94.

Let us now investigate Wien's displacement law with regard to the dependence of the quantity $𝗌$ on the variables $𝗎$ and $\nu$.

From equation [eqn:(101)] (101) it follows, on solving for $T$ and substituting the value given in [eqn:(117)] (117), that $\frac{1}{T}=\frac{1}{\nu }F\left(\frac{c^3𝗎}{{\nu }^3}\right)=\frac{\partial 𝗌}{\partial 𝗎}\mathrm{\backslash Label}[eqn](118)\text{upshape (118)}$ where again $F$ represents a function of a single argument and the constants do not contain the velocity of propagation $c$. On integration with respect to the argument we obtain $𝗌=\frac{{\nu }^2}{c^3}{F}_1\left(\frac{c^3𝗎}{{\nu }^3}\right)\mathrm{\backslash Label}[eqn](119)\text{upshape (119)}$ the notation remaining the same. In this form Wien's displacement law has a significance for every separate monochromatic radiation and hence also for radiations of any arbitrary energy distribution.