Several publications have reported that total column ozone (TCO) may oscillate with an amplitude of up to 10 DU (Dobson units) during a solar eclipse, whereas other researchers have not seen evidence that an eclipse leads to variations in TCO beyond the typical natural variability. Here, we try to resolve these contradictions by measuring short-term variations (of seconds to minutes) in TCO using "global" (Sun and sky) and direct-Sun observations in the ultraviolet (UV) range with filter radiometers (GUVis-3511 and Microtops II (R)). Measurements were performed during three solar eclipses: the "Great American Eclipse" of 2024, which was observed in Mazatl & aacute;n, Mexico, on 8 April 2024; a partial solar eclipse that took place in the United States on 14 October 2023 and was observed at Fort Collins, Colorado (40.57 degrees N, 105.10 degrees W); and a total solar eclipse that occurred in Antarctica on 4 December 2021 and was observed at Union Glacier (79.76 degrees S, 82.84 degrees W). The upper limits of the amplitude of oscillations in TCO observed at Mazatl & aacute;n, Fort Collins, and Antarctica were 0.4 %, 0.3 %, and 0.03 %, respectively. The variability at all sites was within that observed during times not affected by an eclipse. The slightly larger variability at Mazatl & aacute;n is due to cirrus clouds occurring throughout the day of the eclipse and the difficulty of separating changes in the ozone layer from cloud effects. These results support the conclusion that a solar eclipse does not lead to variations in TCO of more than +/- 1.2 DU and that these variations are likely much lower, drawing into question reports of much larger oscillations. In addition to calculating TCO, we also present changes in the spectral irradiance and aerosol optical depth during eclipses and compare radiation levels observed during totality. The new results augment our understanding of the effect of a solar eclipse on the Earth's upper atmosphere.