87.

If we combine equation [eqn:(100)] (100) with equation [eqn:(99a)] (99a) we obtain $\frac{{\nu }^{\prime }}{T^{\prime }}=\frac{\nu }{T}.\mathrm{\backslash Label}[eqn](105)\text{upshape (105)}$

Hence the laws derived at the end of [sect:84a.] Sec. 84a assume the following form:

On infinitely slow reversible adiabatic change in volume of black radiation contained in a cavity, the temperature $T$ varies in the inverse ratio of the cube root of the volume $V$, the frequencies $\nu$ vary in proportion to the temperature, and the radiant energy $𝖴d\nu$ of an infinitely small spectral interval varies in the same ratio.

Hence the total radiant energy $U$ as the sum of the energies of all spectral intervals varies also in proportion to the temperature, a statement which agrees with the conclusion arrived at already at the end of [sect:68.] Sec. 68, while the space density of radiation, $u={\displaystyle \frac{U}{V}}$, varies in proportion to the fourth power of the temperature, in agreement with the Stefan-Boltzmann law.