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By Eurípides do Amaral Vargas Jr., J. A. de Mello Franco

"It is frequently necessary to excavate a tunnel for Civil Engineering purposes, or wells for petroleum exploitation, in laminated rock mass like schists or phyllites or in highly foliated gneisses. The determination of the pre-existing in situ stresses is essential, in order to assure the stability of these excavations. In most cases, the pre-existing triaxial stress field is arbitrary in relation to the tunnel or well axis. For these rock masses the concept of Generalised Plane Strain can be correctly utilized.There are closed form solutions for the calculation of stresses in anisotropic rock masses under Generalised Plane Strain conditions (Lehknitskii, 1981 and Hong , 1994). Based on these analytical solutions, established for the cases of Generalised Plane Strain, a synthetic problem will be formulated: the theoretical in situ stress tensor acting on this rock mass will be determined, with the aid of Bayesian Inverse Problem Techniques, as developed by de Mello Franco (2009). Additionally, the reliability of results obtained will be evaluated, in accordance with the research performed by this author. INTRODUCTIONThe Inverse Problem Technique, as developed in the paper, is based on the definitions and concepts obtained from the current literature and used for the solution of Inverse Problems, but the innovation to be presented is the utilisation of Bayesian Techniques and the determination of the reliability of the results obtained. This will be shown in a synthetic example where the determination of the in situ stress tensor, from strain measurements in a drill hole is supposedly performed. It is assumed that this drill has its axis arbitrarily placed in relation to the rock mass. Generalised Plane Strain conditions will hold for use with problem. The equations of Beltrami – Mitchel, in agreement to Lekhnitskii (1981) and Ong (1994), will be used in this synthetic case, for calculating strains, hypothetically measured in the hole before the final excavations. Finally a synthetic example for the determination of the in situ stress in a fully anisotropic rock mass, based on Bayesian Techniques and its reliability, developed in de Mello Franco (2009) is presented."

Jan 1, 2015

By D. L. Thompson

Foreword The complete history and early development of the Sullivan mine was fully covered in a paper entitled 'The Development of the Sullivan Mine and Processes for the Treatment of its Ores', prepared by the staff of the Consolidated Mining and Smelting Company of Canada, and presented at the Annual Meeting of the British Columbia Division of the Institute at Trail in October, 1924. At a subsequent meeting at Blairmore, Mr. E. G. Montgomery read a paper on the mine, and in 1926 Mr. M. M. O'Brien brought the subject up to date at the joint meeting of the American and Canadian Institutes at Cranbrook. The present paper is necessarily based largely on these earlier accounts. Discovery and Early Development The outcrop was discovered in 1892 and the property was bonded and later sold to the Sullivan Group Mining Company, of Spokane. From 1896 to 1899, surface stripping and test pits (at A) around the outcrop exposed a vien of sulphides with varying amounts of lead and zinc. In some places, a 35 per cent lead ore carrying 15 ounces of silver was found. These lenses were of commercial value. With the completion of the Kimberley branch of the Canadian Pacific railway, in 1900, some systematic development was started. A shaft l00 feet in depth was sunk (at B). Shaft-house, boiler-room, and compressor-plant were erected, and a steam diamond-drill was put into operation.

Jan 1, 1929

By C. Marais

The use of machine vision in the monitoring and control of metallurgical plants has become a very attractive option in the last decade, especially since computing power has increased drastically in the last few years. The use of cameras as a non-intrusive measurement mechanism not only holds the promise of uncomplicated sampling but could provide more consistent monitoring, as well as assistance in decision making and operator and metallurgist training. Although the very first applications of machine vision were in the platinum industry, no automated process control has been developed for platinum group metals (PGMs) as yet. One of the reasons is that to date froth features could not be related to key performance indicators, such as froth grade and recovery. A series of laboratory experiments was conducted on a laboratory-scale platinum froth flotation cell in an effort to determine the relationship between the platinum grade and a combined set of image features and process conditions. A fractional factorial design of experiments was conducted, investigating 6 process conditions, namely air flow rate (x1), pulp level (x2), collector dosage (x3), activator dosage (x4), frother dosage (x5) and depressant dosage(x6), each at levels. Videos were recorded and analysed to extract 20 texture features from each image. By using artificial neural networks (ANN), the nonlinear relationship between the image variables and process conditions and the froth flotation grades could be established. Positive results indicate that the addition of image features to process conditions could be used as sufficient input into advanced model based control systems for flotation plants. Keywords Flotation, machine vision, image analysis, neural networks.

