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By J. D. Austin

Currency fluctuations affect the rand revenues of all exports of mineral commodities, as well as influencing their price on local markets. Of the more than 50 mineral commodities produced by South Africa, about 75 per cent derive 40 to 100 per cent of their revenues from exports. . Although supply and demand are largely beyond its control, management can maximize its revenues despite fluctuating overseas prices and exchange rates by using the right market at the right time. Management can operate in the futures markets, which involve a specific commitment to deliver a specific quantity of a standardized commodity at a set time in the future and at a price that is determined on a futures exchange in open auction; or management can use the options market, in which a producer can insure against the risk of a falling price by taking out a put-option, which gives the holder the right (but not the obligation) to sell the commodity at a stated price at an agreed time in the future. In the forward markets, management has three available tools; forward currency transactions, trading of currency options, and money market hedges. Revenues, currencies of exchange earnings, purchasing power of the rand, and world price trends are shown in over 40 diagrams and tables for the main mineral commodities produced in South Africa.

Jan 1, 1984

By R Kersten

The note describes an exercise on the simulation of the frequency and size of seismic events on the basis of the frequency distribution of the events and their inter-arrival times (Le. the frequency distribution of the time elapsed between events). From the suite of available results, those of one simulation for a period of three months are included. The tentative conclusions drawn from the exercise indicate that the overall seismic activity in an area can be predicted for a time period, that structurally complex areas will have a higher incidence of seismic events than other areas, and that the position and time of an event cannot be predicted by the use of a wide-spread system such as that used at present.

Jan 1, 1985

By S. Visage

By 1984 Iscor's first direct-reduction plant will be operating at the Vanderbijlpark Works, and for the fin;t time the Corporation will have an alternative method to the blast furnace for producing iron from ore. The performance of Iscor's four-kiln plant, which will be the largest coal-based plant in the world producing sponge iron, will undoubtedly be watched with great interest by steelmakers throughout the world. Beneficiation of tin The Southeast Asia Tin Research and Development (SEATRAD) Centre is a regional oganization, formed by the Governments of Indonesia, Malaysia, and Thailand with assistance from the United Nations, to conduct, coordinate, and promote research and training in the various fields of tin production, including geology, prospecting, mining, mineral processing, and smelting.

Jan 1, 1982

By R. G. B. Pickering

The Faculty of Engineering at the University of the Witwatersrand and the Mining Technology Division of the CSIR have co-operated to define the problems associated with deep level mining and in this paper they will identify what they consider to be the critical areas requiring technological solutions. This perspective will then be applied to work currently being carried out by both the organizations and gaps for additional developments will be identified. Finally the Co-operative Research Centre methodology operating in Australia is described. The purpose of this CRC is to provide a vehicle for R&D co-operation to develop and implement technologies which will increase the competitiveness of the mining industry. A further objective is to develop an appropriately skilled human resource base.

Jan 1, 1996

By M. T. Scholtz, I. J. Corrans

Akinetic study of the leaching of pentlandite in acidic ferric sulphate solutions by I. J. CORRANS, (Pr. Eng.). B.Sc. (Chem. Eng.) (Wits.). M.Se. (N.S.W.). Ph.D. (Natal) (Member) and M. T. Scholtz. B.Sc. (Chem. Eng.) (C. T.). Ph.D. (Toronto) (Visitor) A study was made of the kinetics in the leaching of nickel from pentlandite in dilute-acidic ferric sulphate solutions as a basis for subsequent studies on bacterial leaching. The chemical leaching rate was found to be highly dependent on the temperature and the concentration of ferric ions. The proposed mechanism for the leaching process is one involving rate control by chemical processes and mass transport. Good agreement was found between the experimental data and the proposed mechanism.

