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By G. Gaidajis

In this paper, a semi-qualitative methodology is presented and then applied to an aluminium extrusion industrial facility in order to perform an initial environmental assessment. The results of the assessment enable an improved understanding of the environmental performance of the facility and more importantly identify the areas of significant environmental concern. Following, the application of case-specific sustainability indicators related with the areas of significant environmental concern, leads to a more comprehensive sustainability assessment. The applied two-step approach offers a quick and reliable environmental assessment and help focusing on the most environmentally problematic areas. Moreover, the follow-up of the specific indicators seems to be appropriate for the improvement of the environmental performance of the examined industrial facility.

Jan 1, 2008

By D. Menne

A comminution model and a quick laboratory milling test procedure are presented. These allow the determination of milling parameters for the - optimization of ball size and pulp density in operating mills estimation of the performance of new feed stocks in an existing mill - estimation of the expected milling performance for a new project. Information on the estimation of the size of mills to deliver specified amounts of comminution energy, and amount of expected ball, rod, and liner wear to allow cost estimates for new projects, is also included.

Jan 1, 1983

By Walter J. Johnson, Robert L. Chufo

A unique non-contracting coal thickness measurement technique has been developed to measure both the dielectric constant and thickness of a coal seam as part of a sensor array supporting an autonomous coal mining machine. The sensor measures the reflection of an electromagnetic signal from the coal/shale interface. Underground measurements of coal 6- in thick with a dielectric constant of 4 have been confirmed. Measurements were also made of a 31-in thick coal pillar for application of the sensor to highwall mining. The electromagnetic measurement technique, the data reduction process and field test experience will be presented.

Jan 1, 1992

By G. L. Mowrey

In addition to developing various types of coal interface detection systems, the U.S. Bureau of Mines is actively involved in developing a coal rib thickness monitoring system for high wall mining applications. One particular system that appears to show promise uses a ground-penetrating radar system to detect the coal-air boundaries of coal ribs. Based on preliminary laboratory and field tests, results indicate that this method can be applied successfully in highwall mines to maintain a constant rib thickness. The coal seam should be relatively clean in the vicinity of the antenna (e.g., have minimal partings or dirt bands) for best results.

Jan 1, 1995

By W. D. Monaghan, G. L. Mowrey, C. W. Ganoe

In addition to developing various types of coal-interface detection system, the US Bureau of Miner is actively in involved in developing a coal rib-thickness monitoring system for highwall mining applications. One particular system that shows promise in a ground-pentetrating radar system to detect the coal-air boundaries of coal rifts. Based on preliminary laboratory and field tests results indicate that this method can be applied successfully in highwall mines to maintain constant rib thickness. The coal seam should be relatively clean in the vicinity of the antenna (e.g., have minimal partings or dirt bands) for best results.

By W. D. Monaghan, G. L. Mowrey, C. W. Ganoe

In addition to developing various types of coal-interface detection systems, the US Bureau of Mines is actively involved in developing a coal rib-thickness monitoring system for high wall mining applications. One particular system that shows promise uses a ground-penetrating radar system to detect the coal-air boundaries of coal ribs. Based on preliminary laboratory and field tests, results indicate that this method can be applied successfully in highwall mines to maintain a constant rib thickness. The coal seam should be relatively clean in the vicinity of the antenna (e.g., have minimal partings or dirt bands) for best results.

