and also possesses a certain inertial mass and obeys the law of inertia, its mass changes significantly with temperature and it also depends in a certain specifiable way from the magnitude of the velocity as well as from the direction of the moving force in respect to the velocity. However, there is absolutely nothing hypothetical about those properties, as they can be quantitatively derived from known laws in all details.
Given the situation described, by which some views and theorems are stripped of its general nature, hitherto considered to be the strongest support for the usual theoretical considerations of any kind, it must appear as a task of particular importance to single out and especially put into the foreground, those theorems that previously formed the bases of general dynamics, and which also proved absolutely accurate in the light of the results of recent research; for they alone will henceforth be entitled to find use as the foundations of dynamics. But it should of course not be said that the above theorems, noticeably marked as inexact, were to put out of use in future; for in the vast majority of cases, the enormous practical importance of the decomposition of energy in internal and kinetic, or the adoption of the absolute invariance of mass, or the condition of identity of inertial and ponderable mass, is indeed not affected at all by the considerations advanced, and we will never come in a position to dispense with those considerable simplifying assumptions. But from the standpoint of the general theory we must unconditionally and principally distinguish between such theorems, which can be regarded only as approximations, and those which claim exact validity, because today it is unknown to which consequences the further development of the exact theory will lead us: far reaching revolutions, also in practice, have often enough started with discoveries of almost imperceptibly small inaccuracies within a theory that was previously considered as generally exact.
If we therefore ask about the really exact basis of general dynamics, of all known theorems only the principle of least action remains at first, which includes, as it was proved by H. von Helmholtz[1], mechanics, electrodynamics
- ↑ H. Von Helmholtz, Wissenschaftl. Abhandl. III, p. 203, 1895.
