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By Kasimcan Koruk, Julian M. Ortiz

A geological model accounting for uncertainties possesses important advantages for resource estimation. Machine learning algorithms (MLAs) employed on multivariate geochemical datasets open up ways to new methodologies for such geological models with ease in comparison to traditional geostatistical methods. This article proposes a two-step MLA with an ensemble implementation to define geological domains and their uncertainties based on geochemical data. The proposed workflow is applied hierarchically on a dataset from a porphyry copper deposit to perform binary classification that can be attributed to alteration domains.

Mar 1, 2024

By Augusto Andres Torres Toledo, João Felipe Coimbra Leite Costa, Luciano Nunes Capponi, Diego Machado Marques

Short-term mine planning to open pit requires defining diglines to orientate the excavation geometry. In deposits with multiple chemical variables, it is necessary to have more rigorous control over the feeding of the processing plant. This study analyzes the impact of incorporating multiple chemical variables, the risks generated by geological uncertainty, and the number and starting point locations of shovels in the sequential design of diglines. The objective is to maintain and preserve the low-grade variability, required tonnage, and continuity in sequentially selecting blocks. To achieve this, the probability distribution function of each chemical variable is used while attempting to maintain the ore grades as constant as possible. As it is difficult to maintain multiple elements with low variability simultaneously, the relevance of each chemical variable in the economic benefit is identified. Weights are assigned to signal the importance of each element based on its significance in the recovery process. Several diglines, consisting of sequential blocks, were generated on the same seed point to meet the weekly ore demand. Optimizing the stationarity of multiple chemical variables, accessing and reducing the geological uncertainty performed through geostatistical simulation of grades and transfers functions, considering the number and location of shovels, while meeting the operational restrictions of the selected blocks. The optimized digline with the multiple grades as stationary as possible is retained. The process is illustrated in a phosphate mine. The results show that the proposed method is viable and allows for a quick solution.

Jun 25, 2023

By James W. Estep

The sulphur shortage that has occurred in the past two years has directed attention more and more toward sour natural gas reserves, Wellhead values of sour gas vary widely depending upon the acid gas composition, location, market conditions, and necessary processing charges. Preparation of a saleable residue gas is considerably more involved and expensive than that normally encountered in treating a sweet gas. Recent revisions in sales gas specifications have increased capital costs and processing charges. The presence of hydrogen sulphide and carbon dioxide in a natural gas contributes to shrinkage factors that may approach 50%. Fuel required by the gas sweetening process and sulphur slant tail gas incineration also contributes to a further reduction in the volume of residue gas available for sale. The additional processing facilities involving gas sweetening, mercaptan removal, expanded utilities, sulphur recovery and sulphur handling, all demand additional operating and maintenance staff. A favorable sulphur market under certain conditions may justify the processing of sour gas whereby sulphur is either a by-product or a co-product, Five typical cases involving different compositions of sour gas are presented for evaluation. Capital costs, operating problems, and operating costs are presented in detail for full economic evaluation

Jan 1, 1967

By T. Gupta, T. Ghosh

Rare earth elements (REEs) and their compounds are essential in a multitude of mundane and sophisticated applications such as renewable energy technologies, catalysts, medicine, and defense applications. The global supply deficit could be attributed to the destabilization of REE market that has, as a result, incentivized indigenous production of REEs. Cost-effective and environmentally benign opportunities are being explored for the production of REEs from non-conventional mineral sources including coal and coal by-products to stabilize the supply chain. Coal from Healy coal mine and Wishbone Hill deposits in Alaska have been quantified for REEs and were found to possess elevated total REE concentrations as compared to world average levels (60– 70 ppm). The objective of the study was to concentrate the REEs in the froth phase by froth-flotation of the fine size fraction (< 75 μm). A Box-Behnken design of experiment was employed to ascertain the main and interaction effects of operational parameters on response variable by analyzing 3D response surfaces. Experiments were carried out to maximize REE recovery and concentration by modeling and optimization of three operating variables (frother dosage, pulp density (% solids), and collector dosage). Based on the results, the optimum flotation conditions for maximum recovery at an elevated concentration of REEs in the froth fraction was obtained at 4.2% solids and 32.7 ppm of frother dosage for Healy sample and 10% solids and 37.9 ppm of frother dosage for Wishbone Hill coal sample. The quadratic relationship between the input and response variable was found to be independent of collector dosage suggesting good surface hydrophobicity and floatability of the two coal samples.

