1. RECENT experiments by Olszewski on hydrogen (Phil. Mag., May 1902), and on air and nitrogen (Phil. Mag., June 1907), have exhibited results which are not in accordance with theoretical deductions based upon Van der Waal's equation of state (Dewar, Proc. Roy. Soc, March 1904; Porter, Phil. Mag., April 1906; Hamilton Dickson, Phil. Mag., January 1908). An inversion temperature is not necessarily limited by the condition, which was satisfied in the porous-plug experiment of Joule and Kelvin, that the initial and final pressures should be nearly equal. In Olszewski's experiments that condition was widely departed from. Taking account of large differences of pressure, Dickson shows that Van der Waal's equation leads to the result that the inversion temperature must fall when the initial pressure increases, the final pressure being kept constant. Olszewski's experimental results are opposed to this conclusion; and Dickson suggests, as a possible cause of the discrepancy, an appreciable difference between the initial and final values of the kinetic energy. The following reasoning seems to indicate that such a difference would not alter the nature of the theoretical conclusion.