and gas molecules will return its average energy to by absorbing or releasing energy. Hence, in this situation, dynamic equilibrium can only exist when every resonator has an average energy .

We apply a similar consideration now to the interaction between the resonators and the ambient radiation within the cavity. For this case, Planck has derived the necessary condition for dynamic equilibrium ^{[1]}; treating the radiation as a completely random process.^{[2]}

He found:

Here, is the average energy of a resonator of eigenfrequency *ν* (per oscillatory component), *L* is the speed of light, *ν* is the frequency, and *ρ*_{ν}*dν* is the energy density of the cavity radiation of frequency between *ν* and *ν* + *dν*.

- ↑ M. Planck, Ann. d. Phys.
**1**p.99. 1900. - ↑ This condition can be formulated as follows. We expand the Z-component of the electric force (
*Z*) in a given point in the space between the time coordinates of*t*=0 and*t*=*T*(where*T*is a large amount of time compared to all the vibration periods considered) in a Fourier series*A*and_{ν}*α*. Then for the frequencies of the different combinations of the quantities_{ν}*A*and_{ν}*α*there are the (statistical) probabilities_{ν}*dW*of the form:*A*and*α*respectively is independent of the value of other values of*A*and*x*respectively. The more closely the demand is satisfied that the separate pairs of values*A*and_{ν}*α*depend on the emission and absorption process of_{ν}*separate*resonators, the more closely will the examined case be one of being as unordered as imaginable.