By F. G. Miller

To improve coal flotation Bethlehem Steel Corporation&apos;s Research Department has been working on a number of related problems based on both physical and chemical factors. The ideal is of course full understanding of the interrelated effects of both sets of factors. However, detailed studies5 of each physical factor have produced immediately usable results in commercial coal flotation and are providing the bas is for our current work on the effect of chemical factors. Since these detailed studies provided the basis for the present investigation of froth sprinkling, their key results are highlighted here. For example, for a highly floatable bituminous coal, particle floatability was shown to be directly related to the percentage of coal surface available for bubble attachment and inversely related to particle mass. The data also underscored that in a given size range the addition of mineral matter to a particle makes flotation more difficult both by adding to the mass of the particle and by decreasing the amount of coal surface available for bubble attachment. Size also affects particle floatability in that as the size of particles of a given specific gravity increases, mass increases and the ratio between coal surface area and mass of the particle decreases. Flotation tests showed that any recovery of the coarsest particles in a coal feed is accompanied by progressively higher recovery of finer and finer particles. Consequently, fine high-specific-gravity particles are recovered with the coarse good coal. As a result, when the entire 14M x 0 size range is processed by froth flotation, the good coarse coal is contaminated with high-specific-gravity fines. It is the small quantities of these fines that must be rejected from the froth product if flotation efficiency is to be increased above its present level.

Jan 1, 1968

By Thomas Jancic

Two of the open-pit, copper-molybdenum mining operations of Duval Corporation are located in the foothills of the Sierrita Mountains approximately 30 miles southwest of Tucson, Arizona. In March 1959, mining from a moderate sized porphyry deposit known as the "Esperanza orebody" was begun at a rate of 10,000 tons of ore per day. Some five years later, a sizeable group of mineral claims west of Esperanza became available to Duval. Earlier exploration and development drilling in this area by others indicated an orebody of greater size but lower tenor than that of Esperanza. A drilling program conducted by Duval not only verified the results of the prior drilling but in addition, revealed a continuation of the mineralization to the south and east. Thus was developed the Sierrita orebody. Open pit design delineated 414 million tons of ore containing an average copper content of 0.35 percent and a molybdenum content of 0.036 percent. In April 1966, the office of Emergency Planning authorized General Services Administration to undertake a program under the Defense Production Act to en¬courage additional domestic production of copper in the interest of national defense. Duval&apos;s Sierrita Project was brought to GSA&apos;s attention in May 1966 on November 28, 1967, an agreement providing for the development of the Sierrita Property was consummated with GSA. In March 1970, the first copper-molybdenum concentrates were produced in the 72,000 tons-per-day concentrator. Pre-production stripping exceeded the scheduled 105 million tons despite the comparatively short lead time available to equip the mine, build the mine plant facilities, and staff the technical, supervisory, and labor forces. Shortly before the first concentrates were produced, plans were being formulated for a program to increase processing capacity by approximately 15 percent, which entailed increasing overall mining capacity by approximately 50,000 tons per day. This program is scheduled for completion early in 1971.

Jan 1, 1971

By Hugh R. Rhys

The question of the desirability of recovering cullet from MSW in order to recycle it into the manufacturing of glass containers remains a controversial one. The main factors appear to be: 1. The position of the Glass Container Manufacturers Institute (GCMI), as the trade association for most container manufacturers, is that post-consumer cullet is a vital source of raw material. Present requirements are for: a) Flint cullet b) Non-flint cullet of known mix proportions c) Mixed unsorted cullet of known mix propertions c) Mixed or non-flint cullet of unknown mix proportions. A market balance for these products exists, and this might somewhat limit the outlets for (b), (c) and (d), or severely limit the outlet for (d) alone. 2. The color specifications are rather strict. With cullet admixtures of 20% of the melt or more, and the use of decolorisers in a flint furnace discouraged because their action is reducing in a process which requires an oxidising environment, color contamination in a flint furnace is serious.. For amber and green furnaces (reducing) it is less serious, but in order that the quantity of decolorisers may be controlled, the color balance (as a measure of the Fe and Cr content) of the admixtured cullet should be known. 3. Why not simply color analyze, either by a continuous on-stream or off-stream: photo-electronic analysis, or by systematic batch sampling (with some kind off electronic surveillance of the mainstream) and just send mixed, color measured cullet to only amber and green furnaces? The flint would-be simply included in the mix. This is probably technically feasible, but is subject to the market limitations noted in point1.

