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By J. Chipman, N. J. Grant, J. C. Fulton

This paper contains data on the distribution of silicon between liquid iron-silicon-carbon alloys saturated with respect to graphite and CaO-SiO2-Al2O3 slags under 1 atm of CO at 1600°C. The ranges of slag compositions studied were extended from the dicalcium silicate saturated liquidus composition up to silica concentrations at which Sic appeared as a stable phase. IN blast furnace operation it is not to be expected that slag and metal reach equilibrium with one another. Nevertheless, the silicon content of the metal varies with slag composition and with temperature in a manner which would be predicted from equilibrium considerations. Similarly, the distribution of sulphur between slag and metal does not attain an equilibrium state, yet the influence of slag composition is strongly analogous to its effect on the distribution equilibrium. The desulphurizing power of metallurgical slags has been shown to be highly dependent upon the FeO content of the slag. Moreover, the rate of removal of sulphur from slags is influenced by the oxygen potential of the slag-metal system. Thus it was shown by Grant, Kalling, and Chipman1 that the presence of MnO in slags which are low in FeO causes a marked slowing down of the transfer of sulphur from metal to slag. This led to the hypothesis that the slow removal of sulphur by blast furnace slags of more acid composition might be due in part to the effect of SiO2 on the oxygen potential of the system. This was verified in the work of Grant, Troili, and Chipman,' who found that the desulphurizing power of the more acid blast furnace slags could be markedly improved by an increase in the silicon content of the underlying metal. Their explanation of this improvement was that the higher silicon content of the metal decreased the rate of transfer of more silicon and, along with it, of oxygen from the slag to the metal. The slowness of the transfer of sulphur from metal to slag was the result of the slow reduction of SiO2 from slag to metal. Attempts to study the rate of sulphur removal had in the past resulted in very slow rates corresponding to the rates of silica reduction. It has become evident on the basis of these studies that further experimental studies on the rate of removal of sulphur must take these factors into consideration if there is to be a clear understanding of the rate of sulphur transfer under conditions simulating those existing in the blast furnace. It will be necessary, at least in a part of such study, to employ combinations of slag and metal in which the disturbing effect of silica reduction has been eliminated; in other words, to employ slag-metal combinations which are already in equilibrium with respect to the transfer of silicon. In preparation for such studies of desulphuriza-tion, a preliminary program of research on the distribution of silicon between slag and metal has been undertaken. This will ultimately include a comprehensive survey of the effects of temperature and slag composition on the equilibrium distribution of silicon between slag and metal. The present paper is a report on experimental methods employed and on

Jan 1, 1954

THE strike and dip of bedded formations is readily determined by trigonometry if some marker horizon is intercepted by three holes. If no marker can be identified and if orientation of the cores is unknown, as is the usual case in diamond drilling, the determination still can be made readily by the use of a stereonet if the bearing, inclination, and angle the bedding makes with the core axis is known for each of the three holes. Such determination, valid only if the bedding orientation is fairly uniform within the area drilled, is considered simpler, faster, and more effective than any solution previously published. Method: The steps of this procedure are as follows: 1) Mark north and south poles on tracing paper placed over stereonet.* 2) Plot the three diamond drillholes by drawing a line from the center of the net in the direction of the bearings of the holes. Then rotate the paper until each line, in turn, lies along the equatorial diameter of the net; the end of each line is determined by the inclination of the hole measured in degrees from the periphery toward the center of the net along the equatorial diameter. Fig. 1 illustrates a vertical hole and a hole inclined at —23" due east. 3) With the projection of one diamond drillhole along the equatorial diameter, measure from the end of the hole, to the east and then to the west, a dis- tance in degrees equal to the core axis-bedding plane angle. Find two more points by measuring the same number of degrees north then south along the great circle from the end of the drillhole. Draw a circle, the center somewhere along the direction of the projection of the drillhole, to connect these four points. Draw circles for the other two diamond drillholes in the same manner. See Fig. 1 for two circles representing core axis-bedding plane angles of 35" and 23" and Fig. 2 for these plus a third circle representing a core axis-bedding angle of 42" in a hole bearing S 50 W inclined at —52". 4) Rotate the tracing paper until one great circle on the stereonet is found which is tangent to all three of the circles or parts of circles derived in the previous step. Trace this great circle on the paper and join its ends with a straight line passing through the center of the net. The bearing of this line is the strike of the bedding. In Fig. 2 the bedding strikes N 77 E. 5) Rotate the paper until the strike is along the polar diameter of the net. The dip of the bedding is determined by measuring along the equatorial diameter the distance in degrees from the periphery of the net to the great circle derived in step 4. The dip of plane illustrated in Fig. 2 is 55" to the N 13 W. Fig. 3 indicates the solution for three holes whose bearings and inclinations are N 20 W and —43o, due E and —30°, S 30 W and 23" with core axis-bedding angles of 30°, 50°, and 43" respectively. The bedding (stippled area) strikes N 44 W and dips 70" to the southwest.

