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By L. M. Yokum

Tremendous strides have been made in front end loaders in the last fifteen years. Fifteen years ago a 2; cubic yard front end loader was the largest standard machine you could purchase. Today there are two commercially available 15 yard front end loaders and many 10 yard front end loaders. The estimated total worldwide market for all front end loaders over one cubic yard has increased to over 30,000 units yearly. The trend for front end loaders, in general, and for the mining market, in particular, is to larger and larger loaders. Today there are 18 cubic yard and a 24 cubic yard front end loader in prototype form. It is not inconceivable that within another fifteen years that there will be front end loaders in the 50 cubic yard class with design features quite different from today's. These larger loaders are being designed at the demand of the mining industry and the design criteria are being directed at this market area. The costs of these larger loaders will be greater per unit of capacity, and it is the intent of the various manufacturers that they will be more reliable, be easier to service, give greater availability, live longer, and cost less to maintain, than previous loaders. It is also the intent of the manufacturers to compete directly with the large mining shovel as the front end loaders become appropriately larger and more reliable. There has been some trend in this direction in the past with smaller shovels and loaders. In Figure No. 1 are data for U.S. production of front end loaders (5-6 cubic yard class and 10 cubic yard class) and U.S. production of cable operation, crawler mounted power shovels, draglines and cranes (1; to 5 cubic yard class) for the years 1965 and 1970. (Source: Bureau of Census, U.S. Department of Commerce.)

Jan 1, 1972

By N. B. Prenn

Case Studies in Open Pit Design Using Whittle 4D will be discussing the following four examples: 1) Optimization of process plant design using Whittle 4D as a sizing tool. In this case, the home office and project team had different views of the size of the final project. The home office wanted to reduce the size of the project to reduce capital expenditure, while the project team suggested a larger project. Whittle 4D was used to determine Net Present Value and Internal Rate of Return using the Whittle scheduler (FDAN) to schedule many alternatives, and calculate the NPV and return for each alternative. 2) Comparison of pit optimization methods: Lerchs-Grossman vs floating cone. Many pits are developed based on floating cone economics. A comparison of methods in one large gold mine resulted in the stripping ratio of the pit being reduced by 10% in the Whittle 4D optimization as compared to the floating cone optimization. 3) Pit optimization to determine if a new mill is justified. A large heap leach gold and silver mine needed to determine if a new mill was justified. The planning and scheduling would take several man months if completed without pit optimization and scheduling software. Whittle 4D software proved to be very effective in providing optimized pits and a mine schedule in a short time frame. 4) Pit optimization to determine how to mine and size. Open pit optimization determined where the underground operation should start, and whether the material should be processed by milling or heap leaching. One of our clients asked for help in determining where the pit should end and a new underground operation start. We used Whittle 4D to help determine where the pit should end and where to go underground. In addition the operation needed to determine how to process the material.

Jan 1, 1996

By Patrick B. Kenny

Generally speaking, it is safe to address this conference as a conclave of Engineers, Owners' Agents, Governmental Representatives, and Contractors. As a group, we have assembled here to learn of our compatriots engaged in similiar underground operations throughout the United States and the World. We are here to learn of improved methods, higher technology, and better management. Through the acquisition of this knowledge, we each hope we can improve our own particular services, products and projects. This session is dedicated to a discussion of "Costs". The most apparent reason for a discussion of costs at this level is to expose subjects affecting costs and propose methods to reduce them. From that premise a contractor can identify three areas of discussion: design considerations, contract considerations, and governmental considerations. A fourth area of consideration is an introspective view of the contractor's role in the design construct process. Unnecessary costs and risks attributable to these areas are contributing excessively to ever increasing project and system costs. DESIGN CONSIDERATIONS On April 20, 1977 the Metropolitan Sanitary District of Greater Chicago accepted proposals for the Tunnel and Reservoir Plan on Contract A and Contract B. This letting called for construction of over 33 km (21 miles) of the Mainstream Tunnel bored at 9.75 m (32 ft) to 10.67 m (35 ft.) in diameter. Also included were all the appurtenant collecting and regulating structures. The proposal allowed the

