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By J. E. House, C. J. Lewis

In the solvent extraction process, also referred to as liquid-liquid extraction, the clarified uranium-pregnant sulfuric acid leach solution is contacted with an organic extractant dispersed in kerosene; the uranium enters the organic phase and associates itself with the organic extractants. Simultaneously an-ions or cations, as the case may be, leave the organic extractant phase and enter the aqueous phase. The two phases are then allowed to separate by virtue of their immiscibility. Based on the data available, a generalized procedure for the recovery of molybdenum from the sodium carbonate scrub liquor of acid leach uranium mills using secondary and tertiary amine extractants is presented, as is another generalized procedure for the recovery of molybdenum from the bleed stream of alkaline leach uranium mill circuits. Such economic appraisal as can be made at this stage of the development is also indicated. Molybdenum occurs in most uranium ores. Whether the uranium is solubilized by the acid leach route or by the alkaline leach process, some of the molybdenum present in the ore is solubilized along with the uranium. Molybdenum in uranium mill pregant solutions may cause processing difficulties, among which may be mentioned the poisoning of resins, the precipitation of organo-molybdenum complexes, or the build-up of molybdenum in recycle streams. While the uranium milling industry has been successful in applying measures to overcome the problems arising from the presence of molybdenum in the circuits, such measures nevertheless add to the cost of producing uranium yellow cake concentrate. Table I shows the analysis of typical uranium pregnant leach solutions. Uranium recovery by solvent extraction is presently practiced only in conjunction with acid leach circuits, and it may be noted that of about 16,000 tons of uranium ore daily processed by sulfuric acid leach, more than half of this tonnage follows the solvent extraction route. Uranium mills leaching ore with sodium carbonate-sodium bicarbonate solution (the so-called alkaline leach circuit) do not use solvent extraction. In this case the uranium pregnant solution is sufficiently pure to permit the direct precipitation of uranium concentrate with subsequent recycle of the alkaline leach solution. While solvent extraction procedures may be developed which are economically attractive for the alkaline leach uranium process, this has so far not been the case. The earlier uranium mill solvent extraction circuits used organo-phosphate extraction reagents, among which di-2-ethylhexyl phosphoric acid was popular. It should be borne in mind that uranium in its sulfuric acid leach solution exists in an equilibrium involving uranium in both anion and cation forms: uo + 2S0 = [uo2(so4)2] For this reason uranium may be extracted by either cation extractors or anion extractors and this is likewise true of molybdenum. However, the organo-phosphate extractants also load ferric iron which is usually present in the uranium acid leach solution. For this reason, it is necessary to reduce this solution substantially to the ferrous state ahead of solvent extraction using organo-phosphate reagents. The amines, being anion extractors, selectively reject iron and thus render the iron reduction step unnecessary. In the solvent extraction process, also referred to as liquid-liquid extraction, the clarified uranium-

Jan 1, 1961

By Constance Holmes

President Lien presented Mrs. Holmes with the first of speaker appreciation gifts presented by his firm Amax Coal West, Inc. These were books by Rand-McNally entitled The Executive Golfer Guide. Following the coffee break, Clark Moseley presented the first annual Institute Safety Achievement Awards for the safest mines in the eight member state region. The awards were based on: 1. Total man-hours 2. Total number of lost time accidents 3. Incidence rate 4. Number of S&S violations 5. Description of safety program 6. Safety awards received 7. Health and safety training efforts 8. Safety Policies 9. Does the operation take employee suggestions and implement them? 10. Letter(s) of commendation from agencies individuals The awards were judged by the senior/graduate level class of Mine Safety & Health at the Colorado School of Mines under the supervision of professor Edward Hollop. The two handsome traveling trophies were awarded to and accepted by: Surface: Big Sky Mine. Colstrip, Montana Gordon Brannon, Manager of Safety Underground: Skyline Mine, Scofield, Utah Dave Hales. Safety Supervisor and Doug Johnson, General Production [ ]

