It is well known that the Boltzmann-Maxwell Law, which asserts average equi-partition of kinetic energy amongst the various motional freedoms, finite or infinite in number, of suitably conditioned systems, meets with apparently insuperable difficulties in its application to actual gases. Even in the case of gases showing complicated spectra, and therefore possessing numerous vibrational freedoms, the actual values of the ratio of the specific heats never deviate much from values which should, according to the law, be limited to very simple systems. Possible modes of evading this result, such as that supplied by J. J. Thomson's suggestion (Arch. Néerlandaises, 1900, Ser. II. t. v.) that individual molecules may not be concerned in radiation, are too problematical to give much relief.