Jan 1, 1979

By A. Mei, F. Amadini, F. Cernera, D. Baliani, A. Flor, M. La Morgia, F. Sassi

The risk of TBM jamming because of squeezing rock mass or excessive caving (instability of the cavity) conditions is always a focal point while boring long and deep tunnels with shielded TBMs. Mechanized excavation provides a large amount of real-time data, for each machine’s parameters. Several analyses have been executed to assess the correlations between different sets of TBM parameters for the exploratory tunnel. Instead of analyzing the full dataset, a different approach is proposed, with data processed sequentially to simulate the real excavation situation. The probability distributions are recalculated together with their statistical parameters while advancing. This approach is extended also to the training of a Machine Learning model able to foresee the behavior at future rings based on past rings (using a Recurrent Neural Network). The predictions show a promising first step toward creating practical tools that can assist contractors and designers to correlate and predict TBM excavation data. These tools will assist to predict and quantify high risk situations that could arise during excavation.

Jun 13, 2023

By L. J. Nicks

The current U.S. Bureau of Mines research program is addressing the recovery of flake graphite from kish, a steelmaking waste product, and the use of zeolites from abundant domestic natural deposits for efficiently cleaning up mining industry wastewater. The United States is almost totally dependent on imports for its graphite needs, but this may change depending upon the results from a pilot plant being constructed by industry using Bureau technology. Standard mineral processing techniques were applied by the Bureau to recover high-quality flake graphite from kish. It was considered innovative enough to receive an R&D 100 Award in 1992, and its commercialization has the potential to supply the total U.S. demands for graphite many times over. Zeolites have ion exchange properties similar to ion exchange resins, but are less expensive and available in large quantities. Samples of naturally occurring zeolites were tested for their efficiency in removing metal ions from synthetic and industrial waste solutions. The tests focused on defining their selecting, loading, eluting, and regenerating characteristics, and on developing a method for recovering the metal ions as added value products. The results showed that the removal of metal ions with zeolites from acid rock drainage (ARD) solutions is technically feasible and that this technique has the potential for being used in an integrated chemical treatment systems approach either as a primary or secondary cleaning step.

Jan 1, 1995

By R. V. Ramani, W. Miola

The MSHA prescribed method for the determination of quartz in airborne respirable-dust samples from underground coal mines is the P-7 method, a combination of low-temperature, radio-frequency ashing (LTA) and infrared analysis (IR). There is no prescribed procedure for quartz analysis in bulk samples of coal and host rock. Dispersive infrared (IR), Fourier-transform infrared (FTIR) and X-ray diffraction (XRD) methods are most commonly used for the analysis of quartz in powders. Several aspects of the experimental procedures, such as the preparation of the analysis sample from bulk samples, ashing techniques, scanning procedures, peak measurement location, calibration techniques, sample amounts, size consist and data interpretation, affect the results from each of the methods differently. Significant differences in analytical results obtained from X-ray diffraction (XRD) and infrared spectroscopy (IR) on the same samples are reported. All studies point to the need for reliable quartz analysis methods. In a recent research program, a procedure for preparing bulk-coal and host-rock samples for quantitative quartz analysis was developed. Further, the results from X-ray diffractometry and infrared spectroscopy for quartz content on identical samples were compared. Calibrations with pure and mixed standards were used to assess the influence of particle-size distribution, matrix and calibration on the analytical results. In this paper, several issues concerning the measurement of quartz in the samples of coal, host-rock and airborne respirable dust from mines are outlined and quantified.

Jan 1, 1996

By R. J. Sweigard, R. V. Ramani

The effects of postmining land use planning are addressed in this paper. These effects may include savings in reclamation costs and increased value of reclaimed land. However, this may result in greater planning costs and possible delays in production. Therefore, an economic analysis was undertaken in an effort to determine the importance of each potential result and to quantify the overall economic impact of postmining land use planning. A discounted cash flow analysis was performed using a surface mine cost model to analyze the sensitivity of selling price to changes in various postmining land use planning parameters. As a result of this analysis, it was determined that the profitability of a project is most sensitive to delays in production, particularly if the delay occurs after major investments have been made. Many methods have been proposed for evaluating postmining land use alternatives (Sweigard and Ramani, 1981). Both quantitative methods, such as benefit-cost analysis (Brock and Brooks, 1968), and nonquantitative methods have been proposed. The application of one specific analytical method is pursued in this paper.