Jan 1, 1998

By Scott A. Anderson, Benjamin S. Rivers, Derrick D. Dasenbrock, Silas Nichols

Unknown geotechnical conditions are a major source of risk. Unexplored places vastly outnumber the sampled and tested ones, and widely spaced boreholes with intermittent tests and samples are the norm. Sometimes site-specific planning and thought goes into locating these special, tested places, such as basing them on the geologic understanding or anticipated key locations for the structure; more often they are simply evenly distributed. We demonstrate a holographic model that allows viewers to see real data in real space, scaled or not, and to visualize where measurements are taken, what those values are indicating, and where there exists more unknown and more risk. The holographic model shows in an intuitive way, values from Standard Penetration and Cone Penetration tests, and surface geophysics. The mixed reality of this future is that a wide audience – owners, designers, project managers, contractors, and stakeholders interact together in a real space where they see and talk to each other, while at the same time are individually looking all around below or above ground, like a gopher, in a virtual one. Risk in the future will be better managed through more thoughtfully designed investigations and better communication of 3D data in a world of augmented reality. INTRODUCTION This paper explores the use of augmented reality to convey understanding of the subsurface conditions of a bridge site. This is in contrast with the current state of practice where this information is contained in a geotechnical report, and the ideas are also applicable to other structures, earthworks, and excavations. “Augmented reality” describes a situation where a 3D holographic model is displayed for users in such a way that the users experience both the model and the real environment of their setting- such as at a desk, in a meeting room, or in an open space at a project site (Figure 1). The 3D holographic model is used to directly visualize underground features, to see through the earth to the actual locations where explorations are made, samples are obtained, or measurements are taken, design values are assigned, or construction is planned. An immersive model provides the following three powerful functions for users:

Jan 1, 2019

By Robert L. Lagace

The purpose of the work reported herein was to investigate whether available telephone multiplexing equipment offered a means to rapidly upgrade the traffic-handling capacity of present mine telephone systems and provide for selective calling for safer and more efficient mine operation. Common sense was used to decide whether or not an item could be termed "available." Since conventional telephone gear is not designed to interface pager phones for example, existing shelf items would require adapters to compatibly interface these two types of gear for independent operation over the present single twisted pair used in mines. These and similar small items were allowed, but if a system required any extensive design work to adapt it for the mines, we ruled it "not available."

Jan 1, 1975

This study was done to evaluate the economic and technical considerations of using pozzolanic materials in order to guide cement manufacturers, pozzolan producers, contractors, Government organizations, and others interested in concrete construction work. Five hundred and thirty-eight samples of pozzolanic raw materials were taken from 27 central and western States. These samples were evaluated by petrographic procedures, and about 200 of the most promising ones were given a complete series of physical tests (American Society for Testing and Materials) to evaluate further their suitability as a pozzolan. This investigation showed that deposits of natural pozzolan materials were widely dispersed in the central and western parts of the United States but that exploiting these deposits would depend on whether they could compete economically with an increasingly abundant industrial waste product--fly ash.

Jan 1, 1969

By Yi Luo, Jian Yang, Hua Jiang

Surface subsidence induced by underground coal mining activities, especially longwall mining operations, can cause various problems to interstate highways ranging from structural integrity, drivability to safety. Accurate subsidence prediction, correct influence assessments, and effective mitigation measures are the keys to ensure the safety of highway traffic. The surface subsidence prediction program, called comprehensive and integrated subsidence prediction model (CISPM), was developed based on the principle of influence function method and has been validated with a large number of subsidence measurements. In this paper, the techniques to use the predicted final surface movements and deformations for assessing their influence on the integrity and functionality of highway structures (e.g., road surface pavements, concrete slabs, transverse joints, etc.), vehicle dynamics, comfort level, and drivability are presented. A number of mitigation measures to protect the highway structures and to ensure traffic safety are proposed along with an application case.

By Yi Luo, Jian Yang, Hua Jiang

Surface subsidence induced by underground coal mining activities, especially longwall mining operations, can cause various problems to interstate highways ranging from structural integrity, drivability to safety. Accurate subsidence prediction, correct influence assessments, and effective mitigation measures are the keys to ensure the safety of highway traffic. The surface subsidence prediction program, called comprehensive and integrated subsidence prediction model (CISPM), was developed based on the principle of influence function method and has been validated with a large number of subsidence measurements. In this paper, the techniques to use the predicted final surface movements and deformations for assessing their influence on the integrity and functionality of highway structures (e.g., road surface pavements, concrete slabs, transverse joints, etc.), vehicle dynamics, comfort level, and drivability are presented. A number of mitigation measures to protect the highway structures and to ensure traffic safety are proposed along with an application case.

