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By Yan Samuel Ferreira Junqueira

O processo de coqueificação em uma Coqueria do tipo Heat Recovery ocorre pela queima da matéria volátil presente no carvão, principal combustível para aquecimento dos fornos. Uma segunda queima não desejada ocorre pela combustão do coque. Essa queima indesejada é denominada Burn Loss. A quantidade de ar succionada para dentro dos fornos era controlada por um sistema automático que abria ou fechava as válvulas utilizando como principal variável o Tempo. Durante o controle por tempo varias influências e distúrbios que ocorriam no processo não eram levadas em consideração e consequentemente não era utilizado todo o potencial do processo para a produção de coque. O controle desenvolvido pela equipe da Coqueria da thyssenkrupp CSA (tkCSA) chamado de PID Combustão é focado em um sistema de autoaprendizagem, capaz de reconhecer as características do processo e admitir somente a quantidade de ar necessária para cada forno. Cálculos matemáticos, estatísticos e o histórico da temperatura do forno são levados em consideração pelo PID Combustão que otimiza a mistura de gás com ar no forno. Os principais benefícios após a instalação do PID Combustão foram: redução nas temperaturas dos coletores (preservação do ativo), aumento da capacidade de produção do forno (aumento da velocidade de coqueificação) e otimização da sucção ao longo dos fornos no mesmo coletor.

Aug 17, 2017

By C. H. Wright

Introduction The rapidly expanding and increasingly complex Canadian industrial structure, with the mining, metallurgical, and chemical industries as a large integral part, has, in recent years, brought greatly increased importance and value to our industrial minerals. In the modern economy of our mineral industry the importance which is due the non-metallics has been somewhat overshadowed by the great value of our large metal production and, in addition, by the glamour and fascination usually associated with the mining and treatment of gold ores. The term 'Industrial Mineral' is used in this paper in its usual sense and refers to non-metallics other than fuels. Coal and petroleum products, including natural gas, are considered as industrial minerals in those applications in which they are used for strictly chemical process purposes. Certain reduction metallurgical industries are so closely allied to chemical industries that for purposes been of this discussion no attempt has made to differentiate between them. Chemical industry in Canada today is a fairly large factor in our national economy, whereas in 1898, when the Canadian Mining Institute was born, it was very small indeed. Chemical concerns are largely dependent on industrial minerals for raw materials and process supplies and, as the country has developed industrially, so have the demands for non-metallics increased, not only by chemical industry but also by other large consumers, such as the construction and metallurgical industries. At the present time there is a greater than normal incentive prevailing for new discoveries, due to the serious lack of balance that exists in our import and export trade. This fact has resulted in intensive efforts to rectify the situation by locating new deposits and re-assessing those already known in an effort to enlarge and improve our home production of raw materials and also to extend their processing in Canada for our own needs and for export. The rapid advances in science and technology that have taken place since 1900 have also resulted in many cases of beneficiation and utilization of otherwise too low grade materials in order to satisfy current demands. The purpose of this paper is to indicate the history and the trends of the utilization of industrial minerals in established industry and to indicate the important part played by non-metallics in connection with the opening up of new industries. Some consideration has been given to the continual competition between natural and 'synthetic products and to the general tendency towards more rigid specifications.

Jan 1, 1948

By C Jenkins, J Jasper, Y Suryaputradinata, S Lozyk, M J. Hartmann

The primary objective of mining companies is to function as a profitable business by delivering products that fit customer requirements in a safe and sustainable manner. Optimum resource utilisation is a critical focus area to achieve this objective, and the long-term sustainable business performance of a mining company is determined by the extent to which this is achieved. Technology improvements and/or new technology development could improve resource utilisation. However, adding new projects to a Brownfield operation carries risk. Overall project schedules, tie-in schedules and safety risks normally receive adequate attention, but the introduction and integration of new technology to a Brownfield site also carries the significant risk of failure to achieve design performance (quality or throughput). This risk must be addressed via rigorous design phase risk assessments and piloting. Post commissioning, the effective metallurgical integration of any new technology/circuit/process plant into an existing process plant calls for critical assessment, through circuit performance testing, and optimisation to ensure alignment with design criteria. In addition, this approach provides clear focus areas for further optimisation of the new plant and additional opportunity for overall plant optimisation. Roy Hill recently navigated this process successfully, and this paper provides feedback on the journey that led to improved resource utilisation.

Nov 8, 2021

By David C. Oyler

Methane-drainage holes must be completely filled by grout before mining to prevent the emission of large quantities of gas during mine-through, which would constitute an explosion hazard. In November 1980, seven horizontal holes at the multipurpose borehole, a small-diameter shaft drilled as a Bureau of Mines coalbed methane-drainage installation on the property of the Federal No. 2 Mine, Monongalia County, WV, were plugged using a sodium silicate gel grout. This report de- scribes the grout mix and the use of the grout at the multipurpose borehole, and discusses the results observed upon mine-through of the holes in early 1981. Cost data for the sodium silicate grout are also presented.

