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By Zhigan Deng

Cooling crystallization was used to separate iron (III) and nickel (II) from acidic sulfate solution produced by leaching of molybdenum-nickel black shale. The effect of K2SO4 concentration, crystallization temperature, solution pH and crystallization time on recovery of nickel (II) and precipitation of iron (III) was investigated, in order to obtain effective separation of nickel and iron. The optimum parameters determined were as follows: 200 g/L K2SO4, 10 °C crystallization temperature, solution pH of 0.5 and 24 h crystallization. Under these conditions, 97.6% nickel (II) was recovered as K2Ni(SO4)2, 6H2O crystals and only 2.0% of the total iron (III) was precipitated. Recrystallization yielded K2Ni(SO4)2, 6H2O crystals with a purity of 98.4%.

By James Paone

The Bureau of Mines studied the behavior of rocks at the initial state of crater formation that results from the stresses created under a drill bit to determine which mechanical properties of rock are important in rock fragmentation by drilling. Although a definite relation between the drilling strength and relevant mechanical properties has not been established, maximum yield strength of rock is apparently a parameter of drillability of rock. The strengths of rock were considered from the Mohr-Coulomb criterion from which the surface of failure was constructed. The results from previous tri-axial tests on Solenhofen limestone were adopted to verify the criterion of failure. Inelastic behavior of some rock types was observed under a low-velocity impact of a hemispherical bit and under static indentation with a similar bit. Quantitative determinations of strengths of Solenhofen limestone) Indiana limestone, and Tennessee marble were made under static indentation. The maximum yield strength estimated from the average stress over the indented area was used as the crushing strength of rock under a drill bit.

Jan 1, 1966

By H. C. Brunaugh, James Westfield, R. W. Whittaker

"INTRODUCTION The purpose of this circular is to describe the sealing off of a mine fire and subsequent use of carbon dioxide gas to extinguish it.A fire of electrical origin occurred in the Valier mine of the Valier Coal Co., Valier, Franklin County, I11., on March 29, 1949, at about 1:35 p.m. It was discovered about 3:35 p.m. in 5 south west intake airway inby 1 and 2 west panels. The No. 5 southwest airway had caved, and the fire was in the top coal beneath a large fall of rock. All men, except officials, were ordered from the mine. The mine officials decided to seal the fire, and four temporary seals were erected, which isolated approximately 200 feet of 5 south west entry. The seals were completed on March 30 at 2:45 a.m., but on March 31, at 3;40 a.m,, two of them were blown out by an explosion of gas that was produced by the fire. The two seals were rebuilt, the work being completed on March 31 at 12:00 noon, but they were blown out by another gas explosion at 12:10 a.m. on April 1. It was then decided to extinguish the fire with water if possible.To accomplish this, concrete-block dams were constructed. On April 1, about 4:25 a.m., when the dams were about half completed, water was introduced into the fire area through a 2-inch pipe.On April 4, J. G, Crawford, general manager of the Valier Coal Co., notified James Westfield, chief of the Vincennes (Ind.) Branch, U. S. Bureau of Mines, by telephone of the fire in Valier mine and requested assistance to combat it. Westfield, accompanied by F. J. Smith and H. C. Brumbaugh, Federal coal-mine inspectors, went underground and inspected the seals and dams. Later, during a conference with company officials, it was decided that the concrete-block dams were not strong enough to withstand the hydrostatic pressure that would be produced by flooding the fire area. It was then decided to use carbon dioxide gas to extinguish the fire. Four seals were completed, and 5 tons of carbon dioxide gas was introduced into the fire area, which extinguished the fire."

Apr 1, 1950

By Rushikesh Battulwar, Javad Sattarvand, Joseph Seamons, Masoud Zare

In the last decade, new developments took place in the area of indoor positioning (or localization). Since the Global Navigation Satellite System (GNSS) cannot be used in underground mines, other technologies are needed for localization. Positioning and communication options today primarily include Wi-Fi, Bluetooth Low Energy (BLE), Ultra-Wideband (UWB), Radio Frequency Identification Device (RFID), etc. Smartphones and tablets currently have an array of sensors and radios, which can provide valuable information to allow indoor localization via various methods. Where mineworkers could keep smartphones with them, they can be highly effective at enabling localization and navigation. Recent applications of these technologies in underground mines have been thoroughly reviewed and examined for the likelihood of their utility for accurate localization where no other means exist. Some critical challenges and gaps that need to be addressed in future research have been identified.