Jan 1, 1975

By C. L. McKenzie

American Girl Mine is located in the Cargo Muchacho Mountains in the southeastern Imperial Valley of Southern California. Production from the current open pit mine and heap leach recovery system began in early 1989. Previous mining and gold recovery took place commencing in 1987 at the Padre Madre site, situated adjacent to the American Girl site to the southwest. In mid-1990, a 790-tonne-per-day underground gold mine and mill went into production. Approximately 6,500 troy ounces of gold per month are recovered from the combined open pit underground mine operation. Copper in the form of Azurite [Cu3(CO3)2(OH)2] and Malachite [Cu2CO3(OH)2] are abundant in the mined ores (Henshaw, 1942). The high solubility of these minerals in caustic cyanide solutions has a negative impact on carbon adsorption and electrowin processes. This paper presents the results of monitoring programs, process chemistry, and control changes introduced at American Girl Mine to abate production complications in the refinery and measures taken to minimize solution gold losses in the adsorption circuit(s).

Jan 1, 1993

By Linda D. Raedeke

The main platinum-group metal (PGM) deposit in the Stillwater Complex is associated with a stratiform zone formed by magma mixing. In general, the intrusion is a large, layered body of Archean age which formed by repeated magmatic injections in- to a single, large, hypabyssal magma chamber. The Complex is broadly divided into the lower Ultramafic series of olivine ± orthopyroxene rocks (1000-2000 m thick) and the upper Banded series of predominantly plagioclase-rich rocks (24500 m thick). The latter is further divided into Lower, Middle, and Up- per Banded zones. The Ultramafic series, plus most of the Lower and Upper Banded zones formed from repeated injections of an olivine-saturated magma, the rocks accumulating from the floor upward with a crystallization order of olivine, or- thopyroxene, plagioclase, clinopyroxene. The olivine-bearing subzones of the Middle Banded zone formed predominantly from a magma which crystallized in the sequence plagioclase, olivine, clinopyroxene. Olivine-bearing subzone I, with which the PGM mineralization is associated, occurs generally -400 m above the Ultramafic series-Banded series contact. Ore grade mineralization is usually found in plagioclase or plagioclase-olivine cumulates. The platinum-group elements are associated with disseminated base-metal sulfides dominated by the assemblage, pyrrhotite-chalcopyrite-pentlandite. Olivine-bearing subzone I marks an interruption in the crystallization sequence of the Lower Banded zone, with the reappearance of cumulus olivine and an associated change of the crystallization sequence. These changes indicate the addition and mixing of a secondary magma of the same composition as that which later dominated in the formation of the Middle Banded zone. Characteristics associated with mixing include laterally discontinuous but well-developed layers, xenoliths of ultramafic rocks, and sedimentary-type structures such as slum- ping and graded layering. The influx of new magma caused sulfide saturation by one or more of several chemical changes including addition of sulfur, decrease in oxygen fugacity, decrease in FeO, or increase in SiO2. Once an immiscible sulfide liquid was formed, platinum-group elements were scavenged from the magma by the sulfide liquid and segregated.

