The N -dimensional tie-line problem

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Scientific paper

An analytical method is presented for determining whether two mineral assemblages can be related to one another by a balanced chemical reaction or whether their differing mineralogies must be attributed to differing bulk compositions. Projections and other chemographic methods are shown to be equivalent but less general than the method presented. Set theory and vector algebra are used to state the problem and to formulate a solution. Solutions are reached by the methods of linear programming and result in balanced chemical reactions, if such exist. Open and closed systems can be equally well treated, as can various projections, and numerous idealized and natural examples are presented to illustrate the method. It is concluded that chemographic analyses of phase equilibria in pelitic schists presented by (1962), and by (1965), are consistent with the new method, and that the orthopyroxene isograd of the northwest Adirondacks may be as much the result of a metasomatic change of bulk composition as of an increase of metamorphic grade.

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