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By T. Kawashima

The expanding volume of maritime coal transportation is intensifying the problems concerning large vessel service port construction, transshipment and environmental control. The major problem is the transshipment of coal. Customary methods for bulk transfer must be improved and/or new systems developed. Slurry unloading has a key role in the new systems. The present report reviews progress in slurry transportation research which has been done in Japan since the 1960s when large scale experiments for domestic transportation were done. Experiments on the effects of vibration on the slurry cargo and on reslurrying are discussed.

Jan 1, 1982

By K. K. Bhattacharyya

Vast deposits of lignite occur in the Gulf Coast states and northern plain states. Lignite resources are cited to be over 43 billion tons in the Gulf Coast states. An additional resource of 16 billion tons are reported in North Dakota (Jackson, Smith, 1981). All lignite in the U.S. is mined at present by the open pit method. Draglines and scrapers are primarily used to remove the overburden. Bucket-wheel excavators are also being considered for new mines in the planning stages. Lignite seams are mined using front-end loaders, shovels and trucks, or Easi-miners. The depositional environment of lignite is weak sedimentary soils and rock. Ground water is often encountered within the mining depth. Surface water resulting from heavy rainfall or snow melt contributes to the problems of mining. Mining depths of up to 60 m (200 ft) are under consideration. Draglines exert additional loads on the highwalls and spoil piles. The combination of any number of these factors may cause instability of the slopes. Bearing pressure, trafficability, and settlement can also be a problem for excavation and loading equipment.

Jan 1, 1982

By G. M. Wilemon

The U.S. Bureau of Mines has conducted preliminary investigations on the leaching of phosphate ores obtained from deposits in the western United States using sulfuric acid (H2SO4) in the presence of methanol. Phosphate extractions in excess of 80 pct were obtained on an ore sample from Pocatello, ID. Initial leaching studies using the ore as received yielded extraction levels of approximately 35 pct. However, when the sample was ground for as little as 5 min in a rod mill, in methanol, then treated with HzS04, 82 pct extraction was achieved. The R2O3-P2O5 (R2O3 = Al2O3 + Fe2O3) ratio of the starting material was 0.11. Solubilized products after leaching exhibited an R2O3-P2O5 ratio of 0.02, which is well within desired limits. These results illustrate the potential of acid-alcohol leaching for recovering phosphate values from marginal-grade ores and as an alternative to methods involving current beneficiation techniques that yield lower phosphate recoveries.

Jan 1, 1992

By R. Stefanko

Rock bolting as a method of support continues to increase with applications in many other industries in addition to mining. Nevertheless, with nearly 55,000,000 roof bolts installed in coal mines alone last year, this remains as the single greatest use. While bolts have frequently supported ground where conventional timbering could not, there are relatively few design criteria; and trial-and-error procedures prevail. Furthermore, development of suitable instrumentation that is simple to install and readout, sensitive, durable, reliable, safe and economical in evaluating the effectiveness of a bolt over long periods of time lags behind. Therefore, the pull test continues to be the most popular method of evaluating the applicability of a certain type of roof bolt under specific installation conditions. At Penn State in the Department of Mining, research has been conducted for a number of years to measure bleedoff in carefully controlled laboratory experiments as well as in underground investigations.1,2,3,4 Unfortunately, most of the instrumentation developed has been primarily suitable only for research purposes, not possessing all of the aforementioned characteristics desirable for routine underground use. Other groups also have met with restricted success. Therefore, while relatively crude, the torque wrench continues to remain as the most widely used load measuring device. While both field and laboratory tests continue to be conducted, analytical analyses are attempted to discover the more important design parameters in order that more efficient anchorage might be devised.

Jan 1, 1969

By R. Pazhianur

Cathodic Protection using impressed current was employed to reduce the wear of the mill wall during ball mill grinding. Wear rates were determined from weight-loss measurements made on four, I-inch diameter, mild steel coupons installed flush with the interior surface of the mill wall. Grinding tests were conducted on quartz, pyrite and quartz-pyrite mixtures at pH values of 4.6, 7.1 and 9.2. Cathodic protection was shown to reduce mill wear by 40-60010. An examination of the coupon surfaces using scanning electron microscopy showed that cathodic protection greatly reduced pitting corrosion. The presence of a sulfide mineral, such as pyrite, was found to increase the wear rate significantly, possibly due to galvanic interactions. It is also found that the wear rate is significantly higher than the sum of abrasive wear and the corrosive wear, due to a synergistic effect.