By H. Linder, W. H. Dennen

The graphitic carbon content of soils may be used to detect and delimit subsurface graphitic zones. Spectrographic measurement of carbon in C horizon soils from several areas in the northeastern United States shows good correlation with known graphitic bodies. Bodies of graphite and sulfides are readily located by electromagnetic prospecting methods, but these methods cannot generally discriminate between them. Usual practice, therefore, requires follow-up work on electrically anomalous areas by trenching, drilling, or soil sampling in order to determine the mineralogical nature of the conductor. The efficiency and cost of such follow-up is consequently an important factor in prospecting. The presence of buried sulfide deposits is often reflected in concentrations of metals in the superincumbent soil. Simple chemical tests for such metal concentrations have been developed and applied with considerable success. Bodies of graphite or mixtures of graphite and sulfides are, however, very common and a means whereby buried graphite could be detected by soil testing should provide valuable additional information in the search for ore sulfide and graphite deposits. Graphite is a notably stable substance and should persist in soil above graphite-rich horizons. Microscopic examination of soil samples high in carbon, however, failed to reveal any recognizable graphite fragments indicating a grain size in the clay range. Presumably such small particles would have some mobility in a soil by a translocation mechanism similar to that proposed for the movement of clay particles in a soil profile. Experimental data supports this idea since the boundary between background and anomalous soils carbon values is quite sharp, but the anomalous zone is slightly broader than the graphitic source rock. A simple spectrochemical technique for the determination of carbon in geological materials has been described by Dennen,1 and may be directly applied to soils. A modification of this technique which employs an arcing chamber through which nitrogen is passed is recommended to decrease contributions from atmospheric carbon dioxide. Tests indicate that soils over graphitic zones may be strongly enriched in carbon. The spectrochemical determination of carbon depends upon the formation of the cyanogen molecule (CN) from carbon in a sample and atmospheric nitrogen, under the high temperatures associated with a dc arc. Samples for analysis are dried, lumps broken, and screened. A small portion of the -100 mesh fraction is packed into a copper electrode and excited as the cathode of a dc arc. The band spectra of cyanogen are recorded photographically and the density of the bandhead CN 3883A is measured. The limit of detection of the method is about 0.01 pct C and its coefficient of variation is about 15 pct. Soils, of course, contain carbon in other forms than graphite, and the amount of interference from such sources was examined. The C horizon of several soils from Massachusetts, Maine, and Pennsylvania were found to have a carbon content of 0.3 to 0.5 pct by weight. This content is chiefly due to the presence of carbonates and vegetable matter in the sample and may be readily eliminated, or at least

Jan 1, 1961

Gold in the stibnite veins of Costerfield, Victoria, was described in 1922 1, prior to any mineragraphic examination, as (a) free yellow gold (b) free rusty gold and (c) combined gold. The free yellow gold occurs in quartz and will amalgamate with mercury. The free gold of dull, rusty or copper-red colour occurs in massive stibnite and has been stated to resist amalgamation with mercury. The dull colour is only skin deep and the colour is bright when the rusty gold is scratched. The appearance of the rusty gold is spongy or cellular and it generally occurs near small cavities in the stibnite. The suggestion that the cellular character indicated the removal of a certain amount of stibnite leaving a residue of se.condary gold cannot be sustained.It now appears probable that the rusty gold is formed by the primary dissociation of a gold antimonide and is distinct in origin from the normal yellow gold which is deposited with quartz or stibnite from auriferous mineral solutions.The combined gold referred to in the earlier paper was the gold contained in the stibnite as revealed by assay. Such gold was at first thought to be either dissolved in the stibnite or else present as free interstitial particles too minute for observation in transmitted light in thin sections.Subsequent examination of numerous polished,surfaces disclosed the small particles of gold occurring in the grain boundaries in aggregates of fine grained stibnite 2. The assumption that all the gold in the stibnite, as revealed by assay, occurred in this way is now known to be incorrect, because limited amounts of a gold antimonide have been found in the veins.

Jan 1, 1952

By S. Frimpong

The cable shovel excavator is used for primary production in many surface mining operations. A major problem in shovel excavation is the variability of material diggability, resulting in varying mechanical energy input and stress loading of shovel dipper-and-tooth assembly across the working bench. This variability has a huge impact on the shovel dipper and tooth assembly in hard formations. In addition, the geometrical constraints within the working environment impose production limitations resulting in low production efficiency and high operating costs. A potential solution to the above problems is the application of an intelligent cable shovel excavation(ICSE) technology. In this paper, dynamic models of the cable shovel excavator are developed with numerical examples. These models form the basis for developing dynamic shovel simulators for an intelligent shovel excavation technology. The dynamic equations are developed using the Newton-Euler techniques. The path trajectories for efficient excavation, dynamic velocity and acceleration profiles, and dimensioned parameters for optimum feed force, torques and momentum of shovel boom-bucket assembly are modeled and used for efficient excavation. The optimum digging forces and resistances for the cable shovel excavator are modeled and used to predict optimum excavation performance.

