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By Jürgen F. Brune

The Fourth Industrial Revolution, that of digital technologies and their application, is rapidly impacting the mining industry, as it is manufacturing, transportation, agriculture, trade, and most other industries. Mining is about 40,000 years old and has its origins in Africa. Since its earliest days, it has experienced four distinct “revolutions” that each resulted in significant improvements in production, productivity, and safety and health: The First Revolution in the fifteenth through eighteenth centuries brought technologies that improved miners’ lives and health, including pumps, forced and mechanical ventilation with wind catchers and bellows, the wire rope and black powder, to name a few. Many simple, muscle- or water-driven machines have been pictured and described in great detail by Agricola who wrote De Re Metallica in 1556. Agricola was familiar with, and concerned about, accidents where miners fell off rotten, wooden ladders, acrid smoke, and dust that caused respiratory illnesses and diseases. He also knew the dangers of fatigue and recommended that miners should sing aloud to prevent them from falling asleep.

In this study, numerical simulations of yield pillars employing the finite element method with time-dependent Drucker-Prager material model are conducted. The stress control mechanism of yield pillars on weak floor strata is studied. The development of pillar yield zone, the distribution of pillar stress and the development of failure zone in the weak floor strata are investigated. The study indicates that a properly selected yield pillar size may significantly reduce the peak stress induced in the weak floor strata and effectively control the development of failure zone in the floor.

Jan 1, 1999

By W. J. Bronkala

Dense-medium circuits have been installed in many mineral treatment plants since its, original development about thirty years ago. In the intervening, period the process has been thoroughly evaluated and many innovations have been introduced. The Heavy Density. Cyclone is one of the newer systems which has extended the operating range of this process to 65 mesh size. Several different finely divided materials have been used to produce the separating bath but nearly all new plants use a ferro-magnetic medium. The, advantages of magnetic medium include: 1. Smaller recovery plant 2. Lower cost recovery plant both in initial and operating cost 3. Excellent medium stability 4. Dependable medium supply at reasonable and stable cost. Magnetic separators are used to recover this magnetic medium and the smaller plants and lower operating costs are directly related to their use.

Jan 1, 1964

By R. A. Burns

The production of kaolin and calcium carbonate in North America exceeds 13 million tons sold into higher value market segments. With a few exceptions, the markets supplied exhibit mature growth rates. In some market sectors, technology changes have and continue to occur shifting pigment-type consumption and growth. New sources of supply will impact current businesses. New product and process developments for kaolin and calcium carbonates are continuing. Each of these issues is examined in developing a view of the future for kaolin and calcium carbonate in North America.

Jan 1, 1997

By M. L. Clark

Advances in the recovery of gold from heap leaching are being made daily, but of all the systems vital to the maximum recovery of gold from a leach pile, none is more important than the methods used to construct the pile in preparation for the leaching operation. The technology described in this paper illustrates the latest systems developed to minimize compaction in the pile during its construction and reduce the cost of placement of ore on the pile. The Florida Canyon Mine of Pegasus is evaluated in detail to show reasons for its high degree of success to date.

