All that precedes has been by way of preparation. Before taking the final step, which will lead to the law of distribution of energy in the spectrum of black radiation, let us briefly put together the essentials of the problem still to be solved. As we have already seen in [sect:93.] Sec. 93, the whole problem amounts to the determination of the temperature corresponding to a monochromatic radiation of given intensity. For among all conceivable distributions of energy the normal one, that is, the one peculiar to black radiation, is characterized by the fact that in it the rays of all frequencies have the same temperature. But the temperature of a radiation cannot be determined unless it be brought into thermodynamic equilibrium with a system of molecules or oscillators, the temperature of which is known from other sources. For if we did not consider any emitting and absorbing matter there would be no possibility of defining the entropy and temperature of the radiation, and the simple propagation of free radiation would be a reversible process, in which the entropy and temperature of the separate pencils would not undergo any change. (Compare below [sect:166.] Sec. 166.)
Now we have deduced in the preceding section all the characteristic properties of the thermodynamic equilibrium of a system of ideal oscillators. Hence, if we succeed in indicating a state of radiation which is in thermodynamic equilibrium with the system of oscillators, the temperature of the radiation can be no other than that of the oscillators, and therewith the problem is solved.