85.

Returning now to the discussion of [sect:73.] Sec. 73 we introduce the assumption that at first the spectral distribution of energy is the normal one, corresponding to black radiation. Then, according to the law there proven, the radiation retains this property without change during a reversible adiabatic change of volume and the laws derived in [sect:68.] Sec. 68 hold for the process. The radiation then possesses in every state a definite temperature $T$, which depends on the volume $V$ according to the equation derived in that paragraph, $T^{3}V=\text{const}.=T^{\prime 3}{V}^{\prime }.\mathrm{\backslash Label}[eqn](100)\text{upshape (100)}$ Hence we may now write equation [eqn:(99)] (99) as follows: $𝗎={\nu }^3\varphi \left(\frac{{\nu }^3}{T^3}\right)$ or $𝗎={\nu }^3\varphi \left(\frac{T}{\nu }\right).$ Therefore, if for a single temperature the spectral distribution of black radiation, i.e., $𝗎$ as a function of $\nu$, is known, the dependence of the function $\varphi$ on its argument, and hence the spectral distribution for any other temperature, may be deduced therefrom.

If we also take into account the law proved in [sect:47.] Sec. 47, that, for the black radiation of a definite temperature, the product $𝗎q^3$ has for all media the same value, we may also write $𝗎=\frac{{\nu }^3}{c^3}F\left(\frac{T}{\nu }\right)\mathrm{\backslash Label}[eqn](101)\text{upshape (101)}$ where now the function $F$ no longer contains the velocity of propagation.