117.

From these considerations it is evident that the hypotheses whose introduction was proven above to be necessary completely answer their purpose, if they state nothing more than that exceptional cases, corresponding to special conditions which exist between the separate quantities determining the state and which cannot be tested directly, do not occur in nature. In mechanics this is done by the hypothesisL. Boltzmann, Vorlesungen über Gastheorie 1, p. 21, 1896. Wiener Sitzungsberichte 78, Juni, 1878, at the end. Compare also S. H. Burbury, Nature, 51, p. 78, 1894. that the heat motion is a "molecular chaos";Hereafter Boltzmann's "Unordnung" will be rendered by chaos, "ungeordnet" by 116 chaotic (Tr.). in electrodynamics the same thing is accomplished by the hypothesis of "natural radiation," which states that there exist between the numerous different partial vibrations [eqn:(149)] (149) of a ray no other relations than those caused by the measurable mean values (compare below, [sect:148.] Sec. 148). If, for brevity, we denote any condition or process for which such an hypothesis holds as an "elemental chaos," the principle, that in nature any state or any process containing numerous elements not in themselves measurable is an elemental chaos, furnishes the necessary condition for a unique determination of the measurable processes in mechanics as well as in electrodynamics and also for the validity of the second principle of thermodynamics. This must also serve as a mechanical or electrodynamical explanation of the conception of entropy, which is characteristic of the second law and of the closely allied concept of temperature.To avoid misunderstanding I must emphasize that the question, whether the hypothesis of elemental chaos is really everywhere satisfied in nature, is not touched upon by the preceding considerations. I intended only to show at this point that, wherever this hypothesis does not hold, the natural processes, if viewed from the thermodynamic (macroscopic) point of view, do not take place unambiguously. It also follows from this that the significance of entropy and temperature is, according to their nature, connected with the condition of an elemental chaos. The terms entropy and temperature do not apply to a purely periodic, perfectly plane wave, since all the quantities in such a wave are in themselves measurable, and hence cannot be an elemental chaos any more than a single rigid atom in motion can. The necessary condition for the hypothesis of an elemental chaos and with it for the existence of entropy and temperature can consist only in the irregular simultaneous effect of very many partial vibrations of different periods, which are propagated in the different directions in space independent of one another, or in the irregular flight of a multitude of atoms.