116.

Although, according to the statement just made, a decisive test of the different admissible hypotheses can be made only a posteriori, it is nevertheless worth while noticing that it is possible to obtain a priori, without relying in any way on thermodynamics, a definite hint as to the nature of an admissible hypothesis. Let us again consider a flowing gas as an illustration ([sect:114.] Sec. 114). The mechanical state of all the separate gas molecules is not at all completely defined by the thermodynamic state of the gas, as has previously been pointed out. If, however, we consider all conceivable positions and velocities of the separate gas molecules, consistent with the given values of the visible velocity, density, and temperature, and calculate for every combination of them the mechanical process, assuming some simple law for the impact of two molecules, we shall arrive at processes, the vast majority of which agree completely in the mean values, though perhaps not in all details. Those cases, on the other hand, which show appreciable deviations, are vanishingly few, and only occur when certain very special and far-reaching conditions between the coordinates and velocity-components of the molecules are satisfied. Hence, if the assumption be made that such special conditions do not exist, however different the mechanical details may be in other respects, a form of flow of gas will be found, which may be called quite definite with respect to all measurable mean values–-and they are the only ones which can be tested experimentally–-although it will not, of course, be quite definite in all details. And the remarkable feature of this is that it is just the motion obtained in this manner that satisfies the postulates of the second principle of thermodynamics.