Major and trace element patterns established during retrogressive metamorphism of granulite-facies gneisses,NW Scotland

A detailed study of geochemical changes associated with the retrogressive metamorphism of granulite-facies gneisses of the Lewisian Complex of NW Scotland has been made, using nearly 250 gneisses analysed for 24 major, minor and trace elements. The gneiss samples have been divided into 3 groups: (1) granulite facies, (2) granulite facies retrogressed to amphibolite facies but remaining undeformed, and (3) retrogressed (amphibolite-facies) gneisses deformed in shear zones. Element distributions within these groups have been examined using correlation coefficients, and have been compared and tested for significance using Student's t and Fisher z statistics. It is shown that the process of retrogression involved considerable large-scale chemical equilibration. Major-element pairs show marked increases in correlation during retrogression, reflecting considerable reordering of elements into one or other of the main amphibolite-facies minerals: hornblende, plagioclase and (minor) biotite. These correlations are enhanced, but otherwise unchanged, in the deformed gneisses. The retrogressed gneisses have a much more constant Fe/Mg ratio and a more uniform plagioclase composition, while there is a strong correlation between Fe³⁺ and Fe²⁺ throughout the area studied. Trace elements, by contrast, mostly show a significant loss of correlation during retrogression, although Cr and Ni are exceptions. Retrogression occurred as a result of widespread introduction of hydrous fluids up vertical structures in the gneiss complex during the Early Proterozoic. These fluids allowed considerable metasomatic redistribution of elements within the complex as the whole-rock compositions adjusted to the new mineralogy. Throughout the North Atlantic Archaean Craton there is a close association between retrogression of high-grade gneisses and basic magmatism in the form of dyke swarms. It is suggested that the two may be connected, and that the fluids causing retrogression are mantle-derived.     

Discrete calculations of interstellar migration and settlement

Monte Carlo calculations of the expansion of space-faring civilizations are presented for a wide range of values of the population growth coefficient (α) and emigration coefficient (γ). Even for the very low values proposed by Newman and Sagan (α = 10^?4per year; γ = 10^?8per year) the migration wavefront expands at 1.4 × 10^?5 pc per year. Even with this low expansion velocity, such a civilization would fill the Galaxy in about 10⁹ years. Filling times of the order of 60 million years seem probable. The wavefront velocity is approximated by $\text{υ =}\text{Δr}\text{[(}\text{Δx}\text{υ}{}_{\mathrm{<mtext>s</mtext>}}\text{)}\text{+ (}\text{1}\text{α}\text{)}\text{ln}\text{(}\text{2α}\text{γ}\text{)]}$, where $\text{Δr}$ is the average radial distance traveled, $\text{δx}$ the average distance traveled, and υ_s the ship speed. This approximation was derived by Newman.     

Dynamics of close binary systems with mass exchange

The effects of non-isotropic ejection of mass from either component of a binary system on the orbital elements are studied, for the case of a small initial eccentricity of the relative orbit, when all the ejected mass falls on the other component. The problem is transformed to an equivalent two-body problem with isotropic variation of mass, plus a perturbing force which is a function of the intial conditions of ejection of the particles and their final, positions and velocities when they fall on the surface of the other star. The variation of the orbital elements are derived. It is shown that, to first-order terms in the eccentricity, the secular change of the semimajor axis is equal to the one corresponding to the case of zero initial eccentricity. On the contrary, the secular change of the eccentricity is smaller and it depends on the variations of mass ejection due to the finite eccentricity.     

Pierre Mercier (1890–1976)

Sans résumé Insp. cant. eaux VD     

A computer method to calculate the convolution of statistical distributions

It is becoming increasingly important to determine probability distributions of combinations of random variables. Convolution is a technique by which the distribution of a sum of random variables can be determined. This paper presents some simplifications in order to reduce the numerical integrations and computer time. In addition, the method may be used with empirical nonanalytic distributions. While Monte Carlo methods are also appropriate for calculating the distribution, convolution can give at least as much accuracy as Monte Carlo methods with a reduction in computation. Two applications are presented: one approximates the distribution of percent sand in an area, and the other indicates a method of determining sample size when using the distribution of means to approximate normality.