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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 C. R. Boyd

In 1874 I received an appointment in the corps organized by Col. William P. Craighill, U. S. Engineers, to survey the New or Upper Kanawha river for the purpose of ascertaining the practicability and

Jan 1, 1895

By A. L. Slaughter

The Homestake mine, located in western South Dakota, was discovered in 1876. The first reported production was in I 878. Total production through 1965 is 6,554,249 troy ounces of silver and 27,961,276 troy ounces of gold, worth $987,000,000 at present prices. Precambrian sedimentary formations at Lead total 20,000 feet. The Poorman Formation, the oldest, is chiefly ankerite carbonate. The Homestake Formation is iron-magnesium carbonate. The younger formations are argillaceous with some quartzites. The Cambrian Deadwood Formation unconformably overlies the Precambrian. All are cut by Tertiary intrusives. Sideroplesite schist of the Homestake Formation was converted to cummingtonite schist in the zones of higher-grade metamorphism. The Precambrian rocks show the effects of extreme isoclinal folding. A second stage of folding ( cross folds) may have been caused by the Tertiary intrusives. All folds plunge to the southeast. The Homestake ore bodies are pipe-like replacements of the Homestake Formation in zones of cross folding. It is believed that dilatation of the schists has increased permeability in these zones. Chloritization of the schists is the most widespread effect of the mineralization which is divided into four stages. Principal minerals of the first stage are quartz, chlorite, and arsenopyrite; in the second stage, quartz, ankerite, and pyrrhotite. In the third stage only pyrrhotite was deposited. The fourth stage followed the intrusions of Tertiary dikes and deposited mostly pyrite and calcite. Gold accompanies all stages and is always the last mineral to be deposited. It is most closely associated with arsenopyrite of the first stage but can be interpreted as having been deposited during the fourth stage and superimposed on the products of the earlier stages.

Jan 1, 1968

By B. F. Tillson

ALTHOUGH most accidents occur through the A carelessness or misfortune of the workmen; that is no reason why we should not take all physical precautions practicable. The best way to approach the problem of mine safety is to acquire a personal feeling of responsibility for the accident and then plan how it might have been prevented had we known that it was to occur. A statistical analysis of the physical conditions contributory to accidents will give an indication of some of the methods or mechanisms that should be revised or safeguarded. The handling of rock or ore is a common source of minor injuries. Freedom from accident when mucking largely depends on the skill and care of the workman; this also is true, to a certain degree, to loading cars from chutes, but much can be done in the layout of chutes and their equipment to provide equal safety with less skill. Permanent stagings, or rigid units that may be easily assembled, should be provided so that the men handling the chute boards or gates and barring the jammed chunks will have a convenient safe footing for their operations. A stance to the side of the chute mouth is to one in front, because a man will not be liable to be struck by flying lumps or his bar, should it he caught in the mass, yet in many mines the workmen face the chute when loading a car. Fig. 1 shows the operation of a plank chute having special latches which support the chute boards in such manner that they may be conveniently dropped into place to stop the flow of ore.

Jan 1, 1926

By T. R. Wright

THE Corporation operates concentrators in four camps: Casapalca. Morococha, Cerro de Pa-co, and Mahr. The present concentrator at Cerro de Pasco is the newest having been completed in 1943. and that at Casapalca the oldest, having been built originally as a gravity concentrator, in 1889. Prior to 1925 the Corporation's milling operations were confined to the beneficiation of silver-bearing copper ores, and treatment of these ore: by flotation was started in 1918. Although fairly large deposits of complex, fine-grained lead-zinc ores existed, little progress had been made in the treatment of such ores--in Peru or elsewhere-until the early 'twentics. The Casapalca concentrator began the selettive concentration of complex leadzinc ores by all-flotation methods in 1925, or contemporaneously with the commercial development of selective lead-zinc flotation in the United State:.

Jan 1, 1945

By Hermsdorf, Richard P. E.

