is the mean square of the velocity. Integration gives
It is known that the measure of temperature is the mean kinetic energy of the individual molecule and not simply the mean square of its velocity, and we possess here therefore a perfectly precise definition of temperature. We see also from (7) that temperature in a particular gas is directly proportional to either
or
.
MAXWELL further shows without any assumption as to the nature of the molecules, or the forces acting between them, that the derived law of distribution is valid for any gas mixture, but that is it modified when the gas is exposed to the action of external forces.
BOLTZMANN found (Wien. Akad. Sitzber. LXXII B, 1875, p. 443) for monatomic gases that in spite of the effect of external forces (a) the velocity of any molecule is equally likely to have any direction whatever, (b) the velocity distribution in any element of space is exactly like that in a gas of equal density and temperature upon which no external forces act, the effect of the external forces consisting only in varying the density from place to place as in hydrodynamics.