Jan 1, 1988

By G. Rainville, I. Servi, F. Katrak

Despite the severe drought conditions that reduced farm requirements for industrial mineral products, most industrial minerals markets in 1988 continued their growth or, at worst, remained flat. Earlier projections of output declines did not materialize in most segments. Preliminary estimates of demand in Europe and Asia show strong growth for most industrial minerals. Profitability in industrial minerals in North America was best in those minerals that had a significant export market or were not strongly regional. Growth and price trends in the more regional industrial minerals markets in the US such as sand and gravel, crushed stone, and cement, more closely followed the broadly disparate regional economic conditions. For example, sand and gravel and crushed stone grew strongly in the Pacific Coast and northeastern markets but not as much as in the Southeast. Total growth for sand and gravel in 1988 is projected at about 3% above 1987 levels. Combined production is up about 27 Mt (30 million st) to 2 Gt (2.2 billion st). Following the relentless trend of foreign acquisition of US cement companies (currently about two-thirds are owned by foreign interests), several aggregate operations have been purchased by foreign companies. Notable among these in 1988 was the acquisition of Rinker Materials Corp. by CSR of Australia. The acquisition of this Florida-based aggregate and concrete operation will expand the current holdings of CSR in the southeastern US, with operations consolidated under the Rinker logo. In addition, Pike Industries of New England and J.L. Shiely Co. of Minnesota were significant aggregate producers that were acquired by foreign firms. New England's only cement manufacturer, Dragon Products, was acquired by a subsidiary of Cementes del Norte of Spain. Dravo continued to expand its influence in the lime and limestone markets. It became the major supplier of construction aggregates on the inland river system with its purchase of Cyprus Minerals' limestone aggregate operations in Kentucky, Louisiana, and Texas. Although lime production continued to grow from 14 to 15 Mt (15.7 to 16.7 million st) in 1988, lime imports decreased for the fifth consecutive year to 145 kt (160,000 st). In the more export-oriented industrial minerals markets, performance was generally very good for 1988. Soda ash enjoyed an excellent year, with its price up to $102.50/t ($93 per st). This reflected the tight market situation for soda ash, particularly in late 1988. Soda ash production in 1988 was 8.6 Mt (9.5 million st), reflecting the industry's improved efficiency. Particularly significant was the increase in caustic soda prices that led to increased substitution by soda ash. The export market remained at 2.1 Mt (2.3 million st). Phosphate production recovered to the 42 Mt (46 million st) level, a 12% increase despite a soft export market. The price, however, remained soft throughout the year. W.R. Grace sold its interest in its Florida phosphate mine and its phosphoric acid complex as part of its divestiture of the agrichemicals business. The strengthening of the major producers has continued as lower cost capacity has been idled. Future permitting of phosphoric acid facilities and development of reserves will be necessary to maintain current production levels beyond the mid- to late 1990s. Despite new developments worldwide in the titanium minerals market, strong demand has continued to apply pressure to price, with concentrate and slag prices going up. The demand for high quality slag as feedstock for pigment production has resulted in process improvements in South Africa (Richard's Bay) and in plans by Canada to import high quality ilmenite by 1991 to produce a 90% TiO2 slag. Although growth in industrial silica sand applications was small in 1988, concentration in the industry continued. Unimin continued to acquire silica operations. Unimin is now the nation's leading producer of granular silica. The end users of silica have consolidated further. Owens-Illinois purchased Brockway Inc., a leading container glass producer. Three companies now control 75% of the container glass industry. ECC continued to be an aggressive purchaser of industrial minerals operations throughout the world. It acquired Cyprus Minerals' calcium carbonate business as well as two operations in Italy. In addition, ECC continued its aggressive acquisition of kaolin (Australia) and aggregate producers. 1988 was a good year for industrial minerals markets worldwide. More importantly, though, it was a year that showed continuing consolidations of reserve ownership in the industry around the world. Barite AN. Castelli, Baroid Drilling Fluids Inc. US mine production of barite decreased 9.4% during 1988. Consumption (sold or used by grinding plants) increased by 37.9%. Imports are estimated to have increased by 21.2%. World mine production decreased by 9.8%, according to the US Bureau of Mines. The value of domestically produced barite, fob mine, decreased 4.6%, according to the Bureau. The declared value cif US port of all imported ground barite during the first 10 months of 1988 increased from $37.16/t ($33.71 per st) in 1987 to $37.92/t ($34.40 per st), according to Bureau figures. Nevada continued to be the leading producer of barite with 72% of the total, followed by Georgia and Missouri. The Bureau of Mines estimates 69% of US mine production was used as a weighting agent in drilling fluids. The other 31% was used in barium chemicals, glass, or as a filler. Most of the production from Missouri, Georgia, and Tennessee was used in the non-oilfield sector. Of the total consumption used by grinding plants and chemical manufac-

Jan 1, 1989

By D. J. Collins

While the charcoal in pulp (CIP) process was introduced to the mining industry many years earlier, it did not gain widespread recognition until 1973 when Homes take Mining Company installed a CIP circuit at their Lead, South Dakota plant. Since then, a number of mills have been put into production which utilizes activated charcoal for the recovery of precious metals. One of these plants was the Jerritt Canyon mill which Freeport Gold Company commissioned in 1981. It was during the time that the author was employed by Freeport Gold Company that the ideas and concepts presented in this paper were formulated.