Jan 1, 1956

By R. L. Orr, O. D. Sherby, J. E. Dorn

Creep data for pure metals at temperatures above those at which rapid recovery occurs (above about 0.45 the melting temperature) are correlatable by means of the equations and These correlations were applied successfully to data for aluminum, iron, nickel, copper, zinc, platinum, gold, and lead as well as for simple alloys. For a given metal, AH is a constant about equal to the activation energy for self-diffusion. THE early recognition that creep is stimulated by thermal activation prompted numerous investigators', ' to apply the same laws that are valid for the viscous behavior of liquids to analyses of creep data. To a good first approximation these laws are summarized by the equation were i is the creep rate; T, the absolute temperature; R, the gas constant in cal per degree per mol; T, the applied stress; AH, the activation energy in cal per mol; S', a constant dependent on the entropy of activation, the frequency of activation, and the contribution of each activation to the strain; and B', a constant dependent upon the size of the flow unit that is activated. Although Eq. 1 describes the flow of viscous fluids very accurately, its application to the creep of solids has been disappointing. Two reasons for the failure of Eq. 1 for creep are now known: First, the decelerating creep rates during primary creep demand that the internal structures of the metals are changing and that these changes might be reflected by changes in one or more of the three creep parameters S', AH, and B'. Consequently when the conventional methods of evaluating these parameters are employed by comparing the secondary creep rates at a series of temperatures and at a series of stresses, the true effects of temperature and stress are masked because of simultaneous changes in one or more of the creep parameters. Second, as will be illustrated more fully later, three distinctly different types of investigations have shown that the stress term for high temperature creep enters the analysis as and not as t/T. This rather unexpected result points sharply to a significant fundamental difference between the mechanisms for the viscous behavior of fluids and the high temperature creep of metals. More recent extensive investigations",'4 on the creep of high purity aluminum and several of its dilute a solid solutions have shown that where E is the total creep strain; temperature compensated time = for a constant temperature test; t, is the initial stress in a constant load test or the constant true stress in a constant stress test;" and t is the duration of test. • Eq. 2 is valid for either constant stress or constant load tests; but the total creep curve is difierent (i.e. the function, f, is differentl for each test. The fundamental origin of the validity of Eq. 2 is thought to arise from some equivalence of substructures in constant load creep tests at equal values of 0 or E. Both X-ray and metallographic examination revealed that practically identical lattice distortions and subgrain sizes are obtained for the same creep strain under the same load over wide ranges of test temperature.' Furthermore the room temperature tensile properties following equal creep strains at different temperatures under constant loads were also identical, illustrating that identical substructures were indeed obtained.' " A second type of correlation was obtained by differentiating Eq. 2 with respect to time, giving For the secondary creep rate, denoted by i,, But Eq. 2 reveals that 0, is a function of a, alone because the secondary creep rate in a given constant load test is always reached at a fixed value E,". Therefore where is the function that was introduced a number of years ago by Zener and Hollomon." Eq. 4 is not only valid for creep but will permit correlations between constant load creep and tensile data where e, is the rate of tensile straining and (TC is the engineering ultimate tensile strength.

