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INTRODUCTION TO PROBABILITY THEORY The mathematical theory of probability provides the foundation for the interpretations and inferences that can be made from statistical techniques. Probability theory is a broad field of study in itself, and can only be touched on here in order to provide the necessary back- ground for a more complete understanding of statistical analysis. Probability is concerned with the outcome of random events. It had its beginnings in the theory of games of chance which were of great interest to European mathematicians during the last half of the 17th century. The outcome of a random process or experiment is defined as an event. The collection of all mathematical points associated with each event is called the sample space for an experiment. Consider a random experiment having a finite number, n, of possible outcomes, some of which have a characteristic A. What is the probability that A will result from a single

Jan 1, 1980

By Pierre Hines

THE. Owyhee Tunnels in eastern Oregon were started in the early part of 1930, and were completed early in 1932, with the excep-tion of the Magoffin contract. One tunnel is a large water tun-nel, and the other is a small water tunnel; each is approximately tour miles long. Modern equipment was used to full advantage, and remarkably fast time was made during the driving period. The ,J. F. Shea Co., con-tractors, of Portland, Oregon, have broken established records in the smaller tunnel. Their methods are described in detail. The time of a complete round has been reduced by intelligent handling of mechanical shoveling, and this article records some of the useful facts developed. Charles A. Shea (president of the J. F. Shea Co., and secretary of The Six Companies, Inc.) not only granted permission to publish this article, but placed the company's complete daily reports at the writer's disposal. These reports were made out to conform with previous records upon important tunnel work, and enable a comparison to be made of actual averages, rather than ideal cycles, or representative cycles. Gilbert Shea, present superintendent, has been helpful with time, criticisms, and corrections of the information presented. Morton S. Boss, superintendent during the first 15 months of the tunnel work, gave many hours of his time during two visits lasting over two weeks. The whole staff of the J. F. Shea Co. has given encouragement and assistance.

Jan 1, 1933

By Frank Van Horn

INTRODUCTION IN June, 1911, the writer spent a few days in studying the economic geology of the vicinity of Park City. During this rather hurried visit a number of specimens of ore were collected, which have since been examined. The results of these investigations show that bournonite (PbCuSbS3) is present in the ores in greater or less quantity. This fact has never before been reported, as far as can be learned. The failure to recognize this mineral is due to its similarity to tetrahedrite, with which it has probably been confused during a long period of years. Jamesonite (Pb2Sb2S5) has been reported from the region in a rather doubtful manner, but the writer has seen it in notable amounts from several mines, and can offer the first analysis of this mineral from the district. Calamine (H2Zn2SiO6) was found at one mine and has never been recognized and reported from the district.

Jan 8, 1914

By J. E. McDonald, J. G. Eberhart

A model is discussed from which the work of adhcslon .tor liquid transition metals on aluminum oxide surfaces can he calculated, A close-packed (00011 oxygen surface on A12O3 is assumed with two different types of surface sites: one type involving metal-oxygen bonds and the other man der Waals into actions. The work of adhesion is thus expressed as the sum of these two bonsding free energies. Calculated works of adhesion for nickel, titanium, chromium, and zirconium on sapphire agree well with the experimentally determined quantities. The model is extentled to the calculation of the work of adhesion and shear stress required to remove a thin metal film from a sapphire substrate and is in good agreement with experimental values. The obsewed dependence of the work of adhesion on the free energy of oxide formation of the metal is shown to also provide an interpretation of the tittle dependence of thin-film adhesion. THIS paper presents a model for the type of bonding which occurs across a metal-A12O3 interface. The model is used to explain the results of two types of experiments in which such an interface exists: 1) the adhesion of thin metal films on Al2O3 substrates and 2) the wetting of A12O3 by liquid metal drops. The adhesion of thin films to various substrates has been the subject of a variety of investigations.'-' Benjamin and weaver3 and Bowie,6 using the scratch test developed by Heavens,10 studied the adhesion of metallic films to glass substrates. Their observations for noble-metal film adhesion agree well with an adhesion model involving a van der Waals type of bonding between the film and the substrate. For films of metals whose free energy of oxide formation. ?F°f, has a negative value. Benjamin and weaver3 and Bowie6 found a time-dependent adhesion with an initial value that can be interpreted in terms of van der Waals interactions but a larger terminal value which was related to ?F°f, Karnow-sky and Estill7 deposited films on sapphire at elevated temperatures and noticed no time dependence of film adhesion but a similar correlation with ?F°f. Because of the kinetic problems associated with thin-film adhesion it is desirable to examine adhesion in an equilibrium system. The wetting behavior of liquid-metal drops on Al2O3 provides such a system. Systems of this metal-ceramic type have been studied extensively.11 Humenik and Kingeryl2 have measured the wetting of A12O3 (and other substrates) by several metals and have pointed out that the wetting ability of these metals increases with increasing values of -?F°f. It is thus seen that thin-film adhesion and metal wetting on A12O3 are both related to the tendency of the metal to react with the surface oxide ions of the Al2O3 substrate and, because of this, both phenomena should be explainable by an appropriate model for the metal-Al2O3 interfacial bonding. In the sections that follow, wetting and adhesion data on A2O3 are reviewed and a model is presented by which these phenomena can be interpreted. ANALYSIS OF WETTING EXPERIMENTS In an equilibrium system involving a liquid-metal drop on a solid Al2O3 substrate, the work of adhesion, WAD, is defined by the Dupre, equation as WAD = ?s + ?L -?sL [1] where ?s and ?L are the surface free energies of the solid substrate and the liquid drop, respectively, and ?sL is the interfacial free energy. The work of adhesion is the work required to separate a unit area of the solid-liquid interface into two surfaces. The work of adhesion is usually determined from a sessile-drop experiment in which yL and the contact angle, ?, are measured. The Young-Dupr6 equation is then used to calculate WAD Wad = ?L (1+ cos ?) [2] The literature of this subject has been examined and Table I shows work of adhesion data for various liquid metals as measured on A12O3 substrates. The standard free energy of oxide formation of the metal at the temperature of the wetting experiment, ?F°f . is also tabulated in kcal per g-atom of oxygen. The data is grouped according to the gaseous atmos-