Jan 1, 1996

By Nikhil Dhawan, Sanjay Pindar

The limited lifespan, ever-growing demand, and significant lithium and cobalt content are responsible factors for the immediate recycling of discarded lithium-ion batteries. Discharged batteries were dismantled, segregated, and size reduced to recover cathode and anode material. The active cathode material comprises LiCoO2 (65.8%) and LiMn2O4 (34.2%) and was carbothermal reduced with recovered graphite in a microwave furnace followed by water leaching and magnetic separation. A Box Behnken statistical experimental design is used for process optimization. Both cobalt and manganese report to magnetic fraction, whereas graphite and lithium carbonate report to non-magnetic fraction and solution crystal respectively. The final product comprises of cobalt 73% and manganese of 14% with process yield of 36% and saturation magnetization of 76 emu/g.

May 16, 2020

By T. Gelpe

A digital simulator of classification and grinding circuits is used to evaluate the performances of various flowsheets. For a given flowsheet configuration, unit processes dimensions and operating conditions, the simulator calculates the steady-state values of the process variables. A supervisory algorithm is implemented in the simulator to determine the conditions which meet the required criterion on operation, tonnage and product quality. Calculation illustrations are proposed for the design of wet and dry grinding circuits. The performances of various arrangements of cement clinker and sulphide ore grinding flowsheets are evaluated and discussed.

Jan 1, 1983

By M. Sunkpal, K. C. Kocsis

"An underground environment with high air temperature and humidity conditions generated from various heat and moisture sources can significantly affect the thermoregulation processes of the human body. This can lead to a series of heat-related illnesses such as heat exhaustion, heat cramps and heat stroke. The majority of the metabolic energy of a mine worker results in the production of heat. If the human body is to maintain thermal equilibrium, then this metabolic heat must be transferred to the ambient surroundings at the same rate. The heat loss from the human body occurs through a combination of heat transfer processes, such as respiratory heat exchange, convection, radiation and evaporation. If the heat loss from the human body to the ambient surroundings is less than the metabolic heat produced, the excess will be accumulated within the human body, which will result in a rise in the core and skin temperatures. This can ultimately lead to a heat-related illness or a combination of heat-related illnesses. This paper aims to discuss major heat-related issues and provide an overview of various mine ventilation and cooling systems, which can be employed to overcome high levels of heat and humidity in underground mines. In this paper, the effects of heat exposure on the health, safety and productivity of the mine workers are also highlighted. IntroductionMining in the United States remains one of the most hazardous industries, despite significant reductions in fatal injuries over the last century (Coleman and Kerkering, 2007; Saleh and Cummings 2011; Jacklitsch, Musolin and Kim, 2016). Occupational health hazards within the mining industry include hazards that are physical, such as traumatic injury or hearing loss; chemical, such as silica or diesel particulate matter; biological; ergonomic; and psychological (Donoghue, 2004; Saleh and Cummings, 2011). The effects of some of these hazards can be diagnosed immediately, while many, like black-lung and silicosis, will have long-term effects on the health, safety and life quality of mine workers (Donoghue, 2004; National Institute for Occupational Safety and Health, NIOSH, 2000). Among these hazards, exposure to heat and humidity can significantly affect the safety, health and productivity of mine workers, particularly in deep and hot underground mines (Roghanchi, Sunkpal and Kocsis, 2015). Short-term acute heat exposures can cause a rise in the core temperature of the human body, which can result in a heat-related illness or combination of heat-related illnesses. Adverse long-term chronic heat exposure can generate serious occupational heat-related illnesses, such as cardiovascular diseases, mental health problems and chronic kidney diseases. High core body temperatures coupled with dehydration can generate negative behavioral effects such as physical fatigue, irritability, lethargy, impaired judgment, loss of dexterity and loss of concentration (Xiang et al., 2014)"

Jan 9, 2017

The classical slope analysis and a statistical technique were used in order to determine the iron complexes formed in the organic phase during the extraction of Fe(III) from Fe-Ni-Co sulfate solutions with Di-(2-ethylhexyl) phosphoric acid (D2EHPA) in kerosene. Equilibrium constants for the extraction based on these complexes were also calculated. The complexes determined were of the general form (Fe(OH)3-nRn?sHR)x' where n varied between 1 and 2.5 and s between 0 and 3, and both were found to be decreasing as the iron loading in the organic phase increased. Values of 1,2 and 3 were generally found for x, indicating that the complexes were monomers, dimers and trimers.