Jan 1, 1955

By Norman Weiss

Most papers on xanthate have dealt with principles rather than practice. On the assumption that many millmen are interested in knowing where and in what manner the xanthates are being used in mills other than their own, this paper will summarize the results of a recent survey of North American plants. A brief background story and a description of the xanthates will be followed with the results of that survey; then a few observations will be made on storage, feeding, and ore testing. The first xanthate was made in 1822 by Zeise of the University of Copenhagen. With commendable scientific detachment (or perhaps a bad cold) Zeise ignored a more pervading quality of the substance and named it for its color, after the Greek word "xanthos," meaning yellow. During the first 80 years of its recorded existence xanthate found use only in small quantity as an insecticide; after the turn of the century there was some further demand for it in the vulcanization of rubber. It was not until 1922, by coincidence the centennial of Zeise's discovery, that C. H. Keller of San Francisco, seeking sul-phidizing agents, recalled xanthate in connection with his experience years earlier when he had seen this material used in Europe to combat grape phylloxera. His successful tests with the new flotation reagent culminated in the basic xanthate patent (U. S. 1,554,216) in 1925. In the minds of many metallurgists the introduction of xanthate as a flotation reagent is identified with the beginnings of alkaline circuits, the first use of chemical collectors, and the beginning of selective flotation. Actually, these preceded xanthate by a number of years. The alkaline circuit in lead-zinc flotation was introduced by Lyster as early as 1912. In 1922 Sheridan and Griswold made their momentous discovery (Timber Butte) that alkali cyanides and zinc sulphate effectively inhibited the flotation of pyrite and sphalerite in pulps made alkaline with sodium carbonate or bicarbonate. The use of lime to retard pyrite in copper flotation began within two years after Ralston directed attention to its possibilities in 1917. These were the beginnings of modern selective flotation, which was practiced successfully on copper-iron ores at Nacozari in 1922, and at Inspiration, Cananea, and others only shortly afterward. In the lead-zinc mills, selective flotation was of even greater economic importance at that time. The Sunnyside plant of U. S. Smelting, Refining, and Mining Co. used the process earlier than 1920, and Consolidated, Timber Butte, and others soon followed. As a chemical collector xanthate was relatively a latecomer, for the Corliss patent of 1917 covered the first of these, alpha-naphthylamine, and the Perkins patent of 1919 the second, thiocarbanilid. Both of these were in extensive use before Keller's xanthate made its commercial debut in 1923. There is general agreement, nonetheless, that the introduction of xanthate was

Jan 1, 1949

By Norman Weiss

MOST papers on xanthate have dealt with principles rather than practice. On the assumption that many millmen are interested in knowing where and in what manner the xanthates are being used in mills other than their own, this paper will summarize the results of a recent survey of North American plants. A brief background story and a description of the xanthates will be followed with the results of that survey; then a few observations will be made on storage, feeding, and ore testing. The first xanthate was made in 1822 by Zeise of the University of Copenhagen. With commendable scientific detachment (or perhaps a bad cold) Zeise ignored a more pervading quality of the substance and named it for its color, after the Greek word "xanthos," meaning yellow. During the first 80 years of its recorded existence xanthate found use only in.small quantity as an insecticide; after the turn of the century there was some further demand for it in the vulcanization of rubber. It was not until 1922, by coincidence the centennial of Zeise's discovery, that C. H. Keller of San Francisco, seeking sulphidizing agents, recalled xanthate in connection with his experience years earlier when he had seen this material used in Europe to combat grape phylloxera. His successful tests with the new flotation reagent culminated in the basic xanthate patent (U. S. 1,554,216) in 1925. In the minds of many metallurgists the introduction of xanthate as a flotation reagent is identified with the beginnings of alkaline circuits, the first use of chemical collectors, and the beginning of selective flotation. Actually, these preceded xanthatc by a number of years. The alkaline circuit in lead-zinc flotation was introduced by Lyster as early as 1912. In 1922 Sheridann and Griswold made their momentous discovery (Timber Butte) that alkali cyanides and zinc sulphate effectively inhibited the flotation of pyrite and sphalerite in pulps made alkaline with sodium carbonate or bicarbonate. The use of lime to retard pyrite in copper flotation began within two years after Ralston directed attention to its possibilities in 1917. These were the beginnings of modern selective flotation, which was practiced successfully on copper-iron ores at Nacozari in 1922, and at Inspiration, Cananea, and others only shortly afterward. In the lead-zinc mills, selective flotation was of even greater economic importance at that time. The Sunnyside plant of U. S. Smelting, Refining, and Mining Co. used the process earlier than 1920, and Consolidated, Timber Butte, and others soon followed. As a chemical collector xanthate was relatively a latecomer, for the Corliss patent of 1917 covered the first of these, alpha-naphthylamine, and the Perkins patent of 1918 the second, thiocarbanilid. Both of these were in extensive use before Keller's xanthate made its commercial debut in 1923. There is general agreement, nonetheless, that the introduction of xanthate was