Sep 5, 2021

By Gary Cavanough

The spontaneous exothermic reaction of ammonium nitrate explosives with sulphide-containing rocks, commonly referred to as reactive ground, is a site-specific condition that can lead to spontaneous detonations. Mine sites typically carry out regular assessment of ground for reactivity. In Australia, reactive ground testing is conducted according to the Australasian Explosives Industry Safety Group (AEISG) Code of Practice. This paper presents a new method to assess reactive ground. The new method can be completed on the mine site or in the laboratory. The new method allows samples to be tested in hours not weeks, as required when using the method prescribed in the AEISG Code of Practice. The new method also provides an explanation of why ground is reactive or not reactive, Whereas the AEISG Code of Practice provides a reactive, not reactive or marginal results with no understanding of reason for these results. Case studies on the use of weathering agents, pH, sulphide content and carbonate content will be reported. These case studies identify instances where the testing as per the AEISG Code of Practice provides false positive and false negative results. A false positive result will require the use of inhibited products when they are not actually required which increases costs and reduces productivity due to the need to used multiple explosive products. A false negative result increases the risk of an unplanned initiation of a blast hole.

Feb 6, 2023

By A L. Randriamanjatosoa, G Small, C Greet

In flotation simulation models, the effects of pulp chemistry other than pH are often ignored and reduced to particles hydrophobicity or contact angle, neither of which can be measured readily in real time in an operating plant. The flotation response of a given sulphide mineral is known to be influenced and can be improved by changing the chemical characteristics of the pulp during grinding and flotation. The on-line measurement of pulp pH, potential, dissolved oxygen, temperature and oxygen demand of a process stream was completed with the PCM® (Pulp Chemistry Monitor) developed by Magotteaux in this study. The data generated together with relevant plant operating parameters were used to construct an empirical model and simulate the metallurgical performance of the ore. The same approach was also applied to laboratory flotation tests data using various grinding media types. The flotation models better fit the actual data when the chemistry of the pulp is taken into account.CITATION:Randriamanjatosoa, A L, Greet, C and Small, G, 2018. Effects of pulp chemistry on plant and laboratory flotation modelling, in Proceedings 14th AusIMM Mill Operators' Conference 2018, pp 423–432 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Aug 29, 2018

By William Gleason

"There are few people more qualified to speak of the tumultuous times in the global mining industry during the past four years than Newmont Mining Corp. president and chief executive officer Gary Goldberg.Goldberg stepped into his current position in 2012, just before MINExpo 2012. Gold prices had hit record highs not long before that ($54.15/g or $1,856.40/oz on Sept. 8, 2011), expansions were happening around the world and the gold mining sector was still living in the glow of one of its longest upswings in history.That all changed between April 8 and April 15, 2013 when the price of gold dropped by nearly $200/oz ($46.27/g or $1,586.20/oz on April 8 to $40.45/g or $1,386.80/oz on April 15), putting an end to the decade-long mining boom and forcing mining companies like Newmont to re-evaluateeverything.Three years later, with the gold sector recovering, Newmont Mining is not only surviving but is thriving with a pair of mines coming online, Long Canyon in Nevada and Merian in Suriname. On Oct. 1, the Merian Mine went into production on time and more than $150 million under the initial development capital budget.Goldberg, who was one of the featured speakers at the opening session of MINExpo International 2016 on Sept. 26, also spoke with Mining Engineering about the previous four years and the future of the industry.“Mining goes through cycles all the time and gold is no different,” Goldberg told Mining Engineering when asked about surviving the downturn since 2012. “I thought it was important that we take a good methodical and steady approach across the business to determine what was the right thing to do and to set the business up to improve performance. Anyone can cut costs for the short term, but we set out to do it in a sustainable and reliable way. We created a program we call Full Potential to look for sustainable ways to reduce costs and improve productivity. That program has taken more than a billion dollars out of our costs since we implemented it 2013 and that shows up in our results. Our all in sustaining costs are down 28 percent and our productivity is up 39 percent.”During the downturn, Newmont restructured its business model, sold off some assets and created a leaner, more nimble operation. It has paid off with the addition of two new mines and the acquisition of another, the Cripple Creek & Victor Mine in Cripple Creek, CO.“The gold industry had not seen a downturn in 12 years. We had half a generation that had not experienced a downturn, so helping them through that in an organized way and keeping a view toward the long term throughout the downturn was important. We were one of the few companies that continued to invest in assets,” he said."

