According to the theory developed in the preceding section, the nature of heat radiation within an isotropic medium, when the state is one of stable thermodynamic equilibrium, may be regarded as known in every respect. The intensity of the radiation, uniform in all directions, depends for all wave lengths only on the temperature and the velocity of propagation, according to equation [eqn:(300)] (300), which applies to black radiation in any medium whatever. But there remains another problem to be solved by the theory. It is still necessary to explain how and by what processes the radiation which is originally present in the medium and which may be assigned in any way whatever, passes gradually, when the medium is bounded by walls impermeable to heat, into the stable state of black radiation, corresponding to the maximum of entropy, just as a gas which is enclosed in a rigid vessel and in which there are originally currents and temperature differences assigned in any way whatever gradually passes into the state of rest and of uniform distribution of temperature.
To this much more difficult question only a partial answer can, at present, be given. In the first place, it is evident from the extensive discussion in the first chapter of the third part that, since irreversible processes are to be dealt with, the principles of pure electrodynamics alone will not suffice. For the second principle of thermodynamics or the principle of increase of entropy is foreign to the contents of pure electrodynamics as well as of pure mechanics. This is most immediately shown by the fact that the fundamental equations of mechanics as well as those of electrodynamics allow the direct reversal of every process as regards time, which contradicts the principle of increase of entropy. Of course all kinds of friction and of electric conduction of currents
must be assumed to be excluded; for these processes, since they are always connected with the production of heat, do not belong to mechanics or electrodynamics proper.
This assumption being made, the time occurs in the fundamental equations of mechanics only in the components of acceleration; that is, in the form of the square of its differential. Hence, if instead of the quantity is introduced as time variable in the equations of motion, they retain their form without change, and hence it follows that if in any motion of a system of material points whatever the velocity components of all points are suddenly reversed at any instant, the process must take place in the reverse direction. For the electrodynamic processes in a homogeneous non-conducting medium a similar statement holds. If in Maxwell's equations of the electrodynamic field is written everywhere instead of , and if, moreover, the sign of the magnetic field-strength is reversed, the equations remain unchanged, as can be readily seen, and hence it follows that if in any electrodynamic process whatever the magnetic field-strength is everywhere suddenly reversed at a certain instant, while the electric field-strength keeps its value, the whole process must take place in the opposite sense.
If we now consider any radiation processes whatever, taking place in a perfect vacuum enclosed by reflecting walls, it is found that, since they are completely determined by the principles of classical electrodynamics, there can be in their case no question of irreversibility of any kind. This is seen most clearly by considering the perfectly general formulæ [eqn:(305)] (305), which hold for a cubical cavity and which evidently have a periodic, i.e., reversible character. Accordingly we have frequently (Sec. [sect:144.] 144 and [sect:166.] 166)