The thermal–compositional dependence of Fe2+—Mg distributions between coexisting garnet and pyroxene in diverse metamorphic lithologies from two small areas in the Ruby Range, southwestern Montana, has been studied by electron microprobe and multiple linear regression techniques. For coexisting gamet–clinopyroxene, this dependence, which is inferred from independent metamorphic P–T estimates for two areas and thirteen mineral-pair analyses, is summarized by the equation
RT⁢ln⁡KD=(2482±845)+(1509±1392)(XFe−XMg)Gar+(2810±954)(XCaGar)+(2855±792)(XMnGar)

where KD = (XFe/XMg)Gar/(XFe/XMg)Cpx, X = mole fraction, 2482 = 2324 + 0.022P = −ΔGTP(cal) for the gar–cpx Fe—Mg exchange reaction, and the coefficients represent regressed values for garnet mixing parameters (wijGar)⁠. The regressed parameters for Ca and Mn agree well with those calculated by Ganguly (1979); however, the regressed value of wFeMgGar is intermediate to those of Ganguly and O’Neill and Wood (1979).

For nine gamet–orthopyroxene pairs, the best-fit equation is identical to that given above except that −ΔGTP=1391±288 cal for the gar–opx Fe—Mg exchange reaction.

The gamet–clinopyroxene geothermometers of Ganguly (1979) and Saxena (1979) yield anomalously high temperatures for the Ruby Range. If this result is observed in other upper-amphibolite to lower-granulite facies terrains, more realistic temperatures may be obtained from the gar–cpx equation presented here. The gar–opx equation can be used as a relative (but not absolute) geothermometer.

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