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By M. E. Rossi, J. E. Camacho

"Geostatistical conditional simulations are becoming increasingly popular as tools that provide models of uncertainty at different stages of a mining project. They have been used as grade control tools in daily operations to assess the uncertainty of mineable reserves at the project’s feasibility stage, and to assess mineralization potential in certain settings. Other applications include assessment of recoverable reserves, resource and reserve classification, and drill hole spacing optimization studies. All large-scale applications of conditional simulations intend to benefit from the correct (or accurate) characterization of uncertainty, adequately describing the variability observed from the data and its effect on the final objective.The objective of this paper is to compare the ad-hoc uncertainty model provided by a traditional classification scheme with the probability intervals resulting from a conditional simulation model. It is argued that the uncertainty model derived from the use of classification schemes is of little practical use to the mining company or operation. The paper emphasizes differences in uncertainty based on the size of the mining unit considered, the extraction method, and local geological differences. Most importantly, it discusses confidence intervals for these mining units, as compared to the relative precision envisioned by a typical classification scheme.The application described in this paper is taken from a medium-sized Cu open pit and underground mine in northern Chile, and demonstrates the impact of several variables on the resulting conditional simulation models. It also compares a more traditional resource classification scheme applied, and the wide difference in local confidence intervals for each mining unit."

Jan 1, 2004

By K. Miao, W. Mu, M. Sharma, A. Haas, N. Dogan

"The ever increasing demand for cleaner steels with low inclusion content has highlighted the limits of our current knowledge for controlling and predicting inclusion agglomeration and removal during liquid steel processing. Key knowledge gaps in this area result from the complex nature of the problems associated with measuring and visualizing the phenomena studied. Confocal scanning laser microscope (CSLM) allows for continuous in situ observation of micron-size samples in real time, at high resolution, under conditions relevant to the steelmaking process. This paper summarizes some of recent CSLM applications in our laboratory to illustrate the methods of analyzing transient behavior. The reaction between inclusions and slag is given as an example. The dissolution rate of calcium aluminate inclusions in CaO-SiO2-Al2O3 slags has been studied at elevated temperatures: 1500, 1550 and 1600°C as well as thermodynamic/kinetic analysis. It is found that total dissolution time decreased with increasing temperature. The rate limiting steps are discussed. It is shown that the diffusion through a product layer is responsible for dissolution at 1500°C. At higher temperature, dissolution is most likely controlled by both boundary layer diffusion and chemical reaction at the slag-inclusion interface. In this paper, the evidence for and against the theory will be critically examined and repercussions of the theory to steel refining processes will be discussed.INTRODUCTION Inclusion formation during liquid steel refining is an unavoidable consequence of current ladle steelmaking processes. The nature and quantity of the inclusions formed in steel is critical in steelmaking, as it affects both productivity through clogging, and downstream physical properties of the steel. It is therefore crucial to better understand and control the formation, agglomeration and dissolution behaviour of inclusions in a slag in order to improve the removability of inclusions from liquid steel. Most research (Sandhage & Yurek, 1988; Sandhage & Yurek, 1990a; Sandhuge & Yurek, 1990b; Sandhuge, 1991) relevant to the kinetics of inclusion removal has been obtained by using a technique where simulated inclusion material (ceramic rods) is dipped in slag and the dissolution rate is measured. While much has been learned using this approach, the difference in scale from bulk materials to inclusions is likely to have a significant bearing on the dissolution kinetics of inclusions in a slag and will certainly result in a very different influence of capillary effects. Further, the data obtained using an indirect (dip test) procedure relies on a comparison of the initial and final conditions of a sample rather than in-situ observation which can be achieved in a confocal microscope in real time."

Jan 1, 2017

By Jerry Ran

Many large underground mines using the open stoping method have changed their primary applications of consolidated rock fill (CRF) to paste or consolidated hydraulic fill due to considerations of demand in infrastructure and equipment, system reliability, backfill capacity and material sources. However, some smaller or even large mines still use or consider using CRF for backfill purpose due to factors such as capital expenditure, availability or suitability of other fill types or in some cases local regulatory requirements. As demands on CRF applications diminish among major mining companies, there is a lack of recent literature on application of CRF to open stoping in design and operation. There are several methods being used for fill strength design. Results from these methods have been successfully applied to paste or hydraulic fill. However, the design strength for CRF is much higher than that determined by use of these widely accepted methods. In operation, CRF preparation and placement have significant impacts on the quality of placed CRF and therefore the mining performance. This paper reviews the current fill design methods and their applications to open stoping with presentation of the bench marking data, presents fill failure cases and various CRF preparation and placement arrangements and discusses quality assurance and control programs.