AMONG the newer lead smelting and refining plants of the country is that of the United States Metals Refining Co., at Carteret, N. J. Not only is the technical practice here modern and efficient, but exceptional care is taken to assure healthful operating conditions for the employees. One large building houses the entire department, which includes, as its chief units, one reverberatory smelting furnace, one blast furnace, two softening furnaces, one utility reverberatory furnace, two Faber du Faur retorts, five 120-ton kettles, three 60-ton antimouial lead kettles, and one 5-ton kettle for experimental purposes. There is a 10-ton overhead crane in the kettle aisle, which is also used for shipping lead. Other auxiliary equipment is referred to in the outline of operations. A general plan of the plant is shown in Fig. 2, and a general view in Fig. 1. Primary smelting operations are conducted in a 30 by 11-ft. reverberatory furnace with bottom, roof, and upper walls of clay brick, magnesite

Jan 1, 1934

By Robert L. Llewellyn

Preparation of coal begins at the face in underground mines or in the pit with surface mines. Impurities in raw coal can be in the seam itself or in extraneous material taken in mining from the roof or bottom. Raw coal is prepared only to the extent that is necessary to make the product salable. Over 60% of all coal production is processed to some extent in cleaning plants. For underground mines the proportion cleaned is 72% as compared to 42% from surface and 15% from auger mines. Coal supplied for coking purposes is nearly all upgraded by washing, while for the largest market, electric power generation, a high proportion is shipped as a raw product with processing, in whole or in part, only as necessary when excess impurities are mined with the coal. This chapter will deal primarily with plants that process or wash coal to some extent and only incidently with mines shipping raw run-of-mine coal crushed to a top size of, usually, 2 to 4 in., with little, if any, other treatment. ECONOMICS OF COAL PREPARATION During the past decade, major changes have occurred affecting the market, profit, and long-rang planning of the coal industry. Mining companies have become "partners" with consumers at many new and some old mines, both for steam and metallurgical coals. Coal properties have become "assigned" tonnages at mutually agreed upon conditions and prices. Lower unit-train tariffs have been instrumental in helping coal markets to compete against oil and atomic energy. Cod prices for power plants are still on a Btu (British thermal unit) basis but with more emphasis on sulfur content. For metallurgical coal, the lower and medium volatile coals are in demand and the price rises, generally, as the volatile percentage is lower. Moisture affects the Btu value of coal almost the same as ash content, but dusty conditions during loading and unloading are no longer accept-

Jan 1, 1973

By JAMES QATLEY

THE atmosphere, which plays such an important part in the manufacture of iron and steel, is the most variable element involved in its several processes; and particularly is this true of the blast-furnace process, which consumes air in large quantities. At no time since the blast-furnace became an important and widely used apparatus-even when it was operated in the most crude manner-have the variations in composition of the raw materials used been as frequent and as great as the variations in humility of the atmosphere. Important, improvements have been made in the blast furnace and its accessories, such as the hot-blast stoves, the increase in size and change in the shape of the furnace, more efficient blowing engines, the increased protection given to the bosh walls, and the careful preparation of' the raw material, all of which have exerted a pronounced influence on the furnace-operations from a metallurgical standpoint. But during the past eight years little advance has been made in this direction; the fuel-consumption has not diminished, nor has there been any material increase in production. Within that period, however, there has been witnessed the greatest development in appliances for the economical handling of material. So complete has been the work in this direction, that, except in isolated cases, in this country at least., a further extension does not hold out much promise of a satisfactory return on the investment required. It seemed that, with the exception of the gas-engine, we had about reached the limit, for like a strong wall, the atmosphere, with its humility as variable to-clay as when first blown into a primitive blast-furnace, appeared to stand as a Barrier to