Jan 1, 1965

By B. D. Cullity

A distribution of residual stress after plastic elongation is proposed, in which the bulk of the material is strained in compression and a very small portion in tension, This distribution is shown to account both for the X-ray observations and for the effect of plastic straining on magnetic losses in silicon steel. The regions left in compression are tentatively identified with the interiors of the sub-grains revealed by the electron microscope. THIS paper is concerned with the general problem of the nature of the residual stress which is produced in metals by plastic elongation. A particular stress distribution will be suggested which accounts for the main X-ray diffraction observations which have been made. It will also be shown that certain magnetic measurements made on silicon steel can be understood in terms of this stress distribution. X-RAY OBSERVATIONS Uniform straining of a crystal lattice (macro-strain) causes a diffracted X-ray beam to shift its position, and nonuniform straining (microstrain) causes line broadening. If a bar of metal is plastically elongated in the longitudinal x direction and then unloaded, diffracted X-ray lines are observed to be both shifted and broadened.'-= Although the observed line shift indicates the presence of macro-strain, experiments have shown that no macrostrain, in the usual engineering sense of the term, exists.5"7 For example, removal of a layer from one surface of a stretched and unloaded bar does not produce curvature in the remainder of the bar 5'7 Fig. 1 shows the variation of lattice strain in the x direction, as determined from X-ray line shifts, with the applied stress in the same direction. The curve ABC is the normal stress-strain curve of the material, AB being the elastic portion and BC the plastic. In the elastic region AB, the strain measured by X-rays, called the lattice strain, and the strain measured mechanically are both proportional to the applied stress, and both return to zero when the applied stress is removed. Above the elastic limit the lattice strain would be expected to continue to increase along the line BD. Actually, it increases less rapidly with respect to stress, or even decreases, as shown by BE. If the applied stress is then decreased, the lattice strain decreases along EF, which is parallel to AB. As a result, there is a compressive residual lattice strain FA after unloading. STRESS DISTRIBUTION. Since a stretched and unloaded bar does not contain macrostress, it follows that the observed line shift must be due to a special distribution of mi-crostress. Such a distribution is shown in Fig. 2, which shows the variation of the stress u, across a stretched and unloaded bar. The material is assumed to consist of two kinds of regions: regions C, stressed more or less uniformly in compression, comprising the bulk of the volume of the material and responsible for the observed diffrac-

Jan 1, 1963

By D. S. Sanders

IN the four mills of the Cerro de Pasco Copper Corp. in Peru, some 3000 tons of complex sulphide ores are treated daily, with four kinds of concentrates produced: copper, lead, zinc, and pyrite, each containing values in silver, gold, bismuth, and some other metals. Copper occurs in the various ores as chalcopyrite, enargite, tetrahedrite, tenantite, bournonite, and chalcocite; lead as galena; and zinc as sphalerite and marmatite. Small amounts of silver and tungsten minerals are also present. The gangue consist mainly of shale, quartzite, calcite, rhodochrosite, pyrite, and pyrrhotite. In general the values are freed with a relatively coarse grind, about 70 prr cent minus 200 mesh being the finest to which the pulps are ground. In Morococha and Casapalca however. sphalerite particles much finer than this contain inclusions of chalcopyrit r. At Cerro de Pasco the silver and gold are present in all sizes of the ground pyrite.