Jun 1, 2012

By G. Molloy

The purpose of this paper is to demonstrate the value of applying continuous improvement, in particular 5S and standard work, in an underground environment. 5S and standard work are two aspects of Lean manufacturing that have been applied in many industries. At Vale Canada Limited, the focus is to first stabilize the process, commonly through the use of 5S, standard work and other continuous improvement techniques. In parallel with building an engaged workforce, these approaches aim to incrementally stabilize and improve a process. 5S is an employee-driven, systematic methodology to reduce waste in all its forms through attaining, maintaining, and improving workplace organization. Identified as a foundational part of any improvement process, 5S aims to remove wastes that impact on the overall efficiency of the area. Standard work is used to formulate a common approach to how tasks are carried out to ensure consistency. Standardization involves identifying, establishing, and following the best method. The aim is to eliminate the variation that can occur when there is not a pre-defined established standard. Demonstrating the value of 5S and standard work in an underground environment will be achieved by first understanding the overall concept of Operational Excellence and continuous improvement as practiced within our operations. The paper will then cover a real application of 5S and standard work within the underground environment at Thompson, Manitoba.

Aug 1, 2013

By J. L. Barton, R. A. Murray

"This paper looks at how Syncrude Canada Ltd. is utilizing the Conveyor Belt Monitoring technology developed and patented by the Australian CSIRO and licensed to Syncrude by Conveyor Belt Monitoring of North America, Inc. The technology involves magnetizing the steel cables in the conveyor belts and detecting the fields produced by breaks, gaps or cable ends using special sensors which feed the signals into a multi- channel recorder to provide permanent traces of the various events taking place in the steel cable belts.The data is analyzed and combined with existing belt audit programs, to assist in predicting belt life, change-out criteria and belt design, belt loading and construction. All of these applications of the CBM technology leads to better utilization of resources and forms an integral part of the conveying system reliability program."

Jan 1, 1992

By John G. Kuhm

INTRODUCTION The goal of any development drilling program is the drilling of the exact number of holes necessary to adequately determine grade and dimensions of an orebody, no more and no less. This cost of development drilling represents a large part of the total development budget. Any technique which eliminates unnecessary drilling costs produces beneficial results, both to the company and to the person who can claim the savings. This high development cost factor has produced a quantity of research to develop techniques, for efficient control of drilling programs. Recent mining literature is full of articles describing methods for measuring and increasing the effectiveness of these expensive projects. The method described in this paper was developed during the latter part of a major development drilling project at the Christmas Mine of Inspiration Consolidated Copper Company in Gila County, Arizona. It was used to test the need for drilling individual holes but could be expanded to control an entire project. This technique was used at Christmas as a practical means for evaluating adequacy of drilling on an individual hole basis, and it was possible to eliminate several previously approved holes. Application of this method involves an evaluation of geological conditions present and a good bit of common sense. Projects involving large disseminated, rather homogeneous orebodies of the porphyry-copper type would be the most likely candidate for application of the technique. Discontinuous orebodies would not be amenable to this technique. The method is based on the measurement of the linear correlation between the spatial distribution of two sets of data. The Pearson product-moment correlation coefficient is used. This is a standard statistic commonly used to measure linear correlation between two sets of data. The statistical significance of the correlation coefficient at a 95% confidence level is the main criterion for controlling the project. For purposes of reference we will call our technique the "correlation method" in this paper.