Jan 1, 1988

By E. H. Smith

St. Joe Minerals Corp., a subsidiary of Fluor Corp., treats high-grade gold, silver, and copper ore at its El Indio plant at an altitude of 4 km in the Chilean Andes. The ore is complex, being a mixture of massive pyrite-enargite and quartz, both containing very fine gold and silver. Treatment produces a copper flotation concentrate containing high levels of gold, silver, and arsenic, and also dore bullion. Part of the flotation concentrate is roasted to remove the arsenic content, and arsenic trioxide is collected as a by-product.

Jan 1, 1987

"Twin Creeks is a gold mining complex that is part of Newmont’s Nevada operations. The mining complex is composed of two openpits, Mega and Vista, external ore sources and a set of existing stockpiles, all of which provide ore for an autoclave, an oxide mill and a heap leach. Mega pit provides sulfide ore for the autoclave, whereas Vista pit provides oxide ore for the oxide mill and the heap leach. Both pits operate the same mining equipment and their extraction sequence must, therefore, be optimized simultaneously. Stringent blending requirements are associated with the operation of the autoclave for the sulfide ore. Strategic blending optimization on a large scale has brought significant value to the operation by increasing synergies. This paper presents the implementation of a stochastic optimization framework for the long-term production planning at Twin Creeks that simultaneously optimizes mining, stockpiling, blending and processing decision variables. The uncertainty and variability associated with the different sources of material are incorporated in the optimization model by means of stochastic simulations. The stochastic solution generated shows substantial benefits by increasing forecasted recoverable gold, leading to increased cash flows, while reducing the risk of not achieving forecasts by increasing the probabilities of meeting production and blending targets.IntroductionMine operations consist of multiple components such as mineral deposits, stockpiles, external sources, mills and autoclaves. These components represent a mineral value chain, also known in the literature as a mining complex (Montiel and Dimitrakopoulos 2015; Goodfellow and Dimitrakopoulos 2016). The material extracted from the mines flows through the different components and is transformed into sellable products. This flow of material in a mineral value chain involves complex, nonlinear transformations that render the use of industry-standard optimizers difficult. Furthermore, the optimization of a mining complex can be formulated as a mixed-integer, nonlinear optimization program with millions of integer variables representing mining, blending, stockpiling and processing decisions, prohibiting the use of conventional nonlinear optimization approaches. Previous methods that consider the joint optimization of multiple components of the mineral value chain are available (Hoerger, Seymour and Hoffman, 1999; Chanda, 2005; Stone et al., 2005; Wooller, 2005; Whittle, 2007, 2010; Bodon et al., 2010). Although these methods add value by increasing the synergy between the different components of the mining complex, they rely on simplifying assumptions that constrain their efficacy, while ignoring a most critical aspect. The latter aspect includes the geological uncertainty and actual variability of the materials in the mineral deposits mined and are supplied to the related mineral value chain, similarly to conventional life-of-mine planning methods used for individual mines (Dimitrakopoulos, Farrelly and Godoy, 2002; Godoy and Dimitrakopoulos, 2011; Spleit and Dimitrakopoulos, 2017). Additional simplifying assumptions may include: the consideration of a limited number of components, the combination of different methods, the aggregation of variables, fixed production schedules the definition of policies prior to optimization, such as cutoff- grade definition or destination of mining blocks, the linearization of nonlinear transformation functions and/or the disregard for the uncertainty of several critical parameters (Whittle, 2007). The simultaneous optimization of multiple components of a mining complex was introduced by Newmont. Hoerger, Seymour and Hoffman (1999) implemented a mixed-integer programming formulation to optimize Newmont’s Nevada operations. The model is based on the work of Urbaez and Dagdelen (1999) and simultaneously optimizes the extraction of materials from multiple deposits and the delivery of ore to multiple plants, as well as as"

