An elastic solid has, in general, three distinct wave propagation velocities in a given direction. According to a theorem of Fedorov, however, there are only two distinct velocities of propagation associated with an axis of material symmetry greater than binary symmetry. The converse of this theorem is proved herein, namely, that it is only in directions of material symmetry greater than binary symmetry that two distinct velocities occur. This leads to an ordering principle for elastic wave propagation velocities, that is, that the order of the velocities, regarded as functions of the direction of propagation, is invariant.