Jan 1, 1996

By H. T. Clark, S. Feigenbaum

THE importance of measuring the temperature of molten steel in the open-hearth furnace has been recognized for many years. Poor temperature control may be costly to steelmaking operations and lead to a lowered quality of the steel. Low or excessive temperatures may shorten the life of the furnace, ladles and molds. Rates of reactions in the furnace and efficiencies of deoxidizers are known to change materially with a change in the temperature of the metal and slag. Ladle skulls and mold and stool stickers cause steel to be scrapped instead of being converted into useful products. Finally, the structure, segregation and surface condition of ingots are affected by the teeming temperature. Mill investigations of the effect of bath temperature upon steelmaking operations have been largely qualitative in character, based upon observations by practical melting men. The physical chemist has used the empirical information available and has reached reasonable and useful conclusions with respect to the various melting processes. The introduction of a reliable direct- reading pyrometer will permit accurate quantitative evaluation of the effects of temperature and should furnish a more rational basis for study of the thermo- chemistry of steelmaking. The problem is not merely one of making a small number of temperature measurements in the open-hearth furnace. This has been done by several methods to a degree of precision that was apparently satisfactory. Considerable effort by a number of investigators has been directed rather to the development of an open- hearth bath pyrometer that would be both accurate and practical for routine measurements. To be practical, the pyrometer should be inexpensive to operate; that is, the installation, operating and maintenance costs should be exceeded by the tangible benefits to the open-hearth operator. Temperatures from 2800° to 3100°F. are encountered in the open-hearth furnace. The surface of the molten metal is covered by several inches of slag, which prevents direct observation of the metal surface for optical or radiation measurements. Both slag and metal are highly reactive at these temperatures and will attack to a greater or lesser extent any material immersed in them. Adequate protection of thermocouples, which of necessity must be brought to the temperature of the bath, has generally resulted in a large, heavy assembly made up of .brittle materials, unsuited for handling on the open-hearth floor. The lie of the equipment was short and maintenance was an important consideration. EARLIER WORK Any one of a number of physical proper- ties of liquid steel could conceivably be used as a basis for temperature measurement. Efforts to the present time, however, have been confined largely to measuring either the thermal electromotive force generated between two dissimilar materials immersed in the steel or the intensity of radiation from the surface of the steel. These

Jan 1, 1946

By Robin P. Gardner

The mechanistic approach to comminution consisting of incorporating particulate breakage functions into a suitable population balance equation has been developed by a number of researchers over the past decade or so. (1) To date this approach has been developed and demonstrated primarily for batch-operated, laboratory or small-scale ball mills. However, since industrial mills are mostly quite large and operated in the continuous mode; suitable population balance models and methods for obtaining the necessary breakage and other model parameters must be developed. This paper describes and investigates a radioisotope tracer technique for this purpose, Population balance models previously developed(2,3) are adapted for this study.

Jan 1, 1974

By Raymond S. Shrode

Limestone and dolomite production is of significant importance to the Baltimore and Ohio Railroad. Except for coal, more tons of limestone and dolomite are moved by the Railroad than any other mineral raw material. In the territory served by the Railroad, these materials are produced from every geologic system from Cambrian through Pennsylvanian. Some of the operations produce premium stone acceptable for high-specification steel and chemical use; at others, the stone finds application as aggregate materials and for cement manufacture. The Railroad is interested in seeing continued production from the operations it now serves, and in serving operations in a way mutually beneficial to the Railroad and to the producer. In working with producers, the importance of geologic knowledge in prospecting and development of deposits has been clearly recognized. In turn, knowledge of the economic and technological facets of production and consumption is needed for the geologists to participate with maximum efficiency.

Jan 1, 1966

By Stephen Utter

One function of mining is to supply oil shale of the required grade and characteristics to surface retorts. The mining methods must he safe, efficient, and environmentally acceptable. Although the Bureau of Mines no longer conducts research on methods of mining fossil fuels, including oil shale, its many years of activity in that field resulted in a significant body of findings. This article summarizes some of these findings, with respect to oil shale mining. The large areal extent of Green River formation oil shales and the diversity of geologic, hydrologic, topographic, and other conditions, preclude the use of any one single mining and waste management technique. Instead, in most instances, methods and equipment will be chosen to meet site-specific conditions. Such methods include conventional surface mining (open-pit and strip), underground mining (room-and-pillar, sublevel stoping, caving) and in situ extraction (true in situ from surface drill holes and modified in situ from underground retorts containing rubblized oil shale). Combination or hybrid systems may prove suitable. Both surface and underground backfilling of spent shale waste may be practiced. Tremendous amounts of oil shale must be mined, processed, and the waste shale properly disposed of in order to meet projected industry production goals. For example, about 1.4 tons of oil shale averaging 117 L of shale oil per ton are required to produce one bbl of oil. A plant with a daily production of 8 dam' (50 000 bbl) of oil would thus require some 68 kt of raw shale daily. This is more than the average daily production from any underground mining operation.

