143.

For the entropy $S$ of the system of oscillators which is in the state of thermodynamic equilibrium we thus obtain from equation [eqn:(229)] (229) since $N$ and $P$ are large numbers: $S=k\log \frac{(N+P)!}{N!P!}$ and by making use of Stirling's formula [eqn:(171)] (171) Compare footnote to [page:124]page page:124. See also [page:218]page page:218. $S=kN\{(\frac{P}{N}+1)\log (\frac{P}{N}+1)-\frac{P}{N}\log \frac{P}{N}\}.$ If we now replace $P$ by $E$ from [eqn:(231)] (231) we find for the entropy exactly the same value as given by [eqn:(222)] (222) and thus we have demonstrated in a special case both the admissibility and the practical usefulness of the method employed.A complete mathematical discussion of the subject of this chapter has been given by H. A. Lorentz. Compare, e.g., Nature, 92, p. 305, Nov. 6, 1913. (Tr.)

[A System of Oscillators]IVA System of Oscillators in a Stationary Field of Radiation

[The Elementary Dynamical Law] IThe Elementary Dynamical Law for The Vibrations of an Ideal Oscillator. Hypothesis of Emission of Quanta