Jan 1, 1947

By Lane D. Schultz, John D. McLennan, Jean-Claude Roegiers

During construction of the intake tunnels for a nuclear power facility in Ohio, evidence of a potential geological discontinuity was discovered. Assuming that the discontinuity might still prevail underneath the site, it was decided to measure the stress profile across the discontinuity. This information would be used to assess future stability on the basis of predicted shear stresses acting along the fracture. Seven intervals were hydraulically fractured to determine the magnitude and orientation of the stress tensor, in order to infer the shear stresses acting along the discontinuity. The formation consists of tightly interbedded shales. This, in combination with the shallow depths, would be expected to lead to horizontal hydraulic fractures -- a situation which generally provides limited information. Careful testing procedures, and meticulous interpretation, allowed the determination of the horizontal stress components as well as the vertical component, via the initiation and/or propagation of multiple fractures. The measured stresses fall within the range of stress magnitudes and orientation determined in other areas of the northeastern and north-central United States and in southern parts of Canada. In addition, a small stress gradient anomaly was recorded at depth. On a different scale, the measured stress regime is also evaluated in light of the regional geological setting.

Jan 1, 1982

By F. H. Callaway, W. O. Keller

The various theories as to the well spacing-recovery relationship are reviewed in considerable detail and these theories analyzed in terms of their consistency with modern reservoir engineering concepts. It is concluded that the well spacing problem must be analyzed in terms of recovery efficiency and that a positive answer to the relation between well density and recovery efficiency is not available from direct comparisons of the production histories of wells and fields. The results of an engineering analysis designed to permit approximate calculation of recovery efficiencies as a function of well spacing in a depletion type reservoir from basic reservoir data is presented. Results of this type analysis indicate that the effect of well spacing on recovery efficiency in depletion type reservoirs can be expected to be very small. Limitations of this approach are pointed out, particularly with respect to its application in lenticular reservoirs. Testing techniques are outlined which should indicate whether or not a reservoir is continuous between wells and whether or not satisfactory drainage is being obtained with present spacings. A mass of data of this type indicates continuity to exist in most fields. INTRODUCTION The purpose of this paper is to review critically the engineering aspects of the well spacing problem, both from the standpoint of certain concepts and from the standpoint of reservoir mechanics. The well spacing problem is primarily an economic problem in which the optimum well density for a particular field is that density which will yield the greatest oil recovery consistent with justifiable development costs. The well spacing answer in terms of economic conditions, however, is extremely sensitive to the variation in recovery efficiency with well density. The variation in recovery efficiency with 'References given at end of paper. Manuscript received at the office of the Petroleum Branch October 2, 1949. Paper presented at the Petroleum Branch Meeting in San Antonio. Texas, October 5-7. 1949. well density is properly an engineering problem. Different opinions as to the correct answer to this engineering problem is the basis for most of the wide difference in opinion among various members of the industry as to optimum well spacing. This paper will be confined to the engineering problem of the relation between well density and ultimate oil recovery; economic considerations necessary for the evaluation of optimum well density for any particular field will not be discussed. The paper can be logically divided into two parts. The first part deals with a critical examination of the background and logic of the Cutler Rule and of similar studies by other authors and of related well spacing concepts. It is indicated that the variations in recoveries with well density* observed by Cutler and. others can be logically attributed to regional migration. Theoretical justification of the Cutler type relation wherein observed variations in recovery with well density in the same field is attributed to variations in recovery effiiency, in terms of energy relations, is refuted. The second part consists of a review of concepts of reservoir mechanics with regard to the well density-recovery relation. It is indicated that little variation of recovery efficiency with well density can be expected in a depletion type reservoir, unless lenticular conditions prevent communication between wells. The significance of field test data with regard to the existence or non-existence of lenticular conditions is pointed out. THE CUTLER RULE The first published article concerning the engineering aspects of the well spacing problem to receive wide attention was the work of W. W. Cutler' of the U. S. Bureau of Mines, published in 1924. In a study of decline curves from a large *The expression "well density" as utilized herein refers to the number of acres attributed to each well in a uniform well pattern, and is expressed in acres per well. The term "well spacing" Is utilized to denote the average distance between adjacent wells in a uniform well pattern. †Although the Cutler rule is treated critically in this discussion the authors intend no personal criticism of W. W. Cutler or of his hark The currently accepted concepts of reservoir mechanics were no": existent at the time of Cutler's work, as were even the moat basic tools (such as the bottom hole pressure bomb) for observing reservoir behavior.