Jan 1, 1905

By W. A. Forbes

OUR present-day geological surveys show that 36 of our States are underlain with bituminous coal, covering a total area of 496,709 square miles. The North American continent possesses 69 per cent of the world's coal reserves, with the United States alone having an estimated 55 per cent. The American coal reserves, in tons, are calculated to he about 3,500,000,000,000 tons, of which we have exhausted about 1 to 1 1/2 per cent. If this coal were mined at the rate of the 1918 production-a record output of 579;000,000 tons-it would not be depleted for 4,000 years. The more easily accessible and high-grade coals would obviously be consumed much before this; some estimates are 100 years. The natural progress of the nation's industries up to 1910 encouraged on every hand the development of new mines, especially where cheap and easy access to coal measures was coupled with short hauls to the consumer. Over-development resulted, which is perhaps today one of the fundamental causes for the many difficulties faced by the coal industry, which is highly competitive; about 70 per cent of the production cost is labor. Salient statistics for 1930, recently issued by the U. S. Bureau of Mines, follow:

Jan 1, 1932

By G. H. Cutter

SAFETY in mining depends on wire rope to as great, if not greater, extent than in any other industry. Sudden failure of a shaft-hoist rope might easily result in death or serious injury to the operators and workmen, extensive damage to expensive equipment, and a loss in production while repairs are being made. A wire rope is only as good as its component parts. It must be made from wire properly drawn and treated. It must be fabricated on machines large enough and capable of imparting the necessary qualities to meet the stringent service conditions. However, unless the fundamental requirement of good ropemaking is recognized, all other operations, no matter how carefully performed, will not impart reliability and quality to the product. This fundamental requirement is steel that is homogeneous, of high resistance to fatigue, and of a type suitable for rope wire. Most wire-rope manufacturers agree that rope wire should be made from acid-open-hearth steel. It is comparatively easy to meet the same physical properties with basic steel, but such properties are only part of the requirements for good wire. It is absolutely necessary, particularly for rope service such as mining, where reliability is essential, that the wire be uniform throughout its entire length. Most manufacturers feel that this highly important requirement is better met by acid-open-hearth steel.

Jan 1, 1936

By Paul Weir

FOR the first time in 1938, bituminous coal production for the week ending Nov. 19 surpassed that of the corresponding week in 1937, and indexes of industrial activity indicated the possibility that the remaining weeks of 1938 would run ahead of the corresponding weeks of the preceding year. But regardless of this year-end pickup, total production in 1938 was approximately 25 per cent less than in 1937. The estimate of 340 million tons for 1938 places the bituminous industry slightly above the production level of 1933 and approximately 10 per cent above the modem low of 1932. Anthracite production is not subject to the same extent as is bituminous coal to fluctuations arising out of the rate of industrial activity, hence the decline from 1937 has not been so great being approximately 14 per cent under 1937. The estimate for 1938 production is approximately 45 million tons, but this represents the lowest level reached in the last fifty years with the possible exception of several strike years.

Jan 1, 1939

By AIME AIME

MEXICO embraces one of the great metal and petroleum producing provinces of the world. In this respect its history dates back to the overthrow of the Aztec empire by a Spanish force under Hernando Cortes between 1519 and 1.521. Even before then, its richness in silver and other minerals was not unknown. But it was a treasure house for the Spanish conquerors until the country became independent in 1821. It has been computed that in the 400 years following 1521, Mexico yielded 1.55,000 metric tons of silver, worth $3,000,000,000, two-thirds of the entire world production. In 1935 the country accounted for 36 per cent of the world's silver output, 14 per cent of its antimony (in 1934), 13 per cent of its lead, 3 per cent of its zinc and copper, and 21/2 per cent of its petroleum. Contrary to the impression of some, its gold output is now comparatively small, though important in the past. Its oil, as well, formerly hulked much larger than now, in 1921 being one-fourth of the world output.

Jan 1, 1936

By Chester A. Fulton

SUPPLYING as it does a necessity for healthy animal and vegetable phosphate production is a most important industry. We human beings also are animal as this war so surely proves. Unlike many other elements no substitnite is available for phosphorus or its compounds. Marvelous as are modern plastics none can lake the place of phosphorus in making hone structures. As meassured in these times the phosphate industry is not a large industry. Output of phosphate rock, the original source of our agricultural and ,chemical phophates amounts to only some twelve million long tons per annum in the entire world. Phosphates are compounds of phosphorus, which is always found in nature combined with other elements. It never occurs in nature as such. The first choice of the element phosphorus is tie itself strongly to oxygen and then to water moisture - thus becomeing phosphlic acid. This phosphoric acid in turn hunts around for a base such as lime for instance and together they make phosphate of lime.

