Coordinate gauge conditions in theN-body equations of motion in the first-order post-Newtonian approximation of general relativity

The explicit forms of the metric as well as the equations of motion in the first-order post-Newtonian approximation are worked out under several gauge conditions. It is noted that the so-called EIH (Einstein, Infeld, and Hoffman) equation of motion for an assembly ofN finite mass points mutually interacting via gravitation is identically obtained under three different gauge conditions, namely the harmonic gauge, Chandrasekhar gauge and a composite Chandrasekhar gauge used by Misneret al. (1970), even though the solutions for the metric are found to be all different. In one case the metric has a component apparently diverging, but finally generates regular affine connections so that the equations of motions become free from any singularity. By use of the Chandrasekhar gauge and his formulation, the second-order contribution to the acceleration of planets in the limit of test particle motion around the Sun has been calculated, the inclusion of which in the EIH set of the equations of motion would extend the relative accuracy of computing the total acceleration of any planet to better than one part in 10¹⁷.     

THE BLOOMINGTON (LL6) CHONDRITE AND ITS SHOCK MELT GLASSES

The Bloomington meteorite, a 67.8 gram veined, brecciated chondrite, fell during the summer of 1938 in Bloomington, Illinois. Its olivine, orthopyroxene and metal compositions (fo₆₉, en₇₄ and Fe₅₂ Ni₄₈ respectively) and its texture identify it as a brecciated LL6 chondrite of shock facies d. Shock melt glasses occur in Bloomington as sparse melt pockets and veins in clasts and as isolated masses in the black, clast-rich matrix. The vein glasses chemically resemble bulk LL-group chondrites and thus appear to reflect total melting of the host meteorite. The melt pocket and matrix glasses, like those described previously in L-group chondrites, have more varied compositions and are typically enriched in normative plagioclase. All glasses that we analyzed in Bloomington have FeO/MgO and Na/Al ratios similar to those of LL-group chondrites, indicating that melting of this meteorite involved neither a significant change in the oxidation state of iron nor loss of sodium to a vapor phase. Bloomington is a monomict breccia whose components formed in place as a result of a single episode of shock and attendant melting.     

Seismotectonic significance of the 29 January 1989 Etne earthquake, SW Norway

The integrated analysis of geological, seismological and field observations with lineament data derived from satellite images allows the identification of a possible seismogenic fault zone for an earthquake which occurred near Etne in southwestern Norway, on 29 February 1989. The hypocentre of the earthquake was located at the mid-crust at a depth of 13.8±0.9 km which is typical of small intraplate earthquakes. The Etne earthquake occurred as a result of normal faulting with a dextral strike-slip component on a NW–SE trending fault. Available geological and lineament data indicate correlation of the inferred seismogenic fault with the NW–SE trending Etne fault zone. An aeromagnetic anomaly related to the Etne fault zone forms a regional feature intersecting both Precambrian basement and allochthonous Caledonian rocks. Based on these associations the occurrence of the Etne event is ascribed to the reactivation of a zone of weakness along the Etne fault zone. Slope-instabilities developed in the superficial deposits during the Etne event demonstrate the existence of potentially hazardous secondary-effects of such earthquakes even in low seismicity areas such as southwestern Norway.     

Subtidal sea level and current variations in the northern reach of San Francisco Bay

Analyses of sea level and current-meter data using digital filters and a variety of statistical methods show a variety of phenomena related to non-local coastal forcing and local tidal forcing in the northern reach of San Francisco Bay, a partially mixed estuary. Low-frequency variations in sea level are dominated by non-local variations in coastal sea level and also show a smaller influence from tidally induced fortnightly sea level variations. Low-frequency currents demonstrate a gravitational circulation which is modified by changes in tidal-current speed over the spring-neap tidal cycle. Transients in gravitational circulation induce internal oscillations with periods of two to four days.     

Damage to surface structures due to underground coal mine blasting: apprehension or real cause?