Jan 1, 1950

By M. F. Goudge

Production of many industrial minerals reached all-time records in 1965. In keeping with the high level of industrial activity throughout the nation, producers of many industrial minerals operated at capacity or near capacity, notably the producers of phosphate, potash and sulfur. In the case of sulfur, the demand exceeded production and orders were filled, in part, from stocks accumulated in previous years. Industrial minerals as a group continued to increase both in value and quantity at a faster percentage rate than metallic minerals and fuels, The U.S. Bureau of Mines estimated that the value of industrial minerals produced in 1963 was $4318 million vs. $2006 million for metals. Preliminary estimates for 1965 indicate that current value of production was again more than 2% times that of metals, thus making apparent their importance to the industrial life of the nation.

Jan 2, 1966

By Adolf Gurlt

It has long been known that minute quantities of foreign substances, when alloyed with steel, are capable of materially altering its physical properties. Thus, half a century ago, Faraday and Stodart, in England, discovered in the famous Indian steel, known as " wootz," small quantities of aluminum, from 0.0728 to 0.693 per cent., and attributed its extraordinarily good quality to the presence of such minute quantities of that metal. Since aluminum is now produced by electrolytic means on a large scale and at low cost, its addition to cast-steel has been frequently recommended of late. Chromium was alloyed with steel fifty years ago by the celebrated French metallurgist, Berthier, of Paris, and has recently been successfully applied to the same purpose by Holtzer, of Terre-Noire. In 1860 titanium was alloyed with crucible steel by Robert Mushet, of Coleford, the alloy containing up to 0.50 per cent. of titanium, which was extracted from Norwegian ilmenite. The titanium-steel was much vaunted by him for its excellent qualities. Rhodium, a very rare metal of the platinum series, was maintained by Berthier to improve steel materially in strength and hardness. Manganese has always been held by Sheffield steel-melters to provide steel with excellent qualities, and this influence was quite recently investigated by H. M. Howe and L. Campredon. Nickel was tried as an addition by Berthier, not to speak of gold, silver and platinum ; and nickel-steel has recently been brought into prominence by J. Riley and others, who recommend it for its great strength and toughness, particularly as material for armor-plates.