Jan 1, 1988

By H. Wilcox, M. Prichard, Y. P. Chugh

Environmental considerations related to the disposal of coal combustion byproducts (CCBs) and the impacts of deforestation associated with the harvesting of timber for utilization as roof supports in mines should become more severe in the future, as landfill space and suitable timber reserves become more scarce. To help address these concerns, lightweight artificial supports, such as post and crib elements, that use large percentages of coal combustion byproducts as aggregate have been developed for use in underground mines. These structural products show equal or better engineering characteristics than timber, and they have the potential to replace timber support in underground mines. CCB-based ultralight structural material (ULSM) has also been developed and commercialized for use in the construction of ventilation stoppings in underground mines. The bulk densities of these blocks range from 0.40 to 0.64 g/cm3 (25 to 40 lb per cu ft) with more than 75% CCBs. Efforts are also given to develop and demonstrate large volume CCB-based subgrade improvement technique for road construction. Soil treated with SIUC fluidized-bed combustion (FBC) fly ash developed an immediate bearing value exceeding 25% with a swelling strain of less than I %, which is greater than untreated soils, and met Illinois Department of Transportation (IDOT) standard specifications. In this paper, development procedures, engineering characteristics and beneficial uses of CCB-based structural products are given.

Jan 1, 2002

By Andrzej Wala

Constantly increasing demand for energy materials and metal ores brought about tremendous progress in mining techniques which are characterised by a high degree of mechanization and concentration of works. One of the recent trends in underground mining mechanization is connected with an application of heavy machines with diesel engines [l],[2]. The introduction of diesel engines in mining all over world caused not only improvement in economic conditions but also the necessity to prevent contamination of air in the mine by toxic agents in diesel exhaust emissions. A generally used way of eliminating exhaust gases is proper ventilation of the cross cut by means of providing permanent exchange of air that would guarantee in every point of the cross cut and in every moment the decay in concentration of exhaust gases beyond threshold limit [3][4][5][6][7][8][9][10]. The present paper is an attempt to define a mathematical model describing the changes of concentration in cross cut face to which fresh air is distributed by ventilators and tubes in a forcing way. Obtained model should offer its practical adaptability to engineering calculation of the amount of fresh air needed for diluting and eliminating exhaust gases beyond threshold limit. Justness of these models has been confirmed by investigation of the growth of nitrogen dioxide concentration in air environment in some cross cut faces of Kiirunavaara iron ore mine in Kiruna (Sweden).

Jan 1, 1980

By K. Norrena, E. Magri

An important problem in mine operations is the classification of material as waste, low-grade stockpile and ore. This classification must often be made with blasthole data that are widely spaced and that have sampling errors. Geostatistical-simulation techniques combined with basic economic principles allow a procedure for classification that maximizes the expected profit. Geostatistical-simulation methods (Gaussian, indicator or annealing-based) allow the integration of hard and soft data in the creation of alternative, equally probable realizations of the mineral grades. At each location, for each realization one calculates the "profit" if the block were to be classified as ore or waste. The optimal classification is the one that maximizes expected profit (a maximum profit selec¬tion or MPS procedure). In this paper, the authors discuss the theoretical justification of the method and implementation details. The use of blasthole data from different types of mineral deposits, that is, different levels of continuity, are considered. The authors also show the efficacy of the procedure with different levels of sampling error. The increased revenue due to the MPS procedure and improved sampling is shown. The paper shows the geostatistical-simulation procedure and the uncertainty in block grades that result from incomplete and imperfect sampling. The optimal classification is presented. Optimal block classifications are transferred to realizable dig limits by hand-drawing polygonal boundaries. The results of the proposed method are compared to classification based on kriging. Limitations and areas of future work are identified.

Jan 1, 2000

By P. A. Plunkert, D. E. Morse, L. McCartan, S. F. Sibley

Following the recession of 2001, restrained consumer spending, declines in domestic manufacturing and industrial output, and increased unemployment led to a lack-luster year in the domestic economy. In 2002, the U.S. real gross domestic product (GPD) grew only 2.4%. Significant production declines in the U.S. metals industry were registered by copper, lead and zinc producers. Steel producers, despite a slight improvement in shipments, continued to face strong foreign competition, higher energy costs and lower prices for their products. Homebuilding and other domestic construction sectors— major consumers of nonmetallic mineral products such as cement, brick, glass and stone — remained strong enough to help raise the output of industrial mineral materials slightly above 2001 levels. A strong U.S. dollar relative to other national currencies continued to weaken the competitive stance of U.S. metal and non-metal mineral materials companies alike against foreign producers in markets at home and abroad.

