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By R. C. J. Goode

"In my Presidential address last year `The Institute in Retrospect and Prospect', I briefly reviewed the past activities of our Institute, I commented on the dynamic growth of the mineral activity of this country and of the great contribution towards this growth made by members of this Institute. I maintained that there was still further growth to come, pointing out that our future would be very much dependent on the availability and skills of our mining and metallurgical men. This Institute had, therefore, a most important task ahead to ensure that this country would have the necessary skilled engineers to develop our mineral industry so that we would be able to compete successfully in the wide world. In my address I highlighted many of the major achievements of our members and of our Institute. In today's review, I have no wish to repeat myself and I would, therefore, ask members and visitors to regard this review as complementary to my presidential address. I must also refer you to the very full resume of our affairs written for a special brochure in March, 1944, by E. H. Johnson, a founder member, on the occasion of our 50th Anniversary. There is no need to repeat what was given there, rather I will attempt to bring that history up to date. Our Institute was founded under the name of Chemical and Metallurgical Society of South Africa on 24th March, 1894, by a group of chemists and metallurgists The name was changed to Chemical, Metallurgical and Mining Society of South Africa early in 1903, and in July, 1956 became The South African Institute of Mining and Metallurgy. We were not the first technical organisation in South Africa, the S.A. Association of Engineers and Architects having been formed in 1892. In that year also the British Institution of Mining and Metallurgy started in London. A chronological table of some of the more important societies is as follows: British Societies: Society of Apothecaries 1617 Royal Society 1660 Geological Society 1807 Institution of Civil Engineers 1818 Institution of Mechanical Engineers 1847 Institution of Chemistry 1877 Institution of Mining Engineers 1889 Institution of Mining and Metallurgy 1892 Other Societies: Mining Society of Nova Scotia 1887 S.A. Association of Engineers and Architects-later the S.A. Association of Engineers which amalgamated with the Transvaal Institute of Mechanical Engineers 1892 Australasian Institute of Mining and Metallurgy 1893 Geological Society of South Africa 1895 South African Society of Electrical Engineers-disbanded 1904 1897 Mechanical Engineers' Association of the Witwatersrand-later, the

By V. E. Cogho

Optimum Coal Mine comprises numerous defunct, active, and future mining sections. The mine is primarily a large opencast coal mine; however, underground mining activities will be increasing steadily over the next five years. Opencast and underground mining activities have a significant impact on surface and groundwater resources. To ensure that the mine will be able to continue with its mining operations in the catchment, the extent of this impact requires that substantial intervention and mitigation measures need to be implemented to ensure the environmental integrity and economic use of the catchment's water resources. In developing a sustainable long-term mine water management strategy, numerous scenarios had to be analysed. The various scenarios are a combination of water and land management activities. The main components of the mine's integrated water management strategy include: ? Management of water recharge by continual and appropriate rehabilitation of disturbed land ? Beneficial re-use of impacted mine water for coal plant process water and mining operations ? Reclamation and desalination of remaining excess impacted mine water to potable standard. From the mine's long-term water balance, it is evident that the continued implementation of numerous water management actions is required to mitigate the water resources impact in a sustainable manner. In addition, the installation of a water reclamation plant at Optimum Coal Mine (15Ml/day) is a key step for the mine to achieve a zero impact target.

Jan 1, 2012

By N. Morris

In South Africa, diamonds are mined predominantly in rural areas. Kimberlitic diamonds dominate in Limpopo and the Northern Cape Provinces whereas alluvial diamonds are mainly sourced from the North West and Northern Cape Provinces. There are a few large and medium sized diamond companies (De Beers, Petra Diamonds, Trans Hex, Rockwell and Alexkor). There are many smaller companies involved in diamond mining, mostly alluvial diamond mines. The nature of alluvial diamond deposits is that they are aerially more extensive and thus their surface impacts are more pervasive: The recent downturn in diamond prices has resulted in the sudden cessation of mining at many small and medium diamond operations. The South African Mining Charter requires all mines, including diamond mines, to subscribe' to .the following empowerment objectives:

Jan 1, 2010

By Z. Ruetz

Portable X-ray fluorescence (pXRF) analysis has been widely adopted in the geochemical and environmental field as a cost-saving alternative to standard analyses. This paper outlines the efficacy of a method for indirectly quantifying organic copper content in solvent extraction circuits via stripping of the chelated metal with concentrated sulfuric acid in a single contact and subsequent pXRF aqueous analysis. pXRF analysis is common within the mining industry but presents unique challenges with liquid analysis, the most prevalent of which are briefly discussed. This method was developed specifically for mining operations with regional constraints and limited resources. Providing an in-field alternative to flame atomic absorption spectrophotometry and inductively coupled plasma optical emission spectroscopy, this entirely mobile XRF analysis method produces consistent and accurate results within minutes and at a fraction of the cost.