Jan 1, 1984

By Feng Junfa, Du Feng, Li Huamin, Syd S. Peng

"The Ordos coal field is located in the northern midwestern part of China (Fig. 1). Since the mid- 1980s, it has been developed into one of the major coal fields in the world, producing approximately 833 Mt (918 million st) of raw coal in 2013. There were once more than 400 coal mines operating in the region. However, due to the combination of market conditions and implementation of government consolidation policies, the number of coal mines operating in recent years has been reduced considerably, with increasing output.The surface of the Ordos coal field is covered with loess and alluvium layers of varying thicknesses. In many areas, their combined thickness may amount to as much as 100 m (328 ft) underlain by thin bedrock. Many loess and alluvium are aquifers receiving water from rainfalls. There are also gullies of varying depths crossing the coal field. Figure 2 is a typical stratigraphic column highlighting the coal seams and roof and floor rocks of interest.In conjunction with the development of highproductivity coal mines, numerous ground control instrumentation tests have been conducted in the operating longwall panels. Analyses of the results of those tests offer the opportunity to understand the effect of wide-ranging mining and geological factors on the overburden movement. For this reason, trips were made to coal mines of interest to interview mine management and collect their unpublished internal research reports on ground control instrumentation. In addition, literature searches on published thesis/dissertations and papers in the professional journals were performed. Finally, data from a total of 95 fully mechanized longwall panels were collected. The instrumentation involved primarily the monitoring of hydraulic pressures of longwall shields, from which the first roof weighting and first roof caving interval and periodic roof weighting and periodic roof weighting interval were identified and determined. Some panels also included measurements of roofto- floor convergence at the face, roof strata bed separation, longwall face sloughage and the height of caving and fractured zones in the overburden. Those 95 panels were located in 20 coal mines (Fig. 1) congregated along both sides of the Wulunmulun River with the following mining and geological conditions. All together those 20 mines produced more than 224 Mt (246 million st) in 2013, accounting for approximately 27 percent of the total coal production in the Ordos coal field:1. Period of mining: 1991-2013.2. Mining methods: All panels employed the one slice, full-seam natural-caving longwall mining method like those practiced in the United States. All panels were developed with a twoentry system with a single-row of chain pillars measuring 20- x 20-m (65.6- x 98.4-ft) wide.3. Coal seams (Fig. 3): Coal in Ordos coal field is high-quality steam coal, that is very low in sulfur, potassium and ash, but high in Btu. Data were collected in panels mined in a total of 10 seams with 82 panels in four seams and the remaining 13 panels in six seams. The first six seams (1-2, 2-2, 3-1, 3-2, 4-2, 5-2) were mined by the Shenhua Coal Group (the world’s largest coal company) and the #4-2, 5-2, 6R, 62, and 62R seams were mined by both the Shenhua and Yitai Coal groups. In each coal group, the sequence of mining was in descending order. For example, in Shenhua Group, the top seam 1-2 was mined first, followed by the 2-2, 3-1, 3-2, and 4-2 seam in that descending order. In Fig. 3, the top-down sequence of coal seams is listed from left to right in each coal mine group. All seams were near horizontal with dip angles less than 3°."

Jan 1, 2014

By Frederick N. Rhines, Robert F. Mehl

It has been shown elsewhere1 that the data on the rates of diffusion in solid metals are fragmentary and in many cases unacceptable. As a result, relatively little is known concerning the factors determining rates of diffusion and the variations in these rates with temperature. The first form of Fick's law (equation 1 below), in which the diffusion coefficient D is assumed invariant with composition, has been recognized for many years as only an approximation. The differential equation representing the second form of Fick's law (equation 4 below) has only recently been integrated by Matano,2 and unfortunately only in cases where a full diffusion-penetration curve (concentration-distance curve) has been obtained can the Matano solution be applied. The proper analysis of diffusion data is thus confined to the data of Grube and Jedele and of Jedele. 8 These data are essentially for one temperature alone and do not furnish any information on the variation of the activation heat of diffusion, Q, with concentration: no information exists on the variation of Q with concentration within a single solid solution field. 11 Much of the argument concerning the properties of metals that determine D and Q has been drawn from data in which variations of the quantities with concentration are unknown, for these data have been taken from experiments that could not furnish this information. Speculation concerning the properties of metals that may be effective in determining D and Q on the basis of data in which the chosen D and Q values are averages over wide concentration ranges of values at particular concentrations, ranges often of 100 per cent, is likely not to be fruitful.

