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By J. D. McFarlane, V. Robinson

"The paper begins with a brief account of the naturarly occurring resources of gypsum and anhydrite and a discussion of their relative value and utility as sources of sulphur. The fundamental chemistry of recovering sul-phur values from calcium sulphate is discussed. (a) Thermal decomposition -discussed as impracticable; (b) Reduction to calcium sulphide; (i) Total Reduction-The chemistry is outlined and the Dorr-Oliver and Bureau of Mines processes mentioned. The Elcor process is mentioned and certain deductions made from available information.(ii) Partial Reduction-This is stated as the basis of the only proven process, namely ""The Cement -Sulphuric Acid Process."" The possibility of recovering lime is mentioned as an aside, but dismissed for lack of commercial application. The history of the cement -sulphuric acid process is covered briefly and a list of plants in commercial operation included. A brief elementary account of the basic chemistry of cement production is followed by a discussion on raw materials and fuels. A short account of the flow scheme of a typical plant, with notes on the operating peculiarities, precedes an account of product quality. The latest developments which enable by-product gypsum to be used as a raw material are discussed, with an indication of how the flow scheme is modified. A statement of feasible plant capacities is followed by requirements of raw materials, services, labour, etc., and finally some indication is given of capital costs."

Jan 1, 1969

The first metal-mine accident-prevention course was prepared and published in 1942--45 as a series of seven miners' circulars (Nos. 51-57). The scope of the course has been broadened, revised, and brought up to date, and it is being published as a similar series of seven miners' Circulars (Nos. 51-57, revised) on accident prevention in metal and nonmetallic mines. These circulars are: Accident Statistics (Miners' Circular 51), dealing with general statistics on accidents and injuries at metal and nonmetallic mines, including causes, costs, and the uses of investigations and reports of all accidents.

Jan 1, 1957

By Donald F. Hammer, Donald W. Peterson

The Magma mine at Superior, Arizona, has produced over 13 million tons of ore yielding 1.5 billion pounds of copper. It is a mesathermal deposit, and, although the bulk of the ore has come from the Magma vein, most of the recent production has come from replacement deposits in limestone. The mine lies in a Precambrian and Paleozoic sequence of rocks that includes schist, diabase, quartzite, shale, and limestone; nearby, these rocks are intruded by igneous bodies of Mesozoic age that were probably the source of the ore-bearing fluids. Locally, these rocks are overlain by Cenozoic volcanic rocks and conglomerate. Layered rocks at the mine dip eastward about 30°. The area is extensively faulted, and surface faults are grouped into an earlier east-trending set and a later northtrending set. An additional set of diagonal faults that trends northwest and northeast is recognized underground. The east-trending Magma vein-fault, with its splits and branches, is the principal mineralized structure of the district. The bulk of the ore occurs in large ore shoots that plunge steeply westward and are sporadically connected by irregular ore shoots dipping gently eastward. The main ore controls apparently are selective zones of permeability related to the transverse faults. A bed of crystalline limestone near the base of the Martin Limestone (Devonian) is the host for the replacement ore bodies-discontinuous tabular pods dipping eastward parallel to the bedding. Selective permeability is again the apparent ore control, caused both by local hydrothermal solution of limestone and by deformation along faults. The principal copper minerals in the vein are chalcopyrite, bornite, enargite, tennantite, chalcocite, and digenite; these minerals vary in abundance according to a distinct zoning pattern. The upper part of the mine yielded considerable zinc as sphalerite, and the oxidized zone was rich in silver. The chief gangue minerals are pyrite, quartz, and hematite. In the limestone replacement bodies, chalcopyrite and bornite are the chief ore minerals.