Jan 1, 1894

By E. C. Patton

Jan 1, 1947

By E. C. Patton

Jan 1, 1947

By R. W. Nelson

The theoretical basis is presented for energy dissipation methods of measuring permeability in saturated heterogeneous media. Analysis starts with the equation for single-phase flow in heterogeneous porous media which is a first-order partial differential equation in the unknown permeability. This equation is reduced to a system of characteristic equations useful in deriving a differential expression for the permeability as a function of the known potential distribution. For steady flow systems the expression is integrable, giving the permeability integral for direct calculation of the distribution along successive streamlines. The boundary condition in permeability is presented and includes a discussion of the special requirement to assure uniqueness. Theoretical results and necessary computations are incorporated into two general computer programs capable of determining the permeability distribution in two- and three-dimensional steady flow systems. Results are then presented for an energy dissipation analysis using the methods and soltware to determine a field permeability thickness distribution. INTRODUCTION Theoretical work leading to the description of fluid flow in heterogeneous porous media has developed slowly and somewhat sporadically, although the areas of engineering applications predominantly involve flow in nonhomogeneous media. The lack of accurate and economical methods for measuring field permeability distributions has been a major limitation to realistic description of natural flow systems. The economical measurement of permeability using energy dissipation methods may overcome this limitation. Among other things, any permeability measurement method involves consideration of energy dissipation; as used here, "energy dissipation method" denotes the following general approach. The areal energy distribution is measured on an existing flow system in porous media. Then through appropriate analysis of the dissipation of energy in the flow system, the permeability distribution is determined throughout the region using the minimum boundary conditions required to assure a mathematically unique result. This paper presents the theoretical basis for such a method, as well as the techniques and computer software needed to carry out the analysis. The method and techniques are then used in a preliminary field application. EQUATIONS DESCRIBING FLOW IN HETEROGENEOUS MEDLA Heterogeneous as used here implies differing in kind, having unlike quantities or possessing different characteristics. Accordingly, a heterogeneous porous medium has unlike quantities or differing characteristics at different locations. More precisely, if a porous medium is heterogeneous with respect to some property, then that property is functionally dependent on the spatial location. (Media properties are considered here as macroscopic.) Specifically considering permeability k,** then k = G(x, y, z) ,............(1) or the permeability is a scalar function G of the location (x, y, z). Spatial variation of several other properties, of which porosity, dispersivity and medium compressibility are but a few, is implied by the broad title of heterogeneous porous media. The term will be used hereafter to imply only heterogeneity with respect to permeability. The porous medium is considered isotropic as implied by G being only a scalar function. Anisotropy

Jan 1, 1969

By Brij M. Moudgil, John P. Bunch

During hydraulic processing of phosphate matrix enormous amounts of phosphate slimes are produced. Significant portions of mined land are utilized to store the slimes. Some dewatering of the slimes is essential before any reclamation of the storage ponds can be undertaken. Dewatering and reclamation of slimes storage ponds pose many problems which are not encountered in reclamation of other mined areas.

Jan 1, 1977

By Oswald J. Heinrich

SINCE my communication to the Institute at the Baltimore meeting in 1879,* in which I took the lead in emphasizing the importance of a new method in the manufacture of soda, already practiced to some extent in England and on the Continent of Europe, five years have passed. I.then referred particularly to the advantages offered in the United States for this peculiar method, by the ammonia process, namely: 1. At the present time, at least, we have but one mine in this country where rock-salt is mined, namely, at New Iberia, La. On the other hand, we have many localities where brine of various degrees of strength, up to that of cold saturation, is obtained in large quantities. 2. We have excellent fuel, in close proximity to most of the brinecenters. 3. Our supplies of pyrites, to use in the manufacture of sulphuric acid, for use in the manufacture of soda by the Leblanc process, are mostly too far from the brine-centers to permit competition in that line with the more favorable conditions existing in England. 4. Unlike our foreign rivals, we have no large and costly plants, erected on the Leblanc plan, which must be abandoned and exchanged for new but cheaper plants, before the ammonia-soda process can be adopted. 5. We have a constantly increasing demand for soda, which is almost entirely supplied by importation. If slow progress has been made hitherto in this country in the extension of this manufacture (only one plant at Syracuse, erected . under the Solvay patent, having as yet been placed in operation), I still feel gratified in saying that developments in England, and particularly on the Continent of Europe, give ample proof of the