Jan 1, 2011

By David Verrelli, Melissa Kistner, Leanne Smith, Chris Aldrich, Lidia Auret, Warren Bruckard

In this investigation, different mixtures of realgar and orpiment particles were floated in a laboratory batch flotation cell and multivariate image analysis was used to estimate the arsenic content in the froths. The analysis was based on the froth colour, as well as extraction of three groups of textural features, namely those based on grey level co-occurrence matrices (GLCMs), wavelets and local binary patterns (LBPs). Collectively, these features provided better information on the arsenic content of the froths than any one of the individual groups of features. Partial least squares models could explain approximately 78% of the variance in the arsenic by using all the features combined. The colour content, particularly the green component in the red-green-blue (RGB) features, provided almost as much information as each of the three sets of texture-base features individually.

Jan 1, 2014

By Gordon Irons, Kevin Graham, Krishnakumar Krishnapisharody

Ladle or secondary metallurgy in steelmaking is an essential process step for the production of high-quality steel. Professor David Robertson was a pioneer in the modeling of these processes, in particular gas-metal fluid dynamic interactions and the rates of slag-metal reactions. This is now a highly active area of research, and some of the recent developments in this area will be reviewed.

Jan 1, 2014

By L. D. Boughton

Solution mining projects are conducted through one or more boreholes which penetrate en ore body. Proper drilling, completion and maintenance of the boreholes, therefore, is essential to the success of any solution mining operation. Wells drilled for solution mining encounter problems quite similar to problems encountered by the petroleum industry in drilling, completing and maintaining wells for the production of oil, gas or water. Many of the services developed and much of the experience gained by the petroleum industry is applicable to solution mining wells. As in the petroleum industry, each individual wellbore and ore body in a solution mining project provides its own problems. These vary greatly from well to well, and it is not possible to set down data or outline programs that will apply to all wells. Instead, the design of the drilling, completion, production and maintenance programs should be worked out for each individual well. The purpose of this paper, then, is to generally describe materials, equipment and techniques available for these programs and to discuss the purpose and sequence of their use.

Jan 1, 1971

What decision making tools and methods are available to a project owner when there is no clear differentiator between construction alternatives? A team led by a joint venture of Parsons Brinckerhoff and PGH Wong Engineering (PB/Wong) has been providing preliminary engineering services to the San Francisco Municipal Transportation Agency (SFMTA). The SFMTA and PB/Wong team developed several alternative construction methods for the tunnels and stations of the San Francisco Central Subway Project, none of which could be judged clearly better than another using traditional approaches and metrics. The team employed a risk assessment and analysis frame-works as a means of comparative analysis, drawing upon the knowledge of industry experts in the geotechnical, tunneling and construction fields to assist in the effort. This paper presents the approach and results of a cost and schedule risk analysis for two such analyses designed to answer two different questions regarding the advisability of different construction approaches. These assessments paved the way for key decision making in the preliminary engineering phase of the project and formed the foundation for continuing risk management efforts on the project. The focus of this paper is primarily the first two stages of risk management?identification and assessment?and some of the organizational dynamic issues that arise in such efforts.

By Edward C. Peterson

Recent studies indicate that the United States halt substantial reserves of ilmenite, one of the major titanium minerals. However, the studies showed that sources of rutile, another important source of titanium are limited. This paper summarizes and evaluates results and conclusions reached by the various investigations initiated by the Bureau of Mines and others pertaining to the titanium mineral resources of the Nation. Domestic occurrences of ilmenite that are economically exploitable by present-day beneficiation methods are found in Florida, New Jersey, New York, South Carolina, and Virginia. These deposits are estimated to contain 50.3 million tons of titanium dioxide (TiO2). Occurrences of ilmenite that cannot be processed economically under present technological conditions are found in California, Colorado, Minnesota, Montana, Oklahoma, Oregon, Rhode Island, and Wyoming. These reserves amount to 51.1 million tons of TiO2. Reserves of rutile found in the United States are estimated to be 1.8 to 2.1 million tons of TiO2. Other than occurrences in Florida and South Carolina, rutile is found either in small scattered bodies or in deposits where the mineral cannot be recovered economically by present beneficiation methods.