Jan 1, 1968

By Paul F. Kerr

The uranium-producing areas near Marysvale, Utah provide an unusual group of veins and replacement deposits associated with a Pliocene-Oligocene intrusive and extrusive igneous complex. Aside from several scattered occurrences in older volcanics, uranium-bearing veins occur in intrusive quartz monzonite or granite and in nearby rhyolite. The veins in general trend within a few degrees of N55-65°E, are more or less vertical, and are found along the western margins of a quartz monzonite intrusive. The replacement deposits are found in rhyolite intrusives and also in the lower portions of rhyolite flows close to places where veins forming solutions rising through quartz monzonite came into contact with the rhyolite. At least 14 veins have been mined since uranium mining operations began at Marysvale some 16 years ago, while ore has been extracted through about 10 miles of underground workings. The active mmmg area is approximately 3000 feet long and in the central portion 1500 feet wide. Ores have been found over a vertical spread of almost 2000 feet, between the highest occurrence on Jungfrau Hill ( ca. 7200 feet) and the deepest discovery of ore in a drill hole near the Prospector Mine (ca. 5200 feet). Under existing mining and marketing conditions, mining along the veins in the main area appears to have reached an economic limit at about 500-600 feet below the surface. However, orebodies in the rhyolite and in the upper portions of veins close to the rhyolite are subject to active mining. Isotopic dates indicate that the uraninitebearing veins and replacements are late Miocene or Pliocene (ca. 10-13 m.y.), the rhyolite is Miocene (avg. 17.5 m.y.), and the quartz monzonite and granite intrusives are late Oligocene (23.6 to 26.0 m.y.). The older Bullion Canyon Volcanic Series which encircles the area is Oligocene (28 to 31.1 m.y.). Two generations of alteration occur: ( 1) Earlier alunitic veins and replacement bodies are found in the Bullion Canyon Volcanic Series, none of which have produced uranium; (2) Later argillic alteration associated with the introduction of uranium is found along veins, replacing glassy rhyolite dikes and replacing phases of the rhyolite.

Jan 1, 1968

The Florida phosphate industry, which supplies about three-quarters of the domestic phosphate fertilizer, produces tremendous volumes of phosphatic clay wastes (slimes). These clays retain a high percentage of water for extended periods of time. The clays also pose an environmental hazard because the disposal technique involves aboveground storage behind earthen dams. Although much research has been undertaken by numerous organizations to dewater slime, no completely satisfactory solution has been developed. In June 1972, a cooperative effort by the Federal Bureau of Mines and the Florida phosphate mining industry was initiated to develop a solution for dewatering the Florida phosphatic slimes. This report discusses various aspects of the slimes problem, reviews past research, makes recommendations for future research, and includes a bibliography of references and patents dealing with the subject.

Jan 1, 1975

By R. W. Lawrence

A method by which it is possible at an oxidation potential below 680 mV SHE to achieve quantitative conversion of sulphide sulphur to elemental sulphur instead of sulphate in a biological leach of chalcopyrite and bornite has been investigated. The process chemistry, biological phenomena and process flowsheet options are discussed. Several copper concentrates have been evaluated and have been found to be amenable to th process. Results to study the progression of chalcopyrite decomposition during the leach are presented and mineralogical factors affecting the requirement for silver addition are discussed. A chloride addition method for improving silver recovery is described. The results of a small scale continuous leach test have demonstrated that continuous operation can be carried out with high copper extraction and stoichiometric conversion of sulphide sulphur to elemental sulphur.

Jan 1, 1985

Air pollution control regulation$ already implemented or being considered for implementation require substantial investment of capital to remove the sulfur oxides from copper, lead, and zinc smelter gases. There will be an attendant increase in production costs and possibly an associated increase in the price of these metals to the consumer. The total investment and any resultant metal price increase will depend upon the control regulations that ultimately will be adopted by the individual States. Controversy has arisen between the metals industry and governmental control agencies regarding the status of stack gas desulfurization technology and the ability of industry to control sulfur oxide emissions to the degree proposed by some of the more stringent regulations currently under consideration. This paper evaluates the problems involved in achieving various degrees of control over smelter sulfur oxide emissions and the technology available to accomplish the task of assuring clean air. The estimated cost of compliance is reviewed for the copper, zinc, and lead industries, but principal at tent ion is given to the copper situation.

Jan 1, 1971

In 1960, the Secretary of the Interior, acting under the provisions of Public Law 454, 80th Congress, appointed a Lignite Advisory Committee to aid in programming research on coal (lignite) of the north-central area. The chairman of this committee is the Secretary of the Interior or his delegated representative, and in all meetings held during 1960 and 1961, the Director of the Bureau of Mines, Marling J. Ankeny, has presided. The members of this committee were R. W. Rovelstad, President, Baukol-Noonan, Inc., Noonan, N. Dak. W. E. Keller, Vice President, Northwest Division, Truax-Traer Coal Co., Minneapolis, Minn. A. M. Cooley, Professor of Chemical Engineering, University of North Dakota, Grand Forks; N. Dak.

