Some linear and non-linear problems in petrology

Linear mass-balance calculations such as those involved in projections, crossed tie-lines and petrologic mixing can only distinguish between possible and impossible processes, and cannot alone give information on the intensive parameters that operated during rock formation. Non-linear computations involving both mass-balance and mass-action equations can provide insight into both the extensive and intensive controls on rock mineralogy. Approximate extimates of Margules parameters for non-ideal solid solutions may be obtained by calculation using the bulk moduli, shear moduli and molar volumes of the components.