Abstract

The principle of constituent analysis is introduced. Assuming that a component (end member) consists of n variables in percentage form and that m different components (m ≤ n) constitute each of N samples, the samples can be treated as N points in m-dimensional space. Points represented by m end members are characterized by being non-coplanar and non-collinear in m-dimensional space. The amount of the mth end member contained in a sample is calculated as Xm−1i/Xm−1 m, where Xm−1 is the length of (m−1)th orthogonal axis; i and m in subscript Xm−1 are for the sample and mth end member, respectively; and the end members are successively put on the origin of the coordinate, X1, X1X2, X1X2X3,…, and X1X2 …−Xm−1 axes.In a metamorphic rock, m points are equivalent to constituent minerals. If the chemical compositions of constituent minerals and the bulk chemical composition of the rock are known, the method outlined in this paper provides information on equilibrium assemblages and allows computation of the amounts of constituent minerals.

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