Jan 1, 1963

By F. C. Canney

Geochemical prospecting seeks hidden mineral deposits by sampling for variations in the chemical composition of naturally occurring materials. Usually the samples are of soils and other products of weathering and erosion—surface materials extremely susceptible to contamination by human activities. Except when a survey is conducted well away from populated areas, contamination is an ever-present hazard. The program's success is particularly endangered when the contaminants are the elements sought; if these occur erratically throughout an area, spurious anomalies completely unrelated to mineralized areas can be formed. Evenly distributed contamination can be dangerous too, if it raises the background to such a level that true anomalies can no longer be easily detected. Suppose, for example, that in an area where the lead background is 20 parts per million the soil over a lead vein contains 1000 ppm of lead. Here the contrast would be 50 to 1, which is very satisfactory for geochemical surveying. Now if 1000 ppm of lead from some source were added evenly to the soil in this area, the contrast would be reduced to about 2 to 1, and the anomaly would no longer be readily detectable because a threshold of significance twice the value of the background is the minimum generally used for interpreting geochemical data. Of the many possible sources of contamination, probably most important are smelter fumes, which may distribute large quantities of metal contaminants over many square miles of ground. For several reasons, the investigation reported here was begun in the Coeur d'Alene district in northern Idaho: 1) a lead smelter has been operated in this district since 1917 and an electrolytic zinc plant since 1928, and presumably the contamination patterns are strongly developed; 2) to evaluate the usefulness of certain geochemical techniques, V. C. Kennedy and S. W. Hobbs of the USGS had already studied the distribution of copper, lead, and zinc in the soils (both in background areas and other veins) and in the water and plants, providing a criterion for measuring the magnitude and effect of soil contamination; 3) one of the economically important parts of the district lies south of the South Fork of Coeur d'Alene River and within a radius of five miles of the reduction plants near Smelterville (Fig. 1). In this area, and in the entire district, conventional methods of prospecting are hindered by heavy vegetation and thick soil cover, and the possibility of contamination by smelter fumes has discouraged geochemical prospecting. Should data reveal that geochemical prospecting could be done successfully in such an area, a particularly useful tool would be available to mining companies and prospectors searching for concealed orebodies in this economically important part of the district. The field work on which this report is based was done from July 28 to 31, 1955. It should be emphasized that this was reconnaissance study only, and therefore far from exhaustive. Previous Investigations in U. S. : The first geochemical survey known to have been affected by contamination was conducted in 1940—a geobotan-ical reconnaissance made in the Michigan copper district by a private company. Geologists found striking variations in the copper content of oak and maple leaves, but unfortunately the high copper isograds of the study seemed to be related more to the Calumet and Hecla copper smelter fall-out than to mineralized ground.' The leaves of one oak tree near the smelter contained 0.4 pct Cu. Similar contamination was reported by Clarke (Ref. 2, p. 41), who conducted experimental geochemical soil and botanical surveys at Ray, Ariz. He found that the leaves of oak trees growing in unmineralized ground near Superior, Ariz., contained more copper than the leaves of oak trees growing on the capping of the Ray orebody and attributed this fact to contamination from the fumes of the Magma smelter at Superior. According to H. E. Hawkes,3 soils and stream sediments in the Superior area are also severely contaminated. Hawkes' work there has shown a copper content averaging 0.5 pct in the surface horizons of soils within one mile of the smelter stack. Samples taken only a few inches below the anomalous surface samples showed only background copper values. In 1950 L. C. Huff' of the USGS made a geochemical survey in an area near Jerome, Ariz., and found considerable zinc and copper in the soils over unmineralized basalt close to Clarkedale, Ariz., and over limestone close to Jerome. As the amounts were notably greater than could reasonably be expected to be derived from the underlying rocks, Huff suspected airborne contamination from the smelter at Clarkedale. Description of Area: The area sampled in detail (Fig. 1) for the study presented here is one of strong relief. The dominant watercourse is the westward-flowing South Fork of the Coeur d'Alene River. East of Kellogg the South Fork flows in a rather narrow canyon, but its valley floor widens considerably to the west where much of the flood plain is covered by an extensive veneer of mining, milling, and smelting debris. South of the South Fork and between Big Creek and Pine Creek is a mountainous area where