Jan 1, 1981

By M Logsdon, B Johnson, M Fordham

The underground Neves Corvo copper-tin mine in southern Portugal currently disposes of its tailings in a ætraditionalÆ wet tailings impoundment. With the development of new technologies for preparation and transport of thickened tailings or paste, alternative tailings disposal options have become available that provide a more sustainable water management system and a higher degree of environmental protection. In addition, growing European resistance towards subaqueous disposal may well result in mandatory use of dry disposal methods in the near future. Twenty-four tailings disposal alternatives were evaluated through a cost-effective and easily-implementable bench-scale geochemical screening program conducted at site. Since the tailings are pyrite-rich and highly acid generating, particular emphasis was placed on monitoring likely indicators of sulfide oxidation under the various simulated disposal scenarios. Dependent parameters investigated as part of the program included moisture content, use of alkaline additives (lime, cement), use of a bactericide, and agitation. Response parameters included paste pH, specific conductance, and temperature as indicators of oxidation. The testing was carried out for 30 weeks. Results indicate that a number of relationships between the geochemical stability of the samples (ie sulfide oxidation) and sample characteristics can be readily identified. Based on the results of the screening program, a limited number of tailings mixtures have been selected for further long-term testing in field weathering cells to aid in the identification of the optimal mix design for future tailings disposal at the Neves Corvo Mine. This type of testing provides an inexpensive and reliable methodology for semi-quantitative comparison between tailings disposal alternatives, in particular at locations where more rigorous evaluation through long-term, fully replicated testing is not immediately feasible.

Jan 1, 2003

By Enrique Llewellyn

North River Energy Company a previous subsidiary of Republic Steel Corporation commenced development of the Number One Mine in mid-1972. The mine is located in West Alabama and presently employs a total of 632 people. Production capabilities have increased to 1.4 million clean tons of steam coal per year with the newly purchased Longwall System. Washer recovery averages 57 percent. The seam being mined is the Pratt or Corona with an average height of 52 inches and an average cover of 540 feet. The immediate roof is laminated sandstone and the floor is composed of a hard fireclay. Total production out of the mine is provided to Alabama Power Company under a longtime contract.

Jan 1, 1981

By L. G. Austin

A simple finite difference algorithm has been used to compute a simulation model for unsteady-state ball milling. The model considers the mill to act as if it were three fully-mixed reactors in series (one-large/two- small), it incorporates the-Rogers-Austin mass transfer law relating mill hold-up to flow rate through the mill, and it allows for the reduction in breakage rates caused by over-filling of the mill at high flow rates. The computation is rapid and requires only small storage space. Examples are given of use of the model.

Jan 1, 1984

By W. O. Philbrook, A. H. Jolly, T. R. Henry

IN the course of a study of slag-control methods, the authors devised a laboratory technique by which the basicity of basic open-hearth furnace slap could be estimated with sufficient accuracy to make the method of possible interest for slag-control purposes. The process consisted of measuring the slight basicity of an extract of the powdered slag in water. The procedure was presented, for the benefit of those who might care to experiment with it, in a paper submitted in the 1944 McKune Award Contest and presented at the 1944 Open-hearth Conference in Pittsburgh.1 Interest expressed at that meeting and favorable operating experience with the method at a neighboring plant, as described in a related paper by Michael Tenenbaum and C. C. Brown,2 have encouraged us to present further details of the development, technique, and pitfalls of the method and some additional data not included in our first report. At the outset it must be admitted that this method of estimation of slag basicity is not perfect; neither is any other that we know of. It is subject to somewhat greater errors than would be desirable, but compares favorably with other techniques in this respect. It has the disadvantage that it places the final determination of slag basicity in the hands of a laboratory technician rather than the furnace operator, although it can be operated in a control laboratory adjacent to the furnaces. It requires close attention to certain details, as do most laboratory procedures. On the favorable side, it eliminates the "human factor" of personal judgment inherent in estimation from pancakes or powdered samples. The procedure can be placed in practice much more rapidly and presents much less of a training problem than visual methods of estimation. The principle and operation of the method are so simple that it would not be surprising if others have experimented with the same or similar procedures, but we are not aware of any prior publication of details. Our own shop has been operating fairly successfully for several years with the aid of slag pancakes. Since the past year or two have not been favorable for the expenditure of time and energy where the need was not urgent, we have not introduced the new practice for actual slag control and hence do not have extensive operating data. In presenting this method, therefore, we make no claims as to theoretical justification nor guarantees as to practical applicability, but offer it as an empirical observation. We believe it has sufficient merit to warrant its investigation by those just instituting a slag-control program or in search of supplementary methods for judging slag basicity PRINCIPLE OF THE METHOD It is well known that when burnt lime or slaked lime is shaken up with water it

