 1. As we have seen, The H-theorem formed the basis of a renewed claim by Boltzmann to have obtained a theorem corresponding to the second law, at least for gases. A main difference with his previous (1866) claim, is that he now strongly emphasized the role of probability calculus in his derivation. Even so, it will be noted that his conception of probability is still a fully mechanical one. Thus, there is no conflict between his claims that on the one hand, “the problems of the mechanical theory of heat are really problems in probability calculus” and that the probabilities themselves are “derived on the basis of the equations of motion alone”, on the other hand. Indeed, it seems to me that Boltzmann's emphasis on the crucial role of probability is only intended to convey that probability theory provides a particularly useful and appropriate language for discussing mechanical problems in gas theory. There is no indication in this paper yet that probability theory could play a role by furnishing assumptions of a non-mechanical nature, i.e., independent of the equations of motion. However, see Badino (2006, Other Internet Resources) for a very different point of view. 