Jan 1, 1966

By H. J. Gerritsen

From presently available components a portable, rugged, reliable apparatus can be built which will be able to detect methane concentrations of 0.1% and lower in air. Sensitivity and design considerations of the apparatus are given. Ways to build even simpler and cheaper apparatus in the future are indicated. Traditionally the problem of detecting and monitoring the presence of dangerous gases present in small concentrations in air has been a difficult one. Whether canaries,' or sophisticated chemical or thermal conductivity methods are used, they seem to be either slow, cumbersome, or otherwise not completely satis factory. A seemingly natural way of gas detection is to measure the strength of absorption undergone by light of a wavelength that the gas to be detected absorbs. This method has been difficult to apply in view of the low power output over a narrow wavelength range in the infrared from traditional glow bar light sources. Besides, the apparatus to select such a narrow band of wavelengths is quite costly and complex. The use of a laser solves these problems simultaneously. Although a variety of lasers are available to detect a variety of gases (such as carbon monoxide or methane) whose early detection would be desirable, this paper deals exclusively with the use of lasers for methane detection. ABSORPTION SPECTRUM OF METHANE IN AIR The absorption spectrum of pure methane is very well known.2-4 There are four fundamental vibrations, all occurring in the infrared of which only two absorb strongly. They occur at 3.3 µ and 7.7 µ. The absorption spectrum is quite complicated due to the fact that the methane molecule can rotate in a variety of rotational quantum states. These rotational states are furthermore split by anharmonic forces such as the Coriolis force.4 When methane is present in air at atmospheric pressure, much of the very fine structure due to the anharmonic force is washed out since the pressure broadening is of the same magnitude as the splitting due to anharmonicity. For most of the spectrum at 3.3 µ, the rotational lines are typically separated by 0.01µ while the individual linewidth is 0.0001 µ. It is thus very important that the laser emit at a wavelength that coincides with one of these rotational lines. Before elaborating on the point that such a laser exists and how it performs, it is necessary for later discussion to point out that in the

Jan 1, 1967

By C. J. Weiss

"A commercially available Through-the-Earth (TTE) communications system was evaluated at an underground coal mine in eastern Kentucky. This field study was conducted as part of a larger multi-site evaluation of available TTE systems to determine their operational sensitivity. Field testing is being performed along with simulation techniques developed for geophysical surveys. The results of the field test will additionally be used to determine the applicability of these simulation techniques to TTE communications. The mine detailed in this paper was idled at the time of the study, which provided the nearest practical representation of a post-event mine shutdown. For this study, the three following communication modes were tested: surface-to-underground, underground-to-surface and surface-to-surface. Standard deployments of the TTE system using the manufacturer’s recommended procedures were able to achieve clear communications between underground and surface locations. Other arrangements of the units yielded intriguing results, some of which were predicted by computer simulations, others were unexpected. Future experimentation is planned to further evaluate the observed phenomena. INTRODUCTION The ability to establish effective communication between surface and underground personnel after a mine event is essential for both mine evacuation and mine rescue efforts. Current communication technology is reliant on physical infrastructure, such as antennas, cables, and repeaters, located throughout the mine. Such systems are easily disabled during a mine event because of their vulnerability to physical damage. A true emergency communications system would have the ability to function regardless of a mine’s physical state. Through-the-Earth (TTE) wireless communications technology has the potential to provide such a tool. Wireless TTE communications are exceptionally challenging because electromagnetic (EM), or radio, signals are subject to drastic attenuation as they travel through solid strata. In addition to attenuation, EM wave propagation is directly affected by the physical and petrographic characteristics, mineral compositions, metamorphic properties, and the degree of water infiltrations in the strata [1-5]. These strata characteristics are unique to each mine thus making the design of an effective, universally deployable, and reliable TTE communications system very difficult. At present, TTE technology is in the preliminary stages of practical deployment with only a few permissible TTE systems commercially available."

Jan 1, 2015

By I. Longson

As a longwall coalface advances a caved goaf or waste region is left behind. Air flow takes place through this permeable goaf due to the pressure differentials existing across it and en route this leakage air picks up both heat and moisture. A marked deterioration in climatic conditions occurs in the face area at all points downstream of where this leakage air rejoins the main air-stream. This goaf heat source can make a very significant contribution, typically 30-40% to the rate of total heat pickup on an advancing UK longwall coalface with a VST of 40°C and hence on the climatic conditions that prevail at the return end and in the return gate of the face. The magnitude of the rate of heat collection from the goaf depends on a number of factors but it has been established that it is particularly influenced by the prevailing virgin rock temperature and the total flow rate of the leakage air. This paper proposes a model for the goaf based on a packed bed analogy and other assumptions required in order to evaluate the rate of heat pickup are identified. The outlet condition of the leakage air predicted by the model have been shown to correlate with underground measurements taken for a range of different production patterns with the face cutter at various locations on the face. The sensitivity of these predictions to variations in the input data has been tested and is commented on. At this stage of the development the capabilities and predictive limitations of the model are discussed. Further areas of investigation are suggested in order to improve the predictive ability and to extend the versatility of the model.