Jan 1, 1971

By J. Donald Graham, John G. Kuhn

The goal of any development drilling program is the drilling of the exact number of holes necessary to adequately determine grade and dimensions of an ore body, no more and no less. Any technique which eliminates unnecessary drilling costs produces beneficial results, both to the company and to the person who can claim the savings. The method for controlling development drilling programs to be described was developed during the latter part of a major development drilling project at the Christmas mine of Inspiration Consolidated Copper Co. in Gila County, Arizona. It was used to test the need for drilling individual holes but could be expanded to control an entire project. Application of this method involves an evaluation of geological conditions present and a good bit of common sense. Projects involving large disseminated, rather homogeneous ore bodies of the porphyry-copper type would be the most likely candidates for application of the technique. Discontinuous ore bodies would not be amenable. The method is based on the measurement of the linear correlation between the spatial distribution of two sets

Jan 1, 1973

By K. Dzieciol

The paper presents a study about three image correlation methods ?common cross-correlation, mutual information and phase-correlation ? applied to characterize microstructures reconstructed with X-ray tomography. It is shown that phase correlation is not only the fastest, but also the most sensitive method for detection of similar microstructure features, cavities in the present case. A new image correlation indicator is proposed, which takes into account both the phase shift and the amplitude of similar features in compared images. Some preprocessing aspects related to the tomographic reconstruction and filtering out of characteristic noise are also discussed.

Jan 1, 2009

By A. L. Labbe

IT Is well known that the Cottrell process is more easily applied to certain kinds of smoke than to others. The successful Cottrell installations are those treating smokes that carry dust of a mechanical nature; also smoke carrying fume dust that contains an excess of sulfuric acid over that required to combine with the oxides in the dust. But up to the present time the process has not reached a satisfactory economical basis of operation, in the treatment of smoke' containing basic dust. It is not impossible to make a smoke containing basic dust suitable for the process by. humidifying or acidifying. A number of Cottrell plants use these two methods of conditioning smoke previous to Cottrell treatment, which are quite successful, but the use of either results in expensive operation and a substantial loss in metals.. For these reasons, I would say that the baghouse process has not been replaced by the Cottrell process in the treatment of smelter basic smoke. Basic smoke must be given a. preliminary conditioning treatment because the dust is not a conductor of electricity; the water or acid treatment imparts some conductivity to the dust.. The rate at which dust is recovered depends on the proportional amount of power transmitted to the, treater and on the rate at which the smoke passes through; therefore to maintain a maximum constant amount of power across the electrodes of the treater, the same degree of conductivity should prevail, at all times between the surface of the electrodes. For all practical purposes, in the application of this process to lead and copper-smelter smoke, we can consider that the conductivity of the gases is a .constant. The variations in temperature of the smoke have a much greater effect on the solids than on the gases; the only instance where the temperature of the gases plays an important part in the process is at plants using humidifying: The temperature does not affect the conductivity of mechanical dust because such dust has natural conductive properties. However, in the case of smoke carrying acid-fume dust, where the conductivity is imparted to the dust particles by coming into contact with the acid fumes, the temperature is of importance.

Jan 8, 1925

By G. Glinski, K. A. Pericleous

"Recent advances in new computational modelling techniques such as Lattice-Boltzmann and Dissipative Particle methods offer the prospect of simulating complex fluids such as colloidal and dense suspensions in industrial processes. They are referred to as mesoscopic methods since they lie between molecular dynamics at a microscopic atomistic scale «lO-9m) and traditional macroscopic CFD methods (> 1O-2m). The models behave like a 'coarse-grained' gas consisting of fictitious interacting particles, which are much larger than the real molecules of the actual fluid they represent. Inter-particle forces are set so that the collisions collectively mimic the phenomenological transport properties and flow of the underlying fluid at a macroscopic scale.Much of the developmental work to date has focused on laying theoretical foundations based on thermodynamic and kinetic theory. Successful applications include predictions of macroscopic transport properties of complex fluids and flows in porous media and filters. With the constant increase in computational power, these mesoscopic methods are now sufficiently developed to determine their suitability to simulate complex fluid flows in real industrial processes. This work describes the application of meso scopic methods to the stencil printing of solder pastes in the assembly of electronic components. The aim of this work is to assess the ability of these methods to study the transport mechanisms of individual solder particles suspended in the flux solvent as they enter and fill the micro-apertures of a stencil. This paper demonstrates the coupling of such mesoscopic methods to continuum CFD methods to predict the flow of dense suspensions (i.e. solder paste) in industrial processes."

Jan 1, 2001

By Y. Y. Zhou

This paper introduces the application of CRIMM high-gradient magnetic separator in refinement of feldspar powders as well as the supporting technical outfits needed by the refining process with the high-gradient magnetic separator as main equipment. It could reduce the content of Fe2O3 to 0.03% with a deferrization rate of 85.88% from the feldspar raw ore containing 0.17% Fe2O3by using the above refining technology, producing an ultrapure feldspar product.