Jan 1, 2003

By Kim A. Lapakko, David A. Antonson, Jon R. Wagner

This study examined the potential of mixing rotary kiln fines (RK fines), a waste product generated when limestone is converted to lime (CaO), with acid producing mine waste to provide 1) short-term mitigation by neutralizing acid produced by iron sulfide oxidation and 2) long-term mitigation by facilitating the passivation of iron sulfide mineral surfaces. Five loadings of RK fines were mixed with 75 g of Duluth Complex rock to produce neutralization potential (NP) added: acid potential (AP) quotients of 0,0.11,0.22,0.66 and 1.1. The mixtures were subjected to wet-dry cycling laboratory testing for 585 weeks. The rock alone produced acidic drainage, with pH decreasing below 4 after about 20 weeks of reaction and ultimately reaching the approximate range of 3.3 to 3.5; sulfate release did not decrease over time. The RK fines elevated pH and inhibited sulfate release for time periods which increased with the mass of RK fines present. The pH of drainage from the 0.11 quotient (NP added1AP) loading decreased below 6.0 after 75 weeks of dissolution and decreased to 3.6 after 117 weeks, at which time the reactor was terminated. The duplicate 0.22 quotient loadings of RK fines decreased below 6.0 after 95 and 170 weeks. The former was terminated after 117 weeks, and the latter reached a minimum pH of 2.8 after 512 weeks. Drainage pH from the 0.66 quotient decreased below 6 after 581 weeks. For the drainages which acidified, the cumulative calcium release prior to pH decreasing below 6.0 was 92 to 103 percent of that initially present as calcium carbonateloxide in the RK fines. The pH of drainage from the 1.1 quotient typically remained above 8.0 throughout the period of record. Sulfate concentrations in the drainages decreased while the neutralizing fraction of the RK fines was present, but increased after this fraction was depleted.

Jan 1, 2000

By R. M. Williams

Introduction Ring roller mills are efficient size reduction machines embodying the following machine functions: 1) Size Reduction: from a feed size of 2 in. to various size products as fine as 400 mesh, or granulation from 2 in. to 6 mesh containing a minimum of fines. 2) Drying: fluid bed drying of wet feed materials. 3) Conveying: negative pressure air system results in dust-free conveying. 4) Beneficiation: liberation and removal of foreign materials from the auxiliary bottom discharge simultaneously while grinding. Operation Operation of the roller mill system, Figs. 78 and 79, is completely automatic. A feeder introduces raw material into the grinding chamber in the base of the roller mill at a rate determined by pressure variations within the roller mill as material is ground and air conveyed away. The feeder will be activated by the reduced static pressure and introduce unground material into the system, thereby maintaining a constant differential pressure. Plows located ahead of each grinding roll direct the material upward and between the grinding rolls and the bull ring where it is ground to size. The grinding rolls are free to swing out centrifugally, which forces them to bear upon and grind the raw material. Being free to pivot axially, the rolls automatically assume the proper position for grinding and need no adjustment to compensate for wear. Rotation of the rolls is by rolling contact. Once ground to size, material is swept out of the mill by the controlled air flow from the centrifugal main mill fan. Air suspended, the ground material passing through the adjustable spinner separator. In the separator, an accurate size classification is made which allows product-size material to be conveyed away from the roller mill while oversize material is returned internally for additional grinding. By varying the speed of the separator drive, more or less cyclonic action is achieved at this location, effectively controlling product size. Product sized material is removed from the airstream by the cyclone collector. Typically, a conveyor or product storage bin will be located to accept the product as it exits from the bottom of the cyclone collector.