Jan 1, 1989

By C. D. Litton

This paper describes two new gas diagnostic techniques which have been used successfully to determine: 1) the combustion status of underground mines which have been sealed due to fire (Littol1 Ratio); and 2) the location of fires in abandoned, underground mines or waste banks (Kim Ratio). The Litton Ratio makes use of the rate of change of CO, calculated on both an air-free and methane-free basis, from mine gas samples and compares these values with those expected from a normal, combustion-free environment. The Kim Ratio uses the concentrations of total hydrocarbons, C2 ?C5, less the methane, to arrive at ratio values which increase as combustion intensity increases. The details of these two new techniques, their application to real situations, and their limitations will be discussed.

Jan 1, 1989

By D. Olsen

The paper discusses the legislative and practical approach adopted to problems of management of environment in relation to coal mining in a very sensitive area of the south coast of New South Wales. The environmental problems are complicated in this area due to multiple and very often conflicting land usages. The environmental approach in relation to water quality maintenance, noise control and air quality is discussed and methods adopted meet stringent requirements. Requirements of New South Wales Regulations on Environmental Impact Statements (EIS) are described.

Jan 1, 1988

By Richard O. Y. Breese

Geologically and commercially, the term diatomite is applied to the nearly pure sedimentarv accumulation of diatom frustules- the microscopic skeletons of unicellular aquatic algae belonging to the class of golden brown algae, bacillariophyceae. The sediments are fine-grained, siliceous, and consist primarily of amorphous opaline silica with only minor amounts of organic residue, secondary minerals, and co-deposited non-diatomaceous or crystalline clastic debris. In the geological sense, the name diatomite implies sedimentary accumulations that have reached appreciable thickness and when thick enough, such accumulations consequently may have possible commercial potential. Although the term diatomite is popularly and inappropriately applied to any sediment in which there is an abundance of diatom frustules, alternative terminology is more correctly employed to describe the less pure diatomaceous sediments, for example: clay-bearing diatomite or diatom-bearing clay. Synonyms in current usage include diatomaceous earth and kieselghur. More antiquated and obsolete terminology includes tripoli-powder, tripolite, and infusorial earth. Worldwide, diatomites occur within Tertiary to Recent lacus- trine and marine sedimentary facies. Although diatomite is wide- spread throughout the world, deposits that contain high purity, commercially versatile ore are uncommon. Physical properties of the diatom and of processed diatomite that provide unique commercial value in a broad spectrum of market end-uses include ornate fine structure, low bulk density, and high porosity and surface area. Properties of equal importance are mild abrasiveness, high absorptive capacity, insulating ability, relative inertness, and high brightness. End-use markets are diverse and range from insulating brick and absorbents through quality sensitive filter aids and premium quality functional fillers. Notwithstanding both the economic attractiveness of the specialty markets and the commercial versatility of the high purity deposits, deposits of lesser purity are mined in nearly all parts of the world for less demanding uses. Mining costs are minimized through open pit quarrying, but in Europe, Asia, Africa, and South America underground mining methods are also employed. Blasting is not required because diatomite is soft and easily broken loose with mechanized equipment. Following gentle crushing, the ore is dried, milled, and processed into one of three broad categories of products: naturally milled, straight calcined, and flux calcined grades. Each of these principal categories is further subdivided into additional grades through particle size adjustment of the powders. Agglomeration of particles, alteration of fine structure, and color change are achieved through calcination. Flux calcination further accentuates these changes. Production throughout the world is dominated by the United States, followed by Romania, the former Soviet republics, and France. Other major producers include Spain, Mexico, Iceland, Korea, Japan, and Germany. Denmark is a major producer of Moler earth products, which consist of a diatomite-clay mixture. HISTORICAL BACKGROUND The first industrial use of diatomite can be traced back some 2000 years to the Greeks and to the use of diatomaceous earth as a component in lightweight building brick and in ceramic pottery. It was not until the mid-1800s, however, that the unique properties of diatomite were first recognized and the market end-uses explored and developed. One of the most important of the early uses followed the development of dynamite by Alfred Nobel in the mid-1860s, whereupon diatomite was used as a component of the explosive to improve stability and safety. Other early uses included low temperature insulating and refractory bricks and as a component in insulating and fireproofing construction panels. During the 1920s, processing technology underwent a very rapid evolution with the development of calcination, flux calcination, and air classification technologies. Through these technologies, innumerable different size and grade classifications could be made for market applications and for rapidly diversified end- uses. Today, the application of processed diatomite for filter aid is the largest of the quality sensitive end-uses. Specific filtration uses include the clarification of beer, wine and liquor, vegetable oil, syrup and sugar, pharmaceuticals, and swimming pool water, to name a few. As a functional filler and extender, processed diatomite is ideally suited for application in paint, rubber, and plastic formulations. Other filler applications include use as an anti-blocking agent in plastic film, anti-caking agent for fertilizer, thermal insulating material, catalyst carrier, polish, abrasive, pesticide and fertilizer carrier, and chromatographic supports. Throughout much of the world diatomite is still used as a component of insulating brick and as an absorbent.