Jan 1, 1944

By Tracy C. Jarrett

The alloying of various elements with gold to produce different colors is an old art, but the effect of each element or combination of elements is not generally known. Investigations have been made in this field by F. E. Carter,' E. M. Wise,2 and L. Sterner-Rainer.3 It is the intent of this paper to present in schematic diagrams the effects of various elements upon the color and the melting point of gold alloys. In this investigation 2-oz. melts made in a high-frequency inductiorl furnace were used for all tests. The melting points were determined by the use of a calibrated chromel-alumel thermocouple sealed in a thin-walled alundum tube. The couple was then submerged in the molten metal and the freezing and melting points were determined by using a Leeds and Northrup potentiometer. By checking several melts using copper, zinc and gold, it was found that the accuracy of determining the melting point was within ± 5" F. To determine the differences in colors and to classify them, a wet tissue paper was placed over the polished samples and examined under a uniform white light. The 2 by 45 by 0.045-in. samples were cut from 50 per cent cold-worked strip. The original ingot was 3 by % by % in. This visual comparison, although not scientifically exact, served as a quite satisfactory means for determining and classifying these differences. The base alloys, or "hardeners," were first made up and analyzed, after which the gold and silver were added. This method of making up the alloys was chosen so that the same base alloy could be used for the gold alloys of different karats. The first series consisted of gold, copper, zinc and nickel, the copper comprising from 85 to 65 per cent of the content of the "hardener" and the zinc and nickel replacing copper. The second scries consisted of gold, silver, copper, zinc and nickel, the copper comprising from 85 to 65 per cent of the content of the hardener with the silver, nickel and zinc replacing copper. There was no particular reason for choosing these combinations, except that they gave a color range from red-pink to white.

Jan 1, 1940

By Tracy C. Jarrett

The alloying of various elements with gold to produce different colors is an old art, but the effect of each element or combination of elements is not generally known. Investigations have been made in this field by F. E. Carter,' E. M. Wise,2 and L. Sterner-Rainer.3 It is the intent of this paper to present in schematic diagrams the effects of various elements upon the color and the melting point of gold alloys. In this investigation 2-oz. melts made in a high-frequency inductiorl furnace were used for all tests. The melting points were determined by the use of a calibrated chromel-alumel thermocouple sealed in a thin-walled alundum tube. The couple was then submerged in the molten metal and the freezing and melting points were determined by using a Leeds and Northrup potentiometer. By checking several melts using copper, zinc and gold, it was found that the accuracy of determining the melting point was within ± 5" F. To determine the differences in colors and to classify them, a wet tissue paper was placed over the polished samples and examined under a uniform white light. The 2 by 45 by 0.045-in. samples were cut from 50 per cent cold-worked strip. The original ingot was 3 by % by % in. This visual comparison, although not scientifically exact, served as a quite satisfactory means for determining and classifying these differences. The base alloys, or "hardeners," were first made up and analyzed, after which the gold and silver were added. This method of making up the alloys was chosen so that the same base alloy could be used for the gold alloys of different karats. The first series consisted of gold, copper, zinc and nickel, the copper comprising from 85 to 65 per cent of the content of the "hardener" and the zinc and nickel replacing copper. The second scries consisted of gold, silver, copper, zinc and nickel, the copper comprising from 85 to 65 per cent of the content of the hardener with the silver, nickel and zinc replacing copper. There was no particular reason for choosing these combinations, except that they gave a color range from red-pink to white.

