While the oscillator is absorbing it must also be emitting, for otherwise a stationary state would be impossible. Now, since in the law of absorption just assumed the hypothesis of quanta has as yet found no room, it follows that it must come into play in some way or other in the emission of the oscillator, and this is provided for by the introduction of the hypothesis of emission of quanta. That is to say, we shall assume that the emission does not take place continuously, as does the absorption, but that it occurs only at certain definite times, suddenly, in pulses, and in particular we assume that an oscillator can emit energy only at the moment when its energy of vibration, , is an integral multiple of the quantum of energy, . Whether it then really emits or whether its energy of vibration increases further by absorption will be regarded as a matter of chance. This will not be regarded as implying that there is no causality for emission; but the processes which cause the emission will be assumed to be of such a concealed nature that for the present their laws cannot be obtained by any but statistical methods. Such an assumption is not at all foreign to physics; it is, e.g., made in the atomistic theory of chemical reactions and the disintegration theory of radioactive substances.
It will be assumed, however, that if emission does take place, the entire energy of vibration, , is emitted, so that the vibration of the oscillator decreases to zero and then increases again by further absorption of radiant energy.
It now remains to fix the law which gives the probability that an oscillator will or will not emit at an instant when its energy has reached an integral multiple of . For it is evident that the statistical state of equilibrium, established in the system of oscillators
by the assumed alternations of absorption and emission will depend on this law; and evidently the mean energy of the oscillators will be larger, the larger the probability that in such a critical state no emission takes place. On the other hand, since the mean energy will be larger, the larger the intensity of the field of radiation surrounding the oscillators, we shall state the
law of emission as follows: The ratio of the probability that no emission takes place to the probability that emission does take place is proportional to the intensity of the vibration which excites the oscillator and which was defined in equation [eqn:(158)] (158). The value of the constant of proportionality we shall determine later on by the application of the theory to the special case in which the energy of vibration is very large. For in this case, as we know, the familiar formulæ of the classical dynamics hold for any period of the oscillator whatever, since the quantity element of action may then, without any appreciable error, be regarded as infinitely small.
These statements define completely the way in which the radiation processes considered take place, as time goes on, and the properties of the stationary state. We shall now, in the first place, consider in the second chapter the absorption, and, then, in the third chapter the emission and the stationary distribution of energy, and, lastly, in the fourth chapter we shall compare the stationary state of the system of oscillators thus found with the thermodynamic state of equilibrium which was derived directly from the hypothesis of quanta in the preceding part. If we find them to agree, the hypothesis of emission of quanta may be regarded as admissible.