Jan 1, 1994

By F. Kennedy

Consolidation Coal Company (Consol) supports an active R&D effort to improve the safe, productive mining of coal and to utilize coal in an environmentally acceptable manner. Attention will be focused on degasification of coal seams, continuous coal transport systems, earth sciences activities, and coal combustion. Brief mention will be made regarding the SO2 emissions control programs. The research program constitutes about 1.0% of Consol coal sales which positions Consol as the preeminent coal company supporting broad-based research addressing the full spectrum of the various problems associated with utilizing the nation's abundant reserves of economical, readily available fuel.

Jan 1, 1989

By R. W. Brann, R. C. Freas

Franklin Industrial Minerals operates several mines/quarries, including two room and pillar underground mines. Both of these mines are operated as multiple level room and pillar including heading and bench operations on one or both of the levels. This paper focuses on Franklin’s Crab Orchard, Tennessee mine, which produces both high purity chemical grade limestone and crushed stone for construction applications. The high purity chemical specifications for the chemical grade limestone and filler/extender applications are inconsistent with the non-chemical rock being produced to supply the crushed stone market. As a consequence Franklin has developed a unique mine plan and operation to maintain both product balance and a safe and stable working environment.

Jan 1, 2003

By Carolina Bruecker, Axel Preusse

"The topic of ground movements in Germany has been studied extensively in the past, especially in the field of active mines. The active hard coal mines were finally shut down in 2018 in Germany and lignite mining is expected to take place only until 2038. The so-called long-term liabilities of the mine operators in Germany include, among other things, the long-term guarantee of stability and thus the monitoring of ground motion.So far, the economic use of underground mining in Germany was mainly the supply of raw materials. In the future, the underground storage of compressed air, methane, or hydrogen will play an important role in renewable energy supply and climate change. Therefore, underground storage space will become more important and spatial planning is essential to ensure availability of safe underground openings for the various options of environmentally friendly energy storage.However, this renewed usage of underground openings may also bring new and sometimes unknown challenges of geomechanical influence. On the one hand, the aftermath of hard coal and lignite mining will be an increasing challenge in mining subsidence engineering. On the other hand, new possibilities due to underground spatial planning may lead to subsidence and/or heaving of the upper surface.INTRODUCTIONBoth hard coal and lignite have a long tradition in Germany. The Prosper Haniel mine in the Ruhr area was closed at the end of 2018 after 150 years, which signalled the end of hard coal production in Germany. Lignite mining still takes place in the Central German, Lausitz, and Rhineland districts. However, lignite mining in Germany is expected to be phased out gradually by 2038 (MDR, 2019). With the closure of these mines, however, mining damage is not over. The long-term consequences of mining, which extend far beyond the closure of the mines, are associated with the liability and responsibility of the individual mining companies. The so-called eternity burdens on the mining company continue to apply. In the field of lignite production, the discontinuation of dewatering and the resulting possible elevations of the surface will be a relevant topic for the future of mine surveying. The same applies to the hard coal mines, which are partially flooded in Germany and therefore require extensive monitoring of soil movements in the future.The discontinuation of energy from hard coal and lignite calls for a change in the energy mix. With the renewable energy revolution in Germany, the focus is on a sustainable and environmentally compatible climate and energy policy based on renewable energies. Sustainable use of the subsoil, both natural and anthropogenically produced cavities, will play an essential role in the objectives of this policy. For example, disused mine cavities can be used to store electricity from renewable energy sources. (Umwelt Bundesamt, 2018) These functions will again cause classical ground movements such as subsidence and uplift, but will also bring new challenges for the mine surveyor. Challenges can be underground cavity exploration in inaccessible areas or legal aspects of underground competition."