Investigations were carried out at three underground coal mines in India to study the response of surface structures to underground blasting and the likelihood of damage to the structures. The structures in the vicinity of the underground blasting area were single and multistoried residential houses. The amplitudes of vibration due to underground blasting were monitored simultaneously on the ground surface near the foundation of the structures and on various floors of the structures. The vibrations were also monitored near the important surface installations. It was observed that the magnitude of vibration in structures decreased with the increase in the height of the structures. The frequency of blast vibration from underground blasting was higher than the natural frequency of the structures. Little energy was transmitted into the structures, which caused reduction in the vibration level in the structures. The reduction in the vibration levels was up to 45% in the houses. It indicates that the dominant frequency of blast vibration plays an important role in persistence of vibration and its amplification or reduction characteristics in the structures. This paper deals with the effect of the vibrations on structures/houses standing above the blasting faces in underground workings and their potential to likely damage to the structures at different Indian geo-mining conditions.     

Disturbances in an infinite slab due to torsional forces applied on a cylindrical cavity

Summary The paper deals with the disturbances in an infinite slab of finite thickness, the medium being homogeneous, isotropic and perfectly elastic.     

Note on the propagation of waves from a spherical cavity in an infinite solid

Summary The present note, as its title implies, is concerned with the investigation of disturbances in an infinite elastic medium containing an initial magnetic field in the axial direction. The equations ofMaxwell, those of elasticity have been effectively made use of to solve the problem.     

The dissociation constants of carbonic acid in seawater at salinities 5 to 45 and temperatures 0 to 45°C

The pK₁^* and pK₂^* for the dissociation of carbonic acid in seawater have been determined from 0 to 45°C and S = 5 to 45. The values of pK₁^* have been determined from emf measurements for the cell:

Pt](1 − X)H2 + XCO2|NaHCO3, CO2 in synthetic seawater|AgC1; Ag

where X is the mole fraction of CO₂ in the gas. The values of pK₂^* have been determined from emf measurements on the cell:

Pt, H2(g, 1 atm)|Na2CO3, NaHCO3 in synthethic seawater|AgC1; Ag

The results have been fitted to the equations:

lnK^*₁ = 2.83655 − 2307.1266/T − 1.5529413 lnT + (−0.20760841 − 4.0484/T)S^0.5 + 0.08468345S − 0.00654208S¹

InK^*₂ = −9.226508 − 3351.6106/T− 0.2005743 lnT + (−0.106901773 − 23.9722/T)S^0.5 + 0.1130822S − 0.00846934S^1.5

where T is the temperature in K, S is the salinity, and the standard deviations of the fits are σ = 0.0048 in lnK₁^* and σ = 0.0070 in lnK₂^*.Our new results are in good agreement at S = 35 (±0.002 in pK₁^*and ±0.005 in pK₂^*) from 0 to 45°C with the earlier results of Goyet and Poisson (1989). Since our measurements are more precise than the earlier measurements due to the use of the Pt, H₂|AgCl, Ag electrode system, we feel that our equations should be used to calculate the components of the carbonate system in seawater.     

ENSO related modulation of coastal upwelling in the eastern Atlantic

An index of ENSO in the Pacific during early boreal winter is shown to account for a significant part of the variability of coastal SST anomalies measured a few months later within the wind driven West African coastal upwelling region from 10°N to 26°N. This teleconnection is thought to result from an atmospheric bridge between the Pacific and Atlantic oceans, leading to warm (cold) ENSO events being associated with a relaxation (intensification) of the Atlantic trade winds and of the wind-induced coastal upwelling. This ENSO related modulation of the wind-driven coastal upwelling appears to contribute to the connection observed at the basin-scale between ENSO and SST in the north Atlantic. The ability to use this teleconnection to give warnings of large changes in the West African upwelling several months in advance is successfully tested using data from the 1998 and 1999 ENSO events.