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 went on the assumption that the molecules behave like centres of forces. He demonstrated anew the law of distribution of velocities; but the proof had a flaw in argument, pointed out by Boltzmann, and recognised by Maxwell, who adopted a somewhat different form of the distributive function in a paper of 1879, intended to explain mathematically the effects observed in Crookes' radiometer. Boltzmann gave a rigorous general proof of Maxwell's law of the distribution of velocities.

None of the fundamental assumptions in the kinetic theory of gases leads by the laws of probability to results in very close agreement with observation. Boltzmann tried to establish kinetic theories of gases by assuming the forces between molecules to act according to different laws from those previously assumed. Clausius, Maxwell, and their predecessors took the mutual action of molecules in collision as repulsive, but Boltzmann assumed that they may be attractive. Experiment of Joule and Lord Kelvin seem to support the latter assumption.

Among the latest researches on the kinetic theory is Lord Kelvin's disproof of a general theorem of Maxwell and Boltzmann, asserting that the average kinetic energy of two given portions of a system must be in the ratio of the number of degrees of freedom of those portions.