  2. The procedure of dividing \(\mu\) space into cells is essential here. Indeed, the whole prospect of using combinatorics would disappear if we did not adopt a partition. But the choice to take all cells equal in size in position and momentum variables is not quite self-evident, as Boltzmann himself shows. In fact, before he develops the argument above, his paper first discusses an analysis in which the particles are characterized by their energy instead of position and momentum. This leads him to carve up \(\mu\)-space into cells of equal size in energy. He then shows that this analysis fails to reproduce the desired Maxwell distribution as the most probable state. This failure is remedied by taking equally sized cells in position and momentum variables. The latter choice is apparently ‘right’, in the sense that leads to the desired result. However, since the choice clearly cannot be relegated to a matter of convention, it leaves the question for a justification.