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By C. K. Eilerts

Finite difference equations were programmed and used to integrate the second-order, second-degree, partial differential equation with variable coefficients that represents the transient linear flow of gas-condensate fluids. Effect was given to the change with pressure of the compressibility factor, the viscosity, and the effective permeability and to change of the absolute permeability with distance. Integrations used as illustrations include recovery of fluid from a reservoir at a constant production rate followed by recovery at a declining rate calculated to maintain a constant pressure at the producing boundary. The time required to attain such a limiting pressure and the fraction of the reserve recovered in that time vary markedly with properties of the fluid represented by the coefficients. Fluid also is returned to the reservoir at a constant rate, until initial formation pressure is attained at the input boundary, and then at a calculated rate that will maintain but not exceed the limiting pressure. The computing programs were used to calculate the results that would be obtained in a series of back-pressure tests made at selected intervals of reservoir depletion. If effect is given to the variations in properties of the fluid that actually occur, then a series of back- pressure curves — one for each stage of reserve depletion — is required to indicate open-flow capacity and related flow characteristics dependably. The isochronal performnce method for determining flow characteristics of a well was simulated by computation. INTRODUCTION The back-pressure test procedurel is based on a derivation of the equation for steady-state radial flow of a gas, the properties of which are of necessity assumed to remain unchanged in applying the test results. The properties of most natural gases being recovered from reservoirs change as the reserve is depleted and pressures decline, and the results of an early back-pressure test may not be dependable for estimating the future delivery capacity of a well. The compressibility factor of a fluid under an initial pressure of 10,000 psia can change 45 per cent and the viscosity can change 70 per cent during the productive life of the reservoir. There are indications that the effective permeability to the flowing fluid can become 50 per cent of the original absolute permeability before enough liquid collects in the structure about a well as pressure declines to permit flow of liquid into the well. The advent of programmed electronic computing made practicable the integration of nonlinear, second-order, partial differentia1 equations2.3 pertaining to flow in reservoirs. Aronofsky and Porter4 represented the compressibility factor and the viscosity by a linear relationship, and integrated the equation for radial flow of gas for pressures up to 1,200 psi. Bruce, Peaceman, Rachford and Rice5 integrated the partial differential equations for both linear and radial unsteady-state flow of ideal gas in porous media. Their published results were a substantial guide in this study of integration of the partial differential equation of linear flow with coefficients of the equation variable. The computing program was developed to treat effective permeability as being both distance-dependent and pressure-dependent. In this study all examples of effective permeability are assumptions designed primarily to aid in developing programs for giving effect to this and other variable coefficients. The accumulation of data for expressing the pressure dependency of the effective permeability is the objective of a concurrent investigation. FUNDAMENTAL DIFFERENTIAL EQUATIONS DIFFERENTIAL EQUATION OF FLOW Linear transient fluid flow is represented by the partial differential equation,

Jan 1, 1965

By Hermann Wedding

It is now fourteen years since we German ironmasters, in considerable number, visited the United States on the occasion of the Philadelphia Exposition, and found the iron metallurgy of this country, as must be frankly confessed, in an advanced stage of development not previously suspected by us. At that time the United States already occupied, as now, the second rank, with Germany in the third, the product of pig-iron for that year being, in Great Britain, 6550, in this country, 2093, and in Germany, 1850 kilotons.* This relative position has not been changed. The present annual product of the three countries is, in round numbers, Great Britain, 8380, the United States, 7790, and Germany, 4530 kilotons. But the proportion of the United States, which was, in 1876, but 15 per cent. of the world's product, has now advanced to 30 per cent. When we left America in 1876, it was not only with gratitude for cordial hospitality and for the liberality with which our professional colleagues here had opened to our inspection whatever was worthy of notice in our special field, but also with the conviction that we had collected a great treasure of new and interesting information which we could utilize for the benefit of our German Fatherland. Particularly the achievements of the never-to-be-forgotten Holley in the field of Bessemer practice, set us an inspiring example for imitation in our own country. As an expression of our thanks in more practical fashion, I attempt in this paper to sketch what we have done in Germany since