Jan 1, 2013

By K. C. Kocsis

"Diesel-powered equipment has allowed the mining industry to raise production rates and significantly improve productivity, as it is rugged, mobile and reliable, but its widespread use in underground mines has generated concerns regarding the exposure of mine workers to harmful diesel engine exhaust gases and particulate components such as diesel particulate matter (DPM), which has recently been classified as a human carcinogen by the International Agency for Research on Cancer. The agency expressed further concerns that workers’ exposure to high DPM concentrations can increase the risk of cardiovascular, cardiopulmonary and respiratory illnesses. Three emerging technologies could have the ability to replace dieselpowered equipment and remove DPM from underground mines: fuel-cell-powered mining equipment, battery-powered mining equipment and advanced material handling systems. This paper reviews them and assesses whether they have reached the point where the pollutants emitted by diesel-powered equipment can be removed from underground mines through the introduction of zero-emission mining equipment and power systems. Information is also provided from the results of a feasibility study, including a detailed cost benefit analysis, carried out at six Canadian and nine U.S. underground mines, which looked at the possibility of replacing diesel-powered production equipment with fuel-cell-powered equipment. The remarkable pace at which battery technology is progressing is also reviewed, and the feasibility of replacing diesel-powered mining equipment with battery-powered equipment is assessed. IntroductionHazardous pollutants in underground mines. Why is it important to remove diesel particulate matter (DPM) from underground mines? Over the past 40 years, diesel-powered equipment has allowed the mining industry to achieve rising production rates and major improvements in productivity, as the diesel engine is an economical source of power and diesel-powered equipment is usually rugged, mobile and reliable. On the negative side, the toxicity of some diesel exhaust gases is well known (Grenier et al., 2001), and the widespread use of diesel-powered equipment in underground mines has generated increasing concerns about the occupational exposure of mine workers to harmful diesel engine exhaust gases and particulate components such as DPM. Diesel equipment also entails other hazards like heat and humidity. Exposure to excessive heat can cause heat illnesses, such as heat rash, heat exhaustion and heat stroke (Donoghue, 2004; Roghanchi et al., 2016), and a hot and humid underground environment negatively affects the efficiency of the workforce, which may result in a decline in production output (Roghanchi et al., 2017)."

Jan 10, 2017

By V. F. Swanson

A petrographic study was made of the type and sources of mineral contamination occurring on phosphate rock products from Florida. Emphasis was placed on contaminants in the screened rock (+1 mm) since this portion of the product undergoes no physical beneficiation except for scrubbing to remove slimes. Since iron and aluminum con- tent of the finished product affect the salability, special emphasis was placed on identifying types and sources of these contaminants and relating chemical composition to visual characteristics. Wavellite derived from the overburden was the major aluminum contaminant with some aluminum being included as secondary clayballs. Iron occurred as phosphates in the overburden, and as colloidal oxides included in the phosphate pebbles. Chert and limestone contamination were derived from the Hawthorne formation underlying the phosphate matrix.

Jan 1, 1969

By Brian Young, Ben Pantony

Interferometric Synthetic Aperture Radar (InSAR) has played an integral role in many large scale tunneling projects globally. Until recently, it has been regarded as a complementary monitoring tool. On the Los Angeles Metro Purple Line Phase 1, InSAR was proposed as a primary means to replace weekly and bi-weekly surface monitoring requirements on surrounding critical infrastructure. This paper will summarize the statistical analysis approach engaged in order to compare and contrast a year of historical InSAR data to known geodetic survey data, in order to utilize InSAR as an operational monitoring tool on this project.

Jun 13, 2021

By Bernd Hagenah, Eric C. Wang

New tunnels of significant alignment lengths such as mountain tunnels, base tunnels, as well as beneath urban centers pose unique environmental challenges. This paper highlights key environmental considerations for planning, design, construction, and operations by sharing lessons-learned from the authors' extensive project experience on these types of tunnels. Discussion of unique constraints include limited right-of- way, ventilation and emergency egress during the construction phase and revenue service, safety and security, and protection of existing structures. Practical approaches and applied innovative state-of-the-art solutions addressing distinct sustainability challenges and unique requirements are shared from US and international project examples.

Jun 23, 2024

By M. Poulton, J. A. Botín, C. Gatica

"The Chilean minerals industry faces a shortage of 27.000 new skilled professional by 2023. Enhancing the integration of women into the workforce is a possible solution. This study analyzes the state of women in the mining workforce over the past decade. Several key indicators are presented: percent in the workforce, salaries, career profiles, presence at management level, and participation in academia are studied. The study also analyzes the strategies used by government, industry, and universities to recruit and retain women for the minerals industry. The main results show that women represent 7.4% of the mining workforce in Chile and less than 1% of senior positions with a salary gap of approximately 30%. Systematically, women prefer professional programs in geology, chemistry, and environmental areas. The Chilean statistics are compared to data from the United States mining industry. INTRODUCTION The Chilean mining industry faces a significant shortage of professionals for the next decade which compromises competitiveness and productivity. The demand for human capital in mining depends on several factors. First, the age structure of workforce, which determines future retirement needs. Second, minerals market considerations, determining the amount and size of mining projects entering production in the coming years. Third, the evolution, positive or negative, of productivity, mainly driven by technology and innovation, and negatively affected by the declining ore grades. Finally, negative trends in lead times to production of mining projects, due to social opposition, changing regulations and other project contingencies, negatively affecting the demand for human capital. Regarding the supply of human capital, the fast increase in the technology level of the minerals industry and hence, the increase of technical qualification requirements of the human capital generates a rise in the time required for trade and university education of mining professionals, which may cause imbalances in the labor market. According to (Consejo Minero, 2014) human capital gap in Chile by 2023 will be around 27.000 workers for extractive, processing and maintenance jobs, which represents 14% of the current workforce (Figure 1)."