Jan 5, 1976

By H. Gercek, M. Genis

In this paper, the effects of dynamic loads on the geometry of the failure zone occurring around underground openings, excavated in deep and massive rock masses, have been investigated. Following an elasto-plastic stress analysis of a two-dimensional underground opening under static conditions, dynamic loads have been applied. In the static and dynamic analyses, FLAC2D computer program has been utilized. Maximum ground acceleration value is selected as an input parameter. An index determining the relative size of the yield zone around the opening has been used for comparison of instabilities. In diesem Bericht wurden die Auswirkungen von dynamischen Lasten, auf die Geometrie der Bruchzone in der Umgebung von Untertagehohlräumen, die in tiefen und massiven Gebirge aufgefahren wurden, untersucht. Nach einer elasto-plastischen Spannungsanalyse eines zwei-dimensionalen Untertagehohlraumes unter statischen Beanspruchungen, wurden dynamische Lasten aufgebracht. Für die statischen und dynamischen Analysen wurde das FLAC2D Computer Programm verwendet. Die maximale Bodenbeschleunigung wurde als Eingabe Parameter gewählt. Zum Vergleichen der Unstabilitäten wurde ein Index verwendet, der die relative Grösse der Bruchzone in der Umgebung des Hohlraumes bestimmt. Dans ce papier, l’influence des chargements dynamique sur la géométrie de la zone en rupture observée autour des cavités profondes excavées dans des massifs rocheux ont été étudiées. Des chargements dynamiques ont été appliqués, dans le cas d’une modélisation bi-dimensionnelle de l’excavation d’une cavité profonde, sur la base d’une analyse élastoplastiques des contraintes en conditions statiques. Le code de calcul FLAC2D a été utilisé pour les analyses statiques et dynamiques. La valeur maximale de l’accélération du sol est choisie comme paramètre d’entrée. Un indice déterminant la taille relative de la zone sollicitée autour de la cavité a été utilisé pour comparer les différentes instabilités.

Jan 1, 2003

By R. J. Davidson, V. Veronsee

Some of the parameters affecting the elution of gold from freshly loaded activated carbon using pure water as an eluant were studied. The procedure involved pretreatment of the gold-loaded activated carbon with a strong reagent of sodium cyanide and sodium hydroxide, followed by elution of the gold with water. Gold-loaded carbon obtained from three different sources was studied. It was shown that the elution temperature was the most critical parameter, and column operation at I !OCC (gauge pressure of 50 to 100 kPa) is suggested. The effects of variations in the concentration of sodium cyanide required for the pretreatment of loaded carbon and of variations in elution flowrate were also investigated. Both these parameters were found to have only a marginal effect on the efficiency of gold elution. The investigation also indicated that gold-elution rates were affected to a considerable degree by the particle size of the carbon concerned. Higher elution flowrates could be used when carbons of finer particle size were eluted. A modified eluate-collection procedure was also developed during the course of the investigation. Oven-drying of the loaded carbon was shown to have little or no effect on the efficiency of the subsequent gold elution. The calcium and silica contents of the various carbon samples were also determined. It was immediately evident that the calcium content was very considerable in the case of loaded carbons originating from carbon-in-pulp operations. Calcium concentration was particularly high where air agitation had been employed in the carbon-contacting circuit. To some degree, the calcium build-up explains the serious carbon fouling taking place, resulting in a decreased efficiency of gold adsorption. The fouling problem was found to be less severe when mechanical agitation was used. No poisoning by calcium carbonate was observed where the pregnant solution had been acidified before it was contacted with the carbon.

Jan 1, 1979

By D. Rankin, H. J. Stucke, W. K. B. Loftus

Discussion: H. J. Wright (Member): The authors are to be congratulated on presenting such a comprehensive and lucid account of bringing a large diamond mine into efficient production from the grass roots. When one considers the vast amount of planning and hard work that had to be put into the project the authors have done a praiseworthy job in condensing the story, so as to present all the important technical aspects, the logic behind the major decisions and the future thinking on the operations, in a concise and readable form. This was the first experience of De Beers personnel in starting a large diamond mine as an opencast project and nor do they employ a large planning staff, most of the planning being carried out by the executive staff themselves. It is operating most efficiently on a large tonnage and it is neatly and very well laid out. In fact, with its model townships, both for European and Coloured employees, tarred roads, recreation club and its grass golf course, it is like an oasis in the arid climate of the North-Western Cape. The key operation of opencast mining is, of course, the planning of the geometry of the pit. This has been adequately dealt with by the authors. It is of interest to consider some of the consequences arising from complete lack of open pit planning, based on actual operating mines. I refer of course to the present, four producing mines in Kimberley. The Kimberlite pipes were all discovered in a short span of time from the year 1870, onwards. They soon became a hive of activity with diggers industriously working their claims at varying rates. The country rock comprises from the surface downwards, some 90 ft of decomposed dolerite followed by approximately 260 ft of soft Karroo shales, which in turn is underlain by a hard competent Ventersdorp lava, known locally as melaphyre. The average water table was just below the dolerite at a depth of approximately 90 to 100 ft. Only the blue ground was mined leaving the waste rock sides almost vertical, and as the depth increased beyond 100 ft, large falls of sidewall started to take place. The shale was unstable and the falls covered