Jan 1, 2014

By Gregory P. Lorsbach

Significant information about any blast is contained within the seismic signal generated by the blast. In this study, standard digital signal processing techniques are utilized to extract source parameter information from a seismic signal recorded at distances commonly used in compliance monitoring. Specifically, digital seismic data was analyzed using the cross-correladon and autocorrelation functions for the purpose of determining delay timing. The initial results are interpreted to indicate that: 1) Individual delays can be identified analytically but not visually for short delay periods and large source to receiver distances, 2) Delay timing can be resolved to a few milliseconds, and 3) Results can be obtained from data collected at a minimal number of locations.

Jan 1, 1991

By M Fylak, R Wenda

Advanced preparation techniques open new ways for SEM and X-ray diffraction (XRD) investigations on hydrating cementitious systems. In this paper the early time hydration of Portland cement is studied with advanced cryo scanning electron microscopy techniques in combination with in situ X-ray diffraction and heat-flow calorimetry. The application of preparation techniques and analytical methods to Portland cement hydration are presented and discussed. Some aspects of hydration reactions are focused. The reaction products of the first minutes, changes in ettringite morphology, AFm formation during the deceleration period and the visualisation of C-S-H microstructures were special points of interest. X-ray diffraction analyses and Cryo-SEM images gave essential information about phase development, reaction kinetics, microstructure and morphology of hydration products. Portlandite, AFt and AFm phases were detected by in situ XRD. Cryo-SEM analyses enabled high resolution imaging and EDX-analyses of cement particles and reaction products. The results of the different analytical methods were compared to obtain detailed information about crystallisation processes and microstructural development during the first three days of Portland cement hydration.

Jan 1, 2008

By Andrew Neale, Len Anderson, Rob Perry

"P.T Freeport Indonesia's new SAG mill commenced operation in February 1995. The reclaim system consists of four apron feeders and a series of three conveyors. The feeders are used in various combinations and relative speeds to blend SAG mill feed. It was recognized during design of the control system that effective automatic control would require dead-time and gain compensation. The successful implementation of the Dahlin algorithm to provide variable dead-time and gain compensation is described and compared to Pl control.RésumeL'opération du nouveau SAG de P.T. Freeport Indonésie a commencé en Février 1995. Le système de réclamation du minerai comprend 4 alimentateurs à tablier et une série de 3 convoyeurs. Les alimentateurs sont utilisés dans une combinaison variée et à des vitesses relatives différentes pour mélanger l'alimentation du SAG. II a été reconnu pendant la conception du système du contrôle que le contrôle automatique demandera une compensation pour le temps de délai et le gain. L'implantation de l'algorithme de Dahlin a été un succès et ii est comparé avec le contrôle Pl.ResumenP.T. Freeport Indonesia inició la operación de un molino semi autogeno (SAG) en febrero de 1995. El mineral es alimentado desde cuatro alimentadores tipo apron feeders y una serie de correas transportadoras. Los alimentadores se utilizan en variadas combinaciones y velocidades para mezclar apropiadamente el mineral que alimenta al molino SAG. Durante el diseño del sistema de control se detectó que el control automático requería de un tiempo muerto y compensaci6n de ganancia. En este documento se describe la implementación del algoritmo de Dahlin, que ha sido exitosa y ha permitido proveer tiempos muertos variables y compensaci6n de ganancia. Ademas se hace una comparaci6n con el Pl de control."

Jan 1, 1996

By Cemal Can Maslak, Vijaya Bhushan Rao, Vidyaranya Bandi, Karsten Beckhaus

A Large Earth Cum Rock Fill, ECRF Dam is under construction at Polavaram in the state of Andhra Pradesh in India as part of an irrigation project. The Embankment crest width of the dam is 12.5m and base width is of approximately 136.75m with a stepped sloping height of 27m on both upstream/downstream sides. Once the 1.2m Thick Plastic concrete cut-off wall is constructed below the dam along the longitudinal central axis to avoid seepage, this magnificent structure will be supported on a series of Deep Mixing Columns and Stone Columns that are evenly arranged under the footprint of ECRF Dam forming a smooth transition of gradually reducing stiffness moduli of treated ground from the center of the embankment, where the foundation stresses are high, towards the edges in order to be able to progressively limit the settlements under the dam to a specified allowable limit. As such the required post treatment stiffness in case of stone columns is 2 times of the in-situ stiffness of foundation soil, whereas it is expected to be 5 times improvement for Deep Mixing as per project specifications. Laboratory testing and Field Trials undertaken successfully to verify the design.

