The Principle of Constituent Analysis, with Special Reference to the Calculation of Weight Percentages of Minerals in Metamorphic Rocks

The principle of constituent analysis is introduced. Assuming that a component (end member) consists of nvariables in percentage form and that mdifferent components (m ≤ n) constitute each of Nsamples, the samples can be treated as Npoints in m-dimensional space. Points represented by mend 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−1is the length of (m−1)th orthogonal axis; iand min subscript Xm−1are for the sample and mth end member, respectively; and the end members are successively put on the origin of the coordinate, X1, X1−X2, X1−X2−X3,…, and X1−X2 …−Xm−1axes.In a metamorphic rock, mpoints 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.