Jan 1, 1945

By T. F. Dumm, O. Trass, V. R. Koka, L. G. Austin

"The size distributions of carefully screened 2 size fractions of ground materials were determined using a Microtrac laser dif-fractometer. The size distributions were fitted to the empirical function P(x) = 1/[1 + (x50/x)1] where P(x) is cumulative mass fraction less than Microtrac size, x. The standard deviation of A for a 50 second test time was approximately 0.5, so that seventeen test times give a mean with an estimated error within t 0.25 (95% confidence level). Values of were 5.44, 4.82, 4.40 for a coal ground under different conditions, indicating statistically different shape distributions; the average value for mica was 2.91 owing to the high aspect ratio of the particles. The ratio of x50 to the geometric mean sieve size was 1.2 for the coal and 0.70 for mica.1 IntroductionKoka and Trass have presented evidence [1,2] that materials ground in the Szego mill [3] give different shapes depending on the milling conditions. The variations in shape were deduced qualitatively by viewing SEM photomicrographs of selected 1/2 screen fractions. This paper quantifies their observed differences in shape by using measurements of the size distributions of screen fractions examined in a laser diffractometer [4] (Microtrac, Model 7991). The basic concept is that particles of 'a given ""screen"" size will give a wider distribution of ""Microtrac"" size when the particles are flaky with high aspect ratios, and a narrower distribution when the particles approach the cubical and spherical geometries.2 TheoryAustin and Shah [5] have shown that coal screened within a 1. 1/2 upper-to-lower sieve size range will give rise to a much wider distribution of Microtrac size. They found that the screen interval of irregular fragments of comminuted coals or quartz gave Microtrac size distributions which could be described by the simple function"

Jan 1, 1988

By Charles C. Hawes

DETERMINATION OF SILICA OXIDE iron ores usually are found in intimate association with silica and phosphorus compounds. Their quantitative separation and purification sometimes present difficult problems to the chemist. Silicic acids may represent various degrees of dehydration. They are exeedingly weak, but combine with metallic oxides and form some of the most stable oxides in nature, the silicates. When iron ores are treated with hydrochloric acid, they yield practically all their iron. However, apart from rare exceptions, varying amounts of insoluble residues of silica, alumina, lime, magnesia and compounds of phosphorus, sulphur, titanium, chromium and others will be left. If the oxides of silicon, aluminum and titanium are present in small quantities, the insoluble residue is generally very small, but the presence of these oxides is more usual in larger quantities. Therefore, only a special treatment can break the bond between these elements. Ore Residues Acids remove the soluble constituent of the ore, leaving the insoluble residue, which chemically is rock or gangue and must be treated accordingly. Alkali carbonates are used frequently to break up the residue, but other fluxes have also been recommended, such as a number of lead and boron salts. The introduction 0f these salts, which offers certain advantages, requires, however, their removal before the other constituents can be analyzed, and this elimination is sometimes difficult. Usually in quantitative analysis silicates are dissociated by fusing them in a platinum crucible with sodium carbonate, thereby forming sodium silicate, Na2SiO3, sodium aluminate, Na2Al204, sodium titanate, Na2TiO3, and carbonates of other elements. All the carbonates are soluble in hydrochloric acid, but also some silicic acid is formed that must be rendered insoluble. To this end the solution is evaporated several times, as the first evaporation still leaves as much as 5 per cent of the silica soluble. Even after a number of evaporations, minute quantities of silica may be found with the iron and alumina present. Perchloric Acid as an Agent for Dehydrating Silicic Acid Perchloric acid, HC104, (60 per cent), has been used for years as a solvent, but few chemists have used it to dehydrate silica. It is derived from anhydrous perchloric C1207, which is most unstable and dangerous. Perchloric acid is a strong oxidizing agent, which boils at 203°C. It is more effective in rendering silica insoluble than any other known agent, and most rapid in action. After perchloric acid is added to a mixture containing silicic acid, the resultant solution is