Jan 1, 1891

By David Mitchell

MANY of the difficult operating problems of the preparation of coal for market, of sampling coal shipments and in the utilization of coal are caused by segregation in the coal mass. Segregation may be of two kinds: i.e., "size segregation," in which parti- cles of the same size in a mass of coal containing a range of sizes collect to-gether and "density segregation," in which particles of the same density or specific gravity in a mass of particles of varying density gather together. MECHANICS OF SEGREGATION Size segregation cannot take place with closely sized coal. As the size range increases, the tendency for size segregation increases. Similarly, cleaned coal with particles of approxi- mately the same specific gravity have very little tendency for density segrega- tion. The wider the density range of particles and the more particles of different density, the greater the chances are for density segregation. FIG. 1.-SEGREGATION IN A SIDE-FILLED The following discussion deals primarily BIN with coal of a wide size range as screenings and of wide density differ-ences as uncleaned or run-of-mine screenings. If a mass of coal containing particles of a wide size range is subject to the stream action of a moving current of water, the small particles are transported farther than the coarser. Particles of different density in a stream of moving water are subject to the laws of classification, the heavier settling out first. The familiar sluice box of the gold miner and the action of rivers and other streams in classifying material according to

Jan 1, 1937

By R. T. DeHoff, L. J. Buteau, J. Kronsbein

Network topology is introduced and used to describe sinter bodies at various stages of the sintering process. The matrices of incidence, loop-branch. tree-branch, and cut-branch are constructed and their relationship to the three-dimensional void space and the common two-dimensional bounding surface is established. The sintering body is assunzed to remain connected but this is not so with the void space. The topological invariants known as Betti numbers are related to this observed fact and provide parameters which measure the progress of the sintering process. They are extracted from the matrices by means of known algebraic operations. Experimental procedures are given which permit actual construction of the various matrices and determination of the Betti numbers by serial sectioning of the sinter bodies. A sinter body is produced by exposing a large number of metallic particles (0.00001 to 0.3 in. diam) to a temperature that is near but below their melting point. When these particles are maintained at such a temperature for a sufficient length of time, it is found that the interparticle contacts become welded. As time increases, these welds, often referred to as necks, grow. All of the space between the particles constitutes a single connected void; an ultimate consequence of sintering is the breaking up of the void into separated parts. A mathematical apparatus for describing the geometric characteristics of a sinter body at each stage of the process was first proposed by F. N. Rhinesl when he introduced the application of topology to this problem. He described the sinter body in terms of one of its topological invariants, the genus. The most important advantage of a topological description is invariance with respect to continuous deformations. This means that particle sizes and shapes need not be considered, resulting in considerable simplification and generalization of the geometric description. In the case of a sinter body, wherein the internal geometry is particularly complex, the simplification provided by topological concepts is absolutely essential. The important parameters in the Rhines model are the number of particles and the interparticle contacts. The invariant considered called genus is given by Euler's formula for the connectivity of two-dimensional surface of the sinter body. This surface includes the pore-solid interface. The Euler formula is G = C - P + 1 [1] where C = number of interparticle contacts, P = number of particles, and G = genus of the surface bounding the sinter body. In topology the term genus may be used to mean the number of self re-entrant cuts that can be made on a closed surface without dissecting it into more than one connected surface. Its use is restricted to the surface and does not apply to the three-dimensional volume enclosed or excluded by it. In the case of sintering, the volume enclosed by the surface is defined as the sinter body; the volume excluded will be referred to as the void space. There is an intrinsic reason for using genus as a characteristic number associated with a sinter body. The genus is related to the Gaussian curvature by the integral of the product of the principal curvatures taken over the entire surface of the sinter body, as given by

Jan 1, 1965

By James Fiore

The Nuclear Waste Policy Act of 1982 provides a set of rules for proceeding with the identification and selection of sites for a mined geologic repository as well as for interim storage facilities for high level waste in the event storage facilities are needed. The following paper summarizes the sequence of procedures in site selection, and presents the interaction of governmental agencies, the states, the public, and affected Indian tribes in this process. Several agencies have published regulations assocated with the selection of high level waste sites. These regulations set down a diverse collection of requirements designed to ensure public safety. This paper identifies the organizations working to satisfy these requirements, and outlines the role of the geotechnical community in performing data collection activities to support these same requirements.