Jan 1, 1940

CONTENTS PAGE ANDERSON, ROBERT J., and ENOS, GEORGE M.-Corrosion of Brass as Affected by Grain Size. Discussed by Henry S. Rawdon, Robert J. Anderson, Francis B. Coyle, William B. Price, and W. R. Webster 1 RAWDON, HENRYS., and MUTCHLER, WILLARD H.-Effect of Severe Cold Working on Scratch and Brinell Hardness. Discussed by W. H. Bassett, John Livermore Christie, John R. Freeman, Jr., W. R. Webster, William B. Price, Norman B. Pilling, D. J. McAdam, Jr., F. G. Smith, Zay Jeffries, F. E. Carter 3 WILLIAMS, ROBERT S., and HOMERBERG, VICTOR 0.-Relation of Heat Treatment to the Microstructure of 60-40 Brass. Discussed by 0. W. Ellis 14 Corrosion of Brass as Affected by Grain Size Discussion of the paper of ROBERT J. ANDERSON and GEORGE M. ENOS, presented at the New York Meeting, February, 1924, and issued as Paper No. 1282, with MINING AND METALLURGY, December, 1923. HENRY S. RAWDON,* Washington, D. C. (written discussion).-So numerous and so varied are the factors that affect the corrosion of metals that particular care is necessary in corrosion tests to eliminate so far as possible all extraneous factors. It appears to the writer that the question may well be asked as to whether all the necessary precautions have been observed in this investigation. It may be that the points to be mentioned were considered by the authors and found to be insignificant; however, there is nothing in the report to show this.

Jan 5, 1924

By Tracy Jarrett

THE alloying of various elements with gold to produce different colors is an old art, but the effect of each element or combination of elements is not generally known. Investigations have been made in this field by F. E. Carter,1 E. M. Wise,2 and L. Sterner-Rainer.3 It is the intent of this paper to present in schematic diagrams the effects of various ele¬ments upon the color and the melting point of gold alloys. In this investigation 2-oz. melts made in a high-frequency induction furnace were used for all tests. The melting points were determined by the use of a calibrated chromel-alumel thermocouple sealed in a thin-walled alundum tube. The couple was then submerged in the molten metal and the freezing and melting points were determined by using a Leeds and Northrup potentiometer. By checking several melts using copper, zinc and gold, it was found that the accuracy of determining the melting point was within ± 5° F. To determine the differences in colors and to classify them, a wet tissue paper was placed over the polished samples and examined under a uniform white light. The 2 by ½ by 0.045-in. samples were cut from 50 per cent cold-worked strip. The original ingot was 3 by ¼ by ¾ in. This visual comparison, although not scientifically exact, served as a quite satisfactory means for determining and classifying these differences. The base alloys, or "hardeners," were first made up and analyzed, after which the gold and silver were added. This method of making up the alloys was chosen so that the same base alloy could be used for the gold alloys of different karats. The first series consisted of gold, copper, zinc and nickel, the copper comprising from 85 to 65 per cent of the content of the "hardener" and the zinc and nickel replacing copper. The second series consisted of gold, silver, copper, zinc and nickel, the copper comprising from 85 to 65 per cent of the content of the hardener with the silver, nickel and zinc replacing copper. There was no particular reason for choosing these combinations, except that they gave a color range from red-pink to white.

Jan 1, 1939

By J. F. Myers

AT the Regional meeting in Columbus, Ohio, in September 1949, the authors presented a progress report of the first year's operation with a Hardinge tricone mill in closed circuit with a Dorr hydroscillator. The present report covers our findings on this grinding circuit to January, 1950. In order to clarify our position, the authors wish to state that no invention or discovery is claimed. The Tennessee grinding circuit is simply an engineered arrangement of known equipment arranged to incorporate all of the recognized efficiency factors of comminution as they are known today. As we concluded our first report, it was not clear how effective the Tennessee mode of operation would be on harder ores. The only information we had at that time was that the Bond grindability test at 48-mesh gave 6.04 g of undersize per revolution. A later test on the same sample at 100-mesh reduced this to 2.04 g, which is definitely in the harder ore class, and which makes the reported 8.80 kw-hr per ton of -200-mesh produced a very creditable figure.

