It is well known that, in classical theory, Liouville's theorem shows that if an ensemble of systems is distributed over a small element of volume in phase space, the ensemble fills a region of equal volume at all later instants of time. In quantum mechanics, the uncertainty principle is associated with the products of the errors in conjugate coordinates and momenta, and such products can be interpreted in terms of volume elements in phase space. Comparison of these two facts leads to the assertion in the interesting volume on “Statistical Mechanics” recently published by J. E. and M. G. Mayer that “The Liouville theorem is essential for the complete understanding of the uncertainty principle.