Jan 1, 1960

By R. Y. Wan, S. L. Chryssoulis

"Gold associations were established in a·biooxidized, chlorinated CIL residue assaying 0.02 oz Ault and in a biooxidized thiosulfate leach residue assaying 0.01 oz Au/t. A detailed mineralogical study involved: assays of screened fractions; light microscopy; ion probe microanalysis to quantify 'invisible' gold in sulfide minerals; proton probe microanalysis to detect and quantify preg-robbed gold. In the CIL residue, most of the gold is preg-robbed (71 %). In the thiosulfate leach residue, gold occurs mainly as submicroscopic disseminations in microcrystalline quartz (chert). In both residues, the 'invisible' gold in pyrite accounts for a minor fraction of the gold assay. Quantitative determination of the gold occurrence in the two residue samples established conclusively that gold adsorption on carbonaceous matter in the thiosulfate leach is of minor importance.Acknowledgement: published with permission of Newmont Gold Company."

Jan 1, 1997

By G J. Lyman

The theory of sampling has progressed slowly over the last century. The concepts of correct sampling were known to mining engineers such as D W Brunton in the 19th century. It was recognised early in the 20th century that the Poisson distribution of particles carrying the target analyte was the key to the uncertainties between samples of a given mass. However, no efforts were made until the 1980s to determine the entire sampling distribution as a function of sample mass. The variance of sampling was made clear by Gy and others, but none attempted to determine the entire sample assay density function until J H Venter in South Africa applied the method of characteristic functions to the problem.Venter applied the method to a specific case of very low analyte concentrations in samples of very fine particle size where his assumption of constant sample mass was justified. When his general methodology is applied to the more general problem, it can be shown that the assumption of constant sample mass is no longer justified and leads to some anomalous results for sampling variance. Venter’s method can be expanded to allow for a statistically variable sample mass and to take into account the size distribution of particles that carry no analyte.This paper presents the basis of Venter’s work and shows how the approach can be easily modified to yield results for the variance that are consistent, for example, with the work of Gy. It is also demonstrated that the entire sampling distribution can be determined without undue computational burden when sufficient information on the material heterogeneity has been collected.CITATION:Lyman, G J, 2014. Determination of the complete sampling distribution for a particulate material, in Proceedings Sampling 2014 , pp 17–24 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Jul 29, 2014

The Bureau of Mines has successfully used sulfur hexafluoride (SF6) as a tracer gas to measure mine air flows under conditions where conventional methods have failed. SF6 was employed experimentally to measure accurately recirculation of return into intake air caused by leakage through an old stoped area, to check for potential leakage from an adjacent mine, to trace 10,000 cfm of "lost" air from an intake airway, and to measure transit air time through uranium mines. It proved useful as a means of accurately measuring airflow volumes in airways of large cross section and very low flow velocity, and in determining the recirculation resulting from underground cooling plants.

Jan 1, 1974

By T. Moodleya, I. Govender

Despite the widespread use of DEM to simulate particle processes, comparatively little work has been done to evaluate its accuracy. One of the reasons is a lack of available measurement techniques that can capture dynamic information at the momentum transfer timescale which is lower than 10-6 s - typical of the kinetics occurring within the drum. This work makes use of Positron Emission Particle Tracking (PEPT), an in-situ method capable of measuring 3D kinematic data at 1000 frames per second. PEPT measurements are performed using 3 mm and 5 mm mono-size glass beads in a 300 mm diameter rotating drum at critical speeds that are relevant to industry. We undertake systematic ‘tuning’ of DEM with a view to optimising the agreement between experiment and simulation. To ensure an equitable comparison scale, both the DEM and PEPT data are coarse grained within representative volume elements. This work seeks to validate DEM predictions against experimentally derived PEPT kinematic measurements. Keywords: PEPT, nuclear imaging, DEM, Tumbling Mills

Jan 1, 2020

By G. S. Scott

Mine fires have occurred since the mining of coal was begun, and they are still occurring. The resulting economic waste may become considerable (219),3 especially if a fire is allowed to assume major proportions or to get beyond control temporarily. It is important, therefore, to act promptly whenever a fire is suspected and to have every action count. To do this effectively, it is necessary to know at the earliest possible moment and thereafter what is happening in a remote or inaccessible area. It is equally important to know before¬hand what may be expected as a result of any proposed combative measure. The logical method of combatting a fire demands the cooperation of both mining engineer and chemist. They should decide the course of action to be taken, drawing upon the mining engineer's intimate knowledge of the physical structure of the fire area, the cost and time required for proposed operations, and the probable efficiency with which they could be carried out, and upon the chemist's knowledge of the results to be expected therefrom.

