169.

undetermined in the separate particular solutions in such a way that the process may be adapted to any initial state ( t = 0 ) whatever.

If now, as we have assumed so far, the cavity is entirely void of matter, the process of radiation with a given initial state is uniquely determined in all its details. It consists of a set of stationary vibrations, every one of which is represented by one of the particular solutions considered, and which take place entirely independent of one another. Hence in this case there can be no question of irreversibility and hence also none of any tendency to equality of the partial energies corresponding to the separate partial vibrations. As soon, however, as we assume the

presence in the cavity of only the slightest trace of matter which can influence the electrodynamic vibrations, e.g., a few gas molecules, which emit or absorb radiation, the process becomes chaotic and a passage from less to more probable states will take place, though perhaps slowly. Without considering any further details of the electromagnetic constitution of the molecules, we may from the law of statistical mechanics quoted above draw the conclusion that, among all possible processes, that one in which the energy is distributed uniformly among all the independent variables of the state has the stationary character.

From this let us determine these independent variables. In the first place there are the velocity components of the gas molecules. In the stationary state to every one of the three mutually independent velocity components of a molecule there corresponds on the average the energy $\frac{1}{3}\overline{L\mathrm{\backslash Strut}}$ where $\overline{L\mathrm{\backslash Strut}}$ represents the mean energy of a molecule and is given by [eqn:(200)] (200). Hence the partial energy, which on the average corresponds to any one of the independent variables of the electromagnetic system, is just as large.

Now, according to the above discussion, the electromagnetic state of the whole cavity for every stationary vibration corresponding to any one system of values of the numbers $𝖺$ $𝖻$ $𝖼$ is determined, at any instant, by four mutually independent quantities. Hence for the radiation processes the number of independent variables of state is four times as large as the number of the possible systems of values of the positive integers $𝖺$, $𝖻$, $𝖼$.