Jan 1, 1885

Arthur Yates, lecturer in the mining department of the Royal School of Mines, London, died at Blackpool, on Feb. 14, 1923, at the age of 47 years. My first acquaintance with him was made in 1902, when taking over the management of the Redjang Lebong gold mines in Sumatra, of which he was the responsible metallurgical officer. For that position he was well qualified by reason of his previous experience with the Rand Central Ore Reduction Co., in South Africa, and particularly by his early training with the Cassel Gold Extracting Co., owners of the MacArthur-Forrest patents, and the first commercial company formed to work the then recently discovered cyanide process; in this connection, Mr. Yates had the advantage of working under J. S. MacArthur himself. Our association in Sumatra was maintained for six years, when I left. Mr. Yates remained and was eventually promoted to the management of the neighboring Soelit mine. During those six years and in the close association inseparable from life in an isolated mining camp, the sterling qualities which made him so good a man were unmistakable: industry and interest in his work, patience with everybody, a quiet and unassuming demeanor. On the exhaustion of the mine to which he had been promoted, he returned to England in 1913. In 1914, the Mining Department of the Imperial College was fortunate in securing his services. Hardly, however, had he settled down when the war broke out and he spent some years in the Cleveland District promoting the efforts of the Government toward greater output. Returning to college in 1919, Mr. Yates met the full flood of Service students. The qualities which made him a man amongst men in the world made him a man among students in the college; a senior student if you like. But, unsuspected, a dread disease had fastened itself upon him, making itself felt for the first time during the summer course he was conducting in the South Wales coal field, in 1922. Against its relentless onset he opposed the bravest optimism, and when at last he realized that he was going under, and was in fact dying, his pronounced regret was that he was leaving the boys. In his death, at the age of forty-seven, staff and students in the Mining Department have experienced a great loss, that of a reliable friend, and their deepest sympathy goes out to the young widow and son in their irreparable loss. S. J. TRuBcott.

Jan 1, 1923

Arthur Yates, lecturer in the mining department of the Royal School of Mines, London, died at Blackpool, on Feb. 14, 1923, at the age of 47 years. My first acquaintance with him was made in 1902, when taking over the management of the Redjang Lebong gold mines in Sumatra, of which he was the responsible metallurgical officer. For that position he was well qualified by reason of his previous experience with the Rand Central Ore Reduction Co., in South Africa, and particularly by his early training with the Cassel Gold Extracting Co., owners of the MacArthur-Forrest patents, and the first commercial company formed to work the then recently discovered cyanide process; in this connection, Mr. Yates had the advantage of working under J. S. MacArthur himself. Our association in Sumatra was maintained for six years, when I left. Mr. Yates remained and was eventually promoted to the management of the neighboring Soelit mine. During those six years and in the close association inseparable from life in an isolated mining camp, the sterling qualities which made him so good a man were unmistakable: industry and interest in his work, patience with everybody, a quiet and unassuming demeanor. On the exhaustion of the mine to which he had been promoted, he returned to England in 1913. In 1914, the Mining Department of the Imperial College was fortunate in securing his services. Hardly, however, had he settled down when the war broke out and he spent some years in the Cleveland District promoting the efforts of the Government toward greater output. Returning to college in 1919, Mr. Yates met the full flood of Service students. The qualities which made him a man amongst men in the world made him a man among students in the college; a senior student if you like. But, unsuspected, a dread disease had fastened itself upon him, making itself felt for the first time during the summer course he was conducting in the South Wales coal field, in 1922. Against its relentless onset he opposed the bravest optimism, and when at last he realized that he was going under, and was in fact dying, his pronounced regret was that he was leaving the boys. In his death, at the age of forty-seven, staff and students in the Mining Department have experienced a great loss, that of a reliable friend, and their deepest sympathy goes out to the young widow and son in their irreparable loss. S. J. TRuBcott.

