A series of matrix operations is described which enables the following optical data to be calculated for plane polarized light perpendicularly incident on a section of a transparent or opaque mineral: 1. vibration directions and refractive indices of anisotropic transparent minerals: 2. reflectivities and the state of polarization of light reflected from anisotropic opaque minerals. The data needed are the dielectric tensor, its orientation with respect to the crystal axes, the unit cell parameters and the direction of the incident light. The mathematical techniques involve the manipulation of matrices, the determination of eigenvalues and eigenvectors and, for opaque minerals, the manipulation of complex numbers. All operations can be carried out with the aid of some of the recent electronic calculators which have built-in matrix algebra procedures and complex arithmetic.

Chlorine-rich potassium hastingsite occurs in a calcareous pegmatite, a replacement zone and an amphibolite lens within hornblende gneiss on West Ongul Island, Lützow-Holm Bay, East Antarctica. The amphibolite lens and hornblende gneiss were metamorphosed to the kyanite-sillimanite grade of the granulite facies during Proterozoic metamorphism. Chemical analysis (3.27 wt.% Cl), unit cell parameters and optical properties of the Cl-rich potassium hastingsite are given. Cl-rich (> 3 wt.%) calcic amphiboles reported from various rock types are mostly more than 0.9 in (Na+ K) content, more than 0.4 in K/(Na + K) ratio, more than 0.75 in Fe2+/(Fe2+ + Mg + Mn) ratio and more than 1.9 in AlIV content (total iron as FeO and O = 23). The unit cell volume of Cl-rich hastingsite is distinctly larger than that of Cl-poor hastingsite.

Sporadic small garnet granulite and two-pyroxene granulite xenoliths found in the carbonatite tuffs and lavas near Fort Portal, South West Uganda, are chiefly silica-saturated and rich in Al2O3 (> 20 wt. %) and Na2O (c. 2 to 4 wt. %). Three REE patterns are distinguished: LREE enriched—HREE depleted with a positive Eu anomaly; LREE depleted—HREE relatively enriched and flat; and LREE slightly enriched with a very weak Eu anomaly and high overall REE. The xenoliths are considered to represent original basaltic melts and fractional crystallisation products, varying with the dominance of the clinopyroxene, plagioclase or olivine crystallising phase. It is thought that REE abundances were established before metamorphism.

The clinopyroxenes are low-jadeitic augites, the orthopyroxenes, aluminous hypersthenes and the garnets, pyrope-almandine with constant grossularite. Plagioclase varies with increasing metamorphic grade from labradorite to andesine-oligoclase. Scapolite (meionite), alkali-feldspar, quartz, mica, amphibole, rutile and apatite are minor phases and some appear to be metasomatic.

Calculated temperatures of metamorphic equilibration range from 580 to 800°C at pressures > 4 kbar for the two-pyroxene granulites and > 6 kbar for the garnet granulites. A known geophysical discontinuity marking a density change at 16 km in the Western Rift may be due to the presence of two-pyroxene granulite, calculated to become garnet-bearing at depths greater than 23 km. The absence of proven omphacite-bearing eclogite xenoliths (with no plagioclase) indicates that the greatest depth of crustal sampling by the carbonatite in the Fort Portal field is about 25 km which could be the depth of the Moho in this area.

Vivid blue inclusions in white whewellite or weddellite, occurring within the medulla of four lichen species growing on copper-bearing rocks, have been identified as the hydrated copper oxalate, moolooite, CuC2O4. nH2O (n ∼ 0.4–0.7), by infrared spectroscopy and X-ray powder diffraction. The mineral is believed to have been formed by reaction between oxalic acid secreted by the lichen and ground or surface water containing copper.