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We investigate Maxwell's attempt to justify the mathematical assumptionsbehind his 1860 Proposition IV according to which the velocity components ofcolliding particles follow the normal distribution. Contrary to the commonlyheld view we find that his molecular collision model plays a crucial role inreaching this conclusion, and that his model assumptions also permit inferenceto equalization of mean kinetic energies (temperatures), which is what heintended to prove in his discredited and widely ignored Proposition VI. If wetake a charitable reading of his own proof of Proposition VI then it wasMaxwell, and not Boltzmann, who gave the first proof of a tendency towardsequilibrium, a sort of H-theorem. We also call attention to a potentialconflation of notions of probabilistic and value independence in relevant priorworks of his contemporaries and of his own, and argue that this conflationmight have impacted his adoption of the suspect independence assumption ofProposition IV.

Maxwell and the normal distribution: A colored story of probability, independence, and tendency toward equilibrium