35.

From the consideration of a system consisting of a single homogeneous isotropic substance we now pass on to the treatment of a system consisting of two different homogeneous isotropic substances contiguous to each other, the system being, as before, enclosed by a rigid cover impermeable to heat.

We consider the state of radiation when thermodynamic equilibrium exists, at first, as before, with the assumption that the media are of considerable extent. Since the equilibrium is nowise disturbed, if we think of the surface separating the two media as being replaced for an instant by an area entirely impermeable to heat radiation, the laws of the last paragraphs must hold for each of the two substances separately.

Let the specific intensity of radiation of frequency $\nu$ polarized in an arbitrary plane be ${𝖪}_{\nu }$ in the first substance (the upper one in [fig:3]Fig. 3), and ${𝖪}_{\nu }^{\prime }$ in the second, and, in general, let all quantities referring to the second substance be indicated by the addition of an accent. Both of the quantities ${𝖪}_{\nu }$ and ${𝖪}_{\nu }^{\prime }$ depend, according to equation [eqn:(27)] (27), only on the temperature, the frequency $\nu$, and the nature of the two substances, and these values of the intensities of radiation hold up to very small distances from the bounding surface of the substances, and hence are entirely independent of the properties of this surface.