Jan 3, 1969

By T. Tholana, P. N. Neingo

"A mineral resource constitutes the principal underlying asset of a mining company, and must be exploited and managed in such a way that maximum value is derived from it. Various asset management frameworks applicable to physical assets are available. This paper focuses on the extension of an asset management approach, particularly the Publicly Available Specifications (PAS) 55 asset management framework and the International Organization for Standardization (ISO) 55000 series of standards, to mineral assets. It is concluded that PAS 55 and the ISO 55000 series of standards can be extended to manage mineral assets, resulting in an integrated approach to sustainably optimize value from the company’s mineral assets. The benefits include improved returns on mineral assets, maximum mineral asset utilization, creation of an organizational culture focused on quality and continuous improvement, and assurance to stakeholders that the mineral assets are being efficiently managed over their entire life-cycle. In the context of this paper, a ‘mineral resource’ refers to both Resources and/or Reserves as classified by the SAMREC Code. IntroductionMining involves the extraction of valuable mineral resources from the Earth’s crust. A mineral resource is unique among natural resources in the sense that it is a wasting asset, which means that its value depreciates continuously with extraction. In addition, it is often impaired from time to time as commodity price changes (Macfarlane, 2011a). Since a mineral resource is a wasting asset there is a single opportunity available to optimize value from its extraction. Mine planning involves identifying a strategy to exploit the mineral resource in a way that maximizes value at an acceptable risk level throughout the life of mine (LOM). This optimum extraction strategy changes as economic conditions change, particularly commodity prices, as well as with improvements in orebody knowledge as mining progresses. It is the mineral deposit that competitively distinguishes two different mines and dictates the location of a mine; hence the adage ‘the orebody dictates’. Therefore, a mineral resource is the primary tangible asset possessed by mining companies and must be managed in such a manner that maximizes its value at an acceptable risk level (Macfarlane, 2011a)."

Jan 1, 2016

By D. -H. Park, G. -j. Kim, Y. -J. Park, C. -S. Hong, S. -Y. Choo

To evaluate the quantitative tunnel behavior influenced by characteristics of discontinuity, this pa-per executes the parametric study using 2 and 3-dimensional DEM analysis. First of all, this study finds that displacement and the stress of shortcrete are proportioned to frequency of joint and rockbolt axial force is adversely proportioned too. Secondly, it is found that the most sensitive in-put parameter used in Barton-Bandis(BB) model is residual friction angle. Finally, when joint sets are encountered at tunnel excavation face, to identify the most critical joint orientation is very crucial for a stability of tunnel. La thèse a pour but d’étudier les influences sur la stabilité du tunnel, au niveau du réseau de la discontinuité et de la valeur de sa nature aquis par le projet récemment exécuté en vue de mener à l’analyse quantitative de cette stabilité, en appliquant chaque différent paramètre comme la fréquence de diaclase, la constante de résistance des modèles de Barton-Bandis(BB) ainsi que la relation entre le sens d’excavation du tunnel et le réseau de diaclase en 3 dimensions. En fait, cette étude nous a montré que la fréquence de diaclase s’accroît proportionnellement au déplacement et à la contrainte du béton projeté. L’angle de friction résiduel s’est montré le plus sensible à la stabilité du tunnel parmi les modèles de BB. Aussi à travers l’analyse à 3 dimensions, il s’est vérifié que si l’angle de pente du groupe de diaclase est horizontal entre l’axe du tunnel et la direction, il donne une influence importante sur le comportement du tunnel. En particulier, l’influence était la plus importante sur un fond rocheux dont la diaclase horizontale est grande. Um das quantitative Verhalten des Tunnels zu bewerten, eroertert dieses Papier eine parametrische Studie mit Hilfe der DEM Analyse. Auch wird hier eine zweidimensionale Analyse von Ver-bindungen verschiedener Frequenzen in der Gesteinsmasse, eine sensitive Analyse von allen der im Barton-Bandis-Modell (BB) genutzten Parameter und eine Dreidimensional-Analyse mit ver-schiedenen dreidimensionalen geometrischen Veteilungen von Verbindungen ausgefuehrt. Erstens: Die Studie findet heraus, dass Vedraengung und Druck im Shortcrete proportional zur Frequenz von Verbindungen und Axialkraft der Steinbolzen antiproportinal ist. Zweitens: Es wird herausge-funden, dass die am meisten Sensitiven der im BB-Modell angewendeten Eingaben die am Ende uebriggebliebenen Reibungswinkel sind. Und schliesslich wird herausgefunden, dass wenn Ver-bindungsteile an der Tunnelaushoelungsoberflaeche ausgemacht werden, fuer die Tunnelstabiltaet die Identifikation der meist kritischen Verbindungsorientierung sehr bedeutungsvoll.