Jan 1, 1989

By Daniel Magill, Jim Gentry

"Acrylamide chemical grout (C3H2NO) has been successfully used for over 50 years to control groundwater and stop infiltration. This paper will address three unique projects involving the control of groundwater with each study providing special circumstances and geological conditions: encapsulation of radioactive hazardous waste in the United States, a tailings dam for a large copper/gold mine in Argentina and 27 miles of leaking subway in Canada. The primary reasons for selecting acrylamide grout were based on the following characteristics: thinnest chemical grout on the market, a true solution grout which contains no suspended solids in the blended product, flexible gel set times, and a 362 year half-life in soil as determined by the U.S. Department of Energy.INTRODUCTIONChemical grouting has been successfully used for over fifty years to control the movement of groundwater in a wide variety of applications including:•, Hazardous Waste Containment•, Subways & Tunnels•, Mines & Tailings Dams•, Concrete & Earthen Dams•, Underwater Structures•, Beneath/Around Underground Structures•, Mainline Sewers, Laterals, Manholes•, Large Soil Stabilization ProjectsThis presentation will review three projects where chemical grout was utilized to address some very difficult water control challenges, each providing special circumstances and geological conditions:1. Pre-construction seepage control at a mine tailings dam2. 27 miles of leaking subway3. Encapsulation of radio-active hazardous wasteThe reasons for selecting acrylamide grout as the solution for controlling groundwater in these selected projects were based on the following characteristics:1. Acrylamide grout is the thinnest chemical grout on the market2. No suspended solids which allows acrylamide grout to travel anywhere water can travel3. Flexible gel set times from 5 seconds to 10+ hours4. U.S. Department of Energy studies conclude that acrylamide chemical grout has a 362 year half-life in soil and can reduce the permeability of rock/soil to less than 10-8 meters per second (m/s)"

Jan 1, 2017

By Lloyd Williams

1. This investigation shows that the Poplar Creek is the most important bed in Scott County from a production standpoint. Although the Poplar Creek bed contains the largest reserve, the Big Mary has a larger recoverable reserve. Estimates of reserves also have been made for the Pewee, Red Ash, Windrock, Upper Pioneer, Jellico, and White Oak beds. 2. Known measured and indicated reserves of coal, based on a minimum bed thickness of 14 inches and on 1,800 short tons per acre-foot of coal in place, are estimated to be 143 million tons as of January 1, 1954. Of this total, 74 million tons is in beds 28 inches and more thick. Areas in each bed were omitted from the estimate because available data relative to the bed characteristics are too meager for making an estimate that conforms with the definitions of measured and indicated coal adopted for this study. Should future drilling or development prove reserves in these areas, such reserves should be added to the total estimated reserves.

Jan 1, 1956

By George S. Koch

We evaluate the exploration effort by diamond drilling for zinc in central Tennessee and southern Kentucky through a statistical analysis comparing the Middle Tennessee district with the older Tri-State and Upper Mississippi Valley districts. All of the ore deposits are of the Mississippi Valley type and are similar geologically. Through statistical analyses we attempt to answer these questions: Had the drilling density in the Middle Tennessee district been applied to the Tri-State district, how much of the ore in the Tri-State would have been discovered? Had this drilling been done in the Upper Mississippi Valley district, how much of the ore in that district would have been found? Which of these two older districts does Middle Tennessee more closely resemble in intensity of zinc mineralization? Is more drilling warranted in the Middle Tennessee district? Our data base includes tonnage and area distributions of ore deposits in the Tri-State dis¬trict, sizes of ore bodies and probabilities of their recognition in the three districts, and data for the Elmwood mine in the Middle Tennessee district. Our statistical analysis considers the consequences of drilling holes in the three districts on square grids at coarse, intermediate, and fine spacings. We conclude that the drilling pattern assumed for Middle Tennessee would have found some but not all of the ore in the two older districts. We believe that in intensity of mineralization Middle Tennessee more closely resembles the Tri-State than the Upper Mississippi Valley district, and that more drilling is warranted in the Middle Tennessee district.