Jan 1, 2023

By P. T. L. Koh, M. P. Schwarz

A series of parametric studies were carried out for a flotation cell using computational fluid dynamic (CFD) modelling to determine the local response of hydrodynamic performance measures to change in operating conditions. As an example, an Outotec cell was used to carry out the response analysis. The hydrodynamics of the flotation cell has been previously investigated by laboratory measurements presented by Schwarz et al (2019), and a CFD model of the cell was developed and validated using these measurement data (Schwarz et al., 2019). In this work, parametric studies have been performed by modelling the flotation cell at different stirring speeds and gas flowrates, varying above and below standard conditions. Predictions of void fraction, bubble size, bubble surface area flux and particle–bubble collision rate are presented showing the effects of increasing and decreasing stirring speed and gas flowrate around the base case. Generally, the total gas holdup in the flotation cell was found to increase with increasing gas flowrate. The bubble diameter was found to decrease with increasing stirring speed and increase with increasing gas flowrate. The collision rate increased with both stirring speed and gas flowrate. The parametric results show that there is a correlation between the bubble surface area flux Sb which is affected by stirring speed and gas flowrate, and the particle–bubble collision rate. With the collision rate as an indication of flotation collection, it is also possible to show that cell performance can improve more by increasing stirring speed than by increasing gas flowrate in a situation where everything else remains constant. The CFD results can form the basis for a Response Surface Method (RSM) analysis which can then be used for automated optimization of cell performance. Keywords: Flotation kinetics, computational fluid dynamics, bubble surface area flux, particle-bubble collision rate

Jan 1, 2020

By D. D. Aksenova, V. A. Ignatkina, L. A. Samatova, A. V. Lygach, E. D. Shepeta

Calcium minerals such as scheelite, phosphate, apatite are valuable minerals, which have similar flotation properties to the calcium gangue minerals. An additional problem is the fine dispersion and close mineral association of valuable and other minerals. Low polar compounds (non-ionic surfactant), such as fatty iso alcohols, neonol and phosphol, and their combinations with sodium oleate have been studied using flotation of monominerals and ore flotation; ATR IR spectroscopy and TEM for study surface of minerals; UV spectroscopy for control solubility, aggregation and de-aggregation processes. Increase in solubility of fatty acid collectors was confirmed by low soluble (heteropolar) compounds. Oxyethylated esters of phosphoric acid are adsorbed on phosphorite by -O2PO2R2 and on other rock minerals by donation of OH bond. Same effect shows difference of adsorption of fatty iso alcohols on calcite and scheelite. The different forms of adsorption of ionic and nonionic compound on a sparingly-soluble mineral surface creates distinction of the flotation kinetics and technological balance of ore flotation. The results of the separation of flotation of scheelite from calcite depend on the order of pouring into pulp of fatty iso alcohols and oleate, and their ratio in the mixture. Increasing scheelite recovery into rougher scheelite concentrate by 3.6% for both the flotation and sludge classes was obtained. Calcite recovery varied slightly upwards or downwards by 0.8-2.4%. The use of the non-ionic surfactant phosphol in combination with a fatty acid soap allows for obtaining a phosphate concentrate with more than 28% P2O5 content and almost 80% recovery in flotation operation. It is not obtainable with other reagent regimes. Keywords: Flotation, calcium minerals, oleate, fatty isoalcols, neonol, oxyethylated esters, adsorption

Jan 1, 2020

By T. N. Matveev, V. V. Getman, A. Yu. Karkeshkina, L. B. Lantsova, N. K. Gromova

