47.

The law holding for the quantity [eqn:(42)] (42) can be expressed in a different form, by introducing, by means of [eqn:(24)] (24), the volume density ${𝗎}_{\nu }$ of monochromatic radiation instead of the intensity of radiation ${𝖪}_{\nu }$. We then obtain the law that, for radiation in a state of thermodynamic equilibrium, the quantity ${𝗎}_{\nu }{q}^3\mathrm{\backslash Label}[eqn](49)\text{upshape (49)}$ is a function of the temperature $T$ and the frequency $\nu$, and is the same for all substances.

In this law it is assumed that the quantity $q$ in [eqn:(24)] (24) is the same as in [eqn:(37)] (37). This does not hold for strongly dispersing or absorbing substances. For the generalization applying to such cases see M. Laue, Annalen d. Physik 32, p. 1085, 1910.

This law becomes clearer if we consider that the quantity ${𝗎}_{\nu }d\nu \frac{q^3}{{\nu }^3}\mathrm{\backslash Label}[eqn](50)\text{upshape (50)}$ also is a universal function of $T$, $\nu$, and $\nu +d\nu$, and that the product ${𝗎}_{\nu }d\nu$ is, according to [eqn:(22)] (22), the volume density of the radiation whose frequency lies between $\nu$ and $\nu +d\nu$, while the quotient ${\displaystyle \frac{q}{\nu }}$ represents the wave length of a ray of frequency $\nu$ in the medium in question.

The law then takes the following simple form:

When any bodies whatever are in thermodynamic equilibrium, the energy of monochromatic radiation of a definite frequency, contained in a cubical element of side equal to the wave length, is the same for all bodies.