In a series of notes published in Nature during the years 1956-1958, K. R. Popper has expounded his thesis of the "untenability of the widespread, though surely not universal, belief that the 'arrow of time' is closely connected with, or dependent upon, the law that disorder (entropy) tends to increase." Independently of O. Costa de Beauregard, who had used the same illustration before him, Popper considers a large surface of water initially at rest into which a stone is dropped, thereby producing an outgoing wave of decreasing amplitude spreading concentrically about the point of the stone's impact. Popper briefly remarks correctly that the eternal expansion of a very thin gas from a center into a spatially infinite universe does not involve an entropy increase, and the de facto irreversibility of this process is therefore non-entropic. Mehlberg's critical estimate of Popper's own affirmation of non-entropic de facto irreversibility likewise seems to be unconvincing in important respects.