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

In the first part of the paper we investigate Maxwell’s attempt to justify the mathematical assumptions behind his 1860 Proposition IV according to which the velocity components of colliding particles follow the normal distribution. Contrary to the com- monly held view we find that his molecular collision model plays a crucial role in reaching this conclusion, and that his model assumptions also permit inference to a non-reversible equalization of mean kinetic energies, which is what he intended to prove in his widely discredited Proposition VI. If we take a charitable reading of his own proof or Proposition VI then it was Maxwell, and not Boltzmann, who gave the first proof of a tendency towards equilibrium. In the second half of the paper we add a further, not yet investigated, piece to the historical and intellectual puzzle surrounding his derivation. We argue that Maxwell’s prior and contemporaneous work on color vision provided him familiarity with and sensitivity to application of statistical reasoning in physics. This includes an encounter with distributions outside the context of error theory. We also call attention to a notion of independence of variables employed in his works on color vision that might have impacted the mistake he made in his proof of Proposition IV