Jan 1, 2003

By Y. H. Suh, H. C. Lee, D. S. Kim

A progressive karst formation and its influence upon engineered structures in the ‘phil-karst’ rock mass draw a tunnel engineer’s special attention to a long-term stability and the maintenance issues. Karst sinkholes of any size beneath the railway bed cause train wrecks or long interruptions in train traffic during rehabilitation work. The collapse of cave roof, called a ‘doline’, is in general connected to the cave by the gradual dissolving of the rock, developing into subsidence and sink-holes. The principal conclusions obtained from the field experiments are as follows: It is found that the development of karst cavity shows a relationship with a structural geological line and it is necessary to define the dominant directions of joint and geological layer (formation). The relation-ship between the water flow and joint direction can be used as an indicator of cavity presence in their direction. In addition the direction of in-situ stress can play a role in the development of karst cavities. A risk map of karst scenario is produced for the tunnel supporting systems with rock type classifications in water-soluble karstic rock mass. Eine fortschrittliche Karst-Formung und sein Einfluß auf angelegten Strukturen in der Phil-Karst-Felsenmasse wecken einem Tunnelingenieur eine besondere Aufmerksamkeit zu einer langfristigen Stabilität und der Wartungsausgaben auf. Karstensinkhöhlen in irgendeinen Größen unter dem Eisenbahnbett sind die Ursache der Zugeszerstörung oder der langen Unterbrechungen in Zugverkehr während Rehabilitationsarbeit. Der Zusammenbruch von Höhlendach, d.h. ein “doline”, ist im allgemeinen an die Höhle, die durch das allmähliche Auflösen des Felsen zu entstehen ist und sich in die Subsidence und Sinkhöhlen entwickeln, angeschlossen. Die Hauptschlüsse, die von Feldenprüfungen erhalten wurden, sind folgendermaßen: es wird gefunden, daß die Entwicklung von Karstenhöhlung eine Beziehung mit einer strukturellen geologischen Linie zeigt und es notwendig ist, die vorherrschenden Richtungen von Gelenk und geologischer Schicht (die Formung) zu definieren. Die Beziehung zwischen dem Wasserablauf und der gemeinschaftlichen Richtung kann als ein Anzeiger von Höhlungsanwesenheit in ihrer Richtung benutzt werden. Zusätzlich kann die Richtung von In-Situ-Spannung eine Rolle in der Entwicklung der Karstenhöhlungen spielen. Für das Tunnelunterstützungssystem, welches mit Felsentypenklassifizierungen in wasserlöslicher Karstic-Felsenmasse, ist eine Risikokarte von Karstenszenar hergestellt. Une formation progressive de karst et son influence sur les structures tracées dans la masse de roche "phil-karst" retiennent l'attention particulière des ingénieurs de tunnel aux problèmes de la stabilité à long terme et du maintien. Les creux de karst de toute la taille sous le chemin de fer causent les accidents de trains ou de longues interruptions pendant le travail de réhabilitaion. L'effondrement du plafond de caverne qui s'appelle "doline" s'est, en général, connecté à la caverne par dissolution progressive de la roche, en devenant l'affaissement et les creux. Les conclusions importantes venant des experimentations sur le terrain sont suivants: d'abord, le développement de la cavité de karst montre le rapport avec la ligne géologique de la structure et il est nécessaire de définir les directions dominantes du joint et la couche(formation) géologique. La relation entre l'écoulement de l'eau et la direction du joint peut être utilisé comme un indicateur de la présence de la cavité dans leur direction. De plus, la direction sur place peut contribuer au développement des cavités de karst. Le plan risqué de karst s'est produit pour le système d'appui du tunnel avec les classifications du type de roche dans la masse de roche karstique qui est soluble dans l'eau.