Nov 1, 2016

By Charles Stahl

El presente texto describe la comercialización de la plata a corto y mediano plazo. El periodo de corto plazo se refiere a cualquier negociación dentro de un período de 5 minutos y tres semanas, mientras que la de mediano plazo, es la transacción que se produce entre dos y tres meses. Para la comercialización de metales es necesario la confianza y la paciencia como habildidad para el éxito de la negociacion, de forma que se tiene que comerciar con un equilbrio y sin excesos.

Jan 1, 1984

By Patrick R. Taylor

In the search for the development of more "environmentally friendly" and more intensive waste disposal approaches to meet more and more stringent environmental regulations, thermal plasma-based processes are considered one of the most promising alternatives to well- established technologies such as incineration. This paper presents an overview on the research and development status of thermal plasma-based waste remediation technologies. The properties of thermal plasma are described. Due to its unique feature of high-energy intensity and super high temperature, thermal plasma is particularly capable of destroying organic- containing wastes. Its potential and promising application to waste remediation may include: treatment of incinerator ashes; metallurgical dusts (especially, electric arc furnace dust); medical wastes; radioactive wastes; and other Resource Conservation and Recovery Act (RCRA) listed hazardous wastes. Many research institutes and vendors have been involved in the development of thermal plasma-based waste treatment technology encouraged by the cleanup programs supported by the Environmental Protection Agency (EPA), the Department of Energy (DoE) and the Department of Defense (DoD). More recently, thermal plasma-based waste treatment technologies (sometimes called plasma-enhanced pyrolysis) are focused more and more on not only just destroying organic wastes but also on how to practically, and economically recover energy contained in the organic waste materials in addition to the recovery of metals in order to offset the high operating costs.

Jan 1, 2003

By B. Courtaud

Uranium plants are generally located quite far from conversion plants, resulting in high transport costs. One way of reducing such costs involves putting more uranium in each drum by increasing the final product?s bulk density, which can be achieved via mechanical compaction of the powder and/or improved precipitation. For most of its plants, AREVA has adopted the latter approach, involving a new precipitation process applicable to all kinds of yellowcake produced (via uranates, uranium peroxide, etc.) that achieves bulk density of 3 for soda uranate, for example, instead of the 1.5-2 density available via conventional processes. At present, this process is being undertaken on an industrial scale and will become the norm for precipitation processes at all AREVA U plants. In addition to producing dense yellowcake, the process also delivers a product with no fines, a spherical particle shape (which allows for high-quality powder flow) and superior post-precipitation filterability

Sep 1, 2012

By V. A. James

The new electrolytic copper refinery situated at Copper Cliff, Ontario, has been in operation for over a year and a half. This plant is operated by the Ontario Refining Company, Limited. The associated companies behind the enterprise are the International Nickel ?company of Canada, Limited, the American Metals Company, Consolidated Mining and Smelting Company of Canada, Limited, and Ventures, Limited. The plant was an outgrowth of the rapid development of copper resources in the nickel-copper ores of the Frood and other great mines in the Sudbury district, and of the desire to have all primary production units grouped together as compactly as possible. Starting anode furnace operations in June, 1930, and electrolytic refining on July 1st of that year, after a record-breaking construction programme completed in only fifteen months, the plant soon settled into its stride and the usual starting-up difficulties were .rapidly overcome. The rated capacity of the plant, namely, twenty million pounds of refined copper per month, has, of course, never been reached, due to depressed business conditions and latterly to the world copper agreement limiting production. It may be said, however, that the present installation has proved its ability to produce in excess of its rated capacity, and with relatively minor additions to plant and equipment that capacity can be doubled. Owing to the severity of the winters, when temperatures of from 20 to 40 degrees below zero are to be expected, the building of this refinery involved a number of problems in insulation, layout, ventilation, etc., which were rather unusual in copper-refinery construction.