Jan 1, 1984

By Louis Huber

THE Liberty tunnels extend through a very steep hill in Pittsburgh (locally called Mount Washington) for a distance of slightly over a mile. The two tunnels parallel each other and are 59 ft. apart, center to center (Fig. 1). They are for vehicular traffic, and in each there is ample space for two lines of vehicles. Northbound traffic, towards downtown Pitts- FIG. 1.-NORTH PORTAL OF LIBERTY TUNNELS. NOTE THE WINDBREAK AT END OF EAST TUNNEL. burgh, is confined to the east tunnel and southbound traffic to the west tunnel. The South Hills residential district is separated from downtown Pittsburgh by Mount Washington, a steeply rising escarpment south of and adjacent to the Monongahela River. The Mount Washington district immediately south of the Monongahela River has been reached, for many

Jan 1, 1927

By A. J. Teplitz, T. Bardeen

In the course of an investigation of lost circulation, a new tool has been developed which gives a qualitative measure of the relative velocity between the fluid column in the borehole and the tool. The position of a diaphragm in the side wall of the instrument depends on the flow through the device. This position is established by using the conductive borehole fluid in a potentiometric circuit. The instrument has high sensitivity and can detect changes in velocity as low as. 5 ft/min. Lost circulation mud additives do not interfere with the satisfactory performance of the tool. In a number of circulation losses of the pressure induced type, the instrument has shown that the losses were confined to extremely narrow zones (less than I ft), indicating that such ruptures occur in a more or less horizontal rather than vertical plane as has often been assumed. This pinpointing of the zone of loss is important in remedial procedures since it allows the treatment to be applied directly to the point of loss rather than to the entire open hole. The device can also be employed for indicating points of entry of water in producing wells. INTRODUCTION The need for an improved means of locating the positions of lost returns zones became evident during an investigation of lost circulation difficulties in the Gulf Coast area.1 With instrumentation available at the time, it had been learned that, contrary to common belief, the position of the thief zone responsible for a given loss seldom coincided with the point of bit penetration at the time the loss was encountered. In the majority of cases, the losses were found to be occurring at some distance removed from the bottom of the hole —sometimes as much as a few thousand feet. This information, along with other observations made during the investigation, led to improved techniques' for dealing with lost circulation problems. Highlighted, however, among the results of this work and of similar studies subsequently conducted in drilling operations in other parts of the country, was the indication that a considerable portion of the difficulty and expense involved in treating prolonged circulation losses is due to the unsystematic application of remedial measures to one or more apertures of unknown position. Basis of Tests It is worth considering that if the troublesome formation could somehow be transported to the surface where it could be directly observed, there would likely be little difficulty in readily effecting a seal. Although this is a decided oversimplification of the situation, it does appear that the chief obstacles to similar ease of handling of a lost circulation zone in a well are lack of visibility and of ready accessibility. The latter handicap is overcome to a considerable extent by placement techniques already in use, and other procedures now in the process of development are expected to offer further improvement. But in the matter of visual observation, the technique to be presently described appears to afford a quite satisfactory substitute.