Jan 1, 1945

By Charles C. Hawes

DETERMINATION OF SILICA OXIDE iron ores usually are found in intimate association with silica and phosphorus compounds. Their quantitative separation and purification sometimes present difficult problems to the chemist. Silicic acids may represent various degrees of dehydration. They are exceedingly weak, but combine with metallic acids and form some of the most stable oxides in nature, the silicates. When iron ores are treated with hydrochloric acid, they yield practically all their iron. However, apart from rare exceptions, varying amounts of insoluble residues of silica, alumina, lime, magnesia and compounds of phosphorus, sulphur, titanium, chromium and others will be left. If the oxides of silicon, aluminum and titanium are present in small quantities, the insoluble residue is generally very small, but the presence of these oxides more usual in larger quantities. Therefore, only a special treatment can break the bond between these elements. Ore Residues Acids remove the soluble constituent of the ore, leaving the insoluble residue, which chemically is rock or gangue and must be treated accordingly. Alkali carbonates are used frequently to break up the residue, but other fluxes have also been recommended, such as a number of lead and boron salts. The introduction of these salts, which offers certain advantages, requires, however, their removal before the other constituents can be analyzed, and this elimination is sometimes difficult. Usually in quantitative analysis silicates are dissociated by fusing them in a platinum crucible with sodium carbonate, thereby forming sodium silicate, Na2SiO3, sodium aluminate, Na2A1204, sodium titanate, Na2TiOs, and carbonates of other elements. All the carbonates are soluble in hydrochloric acid, but also some silicic acid is formed that must be rendered insoluble. To this end the solution is evaporated several times, as the first evaporation still leaves as much as 5 per cent of the silica soluble. Even after a number of evaporations, minute quantities of silica may be found with the iron and alumina present. Perchloric Acid as an Agent for Dehydrating Silicic Acid Perchloric acid, HCI04, (60 per cent), has been used for years as a solvent, but few chemists have used it to dehydrate silica. It is derived from anhydrous perchloric C1207, which is most unstable and dangerous. Perchloric acid is a strong oxidizing agent, which boils at 203°C. It is more effective in rendering silica insoluble than any other known agent, and most rapid in action. After perchloric acid is added to a mixture containing silicic acid, the resultant solution is

Jan 1, 1945

By A. M. Starfield

SYNOPSIS A description is given of a new computer programme that has been developed for the rapid computation of the changes in temperature and humidity of air passing through mine airways. The programme enables the ventilation engineer to calculate air temperature increases along airways with an ease that is comparable with that of looking up a set of graphs or tables in an engineering hand-book. The pertinent information for a particular airway can be fed to the computer either on a standard punched card, or by typing directly into the computer at a remote terminal teletype unit.

By A. M. Starfield

Discussion J. de V. Lambrechts (Fellow): The author's paper is a brilliant follow-up of an earlier paper by Starfield and Dickson.1 I have no quarrel with Dr Starfield's computerization of a complex problem, but I do not believe that he is getting quite the right answers from his programme. My impression is that his predictions about wet bulb temperature increases in very deep mines are over optimistic; in other words, that it will be hotter than Dr Starfield predicts. This is putting my views in a nutshell. This is not the occasion on which to indulge in lengthy argument about the original paper by Starfield and Dickson, but the present paper is, after all, based directly on that earlier paper and if the one fails, the other cannot succeed. I did level certain criticisms at the first paper and cannot say that the authors' replies were very convincing. I do not think it is a sin to admit that I belong to the old school which believes in thorough field experimentation and practical trials and no amount of mathematical manipulation or physical theorizing, no matter how excellent, can make up for inadequate practical confirmation. This, as I see it, is still the crux of the matter. The original paper by Starfield and Dickson still rests on somewhat scanty practical evidence and I would be much happier if Dr Starfield's computer programme, based on the Starfield-Dickson model, had been checked against a large mass of observations in the practical mining situation. This is what both Wiles2 and myself3 had tried to do previously. What we lacked in mathematics and/or computer aids, I think the present paper by Dr Starfield lacks in practical substantiation. This is no condemnation of the author's paper which, taken by itself, is excellent but I think the final stage is still lacking, namely the bringing together of theory and empiricism in a manner acceptable to all. This may be wishful thinking on my part but I hope, within the next year or so, to come up with a modified Starfield-Dickson model in such a way that the computer answers will agree in the majority of cases with the few hundred field observations which are already on record. It might be a case of applying the proverbial 'Cook's Law' to the Starfield-Dickson model! REFERENCES 1. STARFIELD, A. M., and DICKSON,A. J. 'A study of heat transfer and moisture pick-up in mine airways.' J. S. Air. Inst. Min. Metall., 68, (5), 1967. 2. WILES, G. G. 'Wet bulb temperature gradients in horizontal airways.' J. S. Air. Inst. Min. Metall., 59, (7), 1959, p. 339. 3. LAMBRECHTS, J. DE V. 'Prediction of wet bulb temperature gradients in mine airways.' J. S. Air. Inst. Min. Metall., 67, (11), 1967, p. 595. R. Hemp (Visitor): Dr Starfield's paper has very effectively rounded off one particular aspect of the general problem of heat flow in mines. The ease with which this computer programme can be used to calculate temperature increases in horizontal airways must lead to its wider use in ventilation planning and, in developing this rapid method, Dr Starfield has indeed rendered a valuable service to the mining industry. One could consider further instances of heat flow in airways in which the availability of a rapid computer method would be desirable, e.g. the flow of air down a shaft, where there is an increase in temperature due to adiabatic compression, as well as an increase in virgin rock temperature as the depth increases. However, this particular case would not present any new problems and would merely require an extension of the exisitng work. I should like in this contribution to talk about an aspect of environmental control in mines which, I think, will become more important in the future. It is well known that wet bulb temperatures are subject to fluctuations underground. In some instances, particularly in stopes, the fluctuations, both with time and position, can be considerable. The theoretical work which has been carried out on temperature increases has been aimed at the prediction of mean temperatures, and no account has been taken of fluctuations around this mean. It is questionable whether this approach will, on its own, be sufficient, particularly when temperature increases in stopes are considered. The fluctuations in air temperatures underground arise from two causes. The first of these would be the fluctuations in surface conditions, and here one could list random, diurnal and seasonal fluctuations. The second cause is the multitude of things which vary in a mine and here one could list variations in air flow quantity, sources of evaporation, heat transfer from pump and compressed air columns and, particularly in the stope, variations in air flow patterns. Fluctuations arising from surface temperature variations should be amenable to calculation, and here one envisages figures relating the decay of temperature variation with distance to factors such as air flow quantity. Fluctuations resulting from changes in the mine are perhaps more difficult to tackle theoretically and the best approach could well be to analyse underground observations. In this connection, there is a good case to be made for the increased use of statistical methods in the analysis of underground temperature measurements, and it might be of value to look at current air-conditioning practice. When carrying out cooling load calculations for a particular location it is customary to use design wet bulb