Jan 1, 1932

By Sheldon Wimpfen

La exploración es una actividad que utiliza la prospección geológica, prospección geofísica, sondajes, pozos de exploración o de sondeo, galerías de avance subterráneas, de superficie y socavone. Las etapas de la exploración se desarrollan en cuatro etapas : l evaluación regional, reconocimiento de áreas favorables, evaluación de superficie detallada de las áreas de objetivo. Asimismo, se describe la nueva técnicas de exploración y sus incentivos.

Mar 1, 1980

By T. W. Bingay

The production of both lead and zinc in Canada has steadily increased during recent years until today Canada ranks among the world's leading producers of both of these metals. The high prices which they have commanded have led to an energetic search for new deposits and also to an investigation of abandoned properties which, under the present conditions of better prices and more efficient methods of treatment, offer chances of commercial success. It is confidently expected that during the next few years success in both these lines of activity will further increase Canada's lead and zinc output, giving her a still higher ranking among the world's producers. In 1926, approximately 140,000 tons of metallic lead was produced from ores mined in Canada, and of this, 125,000 tons was refined in Canada at Tadanac, B.C. During the same year the production of metallic zinc from Canadian ores amounted to 68,000 tons, of which 62,000 tons was refined at Tadanac. History Of Lead and Zinc in Canada The production of lead in Canada is much older than that of zinc. The chief source has always been the interior of British Columbia. As earl y as the 'eighteen twenties', Indians and Hudson's Bay Company's trappers had discovered an outcrop of lead ore on the site of the present Blue Bell mine on the east shore of Kootenay lake, but it was not until1865 that active prospecting for lode deposits began. In the early nineties the activity of the silver-lead-zinc region of the Slocan reached its culmination and a steady production has been maintained down to the present time. Up to the end of 1924 the Slocan area produced over 38 million ounces of silver, nearly 300 million pounds of lead, and almost 122 million pounds of zinc.

Jan 1, 1927

By M. R. Tek, K. H. Coats, D. L. Katz

A large number of boundary value problems encountcred in unsteady-state heat transfer, fluid flow through porous media, neutron diffusion and mass transfer involve the solution of a linear, parabolic partial differential equation commonly refcrred to as the diffusivity equation, where U is the dependent potential variable. K is the diffusivity (hydraulic, thermal, neutron, etc.) and 1 is the time variablc. Solutions to Eq. I are available in the literature for a wide variety of initial and houndary conditions. The great majority of these solutions are ohtained for geometric boundaries corresponding to linear. cylindrical or spherical flow models. A typical engineering application where the solution to Eq. 1 is required is the calculation of underground water encroachment across the boundaries of oil or natural gas reservoirs, In this particular area of application, the reservoir boundary is invariably approximated by circular geometry. However. the areal shape of many reservoirs can be better approximated by elliptic rather than circular boundaries. Thus the need for a general method of solving the diffusivity equation in elliptic coordinates arises in this problem as well as in other engineering applications involving elliptic boundaries. The solution to the diffusivity equation usually in volves the Error Function for the linear flow model, Bessel functions for the radial flow model and trigonometric or Legendre functions for the spherical flow model. It is well known that the general solution to the diffusivity equation in elliptic coordinates involves Mathieu functions. The significance of Mathieu functions in the analytical treatment of the diffusivity equation in elliptic coordinates is discussed in the literature However, these references do not providc analytical solutions useful in practical engineering problems. The objectives of this papcr are the development of the equations describing the unsteady-state liquid flow through a porous medium with an elliptic inner boun- dary, the development of a numerical method of solving these equations and, finally, a comparison of the water encroachment quantities calculated from the elliptic flow equation with those calculated from the radial flow equation. While the specific problem treated in this paper relates to unsteady-state liquid flow through a porous medium, the basic equations and computational techniques devcloped will apply equally well to problems occurring in the other areas of engincering interest mentioned previously. The solution given here is limited to a single case in which thc outer boundary encloses an area 100 times that of the inner boundary. DESCRIPTION OF THE FLOW MODEL Fig. 1 shows the flow model upon which the calcu lations presented in this paper are based. The inncr and outer houndaries of the flow model are represented by two confocal ellipses with major and minor axes, respectively, equal to 2a1, 2b1, and 2a, and 26,. The height of the elliptic cylinder flow model is denoted by 17. The following assumptions are employed in the development 01 the equations governing the unsteady-state liquid flow through the described flow model. 1. Uniform porosity and permeability throughout the flow model

