Using data from the Bragg crystal spectrometer on the Yohkoh spacecraft we have compute measures the total intensity, centroid position, and line width for the resonance line of Ca XIX during the rise phase and after maximum for 219 solar flares. The difference between the centroid positions early and late in each flare yields a measure of the line-of-sight velocity shift of the line centroid. We find a trend in the average value of the centroid shift with distance from Sun center suggesting radial mass motions with a characteristic velocity of 58 km s-1. There is a correlation between the rise-phase line widths and the centroid shift. We find no correlation between the centroid shift and the peak intensity, rise time, and total flare duration; and no correlation between the line width and the distance from Sun center, the peak intensity, rise time, and total flare duration. These results do not conclusively support or refute the simple electron-beam-driven model or the thermal model for the rise phase of a solar flare.