A recent result due to Caloi, giving an explicit expression for the ratio of the principal axes of the elliptical motion, generated by a Rayleigh wave, of a particle located on the surface of an elastic half-space, is extended herein to yield a similar formula valid for any point in the solid. A further expression is deduced giving the location of strata on which the motion is purely normal to the bounding plane. Finally, formulas are presented which furnish the maximum value of the displacement normal, and the minimum value of that parallel, to the surface, and their respective location in the medium measured in units of the wave length. Results of numerical computation are given.