Jan 1, 1979

By Charles A. Kumke

In June 1942 , ' the Bureau of Mines selected the Zonia copper mine , near Kirkland , Yavapai County , Arizona , as a property meriting investigation in connection with its search for supplies of strategic minerals for use in the war . The following month , representatives of the War Production . Board conferred with Bureau officials and requested that the property be explored with the object of determining the tonnage and grade of ore that could be brought into production quickly and mined cheaply by open-pit methods . The work wa's designed to verify information submitted by the owners in support of an application for a Government loan. It was essential that the investigations be completed promptly , so that operations might be planned and copper produced for war needs . The investigations called for surface trenching , diamond drilling , and check sampling of underground workings . Unable to purchase equipment for trenching without considerable delay , the Bureau saved time by borrowing most of the necessary items from the Golden Queen mine of the Gold Fields Development Co. at Mohave , Calif. This company , whose engineers had sampled some of the old trenches , had a tentative agreement with the owners to operate and manage the Zonia mine in event the loan was granted . Additional equipment was borrowed from two Governmental agencies . The exploratory work , completed in 16 weeks , was carried on 7 days a week .

Mar 1, 1947

By R. G. Hite, R. G. Rowe

The Crandon deposit, located in northern Wisconsin, is a 65.8 million ton Precambrian volcanogenic massive sulfide deposit which averages 1.4% copper and 5.8% zinc. The deposit is classic in origin, mineralogy and shape. Comprehensive understanding of the geology of both the deposit and the project site has been fundamental to the credibility and success of project feasibility studies and regulatory permit preparation. Mine development in the current investment and regulatory climate requires thorough and timely application of geologic tools. From 1977-1980 geologic activities were focused on the typical objectives of orebody delineation, reserve estimation, depositional geology, and general site investigation. Results from these programs formed the basis for the project's preliminary feasibility studies. Since 1981 further geologic investigations have provided criteria for project design, site management, and operational permitting. Activities have included mine entry position definition drilling, devel reserve modeling, large diameter (150 mm) core drilling for mill pilot samples, rock mechanics testing, and evaluation of the glacial overburden/deposit geohydrology for computer simulation.

Jan 1, 1992

By O. Q. Leone

Excellent metal quality, with lower power requirement, is attained in electrorefining titanium by using internal heating of the fused-salt bath. An internal heater provides more effective heat utilization, simplifies structural components in cell design, and prolongs cell life by eliminating direct application of heat to the cell container. This Bureau of Mines report covers one phase of the research in progress at the Electrometallurgical Experiment Station at Boulder City, Nev., for improving the techniques and lowering the total power requirement for electro-refining titanium metal.

Jan 1, 1959

By Jay F. Colinet

Coal workers’ pneumoconiosis (CWP), commonly known as black lung, is caused by the inhalation of respirable coal mine dust and is a disabling and potentially fatal lung disease with no cure. Historically, CWP has taken a tremendous human and financial toll in the US coal mining industry. Recent health surveillance data indicates that CWP continues to occur at elevated levels. Respirable coal dust exposure must be controlled to prevent the development of CWP. The Pittsburgh Mining Research Division of the National Institute for Occupational Safety and Health (NIOSH) conducts laboratory and mine-site research to identify control technologies that can be used to successfully reduce respirable dust levels. Various technologies, using multiple methods of control, can be applied in order to reduce dust levels. An overview ofCWP’s impact and a general methodology for controlling respirable dust in underground coal mines are discussed in this paper.