Sulfide-type tin deposits in Russia are characterised by the complex mineral composition of ores and dump products of their processing. Tin-sulfide ores contain industrial quantities of copper, lead, zinc, tungsten, silver, rare and trace elements (indium, scandium, etc.). In addition, the ores are characterised by uneven dissemination of sulfide minerals (chalcopyrite, galena, arsenopyrite, etc.) and tin minerals (cassiterite, stannine, etc.). X-ray phase and spectral analysis, scanning electronic microscopy (SEAM), laser SIM and AFM microscopy helped to identify the selective fixing of sodium dibutyl dithiocarbamate (DBDTC) on chalcopyrite and galena, as well as the tall oil fatty acids (TOFA) and IM-50 on cassiterite. For the first time, collectors and flocculants of slurry fractions of silver and tin, thermomorphic polymers TMPF were used to isolate more than 80% silver from the tin tailings of the Solnechny mine into a copper-silver rough concentrate. It has been established that preliminary ultrasonic treatment and desliming according to the 0.02 mm class removes up to 20% of sludge material, which impairs the process of gravity separation. The combined flotation-gravity scheme using new reagent compositions helped to obtain tin concentrate with a tin content of 5.42%, which meets the requirements for further metallurgical processing (at least 5%). This work was supported by the RSF according to the research project No. 17-17-01292. Keywords: Flotation, flotation reagents, tin-sulfide ores, casiterite, adsorption, flocculation

Jan 1, 2020

By D. M. C. Valbom

The introduction of new diamond sorting technologies as well as additional manufacturers I vendors, has increased the equipment selection and combinations available for recovery flowsheet design. This paper describes the methodology used and the benefits realized in the design of recovery plants by ensuring a fundamental understanding of the advantages and limitations of the technology embodied in the equipment, a comprehensive knowledge of the ore body characteristics, and the effective matching of this information in combination with operational commercial requirements.

Jan 1, 2010

By F. S. Hoseinian, D. Deglon, L. leal Filho, M. Safari, T. C. Souza Pinto

This paper investigates the effect of chemical and physical operational parameters on the reverse flotation of Timbopeba itabirite iron ore in a pilot-scale pneumatic flotation cell. Operational parameters include collector and depressant dosages, feed rate, superficial gas velocity and solids concentration. Results show that increasing collector dosage results in an increase in quartz recovery, particularly for the coarser quartz where recovery increases by nearly 30%. Increasing depressant dosage results in a decrease in both quartz recovery and hematite loss, for the coarser hematite particles. Increasing the feed rate has no effect on quartz recovery or hematite loss, suggesting that the pneumatic flotation cell is not residence time constrained. Increasing the superficial gas velocity results in an increase in quartz recovery to an optimum at a Jg of around 0.6 cm/s after which it decreases significantly, particularly for the coarser particles where recovery decreases by as much as 50%. Decreasing the solids concentration does not affect quartz recovery but results in significant decreases in hematite loss. Here, fine and coarse hematite loss decreases from around 25% to 12% and 10% to 2% respectively. Superficial gas velocity and solids concentration are operating parameters which have the largest effect on the flotation performance of the pneumatic flotation cell. Results suggest that this flotation cell should be operated at relatively low superficial gas velocities and solids concentrations. However, these are pilot-scale findings and would need to be tested at an industrial-scale where different operating conditions may be optimal. Keywords: Operational parameters, reverse froth flotation; entrainment; iron ore

Jan 1, 2020

By M. Rudolph, R. Tolosana-Delgado, G. van den Boogaart, M. Reuter, U. Peuker

This paper addresses the challenge to define a concept of entropy (state of order) for a textured particle system. Both the particle texture, the intergrowth respectively, and the particle size influence the order of a particle system. The smaller the particles become, the more particles form the solid system and the more permutations of the structure of the particle bed are possible. The texture within a particle is fixed, as long as it is not subjected to changes due to comminution, flocculation or agglomeration. The paper will present a definition of entropy, which is able to reflect qualitatively and quantitatively the intergrowth and the size (distribution) of the particles. Theoretical examples will show how different breakage mechanisms can be identified using the entropy definition. Furthermore, we will define the specifications for data sets to calculate the entropy of a particle system. Keywords: Milling, mineral liberation, intergrowth, statistical entropy, modelling