Jan 1, 1985

By David A. Grisafe

Divided opinions concerning dredging-permit locations and boating uses on the Kansas River in northeastern Kansas led to a study of the recreation potential on the river by a legislatively mandated interagency group (five agencies) that included the Kansas Geological Survey (KGS). In addition, the KGS conducted its own study of the river corridor, encompassing the development, geology, and economic resources of the corridor (Brady and others, 1998). The corridor area is 12 mi wide and 140 mi long (171 river miles). Included in the study was the potential impact of restric¬tions to river dredging. The Kansas River and its floodplain in northeastern Kansas are underlain by Lower Permian and Upper Pennsylvanian limestones and shales. The river and its floodplain are the major sources of sand and gravel for northeastern Kansas, and the limestones along the river bluffs supply crushed stone and building stone. The population of the 10-county area bordering the river has grown by 20% since 1980, and now comprises nearly 40% of the state's population (U.S. Bureau of the Census, 1996). Projections (Floerchinger, 1992) indicate close to 50% of the Kansas population will reside in these counties by 2025, with a continued increase in the demand for aggregates. Factors such as floodplain width, price and availability of land, and overburden ratios tend to favor river dredging on the lower part of the river, and floodplain or pit dredging on the upper portion. The use of alternate sources of sand and gravel such as the Missouri and Arkansas Rivers would increase sand prices due to transportation costs to much of the 10-county area. In 1996, river and pit dredges along the Kansas River supplied more than 3 million tons of sand and gravel valued at about $8 million to northeastern Kansas. As a result of its study, the KGS had concerns with the idea of large recreation zones on the river that excluded river dredging in areas of presently large population and projected population growth. This controversial issue is likely to recur elsewhere.

Jan 1, 1999

By T. Mudder

The objectives for closure of a hard rock mine include minimizing long term environmental liability, attaining regulatory compliance, and maintaining geotechnical stability, while closing as cost-effectively as possible. Proper planning for closure should come during the feasibility study, design and permitting phases, and during operations as updates. The lack of a proper or updated closure plan can result in severe environmental and economic consequences. Effective mine closure is the result of a combination of innovative concepts, long-term commitments, and multi-party cooperation. The purpose of this paper is to discuss concepts, commitments, and cooperation as they relate to an effective closure plan.

Jan 1, 1999

By Patricia Pride, Kurt Bettger, Jack Raymer

"INTRODUCTION The Jefferson Barracks Tunnel is in the final stages of design and is expected to go out to bid in the summer of 2016. The project is located in south St. Louis County along the west bank of the Mississippi River, about 13 km downstream of the St. Louis Gateway Arch. The project consists of a deep sanitary sewer tunnel, a deep pump station and several intakes. The intakes will divert sanitary flows into the tunnel and the tunnel will convey the flows by gravity to the Lemay No. 3 Pump Station, which will pump them up into the Lemay Waste Water Treatment Plant. The tunnel is about 5.4 km long and will be lined with 84-inch (2.1 m) fiberglass pipe. It drops at a gradient of 0.1 percent from south to north and will be bored through strong limestone using a hard-rock tunnel boring machine (TBM). The diameter of the TBM is anticipated to be about 3.4 m. The Owner’s original concept was for a relatively shallow tunnel so as to minimize construction and pumping costs. The preferred alignment ran close to the river, next to the existing force main, which was to be abandoned. Keeping the tunnel close to the force main would reduce the amount of shallow sewer work needed to connect the existing feeder sewers to the new tunnel. Several geotechnical investigations were performed, with shallowly focused geophysics and the borings all going exactly down the conceptual tunnel depth. Limestone bluffs run along the Missouri side of the river. These bluffs are pockmarked by sinkholes and riddled with karst. Large, well-known caves occur both north and south of the alignment. Karst features, including deep crevices and possible caves, were found in those early geotechnical investigations. Many of these features extended well below the level of the Mississippi River and would have been encountered by the tunnel. If a large crevice or cave were encountered, then the inflow of mud and water into the tunnel could have been large and possibly uncontrollable. Something had to be done to mitigate this situation. Pre-excavation grouting was considered, but the program would have been huge and extremely expensive. Using a closed-face TBM with bolted and gasketed lining was also considered, but that too was both risky and extremely expensive. The Owner could have abandoned the tunnel altogether and built a new force main, but that would have brought a whole new set of problems and was undesirable to the Owner. The last option was to move the tunnel away from the karst."

Jan 1, 2016

By J. H. Daniel

Dust-related respiratory disease remains the major health concern in mining, and health agencies are proposing more stringent standards. The U.S. Bureau of Mines (USBM) is investigating techniques to continuously monitor respirable dust in real-time during the coal or ore extraction process. Continuous monitoring will allow mine operators to evaluate hazardous dust concentrations and adjust the operations to produce less dust. Mine instrumentation applications include machine-mounted and hand-held monitors, personal monitors, and area/environmental monitors. Six dust detection methods have been considered to meet application requirements. These are: light-scattering instruments, a smoke-particle detection technique, correlation of pressure drop across the collection filter with amount of dust deposited, the Tapered-Element Oscillating Microbalance (TEOM) instrument, a method that relates the amount of dust collected on a filter with the vibration of the filter, and beta attenuation measurement of dust. Studies to date have identified the TEOM instrument and the technique of correlating the amount of dust collected with the vibration ofthe filter as having the most promise for success. Development of the machine-mounted monitor is the highest research priority. The application options and progress to date in developing continuous monitoring instrumentation are presented.