By James R. Hein

Manganese nodules from the Cook Islands (CI) Exclusive Economic Zone (EEZ) are compositionally different from other nodule fields. CI nodules have relatively high cobalt concentrations and low nickel, copper, and manganese concentrations (e.g. Hein and Petersen, 2013). This reflects the predominantly hydrogenetic (seawater source) origin for metals in the CI nodules versus dual seawater-pore water sources for most other nodules. The concentrations of many critical and strategic metals have not been previously analyzed for CI nodules, so comparisons with other nodule fields have been limited. To address this, we analyzed a set of nodules distributed throughout the CI EEZ for a complete set of 67 elements, including all of the metals that may be of economic interest, such as the rare earth elements (REEs), yttrium, tellurium, niobium, zirconium, tungsten, titanium, and others (see selected elements in Table 1). In addition, we recalculated the tonnages of nodules and contained metals from nodule abundance areas (in square kilometers) determined by GIS ArcMap calculations based on JICA/MMAJ (2001) nodule distributions. The nodule tonnage calculated and summed from each abundance sector yields a total inferred resource estimate of 9.66 billion tonnes of nodules covering an area of 1.21 million square kilometers; using a cut-off of 6 kilograms of nodules per square meter, yields a median tonnage of 8.59 billion tonnes of nodules covering 687,647 square kilometers (Table 2).

Sep 14, 2011

By W. M. Johns

The geological mapping of Lincoln and Flathead Counties was a five-year project undertaken by the Montana Bureau of Mines and Geology. This paper, written by the Project Geologist of the survey, is primarily concerned with the stratigraphy of the Belt rocks encountered in mapping. Lincoln and Flathead Counties of northwestern Montana are underlain by sedimentary rocks of the Belt Series of Precambrian age. In only a very small part of the area, near Libby and Troy, have economic mineral deposits been worked with any success. Most of the area has been inadequately mapped as to geology. The region is crossed by the Great Northern Railway and served by the Pacific Power and Light Co.; officials of these two companies believed that with better geologic maps, prospecting might be stimulated and lead to the discovery of mineral resources that would contribute to new economic development within the area. A cooperative mapping agreement was proposed jointly by the two companies to the Montana Bureau of Mines and Geology in May 1958, and thus was born the Kootenai-Flathead five-year project. The dual objectives of this project are: 1) the possible location of mineral deposits of economic value, and 2) the ''stimulation of prospecting exploration" by others. This was to be achieved by geologic mapping of some 6800 sq miles and by establishing a field office in Kalispell where prospectors could come to have their rocks and minerals identified and receive geological advice on their problems. This writer has finished four field seasons as Project Geologist and thus became familiar with the Belt section in the Libby, Yaak River, Ural, Thompson Lakes, Pleasant Valley, and Stryker quadrangles (see Fig. 1). Progress on the project is given in annual reports issued by the Bureau.* This *Montana Bureau of Mines and Geology, Bulletins 12 (1959), 17 (1960), and 23 (1961). paper is concerned essentially with the stratigraphy of the Belt rocks so far encountered in mapping. PREVIOUS WORK IN THE AREA Willis28 made the first study of the stratigraphy and structure in the Lewis and Livingston Ranges of Glacier Park just east of the project area. In 1904, Daly made a study of the Belt rocks of the 49th parallel, using the names from bottom up, Creston, Kitchener, Moyie, and Gateway, for rocks ranging in age from that of Prichard to that of basal Missoula group. Walcott26 studied the Belt rocks exposed in the Mission Range (see Fig. 1) and other areas to the south of the area under discussion. Calkins and McDonald made a reconnaissance of northern Idaho and northwestern Montana in 1905. Calkins was the first to use Walcott's term 'Ravalli' as a group name for the strata equivalent to the Burke, Revett, and St. Regis formations (see Table I). Clapp worked on the Belt of western Montana (including Lincoln and Flathead Counties) throughout his lifetime. The Fentons9 studied the Belt of Glacier Park and