Jan 1, 1957

By A. H. Daane, J. F. Haefling

The limits of miscibility in some of the uranium rare-earth alloy systems have been determined in the temperature range 1000°to 1250°C. The solubilities of lanthanum and cerium in uranium are greater than those of the remaining rare earths by a factor of more than two. The solubility of uranium is greater in cerium, braseodymium, and neodymium than in the other rare-earth metals studied. The values found in this study are in qualitative agreement with those which might be expected if the solubility rules of Hildebrand and Scott are applicable. AS interest in nuclear reactors intensifies, many new types of fuels are being suggested in attempts to improve the economics of some of the proposed reactor schemes. To remove some of the difficulties inherent in the use of solid-fuel elements and their reprocessing, many types of liquid-metal reactors have been suggested. One of the more attractive features of several of these reactor concepts is that they include a continuous or semicontinuous process for the extraction of fission products and "bred" fissionable materials from the fuel, utilizing immiscible metal extractants. This would enable a much higher burn-up of fissionable material to be achieved and would present a very attractive economic picture. Several studies have been reported on equilibrium systems in which there exists a high degree of immiscibility between uranium and another metal that might be used as an extractant in such a processing scheme.' Two of these systems in which a high degree of immiscibility exists are those of uranium with the two rare-earth metals, lanthanum, and cerium. Since the rare earths constitute a significant fraction of the fission products, their removal is of prime importance. It is reasonable to believe that this might be accomplished by equilibrating a rare-earth phase with the contaminated uranium fuel in the liquid state. In order to make a more complete study of those systems which would be of interest either as extractants in a liquid-liquid extraction process, or as fission products formed in the fuel, the alloy systems of uranium with lanthanum, cerium, praseodymium, neodymium, and samarium were studied in some detail in the temperature range 1000" to 1250°C; less detailed studies were made with the other rare earths. In addition to being of value to the reactor program, the data obtained in this study should be of help in making a study of the role played by the electronic structures of metals in determining the nature of metallic solutions. The unique electronic structures of the rare-earth elements make them particularly interesting in this respect. EXPERIMENTAL The usual procedure for a solubility determination was to seal equal volumes of uranium and the particular rare earth in a tantalum crucible under an atmosphere of helium; this crucible was then sealed in a stainless steel jacket in an atmosphere of helium. These samples were equilibrated by repeated inverting of the crucibles in a furnace for 15 min at the desired temperature, left in an upright position for 15 min to permit separation of the two phases, and then quenched under a stream of water. In some runs the temperature of the furnace was held 50' to 100°C above the desired quenching temperature while inverting in order to insure good mixing. However, it was found that above 1200°C the crucibles were subject to failure and for these runs the furnace temperature was not raised above the desired quenching temperature. A small amount of tantalum was dissolved in the uranium and the rare earths in these runs, a maximum of 3 wt pct in the uranium phase at 1250°C and up to 1 wt pct in the rare-earth phase at this temperature. On cooling, the major portion of this tantalum precipitated as primary tantalum crystals. Any residual tantalum would probably have a negligible effect on the mutual solubility of uranium and the rare earths in each other. Samples for analysis were cut from each phase with an abrasive cutting wheel; the region near the interface between the two metals was carefully avoided. In the case of the rare earths with melting points above 1250°C no solubility data were taken on the rare-earth phase since this phase could not have achieved equilibrium in a reasonable length of time. (For the same reason no data were taken on the uranium phase below its melting point of 1132°C.) Equilibrium appeared to have been reached in the uranium phase in these cases although the rare-earth phase had not melted. To verify this, samples were melted together in an arc furnace similar to that described by Kroll.2 These samples were sub-

Jan 1, 1960

By W. A. Tiller, J. P. McHugh

THE phase diagram of the Ge-Te system was first investigated by Klemm and Frischmuth.' They arrived at the phase diagram shown in Fig. 1 indicating the presence of a peritectic phase boundary at the 50 at. pct Ge composition. Later, Schubert and Fricke2 obtained data which suggested to them the possible existence of a eutectic at about 55 at. pct Ge. In order to resolve these differences, we have carefully studied this system in the region 40 to 60 at. pct Ge using both the conventional thermal analysis technique and a new solidification technique.3y4 The alloys were prepared from semiconductor grade germanium and 99.999+ Te by reacting the elements in evacuated, graphite coated, vycor tubes. The samples were placed in a thermal analysis apparatus described elsewhere4 and cooling curves were taken of each alloy to determine the liquidus surface. The cooling curve for a 50 at. pct alloy shows two distinct arrests about 1°C apart which

Jan 1, 1961

[Secretary's Note.—The following official tables, prepared by the government of the State of Nuevo Leon, and presented to the Institute at the fifth seseion of its Mexican meeting, held at Monterrey, November 26, 1901, present in compact form a general summary of the mineral and metallurgical industry of the State for the preceding calendar year, together with a statement of the railway-shipments of ores from January 1 to October 31, 1901, which, in the absence of direct official mining and metallurgical statistics (not yet available for that year), clearly indicates an increased activity and productiveness of these industries. In other words, the mines are reported to have yielded in 1900 a total product of 83,960,169 kilos of ore; whereas, the railway is reported to have carried, in 10 months of 1901, a total of 108,318,647 kilos of ore. At this rate, the railway-shipments for 1901 mould amount to nearly 130,000,000 kilos. It is, of course, possible that the railwaystatistics include other freight than ores, or that they include duplications, such as would be involved in the record, first of certain ores transported, and afterwards of the " base bullion " produced therefrom. An accurate comparison is therefore impossible ; yet, after making all reasonable allowances for such items as have been named, it seems safe to infer that the mining and metallurgical industry of this State accomplished in 1901 a substantial progress.]