Jan 1, 2016

By S. E. Phillipson

Four massive pillar collapses in limestone mines, and one in a marble mine, occurred between 2011 and 2021 in benched areas at the Appalachian physiographic province. We characterized the rock mass at 43 limestone mines using the Geological Strength Index and, by plotting the results on a physiographic relief map, determined that GSI values between 55 and 70 preferentially occur in the Appalachian and Ouachita Mountains, which were subject to deformation during the Ouachita and Alleghanian Orogenies. Limestone mines located in formations of similar age in the Interior Plains, where deformation was less developed, are characterized by Geological Strength Index values over 80. We present the results of pillar strength calculations that incorporate the Geological Strength Index from mines that experienced massive collapse, as well as from mines with benched areas that did not collapse, to demonstrate the negative effect that a jointed rock mass has on pillar stability. We suggest that pillar designs, particularly those in which benching will be incorporated, should include allowance for rock mass quality. Because of the preferential dominance of lower GSI values in the Appalachians, we further suggest that pillar designs in this environment may require additional engineering assessment, especially where benching is intended. Lower GSI values may often translate into greater overbreak, which results in loss of pillar volume, corresponding wider back spans, and a decreased width-to-height ratio.

Jun 25, 2024

By A. Taghavi, I. Hassan, A. Solecki

"The Eglinton Crosstown Light Rail (LRT) Project is part of an $8.4 billion investment to expand transit in the Toronto, Canada area and is the largest transit project initiated in Province’s history. Settlement control and impact to over 1400 adjacent structures due to tunnelling was identified early as a critical project risk. The ground conditions along the 10km tunnel alignment consist of water bearing soft ground deposits (clays, sands, silts) which required careful analysis and control during design and construction. This paper will describe the process used to analyze settlements along the numerous of adjacent structures and evaluate achieved settlement results to those used during design. The paper will demonstrate that with the appropriate design specifications, selection of modernized EPB machines, and contractor performance, settlement can be maintained well below typical industry (volume loss) standards, expanding the application and suitability of soft ground tunnelling in sensitive settlement areas. INTRODUCTION The Eglinton Crosstown Light Rail Transit (LRT) Project is part of an $8.4 billion (2010$ CND) investment from the Ontario provincial government to expand transit in the Toronto, Canada area. The project is being developed by Metrolinx, an agency of the Government of Ontario to provide 19 kilometers of dedicated LRT service connecting the City of Toronto from the west to east along Eglinton Avenue. Upon completion in the year 2020, the Crosstown will be the first LRT constructed in Toronto. It will link regional and local transit, cut travel time along the route by half and provide over a thousand jobs during construction."

Jan 1, 2016

By F. G. Miller

In mid-1972 we determined that a fresh approach to coal mining research was needed for the industry as well as for Bethlehem. The reasons to us were obvious: Productivity was in the throes of a steady decline, and labor and maintenance costs were spiraling upward. Yet, despite this predicament, nowhere in the U.S. at that time was there a comprehensive and coordinated research and development plan in the offing. The Bureau of Mines had not yet been charged with such a responsibility, and industry was content to rely on machinery manufacturers for innovations. After studying our own mining practices, the state-of-the-art of mining research elsewhere, and development work by manufacturers, we presented a comprehensive research package to our management at the end of 1972. The ideas and experience of many operating and management personnel in our Corporation contributed to the formulation of the final plan as approved.