Jan 1, 1923

By John W. Cahn

Tile avevage value of the mean curvature of surfaces in a specimen can be precisely delermined by sitrlple measurements performed on random sections or on 1 vojectiotzs of these surfaces. For surjaces enclosing particles, the quanlity is sllown to be velated to the probable tlurrrhev ot particles intevcepted by a random platne and, under certain conditions, to the perimeter of their Projected image and to the increuse in surjace area when the particles grow. Many of the velalionsl~ips are valid for any shape or size of the particles. THE recent growth of the field of stereology or quantitative microscopy is largely the result of the discovery of a limited number of rigorously defined geometrical parameters that can be precisely measured on random sections or projections of a structure without assumption about particle shape.' Such parameters have been the volume fraction and surface area and line length in a unit volume. The present paper introduces the average of the mean curvature of surfaces in a volume, and shows that it can be rigorously measured by counting methods alone. AVERAGE CURVATURE ON A PLANE Consider a curve y = v (x) on the xy plane. The curvature Kp in the plane at any point is given by Kp = (dZy/dx2)/[1 + (dy/dx)2]3/2. The average curvature along the curve may be defined as Kp = (1/L) fKpdl |1] where dl = [(dx)' + {dy)2]1/2 is the length of an element of the curve and .(dl = L is the total length of the curve. The integral on the right-hand side of Eq. [l] will be called the total curvature, It is dimensionless and readily evaluated by substituting d = arctan (dy/dx) to give ah which is the change in direction of the tangents to the ends of the curve, Fig. 1. Hence, Kp = (1/L)(?h) [2] It can also be seen that Eq. [2] is applicable in the limit of sharp corners. Even though the curvature is infinite at a corner, f Kpdl remains integrable and equal to the change of angle. The signs of the quantities Kp and dl are arbitrary and, if the areas adjoining the curve are equivalent, there seems to be no compelling reason to fix the signs. For a closed curve, however, it becomes worthwhile to use the signs to distinguish among different types of areas or phases enclosed. For such a closed curve AO = t2r and As a convention, we shall take the direction of the integration along the curve in such a way that the area or phase under consideration (henceforth called a) is kept to the left side of the curve, Fig. 1. Then Kp is positive where the curve is concave and negative where the curve is convex. For a closed curve Ad - +2n if the curve encloses a, and Ad = —2n if the curve is surrounded by a. PLANAR SECTIONS OF THREE-DIMENSIONAL STRUCTURE OF ISOLATED a PARTICLES Consider next a planar section of a microstructure containing particles of a in a matrix. We place no restriction on shape of connectedness of these particles, and begin by considering the curvature of only the boundary between a particles and matrix' Clumps of contiguous a particles are then treated as a single a particle. The two-dimensional section will show in a unit area na simple closed curves enclosing a particles and nh closed curves of holes, in-

Jan 1, 1968

By James R. Evans

Forecasting demand is an art as well as a science, and much personal judgment is required. National forecasts made for sand and gravel, crushed stone, and/or aggregate may be misleading or unhelpful locally. This is because of significant variation in demand within different geographic and/or political areas in the US, and/or the use of an inadequate data base and forecasting methodology. The best forecasts may be made for local or regional market areas, irrespective of geographic or political boundaries, provided a proper data base is available.1 The Bureau of Mines compiles detailed statistics on commodities sold or used in the construction industries and, therefore, is in an advantageous position to make national aggregate demand forecasts.

Jan 1, 1979

By HENRY FA

HENRY FAY (communication to the Secretary*).-In reply to the discussion of my paper, I wish to take this opportunity to express my appreciation to the Chairman and the various gentlemen who have taken part. I regret that others have not offered criticism, for honest differences of opinion often lead to the truth, and suggest new lines of work. An experiment has been made which bears on Prof. Sauveur's discussion and which helps to emphasize the conclusion that cementation is not a factor in the hardening of: the surface. Dr. Langenberg, of the Watertown Arsenal, has heated for me, in vacuo at 1,000° C., a piece of the metal containing a hard surface. The microstructure shows uniform distribution of carbon throughout the metal, showing that no carbon has been added to .the surface and heating in vacuo has prevented any oxidation of the surface.

Jan 6, 1917

By M. M. Fine

In a laboratory study of grinding and classification of silica sand, a satisfactory means of producing the medium-fine specification sand desired by producers of flint-glass containers was developed. The best procedure consisted of ball-mill grinding and double classification, which gave a properly sized sand containing less iron than the feed.

Jan 3, 1950