Jan 1, 2020

By E. Kumar, L. A. Kumar

"A methodology is proposed to develop an optimization model to understand the impact of transporting minerals, from mines to the final destination, on air quality. Recently, there has been increasing concern about the combined effects of multiple activities over many years, and the regional environmental changes brought about by a single project. Environmental issues in the iron ore industry have highlighted the need to broaden the cumulative impact assessment. In this study, we simulated the optimal routes and quantity of materials needed to meet the destination plant demand based upon environment constraints (level of air pollution), as well as the cost of transportation and availability of materials. Multiple scenarios were developed to analyse the effects of changes in routes, alternative transport system (or multi-modal split), traffic congestion, and the cumulative impacts on air quality. The air quality impact zones of the study area were demarcated using a GIS technique. The expected outcome of the study is the selection of a suitable transport system for a particular site with the least impact on air quality, including the transportation route, relative to the minimum cost of transportation of the minerals from the mines to their final destination. The proposed methodology is evaluated with a case study. IntroductionIn India, the process of environmental impact assessment (EIA) has been focused primarily on the local impacts of projects, without considering regional environmental effects. Environmental clearances for proposed projects are based on reports of local impacts. However, any developmental project poses a potential risk to the environment as a whole, and not just in the immediate vicinity of the project. Recently, there has been increased concern about the combined effects of multiple activities over many years—the regional environmental changes due to development of a single project (Dutta, Mahatha, and De, 2004). Environmental issues throughout the country, particularly in the iron ore industry, have emphasized the need to broaden the analysis to include the combined impacts, or those forecast for a proposed region, on an existing environment. The most significant adverse environmental consequences of iron ore transportation are the deterioration of biodiversity and air quality (Kumar and Ajay, 2015)."

Jan 1, 2017

By R. Weideman, K. du Preez

Biological sulfate reduction has become a successful treatment alternative for acid mine drainage and Mintek is developing biological processes for treatment of highsulfate mine waters. Treatment of these high-sulfate waters is achieved by sulfatereducing bacteria that reduce sulfate to produce sulfide as a product, in the form of H2S and HS− at neutral pH. This introduces the opportunity to apply treated effluents from biological treatment processes for the recovery of metals, such as copper, from metallurgical waste streams. This study models the kinetics of copper sulfide precipitation from a complex bioleach liquor. The results indicated a rapid rate of reaction and the formation of covellite, suggesting the potential to use biogenic sulfide to recover copper as a metal sulfide product.

Jan 1, 2023

By P. J. Petit

Changing mining conditions, legislative issues, rising costs, and the constrained supply of skills and electricity in South Africa, have been some of the criteria forcing mine operators and engineers to review the traditional use of compressed air to power underground hand-held drilling operations in narrow-stope, hard-rock mines. In answering the question, 'What is the best way to power this mine?', they have resorted to trade-off studies with results of limited usefulness, because they are site-specific, and use only a few comparative parameters, based on a small data set. This paper aims to provide definitive, objective and quantitative decision-making approaches to evaluate alternative energy delivery systems for stoping in narrow-reef hard rock mines, based on primary and relevant criteria. These include quantifiable criteria such as capital expenditure, operating costs, resulting financial returns, energy and water usage, production performance, life-of-mine, etc. Other important criteria with qualitative aspects are integrated. These are safety, health and environmental concerns, legislative requirements, business risk, technology change, etc. The paper begins with a review of decision making processes available, and proposes the use of the analytical hierarchy process (AHP) method as a multiple-criteria decision making tool and the decision tree-based on milestone-driven uncertainties, to validate the selection of the energy delivery system. The results of a multiple-criteria questionnaire completed by a variety of industry experts and professionals, such as production and operation managers, consultants, suppliers and techno-financial analysts, are discussed. The evaluation indicates the potential for hydropower to be the best solution for narrow reef hard rock mines, based on current information, mine design layout and production.