Dec 1, 2018

By Daniel W. H. Su

A nearly 305-m- (1,000-ft-) wide sandstone channel was projected to run through the mid panel area of a 457-m- (1,500-ft-) wide longwall panel in a southwestern Pennsylvania coal mine. This sandstone channel was known to cause serious longwallface roof control problems in the mine?s B-panel area in 1998 and 1999; and most recently, it induced many large face cavities and caused a substantial production delay in the preceding panel. For the two B panels mined in 1998 and 1999, hydraulic fracturing of the massive sandstone was conducted to facilitate better caving, thus relieving cantilever compressive stress at the longwall face. Vastly improved longwall face condition was observed and four weeks of mining delay due to bad roof conditions were eliminated. The implementation of the hydraulic fracturing technique, results of underground observation and measurement, and results of numerical modeling were summarized in a paper presented in the 20th International Conference on Ground Control (Su et al., 2001). This article is a summary of the activities that took place during a four-month period (October 2011 through February 2012) at a Consol Energy longwall mine southwestern Pennsylvania to improve face conditions and safety of underground personnel during mining of the 457-m- (1,500-ft-) wide longwall panel. The elevated concern for safety was driven by adverse face conditions encountered while mining the preceding longwall panel. Many of the problems were attributed to a thick and massive sandstone channel. A joint task force consisting of coal operations engineering, Pennsylvania operations engineering and CNX Gas personnel was formed in August 2011, which recommended drilling four hydraulic fracturing holes along the center axis of the sandstone channel to reduce pressure and improve face conditions at the longwall face. To further provide detailed monitoring of the longwall face and to evaluate the effectiveness of the hydraulic fracturing program, the Longwall Visual Analysis (LVA) software (Hoyer, 2011) was installed in early December 2011 to track the face pressure and c

Jun 1, 2013

By T. Sun, J. Kou, D. Tao

"The reduction behavior of low-grade lump hematite ore (100% 20-50 mm) has been evaluated by performing a series of coal-based direct reduction roasting tests followed by magnetic separation under different process conditions such as roasting time, temperature, reductant type and dosage, and grinding stage. To investigate mineralogical transformation and reduction characteristics of lump hematite ore, roasted ores and magnetic concentrates were analyzed by X-ray diffraction (XRD), scanning electron microscopy (SEM) with energy dispersive spectrometer (EDS) and polarizing microscope. The results have shown that a magnetic concentrate with a total iron (TFe) grade of 90.7% was produced at an iron recovery of 83.9% when lump hematite ore was reduced at 1,200° C for five hours using 35% lignite as a reductant followed by two stages of grinding, for 20 min and 30 min each, and low-intensity magnetic separation. The degree of reduction is closely related to the change in the internal structure of the roasted ore. Lignite with a higher fixed carbon content and lower ash generated roasted ore with a more highly porous structure, which provides better permeability of reducing gas. Magnetite, fayalite and wustite were the dominant intermediates of coal-based direct reduction of lump hematite ore. Parts of wustite reacted with SiO2 or Al2O3 in gangue and generated fayalite or hercynite. FeO in fayalite was replaced by CaO to produce wustite, which was finally reduced to metallic iron. However, Fe in fayalite and hercynite produced with low contents of CaO cannot be reduced into metallic iron. Introduction Low-grade hematite ore, characterized by low Fe content and high SiO2 content, cannot be treated by traditional mineral processing methods due to its nonmagnetic property and fine liberation size. The direct reduction (DR) roasting process has been studied and proven satisfactory in treating difficult-toprocess ores, such as low-grade nickel laterite oxide ore (O’Connor et al., 2006; Cao et al., 2010; Guo et al., 2011), high phosphorus oolitic hematite ore (Li et al., 2012; Yu et al., 2013), low-grade hematite ore (Wei et al., 2013;) and iron ore tailings (Li et al., 2010), which greatly expand the resources of usable iron ores (Srivastava and Kawatra, 2009). Therefore, the use of a DR process to treat low-grade hematite ore to produce direct reduced iron (DRI) is of great interest to many researchers of mineral processing and metallurgy (Weissberger et al., 1986)."

