in a very simple manner the general differential equation which expresses the variable distribution of heat in any body whatever, subjected to any influences, by means of the single and easily-obtained relation, which represents the uniform distribution of heat in a right-angled parallelopipedon, considering (geometrically) every other body as decomposed into infinitely small elements of a similar form, and (thermologically) the flow of heat as constant during an infinitely small element of time. Henceforth, all the questions which can be presented by abstract thermology will be reduced, as in geometry and mechanics, to mere difficulties of analysis, which will always consist in the elimination of the differentials introduced as auxiliaries to facilitate the establishment of the equations. Examples of such different natures are more than sufficient to give a clear general idea of the immense scope of the fundamental conception of the transcendental analysis as formed by Leibnitz, constituting, as it undoubtedly does, the most lofty thought to which the human mind has as yet attained. It is evident that this conception was indispensable to complete the foundation of mathematical science, by enabling us to establish, in a broad and fruitful manner, the relation of the concrete to the abstract. In this respect it must be regarded as the necessary complement of the great fundamental idea of Descartes on the general analytical representation of natural phenomena: an idea which did not begin to be worthily appreciated and suitably employed till after the formation of the infinitesimal analysis, without which it could not produce, even in geometry, very important results.