Jan 1, 2012

By N. A. Barcza

This paper describes the development of large-scale thermal-plasma systems, which was motivated, in general, by the potential cost savings that could be achieved by their use as a replacement for the more conventional methods used in the generation of thermal energy. The anticipated cost savings arise not only from the use of plasma-generating devices but from the manner in which they have been interfaced with a furnace to process particular materials, mostly as fines. Thermal-plasma systems fall into two categories: non-transferred-arc and transferred-arc devices. In general, transferred-arc devices have been interfaced with open-bath furnaces in which melting or smelting processes carried out, while non-transferred-arc devices have normally been applied to shaft furnaces. Water-cooled transferred-arc devices are somewhat limited in power (about 5 MW) because of the relatively voltages (300 to 500 V) that can be attained in open-bath furnaces, where very long arcs are undesirable, and because only relatively low levels of current can be carried. Graphite electrodes can overcome the restriction current, and power levels of 30 to 50 MW seem feasible, even with one electrode, if direct current is used. Multiple water-cooled devices are capable of attaining similar power levels, but the capital costs are much higher. Costs due to electrode wear are lower for water-cooled systems, but expensive gases are needed for transferred-arc devices. Mintek conducted extensive pilot-plant work in which water-cooled devices were used initially but graphite electrodes were used subsequently to produce ferochromium from fines. Transferred-arc open-bath configurations were used. This work led to a decision by Middelburg Steel & Alloys (MS&A) to install a 16 MVA furnace of semindustrial scale to produce ferochromium aloys based on the ASEA d.c. arc furnace developed for the Elred process. Non-transferred-arc devices have atained reasonable scale-up to the 6 to8 MW power level, and high-voltage operation, which is inherent in such devices, has enabled lower currents to be used. Nevertheless, multiple systems are still necessary to accommodate large-scale applications, and this can be costly from a capital point of view. The cooling requirements are large, and can represent a considerable loss of electric energy. Shaft furnaces equipped with non-transferred-arc devices are suitable for the processing of materials that have volatile species, e.g. silica or manganese, or where the shaft is used to prereduce oxides that are amenable to gas-solid reactions. It is probably in the treatment of light and refractory metals that plasma technology will achieve its greatest development in the years to come. The energy requirements for the production of these metals are high, and very low oxygen potentials are necessary. These are factors that favour thermal plasma. Much developmental work is still needed in this interesting field. It should be remembered that electrically generated thermal energy is a unique temperature source that, in many instances, cannot be replaced technically or economically by the combustion of a fuel.

Jan 1, 1986

By V. Korobko, M. Byantogtokh, N. Byambadorzh, V. Bysov

A three-stage operative planning of mining operations in ore opencasts is considered. The hierarchy of monthly-weekly, weekly-daily, daily-shift planning is offered. For the fastest elimination and deviations in problematic situations a level is analysed and weekly-daily or monthly-weekly operative plans are being constantly updated. Operative planning is formulated on information received of preparation and working of mining panels. The electronic maps of these panels are considered for automated operative planning. On the data of the registration of blasthole drillings on a panel, the position of blasthole entry, their depth and the number of a line are determined. The geologist specifies boundaries of ore grades by the bored silt. The qualitative characteristics of ores are determined by the chemical analysis of slime or magnetic logging of blastholes. The missing geologic information is obtained by interpolation on the data of detailed and operational explorations. During working of the mining panel the technologists mark the movement of shovels, associating this movement to blastholes. For this purpose technological attributes are used: when was the blasthole drilled, what drill-rig participated in drilling, what shovel was used and when was it worked? Around each blasthole the zone of its influence is built up. It represents a discrete, elementary volume of ore or waste. The discrete form of the data is most convenient, as it allows step-by-step methods to be employed of the scheduled tasks in many and various combinations. The account panel working technology avoids ‘combination’ explosions. The elementary blocks should be placed in a trajectory of shovel movement and the trajectory can not be arbitrary. It’s determined by the technological rules of extracting and loading of mine mass. In linking to blastholes, the trajectory of shovels is simulated by the sum of step-by-step moving from one elementary block to another. For this purpose a geometrical linkage of blastholes is used. At a railway haulage, or complete mining with truck haulage, the trajectory of movement is a shuttle along the front of operations in the panel. At a selective mining of ores the number of possible directions is limited to three: moving of a shovel by idle running along the front of operations in the panel, frontal pull all the way down of the panel, and withdrawal. The technologically acceptable trajectories of shovel movement are stored for the following estimation and selection of the best. The estimation is carried out on mathematical models with criteria on the method of the least squares of deviations based on preset parameters from the plan, uniform loading of shovels, and mixing of ore at unloading points. The equations of balance type and directive parameters of the plan, as well as technological restrictions of solid and of elementary blocks within the limits of a trajectory are the restrictions of the model. Depending on an industrial situation it is possible to choose one of the predetermined models. The presented technique is used for longitudinal shovel bench at the Erdenet ore-dressing company.

