165.

The relations between the intensity of radiation and the temperature expressed in [sect:156.] Sec. 156 hold for radiation in a pure vacuum. If the radiation is in a medium of refractive index $n$, the way in which the intensity of radiation depends on the frequency and the temperature is given by the proposition of [sect:39.] Sec. 39, namely, the product of the specific intensity of radiation ${𝖪}_{\nu }$ and the square of the velocity of propagation of the radiation

has the same value for all substances. The form of this universal function [eqn:(42)] (42) follows directly from [eqn:(274)] (274) $𝖪q^2=\frac{{ϵ}_{\nu }}{{\alpha }_{\nu }}{q}^2=\frac{h{\nu }^3}{e^{\frac{h\nu }{kT}}-1}.\mathrm{\backslash Label}[eqn](299)\text{upshape (299)}$ Now, since the refractive index $n$ is inversely proportional to the velocity of propagation, equation [eqn:(274)] (274) is, in the case of a medium with the index of refraction $n$, replaced by the more general relation ${𝖪}_{\nu }=\frac{h{\nu }^3{n}^2}{c^2}\frac{1}{e^{\frac{h\nu }{kT}}-1}\mathrm{\backslash Label}[eqn](300)\text{upshape (300)}$ and, similarly, in place of [eqn:(275)] (275) we have the more general relation $𝗎=\frac{8\pi h{\nu }^3{n}^3}{c_3}\frac{1}{e^{\frac{h\nu }{kT}}-1}.\mathrm{\backslash Label}[eqn](301)\text{upshape (301)}$ These expressions hold, of course, also for the emission of a body which is black with respect to a medium with an index of refraction $n$.