VIII. The distribution of molecular energy

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Abstract
This paper is primarily an attempt to deal with certain points connected with the application to the Kinetic Theory of Gases of Boltzmann’s Theorem on the partition of energy in a dynamical system. It is found by experiment that the ratio of the two specific heats of certain monatomic gases (e. g., mercury, argon) is 1 2/3. If we admit that the energy of these gases is distributed in the manner indicated by Boltzmann’s Theorem, then this theorem leaves no escape from the conclusion that the molecules of these gases must be rigid and geometrically perfect spheres. A similar difficulty arises in connection with other gases: the number of degrees of freedom which a consideration of the ratio in question leads us to expect a molecule of a gas to possess, is always less than the number which the spectrum of the glowing gas shows to actually exist. Further, Boltzmann’s Theorem excludes the possibility of the ratio of the two specific heats having any values except one of a certain series of values, whereas experiment shows that the ratio is not always equal to one of this series, although it is generally very near to such a value. Finally Boltzmann’s Theorem leaves no room for a variation of this ratio with the temperature, although such a variation is known to exist.

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