Jan 1, 1945

By Arnold Hague

In the short time allotted to me* I can only hope to present to you a brief sketch of the main geological features of the country which you are about to visit. My remarks must, of necessity, be more or less incomplete, as my desire is not so much to elucidate any special problem connected with the many interesting geological questions to be found here, as rather to offer such a general view of the region as will enable you, during your five days' trip through the Park, to understand clearly something of its physical geography and geology. The Yellowstone Park is situated in the extreme northwestern portion of the Territory of Wyoming. Its boundaries, as determined by the original Act of Congress setting apart the Park, are very ill-defined. At the time of the enactment of the law establishing this national reservation, the region had been but little explored, and its relation to the physical features of the adjacent country was but little understood. Since that time, surveys have shown that only a narrow strip, about two miles in width, was situated in the Territory of Montana, but it was also found that a still narrower strip extended westward into the Territory of Idaho. The question of properly establishing the boundaries, -based upon our present knowledge of the country, is now before Congress, and an Act has already passed the Senate, proposing to make the northern boundary coincide with the boundary between Wyoming and Montana, and the western boundary coincide with the Wyoming and Idaho line. The Act under consideration extends the southern boundary of the Park to the 44th parallel of latitude, carrying the area of the reservation southward nine and one-half miles. The eastern boundary is made to coincide with the meridian of 109' 30') adding a strip of country about twenty-four and one-half miles in width along the entire eastern side of the Park.

Jan 1, 1888

The following is an incomplete list of members and guests who called at Institute headquarters `during the period Aug. 10, 1918 to Sept. 10, 1918. Amil A. Anderson, Hill City, S. D. A. A. Holland. H. G. S: Anderson, Hurley, N. Al. Paul S. King, Wilmington, Del. Louis A. Barton, Capt., Engineers, U. S. A. Herbert G. Officer, Washington, D. C. K. Baumgarten, lst Lieut., U. S. R. A. B. Parsons. Charles W. Boise, Belgian Congo. Robert R. Pollock, San Francisco, Cal. Henry C. Carlisle, The Pas, Manitoba. Frank A. Smith, Edgewood, Md. J. Ross Corbin, Boyertown, Pa. Edward C. Thompson, Kennett, Cal. S. Le Fevre, Forest Glen, N. V. Malcolm M. Thompson, Morsemere, N. J. Harold P. Ford, Cleveland, 0. Lester C. Uren, Berkeley, Cal. William L. Hogg, Waynesboro, Va. Harold W. Aldrich has been appointed assistant general superintendent of the Inspiration Consolidated Copper Co. at Inspiration, Ariz. Capt. Percy E. Barbour, formerly with the New York State Troopers, has been granted a leave of absence from the Department for the period of the war, by the Governor, and has been appointed Captain in the Engineer Corps, U. S. A. He served on the Mexican border in the New York State National Guard. A. C. Barke, formerly with the United States Smelting, Refining and Mining Exploration Co., has accepted a position with the United States Fuel Co. at' Salt Lake City, Utah.

Jan 10, 1918

By D. H. Bacon

Our Transactions contain so many suggestions of apparently trivial, yet really important, contrivances for the saving of time and

