The main problem of the theory of heat radiation is to determine the energy distribution in the normal spectrum of black radiation, or, what amounts to the same thing, to find the function which has been left undetermined in the general expression of Wien's displacement law [eqn:(119)] (119), the function which connects the entropy of a certain radiation with its energy. The purpose of this chapter is to develop some preliminary theorems leading to this solution. Now since, as we have seen in [sect:48.] Sec. 48, the normal energy distribution in a diathermanous medium cannot be established unless the medium exchanges radiation with an emitting and absorbing substance, it will be necessary for the treatment of this problem to consider more closely the processes which cause the creation and the destruction of heat rays, that is, the processes of emission and absorption. In view of the complexity of these processes and the difficulty of acquiring knowledge of any definite details regarding them, it would indeed be quite hopeless to expect to gain any certain results in this way, if it were not possible to use as a reliable guide in this obscure region the law of Kirchhoff derived in [sect:51.] Sec. 51. This law states that a vacuum completely enclosed by reflecting walls, in which any emitting and absorbing bodies are scattered in any arrangement whatever, assumes in the course of time the stationary state of black radiation, which is completely determined by one parameter only, namely, the temperature, and in particular does not depend on the number, the nature, and the arrangement of the material bodies present. Hence, for the investigation of the properties of the state of black radiation the nature of the bodies which are assumed to be in the vacuum is perfectly immaterial. In fact, it does not even matter whether such bodies really exist somewhere in nature, provided their existence and their properties are consistent with the laws of thermodynamics and electrodynamics.
If, for any special arbitrary assumption regarding the nature and arrangement of emitting and absorbing systems, we can find a state of radiation in the surrounding vacuum which is distinguished by absolute stability, this state can be no other than that of black radiation.
Since, according to this law, we are free to choose any system whatever, we now select from all possible emitting and absorbing systems the simplest conceivable one, namely, one consisting of a large number of similar stationary oscillators, each consisting of two poles, charged with equal quantities of electricity of opposite sign, which may move relatively to each other on a fixed straight line, the axis of the oscillator.
It is true that it would be more general and in closer accord with the conditions in nature to assume the vibrations to be those of an oscillator consisting of two poles, each of which has three degrees of freedom of motion instead of one, i.e., to assume the vibrations as taking place in space instead of in a straight line only. Nevertheless we may, according to the fundamental principle stated above, restrict ourselves from the beginning to the treatment of one single component, without fear of any essential loss of generality of the conclusions we have in view.
It might, however, be questioned as a matter of principle, whether it is really permissible to think of the centers of mass of the oscillators as stationary, since, according to the kinetic theory of gases, all material particles which are contained in substances of finite temperature and free to move possess a certain finite mean kinetic energy of translatory motion. This objection, however, may also be removed by the consideration that the velocity is not fixed by the kinetic energy alone. We need only think of an oscillator as