# “Will someone say exactly what the H-theorem proves?” A study of Burbury's Condition A and Maxwell's Proposition II

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## Summary

Many historians of science recognize that the outcome of the celebrated debate on Boltzmann's H-Theorem, which took place in the weekly scientific journal *Nature*, beginning at the end of 1894 and continuing throughout most of 1895, was the recognition of *the* statistical hypothesis in the proof of the theorem. This hypothesis is the *Stosszahlansatz* or “hypothesis about the number of collisions.” During the debate, the *Stosszahlansatz* was identified with another statistical hypothesis, which appeared in Proposition II of Maxwell's 1860 paper; Burbury called it Condition A. Later in the debate, Bryan gave a clear formulation of the *Stosszahlansatz*. However, the two hypotheses are *prima facie* different. Burbury interchanged them without justification or even warning his readers. This point deserves clarification, since it touches upon subtle questions related to the foundation of the theory of heat. A careful reading of the arguments presented by Burbury and Bryan in their various invocations of both hypotheses can clarify this technical point. The *Stosszahlansatz* can be understood in terms of geometrical invariances of the problem of a collision between two spheres. A byproduct of my analysis is a clarification of the debate itself, which is apparently obscure.

## Keywords

Clarification Scientific Journal Prima Facie Statistical Hypothesis Technical Point## Preview

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