Sep 1, 2022

By D. S. Yang, Y. D. Wang, G. Watanabe, A. P. Notaro

"Deep soil mixing (DSM) walls reinforced with steel soldier piles were installed for excavation support and groundwater control for the construction of a grade separation structure at the intersection of Warren Avenue and the Union Pacific Railroad in Fremont, California to mitigate traffic conditions during the busy commute hours and for the extension of San Francisco Bay Area Rapid Transit (BART) system. Instead of treating the DSM wall as a temporary structure, the reinforced DSM walls were integrated in the design of the permanent structures including retaining walls, and the abutments and pier of the railroad and BART bridges. The integration of steel members inside the DSM wall as part of the permanent structures is an innovation which facilitates the use of top down construction techniques to speed construction and utilizes the steel soldier piles that would have been disregarded after the use as a temporary shoring wall. This paper will review the background of the project and DSM method and present the design and construction of the DSM wall composite structure for this grade separation project.INTRODUCTIONUsing the concept of mixed-in-place piles initiated in the 1950’s in the United States, Japanese contractors in the late 1960’s and early 1970’s installed single mixed-in-place soil-cement piles along a row to create a wall for excavation support and groundwater control. Due to the high groundwater conditions in most of the coastal cities in Japan, wall continuity and uniformity became the requirements of soil-cement walls for reliable groundwater control to minimize ground movement and impacts to adjacent buildings and facilities. In late 1970s, Seiko Kogyo, Co. Ltd. developed the Soil Mix Wall (SMW) method, which uses a triple auger mixing tool to improve the uniformity and continuity of soilcement wall. The SMW method is considered a wall installation method in contrast to the Cement Deep Mixing (CDM) method, also developed in Japan, for ground stabilization in soft soils, especially in the marine environment. In the U.S., generic terms like DMM (Deep Mixing Method), DSM (Deep Soil Mixing) or CDSM (Cement Deep Soil Mixing) are used by various government agencies and private organizations to describe the soil mixing technologies without differentiating the origin, procedure and application. The method used in this project is called DSM method by the project owner, Santa Clara Valley Transportation Authority (VTA), to produce a single continuous soil-cement wall for use as shoring wall and composite structure. The mixing tool for DSM wall installation can vary from 3 to 6 mixing augers. Due to the need to install steel soldier piles into the DSM wall for resisting lateral forces, high water cement ratio slurry with bentonite is used to produce low strength soil-cement, generally in the range of 70 to 100 psi (500 to 690 kPa), with high fluidity to facilitate the installation of steel soldier piles. To maintain the wall continuity for groundwater control, overlapping of one full DSM column is made between neighboring elements using two types of installation procedures as illustrated in Figures 1a and 1b. Steel soldier piles, as shown in Figure 2, are used to reinforce the soil-cement wall to resist the lateral shear force and bending moment induced during the excavation."

Jan 1, 2015

By Andrew T. McBride, Malcolm S. Powell, Indresan Govender

"Current empirical Semi Autogneous Grinding (SAG) mill models contain assumptions concerning the amount of energy available for particle breakage, how this energy is distributed in the mill media and the rate at which the energy is transferred. Despite these assumptions the JK SAG model is highly functional with a proven track record. DEM provides a numerical framework to greatly improve on these assumptions that were necessary due to a lack of available input data.This paper identifies key outputs of the Discrete Element Method (DEM), such as energy spectra and impact probability distribution. It describes how they can be incorporated into current mill models utilising practical rock breakage data. The rate at which energy is transferred is shown to be dependent on particle position and mill rotational speed and not once per cycle as previously assumed. Based upon this an improved energy transfer methodology is presented. The fundamental outputs of the DEM are validated against experimental three-dimensional particle tracking data, so as to establish whether the DEM produces correct energy transfer predictions on the inter-particle level, which is crucial to this work. • Effective Experimental ValidationAn automated 3D tracking technique is employed to study the motion of plastic particles deep within the charge of a 142mm diameter experimental mill. A Biplanar Angioscope is used to film the mill with X-rays in two planes simultaneously at 50 frames/s, with a shutter speed of 1/3000s. A marked ball within the charge is tracked for over 2 minutes and the resulting digital images processed by a fully automated imaging technique, which locates the 3D coordinates of the particles to within 0.2mm. With over 250 circulations, this provides statistically rigorous and accurate data for verification in the numerical modelling of mills.A series of validation techniques have been developed to compare the experimental trajectory data with the outputs of both 2D and 3D DEM simulations. The techniques describe the shape of the charge and the particle motion within mill, allowing objective comparisons to be made of key features of the charge, such as the equilibrium surface and the centre-of-circulation."

