P_total, {Mathematical expression} and the occurrence of cummingtonite in volcanic rocks

The phenocryst assemblage of cummingtonite, orthopyroxene, quartz, titanomagnetite and ilmenite in rhyolites of New Zealand has been used to calculate P_total and {Mathematical expression}. The values of P_total and {Mathematical expression} depend strongly upon whether an ideal mixing, or an ordered, model is used for the solid-solutions, but in both cases {Mathematical expression} ≈P_total. The rhyolite magma contained over 9 per cent water (by weight) when the cummingtonite phenocrysts precipitated, and possibly as much as 12 per cent, so that it is surprising that one of these rhyolites is a coherent lava. The calculated values of P_total and {Mathematical expression} are very sensitive to uncertainty in both the composition of the solid-solutions and temperature. Calculations show that {Mathematical expression}>0.7-0.8 P_total for cummingtonite to precipitate in rhyolites, and that iron-rich olivine and cummingtonite could only exist in rhyolites over a small temperature range at a pressure near 5 kilobars. Hornblende phenocrysts co-existing with fayalitic olivine in rhyolites accordingly have a very low activity of Mg₇Si₈O₂₂(OH)₂.