Jan 1, 1893

By G. M. Ritcey, A. W. Ashbrook, E. G. Joe

Solvent-in-pulp extraction of uranium from acid leach slurries of flotation concentrates is described. Solvent extraction was carried out in a 10 in. diam pulsed-plate column. The extractant was a 0.1 M tertiary amine (General Mills Alamine 336) in a kerosene diluent containing isodecanol as an emulsion suppressor and third phase inhibitor. In pilot plant operation at the Beaverlodge mill of Eldorado Mining and Refining, Ltd., slurry feeds containing up to 35% solids were processed at a throughput rate of 13.5 tpd of dry feed. Uranium extraction obtained was as high as 98%. Amine losses to the raffinate were approximately 0.07 lb amine per ton of original dry feed. The Beaverlodge Mill of Eldorado Mining and Refining employs a carbonate leach for the extraction of uranium from the ore.',' Prior to carbonate leaching sulphides are removed by flotation to reduce reagent consumption. This flotation concentrate containing some uranium is then leached with sulfuric acid, filtered, and the uranium precipitated with magnesium hydroxide. The precipitate is then returned to the carbonate leach circuit. Although the tonnage of flotation concentrate treated by acid leaching is low, reagent costs are relatively high. Also maintenance costs on the acid leach filtration circuit were beginning to show significant increases. The choice of solvent extraction-in-pulp as an alternative to the present circuit was influenced by the following factors: 1) elimination of acid pulp filtration, 2) increase in overall recovery because of soluble loss elimination, 3) reduction of reagent cost (mill sodium carbonate solutions are used as strip), and 4) production of higher purity precipitate at the mill site. Because a solvent-in-pulp process would be difficult to test on a bench-scale, the Eldorado experience in the use of pulse columns,3-5 mixer-settlers,6 and solvent-in-pulp operations in particular7 was applied directly to the initial pilot plant carried out during the summer of 1965 and followed by the second pilot plant in 1966. The latter work, which is presented in this paper, determined the following factors for anticipated scale-up to plant production: 1) overall uranium recovery by this process, 2) tonnage throughput expected, and 3) solvent losses anticipated for the full-scale plant. The equipment used consisted of a 10 in. diam extraction pulse column and three mixer-settlers for scrubbing, stripping, and acid equilibration. All equipment was designed by Eldorado and much of the pilot plant was built at the mill site. PROCESS CHEMISTRY Feed to the acid leach plant consists of a sulphide flotation1,2 concentrate containing mainly pyrite, uranium and graphite, with a particle size of 90%

Jan 1, 1968

By George S. Rice

Instantaneous outbursts of gas in underground workings are similar in effect to great blasts of explosives, but without heat effects. Fortunately they occur only in a few localities in exceptional coal fields of the world and under exceptional geologic conditions. Such violent outbursts should not be compared with the ordinary outflows of gas into coal mines or with explosions of gas and dust. The phenomenon is essentially one of gas held in circumscribed areas under very high pressure and as a mining face or heading approaches such a place and the mining excavation sufficiently weakens the natural surrounding dam or shell, this is burst by the pressure just as by the discharge of a mass of explosives. The outbursts, so far as known to the writer, have been confined to coal beds and have not occurred in other mineral deposits. Hence, as discussed later, he believes that it is the relation of the gases to the coal material that is a factor in conjunction with others in producing conditions which permit the phenomena to occur when mining is done. The gases in most instantaneous outbursts have been hydrocarbon gases but in two coal fields they have been definitely found to be chiefly or wholly carbon dioxide. One of these localities in which CO2 outbursts have been frequent and have caused loss of life is in the southern part of the Gard basin, near Alais, in southern France. In 1919, the writer visited the Fontaine mine in this field the day following the occurrence of an outburst by which two men were smothered by carbon dioxide and fine dust. After 24 hr. the CO2 had not been entirely removed by the ventilating current. Occasional outbursts of CO2 have also occurred in other small basins in France, causing accidents, as in Puy-de-Dome. However, mines in the Gard basin, north of those in which CO2 outbursts have occurred, have experienced hydrocarbon gas outbursts. In the Lower Silesian coal field, Germany, there is a group of mines which have been subject to many instantaneous CO2 outbursts, some causing serious accidents, but the greatest disaster occurred recently

Jan 1, 1931

By M. E. Wadsworth, R. D. Groves, B. W. Madsen

Experimental results obtained from large-scale (7 ton), long-term (500 days) leaching of low-tenor copper sulfide ores were interpreted by a geometric model involving the movement of a reaction zone through the ore fragments. The postulated leaching mechanism involved mixed kinetics and included diffusion of the reacting species through the host rock and a chemical reaction at the surface of the mineral particles. Ore properties which were considered were Ore particle size and shape, grade of ore, and mineral content. Excellent agreement between the mixed kinetic model and the laboratory leaching results was obtained when -1/2-in. ore particles were not included in the leach. Also, a satisfactory prediction of copper recovery from +1/2-in. ore with a different particle size distribution was made; however, it was necessary to modify the shape factor in the model. Prediction of copper recovery from an ore sample which included the -1/2-in. fine fraction and leaching for 460 days was 56.5%, and the recovery from leaching was 47.0%. The presence of fines caused solution channeling and a deficiency of oxygen which inhibited the leaching rate. Also, compaction of fines around coarser particles interfered with circulation around the ore particles, and bulk solution transport probably was a rate controlling factor.

