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Line widths measurements of the coronal ion Si VIII confirm earlier observations which show an increase in the non-thermal velocity above the solar limb. The present data taken at the equatorial limb, show an increase from 24 km s^-1 at the limb to 28 km S^-1 some 25,000 km above the limb. The electron density as measured from the Si VIII line pair show a decrease from 3.5 10^8 cm^-3 to 1.8 10^8 cm^-3 over the same distance. This data implies that the non-thermal velocity is inversely proportional to the quadratic root of the electron density, in excellent agreement with that predicted for undamped radially propagating Alfven waves.