Jan 1, 2015

By Mandira Madhuchhanda, N. B. Devi, P. C. Rath, R. K. Paramguru, K. Srinivasa Rao

An experimental investigation of the dissolution of three base-metal sulfide minerals, namely, CuFeS2, ZnS and PbS, in hydrochloric acid medium in the presence of manganese dioxide is reported. Polarization measurements and leaching studies were employed in the study. Dissolution occurred in the following three ways: by the cyclic action of the Fe3+/Fe2+ redox couple, by galvanic interaction between Mn02 and the sulfide minerals, and because of chlorine evolution from the system. The later two routes were found more effective at higher HCI levels. PbS appeared to be oxidized easily, whereas CuFeS2 was the most difficult to dissolve. ZnS dissolution fell in between PbS and CuFeS2.

Jan 1, 2002

By L. L. Chasko, D. W. Alexander

Researchers from the National Institute for Occupational Safety and Health’s Office of Mine Safety and Health Research conducted an assessment of the effects that ground control mesh might have on rock and float coal dust distribution in a coal mine. The increased use of mesh to control roof and rib spall introduces additional elevated surfaces on which rock or coal dust can collect. It is possible to increase the potential for dust explosion propagation if any float coal dust is not adequately inerted. In addition, the mesh may interfere with the collection of representative dust samples when using the pan-and-brush sampling method developed by the U.S. Bureau of Mines and used by the Mine Safety and Health Administration for band sampling. This study estimates the additional coal or rock dust that could accumulate on mesh and develops a means to collect representative dust samples from meshed entries.

Jan 1, 2014

By R. L. Beatty

Bond International Gold's Colosseum gold mine was discovered in 1865. No recorded production occurred, however, until the 1930s, with production of about 19 kg (615 oz) of gold. The mine was closed in 1942 as a nonessential industry during World War II. The property was acquired by Dallhold Resources in mid-1986. Construction of a 1.1-million Mt (1.2-million st), carbon-in-pulp (CIP), cyanide mill began in November 1986 and was completed in September 1987. Minable reserves are estimated to be 9.5 Mt (10.5 million st), with an average grade of 2.1 g/t (0.061 oz per st). This article describes the general process flow and plant equipment. And it looks at the maintenance and operational problems encountered in the first six months of operation. Process description Ore is direct hauled from the open-pit mine 1.5 km (1 mile) to the crushing facility. There it is crushed to -152 mm (-6 in.) with a single- stage, 1.5-m x 1.2-m (60-in. x 48-in.), 186.5-kW (250-hp), Fuller-Traylor jaw crusher. The ore is then stockpiled in a 31.7-kt (35,000-st) reclaim ore pile. Lime is added to the crushed product as it is conveyed to a single 6.4-m x 4-m (21-ft x 13-ft), Hardinge semiautogenous grinding (SAG) mill, followed by a single 4.3-m x 7.3-m (14-ft x 24-ft) Hardinge overflow ball mill. After grinding, the slurry is thickened and then preaereated for three hours. Following preaereation, the pulp is leached with NaCN at a pH of 11, also for three hours. The slurry then goes through a seven-stage CIP circuit for 21 hours. Then the tailings slurry is preaereated for three hours before cyanide destruction using the Inco process. Loaded carbon is eluted using an Anglo American strip, followed by electrowinning on stainless steel wire. The stainless steel wire is transferred to refinery cells where the gold and silver is plated on stainless steel plates. Following electrore-fining, the gold-silver foil is removed, melted, and poured into dore bars for shipment. The crushing, milling, refining, and maintenance processes require 37 people. Crushing The crushing area required changes and modifications following start-up. Several areas are of specific note. Structural failures Rubber support cushion blocks located under the coarse ore bin failed. These were replaced with heavier, more durable blocks and have since appeared to be satisfactory. A severe structural vibration was encountered in the entire crushing facility. A mechanical engineer, brought in by the contractor, determined the structure needed more support and cross-bracing.

Jan 1, 1989

By R. K. Sinha, B. S. Choudhary, Desh Deepak, A. K. Mishra, Hemant Agrawal, Shankar Kumar

Despite several methods (empirical, statistical and machine-learning tools) to calculate blast-induced ground vibration, it is not easy to predict and simulate blast vibration precisely under varying blasting loads and strata conditions due to complications in the blasting procedure. In this study, field blast data were simulated in Ansys software using explicit dynamics, and ground vibrations for 20 single-hole blasts were monitored. The densities of emulsion explosives were in the range of 0.9 to 1.15 g/cm3. In the laboratory, rock properties were determined from rock samples collected from the mine site before blasting. The in-hole velocity of detonation (VoD) and density of the emulsion explosive were also determined and used in numerical analysis to know the ground vibrations at specific points. The results of ground vibrations predicted by the model were validated using field data.