Jan 1, 1902

Engineers who are in charge of industrial operations, and their number is legion, sense as much as anyone the present feeling of unrest in the' country and more than anyone else realize the present inefficiency of labor. Undoubtedly the two phenomena are closely correlated and no doubt are due to a multitude of causes which it will be impossible to enumerate. From my experience in mining I estimate that the present efficiency of labor is only about two-thirds of what it was under pre-war conditions. In the mining industry, at least, we have not a large surplus of men looking for work and usually under these conditions men are rather more independent and will not work as efficiently and faithfully as if they felt there were plenty of men ready to take their places. Wages in metal mining have advanced more than the increased cost of normal and sane living. The result is that the men often work fewer days in a month and do not seem to have very much interest in their work while actually engaged in it. Then again, they have been listening to the more or less vague propaganda of the I. W. W. and the radical wing of the socialists, who are harping on the fact that the distribution of newly created wealth is unfair and that the laborer really is not working for himself or his fellow laborers but is carrying on his exertions for the benefit of a small and lim-ited class of exploiters. A continued harping on this view is bound to influence the judgment of even a conservative workman who is not a student of economics and who hears little or nothing upon the other side. I am a great believer in the common sense of the American people and in the long run I do not think that they will be carried away by unsafe doctrines. The trouble with so many of these propagandists of industrial in-equality is that they do not differentiate between production and dis-tribution. Even if we admit that distribution is unfair, unless goods are produced there will be nothing to distribute. A great many unthinking people seem to feel that wages are paid out of a pot which is inexhaustible and do not realize that eventually what comes out of the pot can never exceed what is put into it. The workman is not paid in money but is paid in goods, money as we all know being used simply as a measure of value and a medium of exchange, and that all that can be used to pay the laborer is what he produces.

Jan 11, 1919

By Simon Ash

THE coal-mining districts of Washington are mainly west of the Cascade Mountains; Fig. 1. The mines are on the foot hills of the slope, the lignite fields of Lewis and Thurston counties extending into the valleys west of the mountains. An exception is the Roslyn field, a small but important area on the eastern slope. If western Washington is divided into three areas from north to south, the bituminous coal fields and most of the active operations will be found largely in the middle area. The southern portion contains lignites over a large area. In the northern portion, mining is practically restricted to one mine, the Bellingham, which is working a subbituminous coal seam near the city of Bellingham. The degree of alteration that the coal of a particular field has undergone may be gaged roughly by the position of the field with reference to the Cascade Mountains. The lignites of Tenino, Tono, Mendota, and Castle Rock, on the railway line connecting Seattle and Portland, occur in a region, of low relief, in which the Eocene coal measures have suffered only minor disturbances. Subbituminous coals occur in the foot hills, as at Renton, Newcastle, and Bellingham. Coals high in fixed, carbon are found nearer the mountains, where. the measures have been sharply ,tilted and folded, as at Black Diamond and Carbonado. The two typical anthracite fields are located still higher, in the rugged mountains where outcrops appear both in deep gorges and on ridges at elevations approaching 5000 ft. At. Carbonado is found the only semianthracite seam worked on a commercial basis. The occurrence of this seam in a region of bituminous coal is due to the nearness of an igneous sill, which has changed its character from bituminous to semianthracite.

Jan 3, 1925

By Morris Muskat

THE method of R. W. Moore1 for determining subsurface interfacial depths by means of integrated curves of apparent resistivity has been analyzed theoretically. It is found that the only unique tangents that can be drawn to such curves are the asymptotes at infinite electrode spacing and the tangents through the origin at vanishing electrode spacing. Explicit expressions have been derived for the relationship between the electrode spacing at the points of intersection of these tangents and the thickness of the surface strata as a function of the conductivity parameters for the two-layer and three-layer earths. It is found that in all cases the electrode spacing at the points of intersection will exceed [3/2] of the thickness of the surface layer, and may even become indefinitely large as the resistivity of the deepest layers increases as compared with that of the surface layer. These results do not agree with the empirical findings of Moore that the intersection of the tangent lines fall at an electrode spacing very approximately equal to the thickness "of the surface layer.