Jan 1, 2003

By S Jackson, I Arbuthnot

The use of High Rate Thickeners has gained wide acceptance in the mineral treatment industries. The design of these units is characterized by an efficient deaeration and flocculation chamber, and introduction of the flocculated feed solids into a preformed floc bed zone. By these means the settling process is accelerated and consequently High Rate Thickeners achieve a significantly higher throughput per unit area than conventional thickeners.   The object of a control system on a High Rate Thickener (HRT), as on a conventional thickener, is to obtain the required underflow density and overflow clarity at all feed conditions. The feed conditions which may vary include volumetric and mass feed rate, pulp density, particle size and particle type. A conventional thickener has a large volume and cross sectional area, and changes in performance occur slowly û the operator has time to observe and react to these changes to maintain control. On a HRT, there is a much reduced residence time and therefore control parameters need to be reset more frequently. Although manual control is possible, the use of automatic control systems is therefore desirable to avoid excessive operator attention, while optimizing control of density and clarity. Automatic control of a conventional thickener is usually achieved by an underflow density loop which regulates the rate of withdrawal of underflow. A turbidity meter is sometimes used to measure overflow clarity and regulate the addition of a coagulant or polymer flocculant. These measures are not adequate on a HRT, because they would not give optimum control and could lead to excessive flocculant use. To achieve optimum operation in a HRT, the floc bed level should be maintained above the feed inlet point in the thickener. This bed level has become the key variable around which most control systems have been designed. However, a number of problems have occurred which has resulted in poor control, or only partial control of thickener performance. We will describe some of these problems, and a solution which is simple and effective.

Jan 1, 1990

By R. F. Tenney

The performances of four anthracite-burning stokers have been observed under identical 74-hp. steam boilers. Fifty runs of 12 and 24 hours' duration were made in accordance with the test code of the American Society of Mechanical Engineers (ASME). The capacity of each stoker for burning anthracite has been determined, the heat efficiency at each fuel rate has been computed, and the various significant items of hear loss have been estimated. The operating data and results from each run are tabulated in this report in the form used in the test code. The heat efficiencies and most significant operating data for each run are also presented graphically for each stoker to establish the trends with increasing boiler outputs, The tests show that rice anthracite can be burned on stokers adapted to its use at heat-conversion efficiencies of 82 percent or more under continuous firing. These high efficiencies are maintained with fuel inputs 30 percent higher and lower than the peak efficiency rate. Moreover, a heat efficiency of 70 percent or more is obtained at 50 percent of the optimum fuel rate, even though the excess air into the furnace cannot be held below 150 percent.

Jan 1, 1960

A BRIEF DESCRIPTION OF TELPHER HANDLING AND BLAST FURNACE EQUIPMENT.The various sections will be described in the following order:(a) Telpher Handling and Storage Bins.(b) Blast Furnaces.(c) Slag Disposal.(d) Bullion Handling to Drossing Kettles.(e) Copper Drossing.(f) Copper Matte Furnace.(g) Bullion Delivery to Refinery.(h) Fume Handling.(a) TELPHER HANDLING.The telpher installation is an all-steel structure designed to carry out the work of assembly and delivery of charge materials to the blast furnaces.To simplify description, the primary telpher installation will be divided into three (3) sections:-No. 1 Section. 395 ft. long, running north and south, parallel to the water front, and so located that coke, which...

Jan 1, 1937

By J. W. Spyker, D. H. Filson, W. H. W. Husband

"Large deposits of sodium sulphate exist in southern Saskatchewan in the brines or muddy crystal beds of alkali Jakes. Currently, more than 300,000 tons per year of sodium sulphate are produced from these lakes and sold as salt cake to the paper industry. Most of the production is obtained from the brines of a limited number of Jakes.The Saskatchewan Research Council was requested to develop a process for recovering sodium sulphate from the muddy crystal beds so that this type of deposit could be exploited in the future. A flowsheet was developed with the aid of phase diagram data and the process was studied on a pilot-plant scale using raw material from three different lakes. Satisfactory yields and product purities were obtained in all cases, and an economic analysis indicated that a 100,000-ton-per-year sodium sulphate plant could produce salt cake at a cost of $12.26 per ton for a rate of return upon investment of 16 per cent at current market prices."