Jan 1, 1944

This section of Minerals and Materials analyzes the following three factors affecting the recent performance of the U.S. and world mineral industries: 1) the health of the U.S. and world economies, 2) the level of interest rates and 3) the performance of productivity in both the U.S. mineral industry and the general economy. While these indicators do not exhaust the possible critical factors, they represent an initial attempt to probe some of the considerations underlying the performance of the U.S. minerals and materials industry. The U.S. and World Economies It is essential to analyze the state of the U.S. and world economy because the demand for minerals and materials is a derived demand; that is, since minerals and materials are used in the productive process, the demand for them is a direct function of the demand for the finished products of which they are a basic input. Thus, the demand for minerals and materials is directly affected by changes in present and planned consumption and investment expenditures. The past two issues of this publication have highlighted the generally discouraging performance of the national and inter-national economies. Briefly, the world economy is in the third year of the first long recession in recent history where inflation rates have remained above 5 percent. With many countries either unable or unwilling to support domestic spending while inflation continues, there has been a growing tendency to institute trade-restrictive policies to support domestic demand. The resulting weakened demand conditions in exporting nations have had a direct effect on the mineral industry.

Jan 1, 1982

By James O'Brien, Lyman Frost, Grant Hawkes, S. Elangovan, Manohar Sohal, J. S. Herring, Joseph Hartvigsen, Carl Stoots

"Pressing environmental and energy security concerns have brought much needed attention to economic production of hydrogen as the secondary energy carrier for non-electrical markets as well as to meet increasing demand for crude upgrading and desulfurization. While steam reforming of natural gas is currently the dominant method of hydrogen production, it is depleting a valuable fossil fuel while emitting green house gases. Thus, in the long run, efficient, environmentally friendly, and economic means of hydrogen production using nuclear and renewable energy needs to be developed. High temperature electrolysis using solid oxide electrolyte cells is an exceptionally efficient means of generation of high purity hydrogen. It is also capable of directly converting steam and CO2 into synthesis gas. This co-electrolysis process enables conversion of CO2 recovered from concentrated industrial sources into a feedstock for synthetic fuels production. Use of CO2 provides a means of storing hydrogen in a concentrated and convenient form – a hydrocarbon. This is also an effective storage medium for intermittent renewable energy sources such as wind and solar.Ceramatec, Inc and the Idaho National Laboratory are applying solid oxide fuel cell technology to the production of synthesis gas by high temperature co-electrolysis of steam and carbon dioxide. This technology utilizes solid oxide fuel cell stacks to electrochemically remove oxygen from steam and CO2, leaving a clean stream of hydrogen and carbon monoxide suitable for fuel synthesis. By varying the relative concentrations of carbon dioxide and steam, the hydrogen to carbon monoxide product ratio can be controlled as required by the desired type of synthetic fuel being produced from the syngas. The resultant synthesis gas has been used as the feedstock to produce synthetic methane and Fischer Tropsch liquid fuels.Alkaline and proton exchange membrane electrolysis cells typically operate below 100°C, while solid oxide electrolysis cells operates in the 750-850°C range. This higher temperature improves the efficiency significantly. Practically, it translates into a lower cell operating voltage, 1.1-1.4V for high temperature electrolysis vs. ~1.8V for water electrolysis. Hydrogen production is stoichiometric with current in all types of electrolyzers.Carbon dioxide is a valuable resource as a feedstock for energy storage as a hydrocarbon. There is a vast amount of renewable energy that cannot be effectively utilized as grid electricity, but which could be used to convert CO2 to hydrocarbons, offering a solution to the even more difficult (than supplying grid power) challenge of production of sustainable, domestic transportation fuels. Conventional electrolysis and chemical processes could be deployed to accomplish this conversion. However, high temperature co-electrolysis of CO2 and steam to produce synthesis gas using solid oxide fuel cell technology has the potential of improving the efficiency by nearly 50%. A domestic synfuel industry will enable a much larger reliance on intermittent renewable energy than can be accommodated by conventional electric demand profiles while increasing our energy security."

