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The historical record of large volcanic eruptions from 1500 to 1980, as contained in two recent eruption catalogs, is subjected to detailed time series analysis. Two weak, but probably statistically significant, periodicities of ∼11 and ∼80 years are detected. Both cycles appear to correlate with well-known cycles of solar activity; the phasing is such that the frequency of volcanic eruptions increases (decreases) slightly around the times of solar minimum (maximum). The weak quasi-biennial solar cycle is not obviously seen in the eruption data, nor are the two slow lunar tidal cycles of 8.85 and 18.6 years. Time series analysis of the volcanogenic acidities in a deep ice core from Greenland, covering the years 553–1972, reveals several very long periods that range from ∼80 to ∼350 years and are similar to the very slow solar cycles previously detected in auroral and carbon 14 records. Mechanisms to explain the Sun-volcano link probably involve induced changes in the basic state of the atmosphere. Solar flares are believed to cause changes in atmospheric circulation patterns that abruptly alter the Earth's spin. The resulting jolt probably triggers small earthquakes which may temporarily relieve some of the stress in volcanic magma chambers, thereby weakening, postponing, or even aborting imminent large eruptions. In addition, decreased atmospheric precipitation around the years of solar maximum may cause a relative deficit of phreatomagmatic eruptions at those times.