Factor and canonical correlation analysis of geochemical data from eight fossil fumaroles suggest that six major factors controlled the formation and evolution of fumarolic encrustations on the 1912 ash-flow sheet in the Valley of Ten Thousand Smokes (VTTS). The six-factor solution model explains a large proportion (low of 74% for Ni to high of 99% for Si) of the individual element data variance. Although the primary fumarolic deposits have been degraded by secondary alteration reactions and up to 75 years of weathering, the relict encrustations still preserve a signature of vapor-phase element transport. This vapor-phase transport probably occurred as halide or oxyhalide species and was significant for As, Sb and Br. At least three, and possibly four, varied temperature leaching events affected the fumarolic deposits. High-temperature gases/liquids heavily altered the ejecta glass and mineral phases adjacent to the fumarolic conduit. As the fumaroles cooled. Fe-rich acidic condensate leached the ejecta and primary fumarolic deposits and resulted in the subsequent precipitation of Fe-hydroxides and/or Fe-oxides. Low- to ambient-temperature leaching and hydration reactions generated abundant hydrated amorphous phases. Up to 87% of the individual element data variance is apparently controlled by the chemistry of the ejecta on which the relict encrustations are found. This matrix chemistry factor illustrates that the primary fumarolic minerals surrounding the active VTTS vents observed by earlier workers have been effectively removed by the dissolution reactions. Element enrichment factors calculated for the VTTS relict encrustations support the statistical factor interpretations. On the average, the relict encrustations are enriched, relative to visibly unaltered matrix protolith, in As, Br, Cr, Sb, Cu, Ni, Pb, Fe, and LOI (an indirect measure of sample H2O content). ?? 1993.