By John S. Wakeman

The initial step in the pelletizing of iron ores is the production of green balls. The importance of this step cannot be overemphasized as the physical quality of the green balls has a very significant effect on the subsequent induration process, regardless of the type of the indurating equipment employed. The ability of the green balls to withstand the rigors of handling, distribution, compaction and drying will have an effect on the degree of success of any pelletizing operation. Many factors affect the physical quality of the green balls including the prior processing of the iron ore, the characteristics of the balling feed and the type and quality of the binder used (if any). When working on the development of a new project or studying an existing operation, it is often desirable to determine what effect variations in these factors will have on green ball quality. It is generally impractical to make these determinations on a commercial, or even pilot plant scale, especially when the number of variables to be studied is large. Because of this, many organizations have developed batch techniques for producing green balls to enable them to perform such investigations with a minimum of time and expense. The batch balling method is at best, only an approximation of commercial balling systems. Many practitioners employ the use of pre-formed seed pellets to initiate a batch run. Thus, the growth mechanism encountered in any experiment is essentially snowballing. Unless an instability is introduced into a balling test (such as an excessive initial feed rate or an unusual feed material characteristic) the growth mechanism of coalescence is not present to a significant extent nor is it desirable. In a continuous operation, both mechanisms are present and necessary to sustaining the system. The batch balling technique thus produces pellets in an idealized manner and cannot be used to directly predict commercial green ball qualities. A general relationship does exist however, and the procedure is fairly sensitive to variations in test parameters. Although many refinements to this technique have been introduced over the years, batch balling is still essentially an art and subject to "operator effect". Therefore, to assure consistant and reliable results, skilled technicians who carefully adhere to established practice must be utilized.

Jan 1, 1971

By L. L. Chasko, D. W. Alexander

Los investigadores del National Institute for Occupational Safety and Health’s Office of Mine Safety and Health Research han evaluado los efectos que la malla de control de suelos podría tener en la distribución de polvo flotante de roca y carbón en minas de carbón. El creciente uso de mallas para controlar el desconchado o caída de material del techo y las vigas introduce superficies elevadas adicionales para recolectar el polvo de roca o de carbón. Es posible que el potencial para la propagación de explosión del polvo se incremente si el polvo flotante de carbón no es convertido en inerte de manera adecuada. Adicionalmente, la malla podría interferir con la recolección de muestras representativas de polvo cuando se usa el método de recipiente y brocha desarrollado por la U.S. Bureau of Mines y usada por la Mine Safety and Health Administration para muestreo de banda. Este estudia hace una estimación del polvo de roca o carbón adicional que pudiera acumularse en la malla y desarrolla un método para recolectar muestras de polvo representativas atrapado en las mallas.

Jan 1, 2014

By Philip R. Whitney

Precipitation of hydrous manganese/iron oxides in streams can be readily observed in much of the northeastern United States, and is apparently a common phenomenon in other glaciated areas (1,2,3,4). Deposition occurs when Mn-enriched ground or surface water enters the stream environment and encounters conditions of higher Eh and pH. The preferred location for deposition is in shallow, fast-flowing segments of stream; the oxides usually form as coatings on detrital material. The experimental studies of Hem(5) and a considerable amount of work on marine and lacustrine manganese nodules(6,7,8) suggest that given an appropriate substrate, deposition of manganese oxides may occur even when the water is undersaturated in Mn with respect to the oxides, due to catalysis by organisms or by silicate, carbonate, or ferric hydroxide surfaces. Once begun, manganese oxide deposition is autocatalytic (9). Studies of the distribution of oxides in various size fractions of stream sediments indicate that the thickness and prevalence of the coatings commonly increases with increasing particle size in the coarse sand and gravel size ranges. Figures 1 and 2 show a fairly typical distribution of leachable metals over nine size fractions from 62 microns up to 8-16 mm. The leaching solution used was neutral ammonium citrate with hydroxylamine hydrochloride, which effectively removes the oxide coatings without significantly attacking most silicates, carbonates or sulfides. Figure 1 shows metal content as ppm of the total sample; figure 2 shows' the same data as micrograms of metal per square millimeter of surface area.

Jan 1, 1975