Jan 1, 2003

By Andrew T. McBride, Malcolm S. Powell, Indresan Govender

"Current empirical Semi Autogneous Grinding (SAG) mill models contain assumptions concerning the amount of energy available for particle breakage, how this energy is distributed in the mill media and the rate at which the energy is transferred. Despite these assumptions the JK SAG model is highly functional with a proven track record. DEM provides a numerical framework to greatly improve on these assumptions that were necessary due to a lack of available input data.This paper identifies key outputs of the Discrete Element Method (DEM), such as energy spectra and impact probability distribution. It describes how they can be incorporated into current mill models utilising practical rock breakage data. The rate at which energy is transferred is shown to be dependent on particle position and mill rotational speed and not once per cycle as previously assumed. Based upon this an improved energy transfer methodology is presented. The fundamental outputs of the DEM are validated against experimental three-dimensional particle tracking data, so as to establish whether the DEM produces correct energy transfer predictions on the inter-particle level, which is crucial to this work."

Jan 1, 2003

By C. P. Kelley, T. J. McKeon

Several recent developments in fine screening technology have been implemented at the DuPont Starke, Florida plant allowing enhanced zircon recoveries while minimizing operator requirements and total operational costs. The total design concept came about through the efforts of engineers at Derrick Corporation (Buffalo, New York), DuPont Titanium Technologies (Starke, Florida) and Roche Mining (Carrara, Australia). The use of the Kelsey Jigs for zircon recoveries from the tailings stream requires two wet sizing functions in order to operate properly. The first wet sizing is required on the initial mineral slurry feed to the Kelsey Jig. This sizing is intended to protect the Kelsey Jigs internal screen basket from plugging with nearsize particles, thereby keeping production rates maximized. The second sizing function is intended to recover properly sized garnet ragging material, which inadvertently ends up in the tailings stream leaving the Kelsey Jig. The unique machine design developed by the three partners in this project incorporated both wet sizing functions (protection and garnet recovery) into a single patented high capacity wet screening machine fitted with patented screen surface technology. This screen surface technology allowed for high capacity slurry handling capabilities at separations as fine as 230 microns while experiencing no nearsize blinding and extremely long screen panel life. The high open area urethane screen surfaces utilized in the application typically last 20 to 30 times longer than stainless steel wire surfaces. The stacked machine design minimized total equipment requirements and screen footprint requirements, and reduced power consumption and overall installation costs.

Jan 1, 2005

By Joseph W. Roe

MANY questions arising in the work of the mining engineer may be solved quickly and with sufficient accuracy by the methods of descriptive geometry; but, unfortunately, this subject is more often considered from a mathematical view-point than as an effective tool. for solving practical problems. Some of the principles involved are merged into the ordinary operations of mechanical drawing, and are used unconsciously by the engineer in his every-day work. The rest are stowed away on the book-shelf with his forgotten or rarely-used college text-books. One reason for this condition of "innocuous desuetude " may lie in the unfortunate and often cumbersome notation which it has been found necessary to introduce. If some of these principles can be recalled to the engineer's attention in terms of every-day use they may prove of practical bearing. Recently, in talking with several mining engineers, I used some of the drawing-room methods of a machine-designer, to the evident surprise of those around me. These men were perfectly familiar with the methods, but their application to mining-work had not occurred to them. At their suggestion the present paper is offered, not in any way as a treatise, but merely to suggest a certain point of view, in hope that it may lead others far more familiar with mining-problems to pursue the subject further. I. To FIND THE STRIKE. As the simplest and most fundamental problem, let it be required to find the strike of a vein when the location and elevation of three points on the outcrop are known. It will be assumed for the present that the vein is a plane.

Mar 1, 1910