The Logical Inconsistency of the Old Quantum Theory of Black Body Radiation

The old quantum theory of black body radiation was manifestly logically inconsistent. It required the energies of electric resonators to be both quantized and continuous. To show that this manifest inconsistency was inessential to the theory's recovery of the Planck distribution law, I extract a subtheory free of this manifest inconsistency but from which Planck's law still follows.