Jan 1, 2003

DISCUSSION: The value of incentive payments in the mining industry by K; SMITH Published in the Journal, May 1974 H. P. CARLISLE* The author has drawn attention to one of the most important of mining problems, viz productivity, and in so doing has highlighted, perhaps inadvertently, the difficulty of assessing productivity. Competition for Students Each year the Institute offers a prize (or prizes should the entries warrant it) of up to R100 for the best paper or dissertation on a topic appropriate to the interests of the Institute. Corrigendum The Journal, May 1974, p. 377 We regret that the last portion of A. A. Hazell's contribution to the paper 'The value of incentive payments in the mining industry' by K. Smith was printed in the wrong sequence.

Jan 10, 1974

By J. T. Davies

Note: Melting techniques in the iron foundry by J. T. DAVIES* INTRODUCTION The selection of melting equipment for use in an iron foundry has for several years been the subject of numerous discussions, papers, and conferences. The controversy that has raged throughout the world has been brought about by the following factors: IF AC Symposium The 2nd IF AC Symposium on Automation in Mining, Mineral and Metal Processing will be held from 13th to 17th September, 1976, at the Carlton Hotel, Johannesburg. Advance registration takes place on 12th September, 1976. World phosphates The Minerals Bureau of the Department of Mines has released the second publication in its series of reports on the economic aspects of minerals that are of particular importance to South Africa.

Jan 7, 1976

In order to test the applicability of elastodynamic codes in the modeling of mining related problems, comparisons are made between seismic data and numerical analyses. The dynamic finite difference program WA VE is used for the modeling of a horizontal stope in a deep mine. The slip along a vertical fault situated within the positive excess shear stress lobe of the stope initiates seismic waves. The stope-fault geometry is modeled in both two and three dimensions. The three dimensional non-slip weakening WAVE analyses correlate well with Brune's analytical model. For accurate modeling of the peak particle velocities predicted by McGarr's empirical relationship, it is recommended that a three-dimensional stope -fault model is used, with the amount of slip weakening dependent on the magnitude of the event.

Jan 1, 1995

By Northrop. I. N.

Hardmetals possess extremely high hardness and wear resistance, which render them ideal for applications such as metal-cutting tools, rock-drilling tools, and industrial wear-resistant parts like dies, punches, and seals. However, hardmetals are britle, and show poor resistance to impact and shock. They can therefore rarely be used unsupported, and it is common practice to attach hard metal working parts to a more resilient tool holder or support, which is normally made of steel. . . . Owing to the widely differing physical and mechanical properties of steels and hard metals, the Joining of one to the other is problematic, and the method used must be chosen with care. This paper reviews several methods available for the joining of hardmetal to steel, and discusses the advantages and disadvantages of each.

Jan 1, 1987

By M. A. von Below, I. C. Robinson

A mineral economic analysis of South Africa's mineral-beneficiation industry, comprising both economic theory and case studies, suggests that the domestic market has proved to be a more effective vehicle for promoting the establishment of advanced beneficiation projects than the availability of domestic raw materials. Although the domestic market plays an important role in the promotion of beneficiation by providing a secure outlet for sales, its most vital role is in the development of technological and marketing know-how that may give South African beneficiated products the competitive advantage required to penetrate export markets. The real wealth of a country lies primarily in the skills of its people rather than in its natural resources, and the domestic market plays a pivotal role in the development of these skills.

Jan 1, 1990

By M. Pötsch, M. Blümel, E. A. Button

ABSTRACT: Stiffness controlled test procedures performed with servo-controlled shear systems are the most versatile for simulating the wide range of boundary conditions expected in nature. Examples of a function controlled procedure in addition to dilatation controlled procedures are discussed for different characteristic behaviours. ZUSAMMENFASSUNG: Steifigkeitskontrollierte Scherversuche mit servohydraulischer Steuerung eignen sich gut unterschiedliche Bettungen, wie auch in der Natur vorkommen, zu simulieren. Beispiele für spezielle Steuerungsfunktionen und dilatationsgesteuerte Prozeduren mit verschiedenen charakteristischen Eigenschaften werden diskutiert. RESUMÉ: La rigidité a commandé des méthodes d'essai exécutées avec les systèmes asservis de cisaillement sont la plus souple pour simuler l'éventail d'états de frontière prévus en nature. Des exemples d'un procédé commandé par fonction en plus des procédures commandées par dilatation sont discutés pour différents comportements caractéristiques.