Jan 1, 1962

By V. Aghazadeh, E. Bidari, M. Aazami

In this study, mineralogical and microanalysis characterization, as well as diagnostic leaching and cyanidation tests, were performed to gain a better understanding of the refractory nature of the arsenical zone of a Carlin-type gold deposit and also to evaluate possible treatment routes to maximize gold recovery. The results obtained showed that only 56% of the ore’s gold content is amenable to direct cyanidation. The majority of the remaining gold was found as submicroscopic gold and in association with sulfide minerals, such as orpiment, pyrite, and sphalerite. It was also found that despite the abundance of silicate and carbonate minerals in the arsenical zone, they do not play a key role in the refractory nature of the ore, and gold can be liberated from such minerals by appropriate grinding. The analyses further revealed that orpiment dissolves readily during cyanidation, and this dissolution retards the kinetics of gold extraction. Pyrite and sphalerite were generally found to occur in fine network texture and in association with quartz. Flotation of such auriferous sulfides may be difficult due to their oxidized surface. Fine grinding (−20 μm) was found to be partially effective in improving gold extraction.

May 28, 2020

By F. S. White, E. L. Kinsella

THE solids fluidization process brought out by the Standard Oil Development Co. in the early forties for catalytic cracking of petroleum enabled rapid transfer of large quantities of heat from gases to solids under closely controlled temperature conditions. As the technique developed, it was natural that applications for the process outside the petroleum industry would be sought. The calcination of limestone to ' quicklime requires the transfer of a large quantity of heat at high and closely controlled temperatures. For these reasons, this possible application was one of the first to be investigated. Laboratory work conducted by the Dorr Co. indicated that lime produced by solids fluidization would be of exceptional quality. Calculation of theoretical heat balances showed that savings in fuel could be expected. Accordingly, a pilot plant of 10 tons per day capacity was erected by the New England Lime Co. at Adams, Mass., to substantiate the process. Operation of the pilot plant, previously described,1 showed that excellent lime could be produced with a saving in fuel. The work also indicated the necessity of preparing feed to remove the finer fractions if dust losses were to be held to a tolerable level. A single-stage fluidized solids drier-stripper was developed to accomplish this sizing.2 Subsequently a commercial lime reactor was erected at Adams, beginning operation in June 1949, followed by air sizer facilities completed in November 1951. This paper will describe these two applications of solids fluidization. The raw material for preparation of lime by the fluidizing process is a high calcium crystalline lime stone having the approximate chemical composition shown in Table I. The stone is first prepared by crushing and grinding in conventional equipment to pass a 6-mesh sieve. After crushing, the material is sent to the FluoDry unit for drying and dedusting. Fluidized Drying and Sizing As shown in Fig. 1, the FluoDry unit consists of a 1/4-in. cylindrical steel shell, 9-ft ID by 22-ft 6-in. overall height. Attached horizontally at the bottom is a 6-ft diam combustion chamber, approximately 7 ft 6 in. long. A refractory constriction dome, consisting of first-quality fire brick shapes, partitions the inside into two sections. The lower section is called the windbox and the upper the bed compartment. The vertical wall of the shell is lined with 6-in. first-quality rotary kiln blocks. In the bottom of the windbox a hoppered section is formed with castable refractory to permit the windbox to be readily cleaned via a 6-in. screw conveyor. The combustion chamber is similarly lined with refractory shapes. On the 6-in. diam section, 4 1/2 in. of insulating brick, HW-26, are used. The inner combustion chamber is lined with 4 1/2-in. Korundal brick to withstand the high flame temperatures encountered. An 8-in. steel feed pipe, entering vertically through the top and fitted with an air-operated cone valve,