Jul 30, 2020

La presente investigación revela aspectos sobre los métodos geoquímicos aplicados a la exploración de depósitos minerales, como las aplicaciones prácticas e indicaciones sobre de las diversas técnicas empleadas en el campo y y laboratorio. La exploración química de los depósitos minerales como método de prospección, comprende la investigación e interpretación de anomalías químicas relacionadas a la mineralización dentro de varias sustancias naturales como rocas, aguas y vegetación para así localizar depósitos minerales ocultos. La naturaleza de estas anomalías se divide en dos grupos: las anomalías primarias formadas durante el periodo de mineralización y las secundarias, formadas por la destrucción y dispersión del depósito metalífero durante el ciclo de intemperismo y erosión. Sin embargo, existen algunas anomalías de naturaleza "residual" o "vestigial", las cuales son descubiertas mediante el muestreo sistemático de rocas o de los suelos que de ellas derivan. A esto se suma, la dispersión de elementos en solución puede dar origen a muchas variedades de anomalías secundarias que tienen importancia en la exploración geoquímica como las dispersiones secundarias en las aguas de fuentes, pozos y aguas corrientes, en las cajas de cuerpos mineralizados; en coberturas de carácter no residual sobre y cerca de depósitos mineralizados y aquellas dispersiones secundarias en vegetales. Paralelamente a esta exploración geoquímica, tenemos otras métodos comom los técnicas colorimétricas, basadas en reactivos que indican cambios de color y los de análisis espectográfico, que complementan paulatinamente dicho proceso minerológico.

Jul 20, 1956

By M. Kaitz

A continuing discussion in both the petroleum engineering and economic literature is directed to the difficulties encountered in the use of discounted cash flow rate of return (DCF) as a measure of investment worth. Although useful in most Instances, DCF has been criticized because it is time-consuming in its trial-and-error solution, theoretically invalid, not adaptable to cash flow streams yielding multiple return solutions and not entirely reliable in selecting between mutually exclusive investments. The theoretical invalidity of DCF stems from the reinvestment assumption implicit in the calculation that earnings are reinvested at the DCF rate. The emerging consensus of the economic literature is that the net present value or the present worth of the net cash flow stream (discounting at the average opportunity or cost of capital rate) is more correct and reliable. Other criteria proposed have been ratios of net present value divided by initial investment or by present value of all investments in a project. All of these criteria are simple to determine and explicitly assume a reinvestment rate for [he income generated by a project. This paper develops and discusses a theoretically valid profitability criterion which is simple to compute and retains the appeal of a percent return on investment. It is called "percentage gain on investment" or PGI. It measures the gain an investment is expected to realize over like capital invested in the average opportunity and explicitly considers reinvestment potential. Why add another Concept to the large array of investment criteria now available, any one of which, or perhaps a combination of several, appears to embrace the form's (or individuals) objectives? The answer is that not one of the existing criteria provides both a readily comprehensible and theoretically valid measure of risk coverage that has general application. The proposed PGI does fulfill these requirements. INTRODUCTION An ancient expression warns that "one must yield to the times" — there are better ways of doing things. A review of the petroleum engineering and economic literature on one topic alone, measurement of investment worth, certainly is witness to this truth. In use for a number of years, the DCF has recently received attention, directed mainly to its theoretical invalidity. Several alternatives to DCF have been proposed to provide a valid, simply determined criterion to describe investment worth and to overcome the criticisms previously mentioned. This paper introduces another method called percentage gain on investment (PGI) and is proposed as but one of several yardsticks that should be used in making investment decisions. MEASURES OF INVESTMENT WORTH This paper will consider only those criteria which give weight to the time pattern of future earnings. These criteria are usually compared with an average opportunity rate or cost of capital of the firm to judge the relative worth of the investment. For purposes of demonstration, a 9 percent average opportunity rate will be used throughout this paper. Implicit in the DCF calculation is the assumption that earnings are reinvested at the DCF rate. Some argue, though, that there is no reinvestment assumption,' that the DCF rate is simply that maximum rate of interest one can pay on the investment over the life of the project and break even. The determination of DCF is accomplished by discounting the net cash flow stream at that rate (DCF) which will yield zero. The question is: why should reinvestment potential be explicitly considered in calculating return on investment or other criteria measuring economic worth? Perhaps the answer lies in consistent or equal treatment of future cash flow. It appears entirely illogical to give different present worth value to $1 received, say, 10 years from now, which is the circumstance resulting in comparing projects with different DCF returns. In fact, $1 received in 10 years has the same value regardless of which project generated the income. DCF return thus favors investment projects which are expected to provide early income as compared to those providing long-term income. Not surprisingly, the controversy on reinvestment assumption is an old one. Hoskold' discussed this same problem in 1877. He considered the future income from mineral properties as an annuity or a series of fixed future payments. (As will be demonstrated, his equation can be modified for variable income.) Prior to Hoskold, the value or what one could pay for the mine, was determined with the use of standard, single-interest tables. Here is what Hoskold said with regard to these tables. "This table, and others of its kind, to be found in most works on annuities, is constructed correctly according to