Jan 1, 1944

By K. V. Hoover, D. M. Lapham

In Pennsylvania, 310 sampled sites of clay and shale have been studied with regard to potential use, lithology, physical properties, fired properties, major-element chemical analyses, and quantitative five-component X-ray mineralogy. Approximately 80% of the samples are of some potential use. Binary correlations of test data vs. potential use indicate that certain empirically determined parameters may be critical. These are: lithology, particularly for medium to superduty refractories and lightweight aggregate; kaolinite content for refractories vs. low-temperature fired product sources; quartz analyses with an apparent necessary minimum quantity for brick; quartz content, which is low in high grades of lightweight aggregate; mica content, which is low for refractories and possibly high for lightweight aggregate; total iron, which is low for refractories and shows a 4.0% minimum for lightweight aggregate; carbon dioxide, which is low for refractories, beneficial in lightweight aggregate, and probably restrictive for some tiles; chlorite-vermicalite, which is low for refractories and possibly beneficial in lightweight aggregate. In Pennsylvania, clay and shale materials constitute one of the state's major economic mineral resources. To date, the testing program indicates considerable development potential in brick, tile, and lightweight aggregate industries and perhaps a future potential for aluminum from shales that exceed 20% AID..

Jan 1, 1972

By J. Ostachowicz, B. Holynska, M. Lankosz

The paper presents an analyzer and the method for the continuous determination of weight percentage of ore grains with diameter smaller than 75 µm in mineral slurries. The method is based upon the measurement of characteristic x-rays of copper excited by primary radiation of two different energies 16.5 keV and 60 keV from Pu238 and Am241 sources respectively. Additionally the backscattered primary radiation is measured in order to correct the variations of the solids content in the slurry. Since the particle size distribution of slurry can be described by the Rosin-Rammler formula, some calculations have been carried out in order to evaluate the influence of distribution parameters upon the results of the measurements of weight percentage U75 of particles smaller than 75 µm. The influence of solids content and of the copper concentration variation on the results has been also evaluated.1 It resulted from the calculations that the ratio rl/rz, where rl and r2 are the relative intensities of copper characteristic x-rays excited with 16.5 keV and 60 keV photons respectively does not depend on the copper content within the range 1 % to 4% of copper and is slightly dependent on the solids weight fraction and its chemical composition. The change of the dispersion parameter of the Rosin- Rammler distribution from 0.5 to 0.9 results in a change of value of U75 of approximately 3.0%. The results of calculations have been confirmed by the results of laboratory experiments. Therefore, a prototype of industrial analyzer for continuous determination of weight percentage of particles smaller than 75 µm has been designed and made. Its schematic drawing is shown in [Fig. 1]. Slurry is flowing down through steel flow-cell of the length equal to approx. 2 m. In the center, two XRF measuring heads (1) and (2) are located. Each of the heads comprises a rigid waterproof cover (3) with the mylar window (4), in which a proportional counter of resolution 15% for 6.4 keV is mounted with a preamplifier (5). The low- energy isotope source (6) is centrally located above the detector

Jan 1, 1980

By A. Eilers

The year 1874 marks a decided advance in the metallurgy of the West, in two directions. On the one hand, the technical management has been very materially improved, and on the other, the production has been largely increased over that of the previous year. The technical improvements of greatest importance are the introduction of condensation-chambers, or flues, at several works, and the further treatment of the lead matte produced in the ore smelting. These two are of general importance, and although by no means introduced at the majority of works, their adoption at the few where their great importance has begun to be understood will no doubt bring about their universal introduction. To these may be added a third step forward, which for some localities is vital enough, though for others it must still remain doubtful whether it is to be regarded as an improvement or not. This is the introduction, at several