Jan 1, 1952

By Charles Trotter

An instrument has recently been developed for determining the inclination and azimuthal direction of boreholes. This instrument is known as the Tro-Pari Instrument and is the invention of C. Trotter and G. Pajari of Sudbury, Ontario. Description The instrument is characterized by a unit mounted in gimbals and provided with a clockwork mechanism to clamp a compass to indicate azimuthal direction and simultaneously to clamp the unit in its plumb position to indicate inclination (Fig I). By means of a timing ring suitably calibrated in 5-min divisions, the unit may be set to lock after a lapse of time sufficient to allow the placing of the instrument at the desired point in the drill hole where readings are to be taken. The maximum time Lapse obtainable with the instrument designed for use in EX or AX size holes is I hr 30 min which is considered to be ample time to lower to the greatest depths that may be drilled with this size of equipment. Larger sizes could be developed for larger diameter holes such as BX and NX sizes or the larger oil-well sizes and a correspondingly greater time lapse could be provided for. Up to the present time only the EX-AX size has been built. Operation Assuming a borehole is to be surveyed at 1000-ft depth and assuming it will take 30 min to lower the instrument to this depth, the timing ring is rotated through seven divisions which represent a time lapse of 35 min (5-min leeway) and is then returned to its zero position. This operation imparts energy to a spring which drives the clockwork mechanism. Simultaneously the compass needle is freed to swing to its magnetic north-south position and the encased mechanism is freed to hang plumb within a semicircular portion of the frame which is graduated in degrees after the fashion of a protractor. This semicircular protractor portion has a V-shaped notch at each degree division of its inner periphery. The instrument, now in its free position, is inserted in a bronze container made to suit the size of hole to be surveyed (Fig 2). Soft rubber washers are provided within the container to prevent undue shock. The container is connected to the drill rods with three 5-ft lengths of brass or aluminum alloy rods separating it from the steel rods in order to prevent distortion of the magnetic field. The assembly is then lowered to the desired point where readings are to be taken and is allowed to remain at rest until a period of time has elapsed slightly in excess of the time for which the timing ring was set. In the example cited above, when the 35 min has elapsed the compass needle is locked in its north-south position and the protractor locking pin is extruded and locks in the V notch opposite its plumb position. The device may now be removed from the borehole and it will remain in this locked position in spite of jarring or shak-

Jan 1, 1949

By D. R. de Fontaine

By computing the values of the resolved shear stress for a great many orientations of the tensile axis on all 12 (111) <110> slip systems, Taylor and Elam&apos; were able to map out a stereogram of slip systems, given here, Fig. 1, in Diehl&apos;s notation (see, for example Hauser and Jackson&apos;). The purpose of the present note is to derive such a stereogram by mathematical reasoning and to give a simple method of defining the system with highest resolved shear stress for any direction of the tensile axis, thereby eliminating tedious computation of the Schmid factor. Let the tensile axis, of direction cosines [xyz], make the angles 0 and relative to the slip plane normal [HKL] and the slip direction [hkl] respectively. Fig. 2 shows a simple cubic cell whose edges define a Cartesian coordinate system. Let A be a unit vector of origin 0 supported by the tensile axis. Its end point [xyz] then lies on a sphere of unit radius, on the positive hemisphere of which the planes z = 0, x = y, y = z limit the so called primitive triangle of a standard [loo] stereographic projection. For any point of this triangle, the following hold: 0«2 «y *sx « 1 [l] Now, for given [xpz], the most highly stressed system will be the one for which the following expression of the Schmid factor has the largest possible value: (HKL) belonging to the form (111) and [hkl] to the form <110>, the denominator on the right hand side of Eq. [2] is equal to 1.fi.a. The unknowns H, ... h, . . . can now be determined by correctly distributing +1 and -1 to H, K, L, and +1, -1,O to h,k, 1 giving the numerator of Eq. [2] its greatest positive value (the angles 0 and cpare chosen acute) subject to the condition: Hh+Kk+Ll = 0 [3] since the slip direction must lie in the slip plane. Condition [3] can be satisfied only by having one of its terms vanish and the other two equal to +1 and -1. Taking the case of the tensile axis lying in the primitive triangle, x2y, z and therefore Hh will be chosen equal to +1 with H = h = +1 in order to retain a maximum of + signs. There remain two alternatives: either 1 = 0 or k = 0. 1) take 2 = 0 Then Kk = -1 and the numerator of [2] becomes: Retaining a maximum of + signs gives L = k = +1 and becomes: 2) take k = 0 Then L1 = -1and, likewise, the numerator of [2] becomes: xz - z2 + xy + yz [5] But the difference [5] - [4] can be written: (y - z)(x+y +z) [6] positive or zero by virtue of [I]. If [6] is positive (y > z), then the largest possible value for the numerator of [2] for any xyz inside the primitive triangle is given by [5], i.e., for: That is to say, the active slip system corresponding to an orientat:~on of the tensile axis inside the primitive triangle is:

Jan 1, 1962