Jan 1, 1966

By E. M. Cohn

The literature dealing with the electrical conductivity of solid dielectrics, including all its aspects and its relationships to other physical properties of these materials, is extensive and scattered in many books, phamphlets, and periodicals. It is believed that most of the important contributions to this field up to October 1943 have been listed and abstracted in this circular. Also included are some general references on static electricity. Methods of removing static charges are described; methods of and conditions for measurements of resistivity are discussed; equations for the calculation of resistivity are given; and methods of resistance measurements in Situ are reviewed. Data on the variations of resistivity with changing conditions as well as explanations for them have been collected, and three tables showing the resistivity of various dielectrics at different humidities are included. The appendix contains a short development of the mathematical formulation of the charging and discharging currents due to interfacial polarisation. INTRODUCTION Methods for Removing Static Electricity Of the various means employed for preventing or removing accumulations of static electricity in industrial processes, grounding is the most common and most generally effective. It is a precaution readily applied to stationary machines anti may often be utilized to good advantage to rid persons and portable equipment of an acquired charge. There are many situations, however, in which direct low-resistance grounding cannot be used, either because the charged bodies are insulators or are inaccessible, or because contact to a ground lead might give rise to a hazardous spark. If the charged body is a conductor, contact made to a neighboring conductor, even though the latter be insulated from ground and of relatively small capacitance, may also result in the occurrence of an incendive spark. In such instances, static electricity can sometimes be removed most satisfactorily by means of strong atmospheric ionization produced by radioactive material, X-rays, ultraviolet light, or A. C. high-voltage brush discharge. Where no danger exists from flammable

Jan 1, 1944

By David Norval

Water solidification of mattes, metals, alloys and certain slags with high metal entrainment has customarily not been practiced due to the belief that such processes are too dangerous and unproven in the Pyrometallurgical Industry. Slag granulation on the other hand is extensively applied, although in some cases crudely, with disastrous effects, as a result of not recognising the high heat capacities prevalent in slags. This paper will examine the most common air solidification processes and compare such processes with water solidification, mainly slag and matte granulation processes and design criteria for safe and reliable operation. Finally, purpose designed granulation and solidification processes will be discussed taking into account specific applications and the individual signatures of alloys and slags, emphasising that no slag, matte or alloy responds in similar fashion to a granulation practice.

Jan 1, 2006

By Donald F. Smith

This report describes the construction and calibration of two ice calorimeters and includes results of high-temperature heat-content measurements, made by the Federal Bureau of Mines, on rubidium fluoride, hafnium tetrafluoride, cesium chloride, and cesium iodide. The heats and entropies of fusion of rubidium fluoride, cesium chloride, and cesium iodide have been calculated at their respective melting points using equations derived from the experimental heat-content data. Hafnium tetrafluoride did not melt within the range of temperatures investigated. Heat and entropy of transition of cesium chloride from the alpha to the beta form were also determined. INTRODUCTION Free-energy data usually afford the cheapest and quickest means of determining the feasibility of experimentally untested reactions. For known reactions, free-energy data show the variation of the equilibrium constant with temperature and make it possible to calculate, without experiment, the maximum ratio of product to raw material for a given chemical process.

Jan 1, 1961

By Ginger S. Evans

This report documents a preliminary hydrologic investigation of an area where longwall mining methods are to be used. The scope of work includes: determination of physical and chemical characteristics of major soil types in the area; determination of physical and chemical properties of surface water bodies; collection of geologic characteristics, including stratigraphy, structure, and detailed aquifer descriptions; collection of 10 years' meteorological data and installation of a weather station; and a detailed ground-water investigation that includes completion of observation wells, aquifer testing, water quality sampling, and analysis using a 3-D computer model. The Trescott model developed by USGS was used to simulate steady-state aquifer conditions. Input data from 8 multiple-completion monitor wells were used to model an area of approximately 10 square miles. Two layers, coal and overburden, were simulated, both confined. Model results showed good agreement with know piezometric data, desaturated areas, and flow from springs. The study area was found to have very low-yield bedrock aquifers with transmissivities ranging from 5 to 320 ft2/day for the coal (depths from 500 to 1,200 ft) and from 499 to 576 ft2/day and fractured sandstone units (depths less than 100 ft). Annual precipitation and recharge are very low, 10 to 11 inches and 0.25 inch respectively. The area has very high relief and large areas of rock outcrop. No perennial streams are present on the site.

