A further interesting confirmation of the law of radiation of black bodies for long waves and of the connection of the radiation constant with the absolute mass of the material
molecules was found by J. H. JeansJ. H. Jeans, Phil. Mag. 10, p. 91, 1905. by a method previously used by Lord Rayleigh,Lord Rayleigh, Nature 72, p. 54 and p. 243, 1905. which differs essentially from the one pursued here, in the fact that it entirely avoids making use of any special mutual action between matter (molecules, oscillators) and the ether and considers essentially only the processes in the vacuum through which the radiation passes. The starting point for this method of treatment is given by the following proposition of statistical mechanics. (Compare above, [sect:140.] Sec. 140.) When irreversible processes take place in a system, which satisfies Hamilton's equations of motion, and whose state is determined by a large number of independent variables and whose total energy is found by addition of different parts depending on the squares of the variables of state, they do so, on the average, in such a sense that the partial energies corresponding to the separate independent variables of state tend to equality, so that finally, on reaching statistical equilibrium, their mean values have become equal. From this proposition the stationary distribution of energy in such a system may be found, when the independent variables which determine the state are known.
Let us now imagine a perfect vacuum, cubical in form, of edge l , and with metallically reflecting sides. If we take the origin of coordinates at one corner of the cube and let the axes of coordinates coincide with the adjoining edges, an electromagnetic process which may occur in this cavity is represented by the following system of equations: $\mathsf{E} {x} &= \cos\frac{\mathsf{a} \pi x}{l} \sin\frac{\mathsf{b} \pi y}{l} \sin\frac{\mathsf{c} \pi z}{l} (e } \cos 2\pi \nu t + e_{1}' \sin 2\pi \nu t), \ \mathsf{E {y} &= \sin\frac{\mathsf{a} \pi x}{l} \cos\frac{\mathsf{b} \pi y}{l} \sin\frac{\mathsf{c} \pi z}{l} (e } \cos 2\pi \nu t + e_{2}' \sin 2\pi \nu t), \ \mathsf{E {z} &=