Jan 11, 1969

By J. J. leR. Cilliers

ABSTRACT The recently introduced concept of negative taxation complicates estimation of the distributable profit of certain South African gold mines, and an assisted mine could operate at a working loss and yet produce an overall profit for distribution amongst its shareholders. A simple diagram is presented from which the approximate working profit or loss, taxation payable or tax credit received, and the distributable profit of an assisted mine can be estimated directly for any combination of the four main variable operational factors: tonnage milled, recovery grade, unit cost and capital expenditure. INTRODUCTION The effects on the working profits of South African Gold mines caused by changes in unit working costs, recovery grade, tonnage milled and capital expenditure are readily estimated. For normal tax- and lease-paying mines the distributable profit is related to the working profit and the latter is a commonly accepted comparative measure of the profitability of an operation. However, the recently introduced concept of State assistance in the form of negative taxation1, i.e. a tax credit, for mines with a life of less than eight years complicates such estimates. A requirement of State assistance is that an assisted mine must lower its normal pay limit by 16 to 20 per cent, and it will be possible for a mine to operate at a working loss and yet produce an overall profit for distribution amongst its shareholders. In the case of an assisted mine it is therefore necessary for management to judge the effects of changes in unit costs, grade, etc., in terms of distributable profit instead of working profit. This will require repeated calculation of tax to be paid or tax credits that will be received under the numerous possible combinations of the four main variable factors. However, with the aid of the diagram illustrated in Fig. 1, it is possible to assess at a glance the practical effect of these variables on the distributable profit of an operation not subject to tax on the normal formula, or small mine formula, with sufficient accuracy to decide whether a detailed analysis is required. USE OF THE DIAGRAM From the central point 'X' in Fig. 1, a range of tonnages milled per annum has been plotted along the north-bearing axis, a series of costs per ton milled in the northwestern quadrant, recovery grades in the northeastern quadrant, and capital expenditures in the southwestern quadrant. Starting from the tonnage milled per annum, a line is drawn east and west across the two northern quadrants up to the points where it reaches the desired cost- and grade-lines. From these points two north-south lines are drawn into the southern quadrants. A further line is drawn to the east from the point where the western north-south line crosses the desired capital expenditure. Distributable profit is read off in the southeastern quadrant where this line intersects the eastern north-south line. Every possible combination of