Jan 1, 1983

By A. Roberts

This paper reviews progress in equipment design and in the techniques applied to mine lighting in Great Britain. The incidence of the disease miner's nystagmus, which was a major source of concern only a few years ago, has now diminished, largely owing to improvements in standards of lighting in mines. The reorganisation of the coal mining industry, involving increasing mech-anisation, together with new safety legislation, has brought about the widespread use of mains electric lighting underground. An account is given of some of the results of research to determine the lighting conditions needed for compliance with the compulsory legal requirement of "sufficient and suitable" general lighting at specific localities in British mines. Some details are given of the techniques applied and the results of recent research in the problem of glare from miners' cap lamps. Of the various factors in the working environment of the miner, it is true to say that lighting is seldom given attention comparable with that devoted to other factors, such as dust, heat and humidity, or atmospheric gas content. No doubt one reason for this lies in the ability of the human eye to adapt itself to low brightness levels. Be that as it may, the fact is that at the turn of the 20th century the miner's working light improved little throughout the centuries during which mining technology has developed. Indeed, in coal mines which encounter a methane explosion hazard, flame safety lamps, with a luminous intensity less than one candle power, were virtually the sole means of lighting during almost the whole of the 19th century. The 20th century has witnessed a substantial improvement in lighting techniques underground in coal and metalliferous mining. In Great Britain the general pattern has been one of standards periodically raised by the implementation of Statutory Regulations imposed under successive hlines Acts, but it is fair to add that the more progressive mining companies usually anticipated the Statutory Regulations, which when they have been put into effect have served to turn into general practice what was already being done at the better mines. In earlier years, official requirements were limited to the specification of approved lamp designs, with stipulated minimum values of luminous intensity and light output, but more recently the necessity of satisfactory maintenance of standards during service has been recognized, and the current regulations not only require that a maintenance organisation should exist, but also specify a maximum permissible depreciation below initial approval standards.'

Jan 1, 1961

By E. H. T. Whitten

Fundamental principles of trend surface analysis are briefly reviewed. Recent analyses of several granite masses illustrate the method of estimating the quantitative regional composition and also variation trends. Mineralogi-cal, bulk chemical, and other quantitative variates can be employed. Such results should improve gravimetric surveys (etc.) relying on correction terms based upon estimated rock composition. For the first time realistic estimates of the mean composition of rock bodies can be made with the aid of trend components. Deviation maps hold promise for delimitation of disseminated mineralized areas. Deviations comprise residual "anomalies" after removal of trend components. In petrogenetic work such deviations have been shown to reflect local influences (e.g., contamination of magma by assimilation of xenoliths or country rocks of the envelope). Similarly, mineralization should be reflected as deviations standing out from background trends. Actual examples are given. Present results largely involved projection of data onto a horizontal plane, but if sufficient data are available use of three spatial coordinates increases accuracy for prediction in "unexposed" areas. Regression analysis shows that statistical correlations between variates for regionally distributed specimens are often strong (particularly with percentage data). Hence, in preliminary surveys more easily determined variates may sometimes be employed to gain first estimates of the distribution of components more economically significant. The sampling plan is of paramount importance. Unless a suitable sampling plan is devised and adhered to rigorously during collection of the samples, all subsequent analysis is liable to strong bias and to yield spurious estimates of the truth. For a wide variety of purposes it is becoming necessary to assess the quantitative composition and variability of rock masses and mineralized zones of various types. In petrology and petrography this is something of a break with tradition, because virtually all descriptions heretofore have been qualitative. Although vast amounts of qualitative data have been compiled, little is known about the quantitative behavior of rock components. However, if variability of rocks could be understood and expressed with sufficient accuracy, there would be considerable advantage to both economic and petrogenetic problems. For example, if, on the basis of a limited series of observations, the three-dimensional geometry of a disseminated orebody (or ore-bearing formation) could be predicted accurately, it would be possible to extrapolate with confidence the structure into unexposed areas. The following example based upon the geometry of an igneous cone sheet illustrates the point. The significant rock-unit gives outcrops at a number of points on the exposed surface ABCD (Fig. 1A). Study of n exposures may enable a geologist to predict that the rock-unit is circular in form and thus indicate where the unit can be expected in unexposed terrain. Such observations are made at sites with u, v coordinates, but, if subsurface information is available at sites with uvw coordinates, it will eventually become possible to predict accurately the three-dimensional form of the rock mass. Geologic rock masses or mineral deposits are not generally as regular and symmetrical in geometric form as the body illustrated in Fig. 1A. However, even where the broad limits of a major rock mass are known, a more acute problem arises in attempting to obtain detailed quantitative estimates of its internal variability; it is difficult to predict the variability of a mass from a limited number of observa-

Jan 1, 1961