Jan 1, 1976

By Sakshi Hazuria Anderson, Angela Binder, Oscar Jaime Restrepo Baena, Simit Raval, Sandra Nowosad

As the mining industry faces times of change, new challenges arise to ensure raw material supply for the younger and future generations. Different scenarios are currently shaping the way we mine and teach mining engineering. Led by an increasing demand for raw materials, net zero requirements for improving long-term operation performance, technological advancements such as automation and digitalization, safety improvements, environmental considerations and a need for social acceptance, mining is pursuing to change and adapt to these requirements at a faster pace. Such changing times raise new concerns, one of the most relevant is the lower number of students interested or enrolling in mining engineering and related fields leaving mining engineering as one of the less preferred career options between the younger generations. Nonetheless, it is essential to continue addressing and supplying the skill sets that are suited to the contemporary and future mining industry. To this end, globally, academia is currently undergoing several initiatives such as curricula updates and adaptation, up skilling, improving teaching practices and techniques, including e-learning techniques, enhancing industry-academia and inter-university collaboration, and much more. In countries like Australia, where mining plays a crucial role in the economy, the need for curriculum updates is more pressing than ever. As the mining industry evolves with new technologies and sustainable practices, there is a growing demand for a workforce skilled in these modern approaches. Recognizing this necessity, universities such as the University of New South Wales and Curtin University have taken significant steps to revamp their educational programs. By updating their academic offerings, both universities aim to equip graduates with the necessary skills to drive innovation and sustainability in mining, supporting Australia’s development as a leader in this critical sector. Moreover, the selection of topics that drive curricula update and the focus of the research institutions in mining engineering must extend beyond mere technological and technical aspects to include social and ethical dimensions. In this context, the Universidad Nacional de Colombia, in association with the Colorado School of Mines, has introduced the topic of Humanitarian Engineering (HE) in 2020. HE is a socio-technical approach that focuses on developing engineering solutions that promote the sustainable development of communities addressing their basic needs and aiming to improve their quality of life (10, 18). By focusing on sustainable development, community engagement, and equitable resource distribution, HE helps the industry build positive relationships with stakeholders, reduce conflicts, and foster social license to operate. As the mining industry seeks sustainable and socially responsible practices, future engineers require training in this area to understand the broader impacts of their work, fostering a mindset that prioritizes community well-being and environmental stewardship alongside technical proficiency.

Feb 1, 2025

By Joseph W. Murray

Prior to 1950 Magma&apos;s ore production came from two parallel, steeply dipping, east-west striking mineralized faults, one called the Main or Magma vein, and the other the Koerner vein, which lay about 1100 feet to the south, This vein system has been explored and mined over 9000 feet horizontally and 4800 vertically. In 1950 continued exploration led to the discovery and subsequent development of replacement ore bodies in the Devonian limestone zones adjacent to the veins. These replacement deposits occur in the eastern part of the Magma Mine, and follow the strike and the 30" east dip of the host limestone. Strike length of the ore bodies varies from 250 to 500 ft., and thickness from 15 to 125 ft. The ore bodies are large tabular masses with chalcopyrite and bornite being the dominant ore minerals. Hematite and pyrite are the most abundant gangue minerals. Incompetent limestone, shale, or a porphyry sill hanging wall is charactertistic of substantial portions of the replacement beds. In many instances the ore itself is blocky, badly fractured, and intermixed with layers of limestone gouge, pyrite and hematite.

Jan 1, 1973

By R. E. Hamilton

Automation is a word whose meaning has been broadened by popular usage to include any labor saving device. We with restrict our usage to the replacement of human judgement by instrumental measurement and mathematical analysis in the control of industrial processes. Mineral concentration is an area which has resisted automation because of the great difficulty in developing measuring instruments which can exist in the rugged environment and can measure useful properties with acceptable accuracy. This is not the only factor limiting progress, but until recently it has been of over-whelming importance. The development of on-stream X-ray analysers, magnetic flowmeters and nuclear density meters for mineral slurries has eliminated this obvious barrier and is enabling us to locate and attack the less obvious problems which still limit our ability to automate concentrators. If we examine the history of automation in industries which are highly automated we find that it has usually gone through three distinct phases. The first phase has been regulation. This is the simplest form of control and involves manipulating some variable whose value is of no importance in order to maintain the value of some other variable which is important at a constant specified value in spite of disturbances which may occur in other variables which affect it. A simple example is the use of a control valve to maintain a constant flow of fluid in a line in spite of changes in pressure in the vessels at the ends of the line. The position of the valve stem is of no consequence, as long as it is within its operating range. Unfortunately we soon run out of variables which can be

Jan 1, 1971