Here is presented a mathematical method which enables us to evaluate the degrees of lanthanide tetrad effects from the data involving all of REE. Each of the four spans corresponding to four subgroups, La-Nd, Pm-Gd, Gd-Ho, and Er-Lu, is approximately fitted to a quadratic function and the resultant quadratic coefficient is employed as a numerical indicator for the tetrad effect. For the purpose of approximation by a quadratic function, the least-squares method is used under the constraint that the first and second quadratic curves intersect at the middle point between Pm and Sm, and that the third and fourth ones intersect at the middle point between Ho and Er. Since, mathematically, the subject is a problem on the conditional extremum, the method of Lagrange undetermined multipliers should be used. It is noted that the degrees of four tetrad effects can be evaluated simultaneously. This method can lead us to the mathematically well-defined estimation of the tetrad effect.

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K/Ar age data, whole-rock major, trace and rare earth element geochemistry, ⁸⁷Sr/⁸⁶Sr and ¹⁴³Nd/¹⁴⁴Nd isotope chemistry, and computer modelling have been used to clarify the timing and petrogenesis of late Miocene igneous activity on Oki Dozen Island in the Japan Sea. Commencing at about 7 Ma, quartz syenite was intruded on the southeastern part of present-day Nishinoshima. At the same time, compositionally similar magma (trachyte) was erupted as lava and pyroclastic flows. At approximately 6 Ma, alkali olivine basalt-trachyandesite was erupted, forming a volcanic shield (somma phase). Following this, the locus of volcanic activity, and the composition of the magma changed, with eruption of trachyte and rhyolite from satellite vents (parasitic phase). Dikes, compositionally similar to extruded magma, were intruded throughout this volcanic episode. K/Ar dating cannot resolve the individual phases of volcanic activity, which partly overlaps with late Miocene volcanism on Oki Dogo. The composition of somma and parasitic phase volcanics were controlled by fractionation of observed phenocryst phases, but decoupling of trace elements and small isotopic shifts indicate the transition from somma to parasitic volcanism was not a closed-system process. Syenite and comagmatic central cone trachyte are compositionally similar to anorogenic granitoids, and may result from melting of a felsic lower crust by upwelling basaltic magma. Despite weak age overlap, divergent trace element and isotopic trends, and small differences in rare earth element chemistry indicate that alkalic volcanic rocks on Oki Dozen and Oki Dogo tapped different mantle sources.

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Bulk carbon isotopic compositions of 26 Antarctic carbonaceous chondrites (33 specimens) are reported and discussed with relevance to the processes involved in their alteration and the existence of solvent-extractable organic matter. The δ¹³C values (relative to PDB) vary from -16.6 to +0.9‰. The average value (-6.2‰) is higher than that for non-Antarctic carbonaceous chondrites by -6‰. The difference may be explained by contamination of terrestrial organic carbon on non-Antarctic chondrites and/or different populations of parent bodies. Most Antarctic carbonaceous chondrites have an apparent trend (“a major sequence”) that the δ¹³C value becomes higher with increasing carbon content. The trend is likely to beexplained by a mixing model of two components; isotopically heavy and labile component (solvent-extractable organic matter and carbonate), and isotopically light and inert acid-insoluble component (kerogen-like matter). In addition, an unique group (altered specimens) is characterized by relatively high content and isotopically light carbon. For seven CM chondrites, δ¹³C values of residues after the hot H₂O and HCl/HF treatment are also reported. Despite considerable isotopic variations of bulk carbon, the δ¹³C values of acid-insoluble residues may be classified into two groups; isotopically light (-15 to -13‰) and heavy (-9 to -7‰) ones. Most kerogen-like matters belong to the light group, which are isotopically similar to non-Antarctic kerogen-like matter. The altered specimens have isotopically light bulk carbon (∼-15‰), which is similar to those of their kerogen-like matter; they probably lost heavy components such as solvent-extractable organic matters (e.g., amino acid and carboxylic acid) and carbonates during aqueous alteration and thermal metamorphism on parent bodies. This is in accord with mineralogical and oxygen isotope studies. The presence of solvent-extractable organic matter is one of the important factors controlling bulk carbon isotopes in carbonaceous chondrites.

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Molar absorption coefficients of water in glasses of arc magma compositions have been determined for ∼2.8 μm, ∼2.2 μm, and ∼1.9 μm bands. Excellent agreement was found between the water contents calculated from the absorption peak heights and those determined by H₂ manometry when the following molar absorption coefficients (m³/mol m) are used for different glass compositions: ε_2.8μm=6.4±0.1, ε_2.2μm=0.085±0.007, and ε_1.9μm=0.084±0.006 for tholeiite and high-Al basalt glasses; ε_2.8μm=6.8±0.1, ε_2.2μm=0.094±0.006, and ε_1.9μm=0.16±0.03 for dacite glass. With IR spectroscopy using these coefficients, water concentrations up to ∼3 wt.% in the arc basalt and dacite glasses can be determined accurately.

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The concentrations of five chalcophile elements (Pb, Cd, In, Tl and Ag) and the lead isotope ratios in ancient ices from the Taylor Dome near coastal Antarctica, have been determined by the isotope dilution-thermal ionization mass spectrometry (ID-TIMS), with ultra-clean laboratory techniques. The samples were selected from segments of cores, one of which included a visible ash layer. Electric conductivity measurement (ECM) or dielectric properties (DEP) gave distinctive sharp peaks for some of the samples chosen. Exterior portions of the sample segments were trimmed away by methods described here. Samples were evaporated to dryness and later separated into fractions for the five elements using an HBr-HNO₃ anion exchange column method. The concentrations are in the range 2.62-36.7 pg Pb/g of ice, 0.413-2.83 pg Cd/g, 0.081-0.34 pg ln/g, 0.096-2.8 pg Tl/g and 0.15-0.84 pg Ag/g, respectively. The dispersions in duplicate analyses are about ±1% for lead and cadmium, ±2% for indium, ±4% for thallium and ±6% for silver, respectively. The concentrations of lead obtained are commonly higher than those in the present-day Antarctic surface snows, but the isotope ratios are distinctively higher than those of the present-day snows and close to those of the other ancient ice collected from a different Antarctic area.

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In order to evaluate the possibility of radiation-induced wall-rock hematitization of moderate low-temperature hydrothermal uranium deposits, simulating experiments on the radiation-induced oxidation of ferrous iron with gamma-rays have been conducted in aqueous solutions at 25 and 200°C. The results show that the groundwater radiolysis is capable of oxidizing ferrous to ferric iron which will subsequently precipitate as iron oxy-hydroxides.

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