Jan 1, 1976

NEW MEMBERS The following list comprises the names of those persons who became members during the period Apr. 10, 1916 to May 10, 1916. ALLEN, WILLIAM R.... Pres., Boston and Montana Development Co., Butte, Mont. BARKER, EDGAR EARL, Min. Engr. Mine Supt., Chile Exploration Co., Chuquicamata, Chile, S. Amer. BAYLESS, JOHN Z., Met. Engr Alaska Gastineau Min. Co., Thane, Alaska. BLACKWOOD, ARTHUR E., Mgr., Sullivan Machinery Co., 30 Church St., New York, N. Y. BREYER, FRANK G., Chief Testing Dept., The New Jersey Zinc Co., (of Pa.), Palmerton Pa. CARPENTER, JAY A., Mill Supt... . West End Cons. Mining Co., Tonopah, Nev. CORLESS, GEORGE BRADFORD, Geol., Missouri Bureau of Geology and Mines, Joplin, Mo.

Jan 6, 1916

By Persifor Frazer

The accompanying diagrams represent a lamp provided with certain improvements which render it more serviceable for the use of the engineer or other mining official who is often compelled to visit several mines a day remote from each other, and may be called on to use the magnetic needle in any or all of them. These requirements demand that the material of which it is made should be copper, and that it should be capable of being closed oiltight, for emptying and refilling the lamp at each mine would be a less expeditious as well as a less cleanly process, and transporting a lamp of the ordinary kind over rough roads on horseback or in wagon, would result in spilling the greater part of its contents. The general form of the lamp, including the false back to keep

Jan 1, 1882

By E. A. G. Colls

Discusses corrosion in Trail chemical plants producing ammonia, sulphuric, nitric and phosphoric acids, ammonium phosphates, sulphate and nitrate, together with miscellaneous allied material problems and their solution using erosion or corrosion proof materials. Conclusion, that for work of this nature, most costly material may well be cheapest in the long run.

Jan 4, 1950

By L. D. Godshall

A great deal has been written of late regarding the loss of silver in assaying; very discordant results have been published by different writers, and much uncertainty exists concerning even approximate losses in a careful determination of silver, as represented by a fire-assay. In the present paper it has been the aim of the writer to determine as accurately as possible the losses sustained by silver, under certain specified conditions, during the process of cupellation. Such losses are well known to be due to absorption by the cupel and volatilization. The conditions, however, which govern these losses are not believed by the writer to be so well understood. The most important of these are : 1. The effect of variable quantities of silver used. 2. The temperature of cupellation. 3. The character and quantity of impurities in the lead button. 4. The weight of the lead button. 5. The nature of the cupel. The following experiments were made for the purpose of demonstrating, as nearly as possible, the total loss of silver in cupellation under the most favorable conditions to be obtained in commercial assaying. Chemically pure silver and pure lead were taken. The latter was obtained from test-lead, first melted into a bar, from which pieces of the desired weight were cut and accurately weighed. The experiments recorded in this paper were planned by the writer, but executed throughout by Mr. J. N. Walker, whose ability as an accurate, careful and painstaking assayer is too well known and recognized throughout the West to require any further endorsement from me.

Jan 1, 1897

By P. T. Carter, A. B. Murad, H. B. Bell

N. A. Gokcen (Michigan College of Mining and Technology, Houghton, Mich.)—The activities of silica, represented in Fig. 5 for the systems MnO-SiO2 and CaO-SiO2, are in disagreement with the established binary phase diagrams. At Ns102 = 0.50 in MnO-SiO2, and at Ns102, = 0.65 in CaO-SiO2, each binary system is saturated with respect to silica at 1550°C, and therefore as102, is unity in each case. The curves for as102 (FeO-SiO2) and as102, (MnO-SiO,) should nearly co-

Jan 1, 1953

The Army Reorganization Act, which became effective July 1, 1916, contains a provision authorizing the organization of an Officers' Reserve, in which will be included a Corps of Reserve Engineers. There will also be an Enlisted Reserve of skilled workmen in technical lines. The special provisions of the bill relating to the Engineer Officers' Reserve were formulated with the help of the Joint Committee of the several national engineering societies, which has been at work on the matter for over a year with the War Department and Committees of Congress. Recognizing that engineering science is the basis of success in modern

Jan 8, 1916

By David M. Hopstock

The performance of the most common type of low-intensity dry magnetic separator is analyzed on the basis of fundamental physical principles. Expressions are developed for estimating the optimal choice of design and operating parameters for beneficiation of magnetite ores. By proper choice of these parameters either a high-grade concentrate or a low-grade tailing can be produced from an incompletely liberated feed.

Jan 1, 1976

By Fred N. Kissell, Natesa I. Jayaraman

Introduction This paper describes a recent Bureau of Mines research project that resulted in a simple procedure for reducing the dust exposure of longwall shearer operators. This project involved the development and testing of a water spray and passive shield system to hold dust against the face and away from the shearer operators. This system is known as the Shearer- Clearer.

Jan 1, 1981