Jan 1, 2003

By P. D. K. Robinson

In the second of a series of five colloquia with the theme Rescue 91 ..Survival Initiatives for the Mining Industry, the emphasis was placed on the harnessing of improved technology for the benefit of all the industry. The Colloquium was held at Mintek, Randburg, and attracted some 150 delegates and speakers from a cross-section of the industry. Eight papers were presented, and panel discussions were held to round off the morning and afternoon sessions. The purpose of the Colloquium was to allow mines and other groups to put forward innovative schemes in the management of technology that could be shared by everyone in their determination to ensure the survival of the gold-mining industry in the current difficult times. PAPERS The papers presented were as follows: The introduction of detachable bits at Cooke No. 1 Shaft, by C.A.F. Sweet of Randfontein Estates Survival through cost-saving measures in the engineering field, by E.J. Jurgensen of Freddies Survival through innovation, action, and a positive vision for the future, by G.C.V. Wade of Vaal Reefs Measuring misaligned guides, by H. Sperling of CSIR Rock-crushing innovations, by E. Trueman of Nordberg Improved explosives technology-has it been worth the effort? by RA. Lindsay of Sasol Cost savings through corrosion monitoring, by M. Tullmin of CSIR Enhanced efficiencies through technical developments in the survey departments, by D. Maree of Beatrix.

Jan 1, 1992

The April General Meeting of the Institute was held in Kelvin House, Johannesburg, on 15th April, 1970, at 4.30 p.m. Mr J. K. E. Douglas (President) was in the chair. There were also present eight Fellows: Dr J. M. Bereza, H. Britten, R. C. J. Goode, C. E. Mavrocordatos, P. W. J. van Rensburg (Council Members), C. A. Border, D. E. French and S. D. Hill. Four Members, J. A. Boyd, P. Crawshaw, D. P. Hugo and A. H. Munro. Two Associates, including I. Robinson. Eleven Visitors, including A. B. Gould, P. M. Haupt, B. Needleman and A. F. Wentzel. Secretary, D. C. Visser. Total Present, 27. OBITUARIES The President: "It is my sad duty to announce the death of the following: Leslie Richard Ulyate, Fellow, who joined the Institute in 1939 and passed away on 10th March, 1970. Stanley Sterling, Fellow, and Corresponding Member for Canada, who joined the Institute in 1926 and passed away on 25th March, 1970. As a mark of respect to the memory of the deceased and in sympathy with the bereaved I would ask you all to rise and observe a few moments' silence." MINUTES The President: "May we confirm the minutes of the General Meeting, held on 21st January, 1970, as published in the March, 1970, issue of the Journal?" Agreed. MEMBERSHIP The President: "I have much pleasure in announcing that the names of the undermentioned candidates, having been published in accordance with By-Law 5.2.2., Council has elected them to membership of the Institute in the following grades: Associate: Rupert George CaIcott. Students: Clive Martin Davis, William Machiel Eksteen, Cecil John Tainton. From Student to Member: Dirk Johannes Hugo. "I welcome the newly-elected members to the Institute and congratulate the member who has been transferred to a higher grade." TALK AND FILMS The President: "Mr Ballantyne may I call on you to present your talk and films on the 'Continuous casting of steel'?" After the presentation of Mr Ballantyne's programme the President said, "Thank you very much indeed for your talk and films, Mr Ballantyne. This is a fast developing subject and we appreciate having such up-to-date information being made available to us, particularly those of us who are unable to go overseas for this purpose. We trust that you won't let the matter rest here, but will put everything down in a paper which we can publish at a later stage for the benefit of our members. Thank you once again." CONCLUSION The President: "I wish to thank members and visitors for their attendance, and now declare the meeting closed." The meeting closed at 6.10 p.m.

By O. L. Papendorf

The method presented in this paper can be used, instead of lengthy cash-flow determinations, for the calculation of present values in the face of physical growth and inflation.

Jan 1, 1981