By Gordon M. Matheson, Charles V. Logie

The current state-of-the-art design of mine pillars can be grouped into empirical and numerical design techniques. Numerical design techniques are based on sophisticated computational techniques which analyze the stresses and strains through the interstices of a pillar. Empirical techniques are less exact, but have been widely used, particularly for coal mine pillar design, because of their ease of computation. Over the years numerous empirical equations have been proposed to calculate the ultimate strength of coal mine pillars. This paper presents a review of the various equations which are most frequently utilized and examines the fundamental assumptions, limitations and applicability of the design formulae. The review intends to provide the practicing mining engineer with an understanding of the assumptions and mathematical basis of each equation to aid in the selection of the criteria most applicable to his specific design problems. Recommendations are made of the empirical equations that are presently most acceptable for design.

Jan 1, 1983

By G. Thomas, O. Johari

MEIERAN and Richman' have proposed a method for the determination of electron-diffraction patterns from twinned bcc crystals. It is the purpose of this note to present a general method capable of predicting the positions of all reflections from both matrix and twin regions for all possible orientations of cubic crystals. The method has been verified for twinning in explosively deformed copper, and is found to be a very useful tool when used in conjunction with stereographic projection, and dark-field electron microscopy. Let an isometric crystal be twinned in any (hkl) plane. The twinning can be considered either as a reflection in the twin plane or as a 180-deg rotation about the twin axis. In reciprocal space, the 180-deg rotation about the twin axis would place a given point p, q, Y to a new position P, Q,R, such that both will be equally inclined to the twin axis. This is represented in Fig. 1. If the coordinates of three such pairs of points are determined, the matrix of the transformation can be obtained.' It is also seen that such pairs would satisfy another condition, i.e., the vector [p,q,r] plus the vector [P,Q,R] will yield a multiple of hkl, i.e., the indices of the twin plane, because in isometric systems the axis [hkl] is perpendicular to the plane (hkl). This can be simplified by taking the points along the three axes. If a point h2 + k2 + 12, 0, 0 is taken along the x axis, it is seen that its new indices should be so as to yield a sum 2h2, 2hk, 2hl,i.e., 2h(h,k,1). (Also the points h2 - k2 - 12, 2hk, 2h1, and h2 + k2 + 12, 0, 0 are equidistant from the origin and both points make equal angles with the twin axis, i.e., cos-' h/dh2 + k2 + l2.) Similar operations for the points yield respectively, after the 180-deg rotation about the twin axis. Following the method due to Buerger,' the matrix of the transformation is obtained as follows: Using this matrix the indices of any other point in reciprocal space can be determined. This matrix is much simplified for (111) twinning commonly encountered in fcc metals, since are each equal to —1; hence

Jan 1, 1964

By J. D. Bateman

At Giant Yellowknife, where high grade gold-bearing orebodies are highly irregular in shape, geology has been applied extensively to the mining of ore. The classical functions of the mine geologist in the fields of exploration and mine development have been extended to guide ore extraction, ensuring "clean" mining and effectively reducing waste dilution.

Jan 12, 1951

By Eckley B. Coxe

Having been appointed, on February 19th, 1890, a member of the Commission created by the Legislature of Pennsylvania for the purpose of investigating the " Waste of Coal Mining, with the View to the Utilizing of the Waste" (waste in this case referring specially to the small sizes of anthracite heretofore thrown away), my attention was naturally directed to the mash economical method of burning these small sizes.* Although I had been Familiar with the burning of anthracite for • many years, I found when I came to study the matter carefully that I was far from thoroughly understanding it, particularly with reference to the hurning of the smaller sizes, and that the literature of the subject, which was not very extensive, had more of a tendency to confuse than to enlighten me. I began therefore to investigate the subject so as to arrive if possible at some definite principles applicable to the question. With the aid of my assistant, Mr. John R. Wagner, I began at Drifton a series of experiments upon the burning of small anthracites. We first erected a small furnace with a grate 3 feet long and 2 feet wide, with which we experimented about two months. From the information thus acquired, we designed and built another furnace of about the same size, which gave us facilities for extending our investigations still further. After experimenting several months with the second furnace, we built a third one, which was much larger, having a grate area of about 68 square feet, which was exactly the size of the grate used in the boiler-plants of' Coxe Bros. &

Jan 1, 1894