48.

We shall finally take up the case of diathermanous ([sect:12.] Sec. 12) media, which has so far not been considered. In [sect:27.] Sec. 27 we saw that, in a medium which is diathermanous for a given color and is surrounded by an enclosure impermeable to heat, there can be thermodynamic equilibrium for any intensity of radiation of this color. There must, however, among all possible intensities of radiation be a definite one, corresponding to the absolute maximum of the total entropy of the system, which designates the absolutely stable equilibrium of radiation. In fact, in equation [eqn:(27)] (27) the intensity of radiation ${𝖪}_{\nu }$ for ${\alpha }_{\nu }=0$ and ${ϵ}_{\nu }=0$ assumes the value ${\displaystyle \frac{0}{0}}$, and hence cannot be calculated from this equation. But we see also that this indeterminateness is removed by equation [eqn:(41)] (41), which states that in the case of thermodynamic

equilibrium the product $q^2{𝖪}_{\nu }$ has the same value for all substances. From this we find immediately a definite value of ${𝖪}_{\nu }$ which is thereby distinguished from all other values. Furthermore the physical significance of this value is immediately seen by considering the way in which that equation was obtained. It is that intensity of radiation which exists in a diathermanous medium, if it is in thermodynamic equilibrium when in contact with an arbitrary absorbing and emitting medium. The volume and the form of the second medium do not matter in the least, in particular the volume may be taken as small as we please.

Hence we can formulate the following law: Although generally speaking thermodynamic equilibrium can exist in a diathermanous medium for any intensity of radiation whatever, nevertheless there exists in every diathermanous medium for a definite frequency at a definite temperature an intensity of radiation defined by the universal function [eqn:(42)] (42). This may be called the stable intensity, inasmuch as it will always be established, when the medium is exchanging stationary radiation with an arbitrary emitting and absorbing substance.