Jan 1, 2019

The stability of mine roofs in permafrost zones is determined mainly by temperature and ice content. The deformation resulting from creep and temperature dependent physical properties of frozen rockmass is the dominant component of total deformation. Roof bolts can consolidate the roof and control its deformation. In this paper, a finite element model for analysis of the effects of roof bolting in a frozen rockmass is presented. The model includes the variables normally encountered when analyzing the effects of roof bolting in rocks. It also accounts for properties unique to frozen rockmass, creep deformation and the change in Young's modulus with changing temperature. The model shows that, as bolt spacing decreases, there is a trade-off between increased roof stability from increased mechanical support and decreased stability from increased conduction of heat into the frozen roof. This result was expected, and shows that, for a given set of rockmass conditions, including ice content, temperature, particle size, etc., there is an optimum bolt length and bolt density for minimum roof deflection.

Jan 1, 1996

By E. A. Metz

Silicon dioxide, silica, is the most common oxide in the earth' s crust. The health effects of silicon dioxide dust have been known since Biblical times. Agricola's book, published in the mid 1500's on occupational medicine, described a lung disease that afflicted miners. He observed a disease in miners that caused shortness of breath, coughing and wasting. Add fever, chest pains and fatigue and we have the current symptom complex of silicosis. As we approached the 21stcentury, the Labor Department began an aggressive campaign to combat silicosis-a preventable disease. Unfortunately, many publications do not clearly differentiate the polymorphs of silica known to mineralogists. Crystalline silica, i.e., alpha quartz, tridymite and cristobalite need to be considered differently from the amorphous forms of silica. Freshly fractured surfaces of the silica and host specific responses will be examined. Recent research focuses on the biologic interactions of free radicals generated by mineral particles. This results in cell injury and DNA damage, in turn leading to fibrogenesis and possibly carcinogenesis. In addition to particle-cell interactions, emphasis is given to lung defense mechanisms.

Jan 1, 1998

By Richard L. Stein

INTRODUCTION Increasing a miner's chance of surviving a disaster requires advance planning for emergencies, adequate training of personnel, and the provision of proper survival equipment. It is extremely important that fires and toxic gases be detected early, and that warning systems such as stench, audible and visual alarms, and communications systems be provided to allow timely escape. However, situations do occur where timely warning is not provided and immediate escape is not possible, regardless of the precautions that are taken. Under such circumstances, a combination of new per¬sonal protective devices and old techniques can provide protection that is adequate to save a miner's life. SELF-RESCUE EQUIPMENT Self-rescuers are devices which provide a short-term supply of respirable air under the potentially lethal con¬ditions following a mine disaster. Functioning either as filtration devices for the elimination of carbon monoxide (CO) or as oxygen supplies, self-rescuers allow an endangered miner a limited amount of time in which to effect an escape or reach a place of temporary safety. Carbon-Monoxide Self-Rescuers For almost 50 years, filtration self-rescuers have protected miners' lives following explosions or fires. Designed to eliminate carbon monoxide from inhaled air, the first of these devices was approved in the 1920s and has evolved into the two units that are approved today-the Mine Safety Appliance (MSA) W-65 and the Draeger 810. Both of these units rely on the cata¬lytic conversion of very toxic carbon monoxide to rela¬tively safe levels of carbon dioxide (CO,). As shown in Figs. 1 and 2, both of these filtration self-rescuers operate in the same manner. On inhalation, the mine air passes through both coarse and fine filters that remove the dust, preventing the dust from coating the chemical beds or entering the miner's mouth. The air then passes over a drying agent that removes water vapor; this is required to prevent the water vapor from poisoning the catalyst. Subsequently, the dried air passes over the Hopcalite catalyst, where carbon monoxide is converted to carbon dioxide. Then, the air passes through a heat exchanger that reduces the temperature of the inhaled air. Finally, the air is inhaled by the user. Air exhaled by the user passes through the heat ex¬changer and exits the device through an expiratory valve. Both units of this type are subject to certain limita¬tions: 1) The units do not protect the user against oxygen¬deficient air; when air is inhaled through this type of self-rescuer, the device only removes the carbon mon¬oxide. If the mine air contains less than 15% oxygen, anoxia is inevitable. Symptoms of anoxia include dizzi¬ness, shortness of breath, quickened pulse, and deeper and more rapid respiration while the victim is at rest. During heavy exertion such as would be expected dur¬ ing escape efforts, a 15% oxygen level can cause loss of consciousness. 2) The units do not protect against excessive levels of carbon dioxide. Available data on carbon monoxide and carbon dioxide concentrations following explosions or fires are limited, but there are indications that the carbon monoxide concentration can rise to 2% and the carbon dioxide concentration can reach 5 or 6% of the mine air (by volume). In some situations, the in¬haled air could contain up to 6 or 7% carbon dioxide. At a carbon dioxide concentration higher than 2%, breathing patterns can be affected adversely. At a con¬centration of 6 or 7%, the effects include severe respira¬tory distress, with unconsciousness resulting from exer¬tion such as that needed for escape activities. 3) The units do not protect against high inhalation temperatures. The catalytic oxidation of carbon mon¬oxide to carbon dioxide is an exothermic reaction that evolves a large amount of heat. As the carbon monoxide concentration increases, the temperature of the inhaled air also increases. Available data show that above 1.5% carbon monoxide, the air inhaled through some self¬rescuers can be as high as 90°C (194°F). At those

