It is pointed out that the usual mathematical description of the slow flow of viscous liquids within rigid boundaries indicates that such motion is reversible in time. The equations of a mixing transformation, in the geometry of the Couette viscometer, are given. The motion is ideally quite reversible, but because the fluid consists of molecules subject to thermal agitation, the pattern is smeared out in time. Observed unmixing by reversal of motion, although striking, is not perfect.