 Succinctly, and rephrased in modern terms, the argument is as follows. Apart from \(\Gamma\), the mechanical phase space containing the possible states x for the total gas system, we consider the so-called \(\mu\)-space, i.e., the state space of a single molecule. For monatomic gases, this space is just a six-dimensional space with \((\vec{p}, \vec{q})\) as coordinates. With each state \(x\) is associated a collection of \(N\) points in \(\mu\)-space.