Jan 1, 1982

By George E. Aiken

Agglomeration developments in the iron ore industry of North America are closely related to shifting patterns in commercially acceptable ore grades and even the definition of iron ores. These relationships have occurred mainly during the last 20 years. Many of these changes are an outgrowth of events which involved the history of the Mesabi Range. Although magnetic taconites had been discovered in the Lake Superior area about 1870, they remained unworked in part for lack of concentration methods and a generally unfavorable economic climate. Some 20 years later the rich Mesabi hematites were found beginning the era of direct shipping ores which continued through World War II. These Lake Superior iron ores included reserves of an estimated three billion tons. Following World War II, decreasing ore grades and rising costs began to force the closing of many underground iron mines. The early 501 s saw the beginning of the decline in direct shipping ores and a spurt in production of natural iron concentrate s. However, the market for unprocessed concentrates began to decline in the early 601 s as agglomerated products and foreign ores began to dominate the U. S. market.

Jan 1, 1972

By Georges E. Vaillant

Air pollution control in primary aluminum smelter . Various processes are known for air pollution in electrolysis plants. Mainly two systems have to be taken into consideration: -Treatment of concentrated gases collected directly from hooded pots. This is normally achieved by either dry or wet process. This is not the object of this paper as these processes have been already described. -Treatment of low concentrated fumes. A certain amount of gaseous and solid fluoride (35 % of total fluor pollution) goes out of the hooded pot. Gases commonly called secondary fumes are generally treated by wet process. The object of 'this paper is to describe two plants with specific treatment for secondary fumes. 1/ A plant in operation in Vlissingen (Netherlands) for PECHINEY. 2/ Presentation of tests carried out by a specialized Company. The results of such tests have been used for the design of the scrubbers presently under construction for ALUMINIO ESPANOL San Ciprian (Spain).

Jan 1, 1978

By Jack J. K. Daemen

A wide variety of subsidence prediction methods exist. They can be classified into empirical methods and mechanistic models. The empirical methods include profile functions and influence functions (Brzuner, 1973a,b; Kratzsch, 1974; Berry, 1978; Hood et al., 1981), the two empirical approaches of most practical value, if only be- cause they are readily programmed on calculators or computers. The profile functions have the advantage that they allow for ready determination of the necessary empirical parameters from field observations. They have the disadvantage of being restricted to subsidence calculations at a very limited number of points or lines above very simple (rectangular) mine geometries. This reduces greatly their practical applicability for damage predictions, which usually require estimates of strains, slopes or curvatures at structures that have arbitrary position and orientation with respect to planned mine excavations. Influence functions can be used to calculate subsidence at any point near an excavation of any in- seam outline. The main difficulty associated with empirical influence functions is the lack of uniqueness in the relation between subsidence and its cause, the convergence distribution over a mined excavation and its immediate surroundings. A secondary practical difficulty is the need for fairly arbitrary adjustments near the excavation edges, usually in the form of compensation zones (e.g. Brsuner, 1973; Hood et al., 1981). Determination of the appropriate empirical constants in influence functions is facilitated greatly when a direct mathematical connection exists between influence and profile function (several examples are given by Brauner, 1973 and by Hood et al., 1981), so that field data can be used to determine the parameters through backfitting of the profile functions, which is considerably simpler and more direct than backfitting of influence functions.

Jan 1, 1982

By V. L. Magnus

The text of this chapter was not received in time for printing.

Jan 1, 1979