Jan 1, 1995

"INTRODUCTION Foam, unless intentionally created, in any industrial process presents operational problems, or at a minimum, is a nuisance. Some foam problems are unique to a given industry and others are common across many industries. A few problems foam presents to any particular industry are: (a) Poor Housekeeping, (b) Environmental impact, (c) Safety Hazards, (d) Slower Production Rates and, (e) Reduced quality of the end product. Defoamers address these issues. Sadly, the assumption in most industries is all defoamers are alike. In reality, a lot of chemistry is involved in the manufacture of even the simplest defoamer sold today and rarely are any two defoamers “just alike”. Today’s defoamers can include polymer chemistry, fatty esters, alkoxylated alcohols, silicone chemistry, silicone surfactants, ethoxylated and propoxylated block polymers, and a tremendous amount of emulsion chemistry just to name a few. This paper will discuss the various types of defoamers, defoaming mechanisms, the advantages and disadvantages of defoamer selections, and how to choose the proper defoamer for your application. Before a discussion of defoamer can be brought about, foam generation and composition must be discussed. WHAT IS FOAM? Foam is a colloidal suspension of a gas dispersed in a liquid. Most often foam consists of air dispersed in water. If a stream of air is introduced into a liquid, the bubbles produced assume a spherical shape. As the density of the bubble is less than the liquid the bubble rises. When the individual bubbles reach and pass through a surfactant free liquid they collapse. Air from the bubble dissipates and the liquid previously surrounding the bubble flows back.It should be noted a pure liquid will not foam. In the case of air dispersed in water a surfactant is necessary to make the water support a stable foam. A surfactant is a term used to describe a surface active agent; a compound with a hydrophilic end and a hydrophobic end on the same molecule."

Jan 1, 2016

By I. M. Stewart

In a proposed rulemaking regulating asbestos, nonasbestos varieties of Tremolite, Anthophyllite and Actinolite would be excluded from the regulations controlling permissible exposure to asbestos fibers. This proposed rulemaking is perceived as improving the scientific basis of the regulation of asbestos because it recognizes that there are no scientific data, either mineralogical or health related, which support the regulation of nonasbestos Tremoiite, Anthophyllite and Actinolite in the same manner as asbestos fibers. However, the proposed regulation, while representing a major advance in the treatment of AT A for regulatory purposes, does not provide an adequate analytical method for distinguishing between asbestos and nonasbestos particles, nor an adequate description of the regulated minerals. This paper addresses those topics, recommending that OSHA include an appropriate mineralogical definition, and implement a discriminate counting procedure to distinguish asbestos from nonasbestos particles.

Jan 1, 1992

By James Douglas

For the past several years, inflation has placed increasing pressure on our economic system. The total effect of inflation is complex when combined with other factors which affect the economics of equipment. A mathematical model is described herein which can be programmed on a computer to determine the effect of inflation on economic life and profits after taxes. The computer output results in graphic plots which clearly show the relation of various percentages of inflation to life and profits. Inflation has become a common topic of conversation in the recent past. What is it and how can it be measured? What effect does increased inflation have on equipment policy? Research now in progress at the Construction Institute at Stanford University is beginning to unravel some of the mystery of inflation. As a start, let us answer the first question by defining the word inflation. The dictionary says that inflation is "an increase in the volume of money and credit relative to available goods resulting in a substantial and continuing rise in the general price level. It appears, in fact, that we are in an inflationary spiral which is "a continuous rise in prices that is sustained by the tendency of wage increases and cost increases to act on each other." 3 Inflation behaves just like compound interest. It takes more dollars of future years to buy an equal amount of a given commodity, be it a material or a service. Let us assume an annual inflation rate of 5 percent. Assume that 1Associate Professor of Civil Engineering, Stanford University, Stanford, California. 2Webster's Seventh New Collegiate Dictionary, Springfield, Mass., G. and C. Merriam Co., 1969. 3Ibid.

Jan 1, 1972