Jan 1, 2003

By C. van Buuren, R. F. Sandenbergh, P. J. Pieterse

Gold extraction from double refractory ores using conventional cyanidation has proved challenging due to the presence of carbon within the ore. Carbon particles may adsorb leached gold resulting in gold losses to tailings, i.e. preg-robbing the gold. Some of the preg-robbed gold may be recovered by the application of the HiTeCC process on CIL tailings. The process developed by Metso Outotec involves caustic conditioning of the tailings followed by high temperature desorption and simultaneous adsorption onto virgin activated carbon of the aurodicyanide. The aim of this paper was to develop a model for the HiTeCC process which could be used to support design and optimisation of the process, based on the adsorption characteristics of the preg-robbing and activated carbons. It was found that accurate experimental isotherms can be used to predict the behaviour of preg-robbing adsorbents. Comparing the sorption isotherms for preg-robbing ores and activated carbon indicated similar dependencies on temperature and ionic composition. Applying boundary layer diffusion models coupled with experimentally determined isotherms for preg-robbing ore and activated carbon, the HiTeCC process was successfully simulated at experimental and plant scale. Gold recovery of the HiTeCC process is most sensitive to the temperature of desorption and gold loading of the activated carbon, with increased temperature improving recovery. The gold loading of the activated carbon in the process should always be maintained lower than that of the normalised pregrobbing carbon gold loading to ensure favourable conditions for adsorption onto the activated carbon. Caustic conditioning stabilises adsorption and is therefore not necessary during the desorption stages of the process, but potentially improves recovery during adsorption. Keywords: Preg-robbing, refractory gold ores, HiTeCC, aurodicyanide

Jan 1, 2020

By M. Borowski, N. Szlazak, D. Obracaj

Methods of research and control of the intensity of gas inflow to undersoil layers, after the mines were abandoned are presented in the paper. Gas migration causes them to penetrate to lower storeys of buildings and earthen structures being a menace to people's health and life. The results of measurements of gas concentration in undersoil layers, gas emission to atmosphere and their accumulation in buildings on the territory of closed down mines are presented.

Jan 1, 2003

By Y. Jiao, V. S. Thompson, D. W. Reed, Y. Fujita, J. E. Aston

Rare earth elements (REE) are vital components in modern electronics and green technology products. Supply is tight and global demand is expected to increase, leading to high risk for the economic and national security of countries largely dependent upon foreign supplies. Recycling of REE from consumer and industrial waste materials is a possible way to help meet demand. We have shown previously that biohydrometallurgy can play an economically and environmentally sustainable role in REE recycling, particularly if agriculture or food wastes are used to produce organic acid bioleaching agents. A challenge for organic acid-based bioleaching is the incomplete conversion of the carbon substrate to an optimal organic acid biolixiviant with high REE extraction capability from a variety of REE-containing feedstocks (e.g., mining wastes, magnets from end of life products, spent batteries, etc.). To help meet this challenge a metabolic model was developed for Gluconobacter oxydans to identify options for improving sugar conversion to organic acids. Model predictions were consistent with laboratory data for the microbial consumption of glucose and production of gluconic acid, and suggested that providing growth conditions with relatively high C:N molar ratios could result in lower pH biolixiviant production and thus improve bioleaching. Keywords: Gluconobacter oxydans, bioleaching, metabolic modelling, rare earth elements summaries 2019: U.S. Geological Survey, 200 p., https://doi.org/10.3133/70202434.

Jan 1, 2020

By L. A. Vermeulen, C. P. Campbell, D. D. Howat

The production 01material liner than 75 µm in a number of open-circuit mills was investigated. The mils ranged from laboratory rod and ball mils treating a variety 01 ores to large industrial rod mils treating gold and copper ores. It was shown that the dependence on feed rate 01 the production 01 material liner than 751J.1T1 can be accurately described by a simple formula that was derived in previous work. In some 01 the systems reviewed, it proved possible to assess the feed rate 01 ore to the mil at which the rate 01 production 01 material finer than 75 µm can be maximized.

Jan 1, 1991

The following corrections should be made to pages 346 and 347 of the December 1981 issue (vol. 81, no. 12) in the paper by O. L. Papendorf entitled 'A note on rapid determinations of present values in the presence of growth and inflation'. (1) Equation (2) on page 346 should read as follows:

Jan 1, 1982