Boltzmanns generalization of the Maxwell distribution law

For this very general case Boltzmann s generalization of Maxwell s law states If At denotes a very small range of variation in the state of a molecule—so characterized that the coordinates and velocities of all atoms are enclosed by suitable limits,38 similar to limits (2a), (2b), (2c)—then for the case of thermal equilibrium 

A comparison with Eq. (1) shows that, as far as the velocity distribution is concerned, Eq. (3 ) agrees with the Maxwell assumption. Hence we call Eq. (3) the Maxwell-Boltzmann distribution law.40 

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