39.

The second formula [eqn:(41)] (41) establishes a relation between the intensities of radiation in the two media, for it states that, when thermodynamic equilibrium exists, the specific intensities of radiation of a certain frequency in the two media are in the inverse ratio of the squares of the velocities of propagation or in the direct ratio of the squares of the indices of refraction.G. Kirchhoff, Gesammelte Abhandlungen, Leipzig, J. A. Barth, 1882, p. 594. R. Clausius, Pogg. Ann. 121, p. 1, 1864.

By substituting for ${𝖪}_{\nu }$ its value from [eqn:(27)] (27) we obtain the following theorem:

The quantity $q^2{𝖪}_{\nu }=q^2\frac{{ϵ}_{\nu }}{{\alpha }_{\nu }}\mathrm{\backslash Label}[eqn](42)\text{upshape (42)}$ does not depend on the nature of the substance, and is, therefore, a universal function of the temperature $T$ and the frequency $\nu$ alone.

The great importance of this law lies evidently in the fact that it states a property of radiation which is the same for all bodies in nature, and which need be known only for a single arbitrarily chosen body, in order to be stated quite generally for all bodies. We shall later on take advantage of the opportunity offered by this statement in order actually to calculate this universal function ([sect:165.] Sec. 165).