Jan 1, 2010

By Mattos J. L. C

Drilling and blasting with explosives in mining operations near communities require careful planning to mitigate socio-environmental impacts. Ground vibration, noise emission, flyrock, and dust dispersion are factors that may trigger conflicts with local populations. However, large-scale operations demand high productivity and intense material handling, making it essential to balance operational performance with impact control. The adoption of best practices, combined with advanced monitoring and mitigation technologies, enables sustainable mining even in proximity to inhabited areas. This study proposes the use of double and triple-deck blasting techniques with large-diameter boreholes (12 ¼” – 311 mm), addressing the sizing of charges and decks, as well as measures aimed at reducing noise perceived by nearby communities. The approach seeks to maintain the use of large drilling rigs already present in the operation, avoiding costs related to premature equipment replacement or expensive alternatives, while minimizing environmental and social impacts and promoting a more balanced and responsible mining model.

Jan 26, 2026

By Pascal Deschamps

"INTRODUCTION During the last decades, many underground facilities for the storage of hydrocarbons have been excavated worldwide and the technology is fully mature. Similarly to other underground structures, the initial basic design has to be adapted along with the work progress, in order to cope with the actual site conditions and in particular the geology, hydrogeology and associated rockmass quality. In addition, Client’s or underground Contractor’s constraints (such as resources availability, schedule or cost impact) may vary from design to construction and require last minute adjustments. Engineers are required to introduce flexibility and anticipation of unexpected situations (similar to the above-mentioned) while conceiving large underground facilities. Although most of the cases require only minor adaptations, crucial parts of the facility have sometimes to be considerably modified and reviewed. This article will present four cases evidencing how the design of one of these essential structures - the concrete plug – has been adjusted during site implementation without impairing the initial performances. Hydrodynamic containment The product containment of the unlined caverns discussed here is ensured by the principle of hydrodynamic containment. A permanent water flow is naturally or artificially maintained with an orientation toward the storage cavern and then, neither product-tight membrane nor lining are required. The hydraulic gradient (and the associated water flow lines), being directed from the surrounding mass toward the cavern, prevent from outward migration of the product. If the hydraulic gradient is not sufficient or if the water table is evidencing instability, water can be artificially injected into the rockmass through purpose-built boreholes, drilled from dedicated galleries. This water injection system, called the water curtain, is generally located several tens of meters above the level of the cavern. This principle is illustrated here after."

Jan 1, 2016

By Raj K. Rajamani, James R. Nagel, York R. Smith

In this work, we examine the efficacy of Electrodynamic Eddy Current Separation (EECS) to recover valuable materials from end-of-life solar panels. Traditional rotary-based eddy current separators are capable of excitation frequencies of 1 kHz or less and struggle to economically separate particles smaller than 1 cm. A new design of eddy current separators has been developed at the University of Utah which has no mechanically moving parts. The design is capable of excitation frequencies up to 50 kHz, allowing sorting of particles as small as 1.0 mm. Recently, we have been successful in separating mixtures of Si/Al and CdTe/Al particles (1–3 mm) with recovery and grades greater than 85%, an energy demand of 68 kWh/short ton of sorted material, and throughput of roughly 10 kg/h. Current and future challenges utilizing this method for valuable material recovery from end-of-life solar panels are discussed.

Mar 1, 2017

By William E. Robinson

Why did it fail? My first reaction when assigned this topic was to say: because somebody "goofed"--then thank you all for letting me say those few words, then promptly sit down. All of you have been bandying this problem around for many years--so all of a sudden I should come up with the solution. Well, While I might not provide you with your particular answer, I think I can show you some of the resolutions to it. Somewhere along your path of experience you may have discovered that a good formula for starting a fight is to tell a group of dedicated (Nordberg Crusher) users they should be using (Allis-Chalmers), or a group of (Allis-Chalmers) 'users they should be a (Traylor). Now, if you really want a melee, get both groups together and tell them they should be using a (Stedman Cage Mill). This is one sure way you can learn how great minds arrive at logical, well thought-out conclusions, based on all the relevant facts. Why did it fail? I could go on for hours giving you specific reasons why. One of my engineering professors used to start his new class off each year by writing on the blackboard--four and two, then turn to the class and ask: What is the problem? One brave scholar would venture to answer 8. His head would shake no. Another would dare 6. Again, a head shake. Now that the ball had gotten rolling, a number would vocally decide it had to be two, which produced only another shake of the head--no. All of them had missed the question he had asked : What is the problem? What he had gotten ,were some of the possible answers to the problem.

Jan 1, 1977