Jan 1, 1950

By Ralph W. Smith

DEVELOPMENT of the lime industry- in Ste. Genevieve County began in a crude way in 1840. According to information furnished by the Missouri Bureau of Geology, in the early days small vertical kilns built of stone were used, and wood was the fuel. Modern development began in 1904 when one company introduced steel shells lined with firebrick. Within a few years two more companies erected similar plants, and in 1925 a fourth company began operations. Thus there are today four lime companies at Ste. Genevieve, all operating at high capacity and with a gradually increasing production. GEOLOGY The limestone of Ste. Genevieve County, which has the chemical composition and purity required for lime burning, is the upper 80 or 90 ft. of Spergen formation. The Missouri Bureau of Geology, in its geological map of Ste. Genevieve County, gives the Spergen formation a total thickness of 160 ft., but only the upper portion is pure enough for lime burning, with an average raw-stone analysis of 98.7 per cent CaC03; 0.35 Si02; 0.3 R203; 0.35 MgCO3; 0.3 S03. The Spergen, one member of the Meramac group, Iowa series, of the Mississippian system, underlies an area approximately 12 miles long north and south, by 5 miles wide east and west (Fig. 1) in Ste. Genevieve County. The entire eastern two-thirds of Ste. Genevieve County is sedimentary, the formations dipping gently toward the east on an average grade of about 4 per cent, or 2 ½ º. Thus the outcrops of the various sedimentaries run approximately north and south. A line running west from Ste. Genevieve crosses the outcrops of the sedimentaries, ranging from the top of the Mississippian to the Ozarkian geological system in a space of 12 miles. Thus with the gentle dip of 2 ½ º the 160-ft. thickness of the Spergen formation stretches out in its outcrop so that it is approximately one mile

Jan 1, 1938

By L. S. Darken

IT has long been recognized that the driving force in an isothermal diffusion process may be regarded as the negative gradient of the chemical potential (partial molal free energy) of the diffusing substance. This equivalence is exactly analogous to the fact that a mechanical force is the negative gradient of the potential energy. Nernst1 in 1888 expressed these driving forces in terms of osmotic pressure, which is directly related to the chemical potential and free energy. The relationship between the diffusivity, mobility and activity coefficient of electrolytes in aqueous solution has been developed in great detail by Onsager and Fuoss2 with results which have recently been confirmed experimentally by Harped and Nuttall.3 This interpretation of the driving force in isothermal diffusion has been discussed earlier by the author 4.6 who pointed out4 that "for a system of more than two components it is no longer necessarily true that a given element tends to diffuse toward a region of lower concentration even within a single phase region"; departure from the behavior of an ideal solution may be so great that the concentration gradient and the chemical potential gradient, or activity gradient, may be of different sign, thus giving rise to "up hill" diffusion. Since, in the discussion of that paper,4 some skepticism as to the validity of this conclusion was expressed, it seemed desirable to adduce experimental evidence to support it. Evidence of such diffusion in nonmetallic systems has already been reported. For example, it was observed by Hartley11 in a series of experiments in which sodium chloride diffused from a saturated solution in about 5 pct acetone in water into a solution virtually free of salt but with essentially the same acetone concentration. Specifically, a wine glass containing crystalline salt and saturated solution was totally immersed in a large glass cylinder containing the acetone-water solution without salt; the difference in specific gravity was such as to prevent convection. Diffusion of salt was accompanied by a marked depletion 0f acetone in the wine glass; after 3 days the acetone concentration decreased from 5.37 pct at the top of the glass, where the salt concentration was low (0.93 pct), to 1.84 pct at the bottom where the salt concentration was high (21.64 pct). This "uphill" diffusion was found to be such that the partial pressure (activity) of acetone was essentially equalized throughout the system when a steady state gradient of sodium chloride was maintained. In order to demonstrate the existence of such diffusion in metals, a series of four weld-diffusion experiments was made. In these measurements pairs of steel of virtually the same carbon content, but differing markedly in alloy content, were welded at the end and held at 1050°C for about two weeks. Subsequent analysis showed that carbon had diffused so as to produce an inequality

Jan 1, 1948