§ 1. Mechanical Analogy.

If the form deviates from the simple shape, waves must arise that increasingly run into one another, so that the kinetic energy original: "lebendige Kraft," a historical term for kinetic energy of the original visible motion must finally dissolve into that of an invisible wave motion. This mathematical consequence of the equations describing the phenomena leads, so to speak, of its own accord to the hypothesis that those vibrations of the smallest particles—into which the ever-diminishing waves must eventually transform—are identical with the heat generated according to experience, and that heat in general is a motion in small dimensions invisible to us.

Added to this is the ancient view that bodies do not fill the space they occupy continuously in the mathematical sense, but consist of discrete small bodies, the molecules individual units of matter, which are completely imperceptible to the senses due to their smallness. Philosophical reasons support this view. For a true continuum original: "Continuum," a continuous sequence where adjacent elements are not different from each other must consist of mathematically infinite parts; however, a truly infinite number in the mathematical sense is indefinable. Furthermore, if one assumes a continuum, one must regard the partial differential equations mathematical equations involving multiple variables used to describe physical change for its behavior as the originally given data. As desirable as it is to strictly separate the partial differential equations—as the elements most completely controllable by experience—from their mechanical justification (as Hertz Heinrich Hertz (1857–1894), a physicist who clarified the electromagnetic theory of light emphasizes this specifically for the theory of electricity), a mechanical justification of the partial differential equations based on the average values determined by the coming and going of small particles nevertheless extraordinarily increases their clarity. So far, no mechanical explanation of natural phenomena other than atomism the theory that all matter is made of indivisible particles has been found.

Moreover, a certain discontinuity of bodies has been established through experience by numerous, even quantitatively consistent facts. Atomism is particularly indispensable for visualizing the facts of chemistry and crystallography. The mechanical analogy between the facts of those sciences and the grouping relationships of discrete particles certainly belongs to those whose...