100.

As to how the entropy radiation $𝖫$ depends on the energy radiation $𝖪$ Wien's displacement law in the form of [eqn:(119)] (119) affords immediate information. It follows, namely, from it, considering [eqn:(133)] (133) and [eqn:(24)] (24), that $𝖫=\frac{{\nu }^2}{c^2}F\left(\frac{c^2𝖪}{{\nu }^3}\right)\mathrm{\backslash Label}[eqn](134)\text{upshape (134)}$ and, moreover, on taking into account [eqn:(118)] (118), $\frac{\partial 𝖫}{\partial 𝖪}=\frac{\partial 𝗌}{\partial 𝗎}=\frac{1}{T}.\mathrm{\backslash Label}[eqn](135)\text{upshape (135)}$ Hence also $T=\nu F_1\left(\frac{c^2𝖪}{{\nu }^3}\right)\mathrm{\backslash Label}[eqn](136)\text{upshape (136)}$ or $𝖪=\frac{{\nu }^3}{c^2}{F}_2\left(\frac{T}{\nu }\right).\mathrm{\backslash Label}[eqn](137)\text{upshape (137)}$

It is true that these relations, like the equations [eqn:(118)] (118) and [eqn:(119)] (119), were originally derived for radiation which is unpolarized and uniform in all directions.

They hold, however, generally in the case of any radiation whatever for each separate monochromatic plane polarized ray. For, since the separate rays behave and are propagated quite independently of one another, the intensity, $𝖫$, of the entropy radiation of a ray can depend only on the intensity of the energy radiation, $𝖪$, of the same ray.

Hence every separate monochromatic ray has not only its energy but also its entropy defined by [eqn:(134)] (134) and its temperature defined by [eqn:(136)] (136).