Variations in total electron content at high heliographic latitudes, observed during the 1995 solar conjunction of the Ulysses spacecraft when the radio ray path was embedded in the southern coronal hole, were interpreted by Woo and Habbal [1997b> as polar plume structures extending to at least 30 solar radii from the Sun. Somewhat surprisingly, we detected a 24-hour sinusoidal oscillation of the total electron content with a peak-to-valley amplitude of about 10%. Model calculations were performed under the assumption that these electron content variations are indeed the signature of plumes moving in and out of the radio ray path. If the density contrast between plume and interplume regions is low, then the plume structure must occupy a significant fraction of the radio ray path. If the plume extent along the line-of-sight is similar to their observed width in the plane of the sky, then the density contrast is very high (factor 8 or more). Neither scenario seems reasonable under the given geometry. A more likely explanation for this 24-hour variation would be an unaccounted bias at one of the ground stations which imposes an apparent diurnal periodicity onto the measurements. In short, there is no evidence for high latitude coronal plumes in radio sounding data near 30 solar radii. ¿ 1998 American Geophysical Union