Jan 1, 1938

By Frederick N. Rhines, Robert F. Mehl

It has been shown elsewhere1 that the data on the rates of diffusion in solid metals are fragmentary and in many cases unacceptable. As a result, relatively little is known concerning the factors determining rates of diffusion and the variations in these rates with temperature. The first form of Fick's law (equation 1 below), in which the diffusion coefficient D is assumed invariant with composition, has been recognized for many years as only an approximation. The differential equation representing the second form of Fick's law (equation 4 below) has only recently been integrated by Matano,2 and unfortunately only in cases where a full diffusion-penetration curve (concentration-distance curve) has been obtained can the Matano solution be applied. The proper analysis of diffusion data is thus confined to the data of Grube and Jedele and of Jedele. 8 These data are essentially for one temperature alone and do not furnish any information on the variation of the activation heat of diffusion, Q, with concentration: no information exists on the variation of Q with concentration within a single solid solution field. 11 Much of the argument concerning the properties of metals that determine D and Q has been drawn from data in which variations of the quantities with concentration are unknown, for these data have been taken from experiments that could not furnish this information. Speculation concerning the properties of metals that may be effective in determining D and Q on the basis of data in which the chosen D and Q values are averages over wide concentration ranges of values at particular concentrations, ranges often of 100 per cent, is likely not to be fruitful.

Jan 1, 1938

By G. S. Rice

The recommendations of the Bureau of Mines on rock dusting practices are embodied, except in a few details, in the Recommended American Practice for Rock-Dusting Coal Mines to Prevent Coal-Dust Explosions, approved by the American Engineering Standards Committee. December 30, 1925. It is specified that the dust to be used is of a elm that all will pass through a sieve having 20 meshes per linear inch and that 50 per cent or more will pass through a sieve having 200 meshes per linear inch. Thus the coarsest size of dust and the minimum proportion of fine dust are specified, but the specification does not indicate whether a larger proportion of fine dust would be desirable. There have been advocates of the use of that size of rock dust of which the particles would all approach 200-mesh in fineness. Explosion tests were made in the Experimental mine in the earlier period of testing which indicated that the finer rock dust is somewhat more effective under test conditions, but not sufficiently so to Justify the cost of finer grinding of the dust; also there are some disadvantages of finer dust described hereafter.

Jan 1, 1930

By L. Chunpongtong

One of the challenges of mine planning is to determine the most cost-effective replacement time for aging equipment. The lifespan of equipment, such as haul trucks and shovels, deployed in mining operations varies due to the nature of the material and ground conditions in which it operates. For engineering economists dealing with aging equipment, the options become an economic trade-off between higher maintenance cost versus the cost of new equipment. The discount rate plays a significant role in this decision; the higher the rate, the longer the economically optimal lifespan. Therefore, the ultimate question is: ?How can the relationship between the discount rate and the economically optimal lifespan be expressed mathematically??

Aug 1, 2013

By Jon Kellar, Samuel Kessinger, Prasoon Diwakar

Tantalum (Ta) and niobium (Nb) are extracted from many different ore types. The major economic orebody mined for tantalum and niobium consists of tantalite ((FeMn)Ta2O5) and columbite ((FeMnNb2O5)) in a solid-solution mineral commonly referred to as “coltan.” The largest supplying region, The Democratic Republic of the Congo (DRC), is unfortunately also the most ethically compromised source for this critical mineral. Officially, the U.S. government has deemed coltan ore from the DRC a “conflict mineral” [1]. The lack of pragmatic and effective local mining regulation in Central Africa, when coupled with high levels of violence and corruption, has spawned a widespread, illegal, unethical and, most importantly, unsafe economy. This illicit economy is centered around first, illegally mining these valuable conflict minerals and second, smuggling these minerals into the global supply chain. Handheld spectroscopy devices could provide further transparency to these opaque supply chains, giving miners, traders and refiners the ability to authenticate the provenance of the minerals they encounter, and allowing companies to prove compliance with the regulatory agencies attempting to curtail illicit mining.

Mar 1, 2025

By Dale Verran, Jared Orynik, Chad Sorba, David Bronkhorst

Denison Mines Corp. (“Denison”) has a 90% interest in the Wheeler River Uranium Project (“Wheeler River”) located along the eastern edge of the Athabasca Basin in northern Saskatchewan between the Key Lake mill and the McArthur River uranium mine. The project is host to the high-grade Phoenix and Gryphon uranium deposits, discovered by Denison in 2008 and 2014 respectively, which include combined Indicated Mineral Resources of 132.1 million pounds U3O8 (1,809,000 tonnes at an average grade of 3.3% U3O8). The Pre-Feasibility Study (“PFS”), completed in accordance with NI 43-101 in September 2018, is highlighted by the selection of the In-Situ Recovery (“ISR”) mining method for the development of the Phoenix deposit, with an estimated average operating cost of $4.33 (US$3.33) per pound U3O8. Phoenix is the highest-grade undeveloped uranium deposit known globally, including Indicated Mineral Resources of 166,000 tonnes at 19.1% U3O8 for 70.2 million pounds U3O8. The paper aims to provide a summary of Wheeler River and an overview of the proposed development of the Phoenix and Gryphon deposits according to the PFS completed for the Project. Further details regarding the PFS, including additional scientific and technical information are described in greater detail in the NI 43-101 Technical Report titled "Pre-Feasibility Study for the Wheeler River Uranium Project, Saskatchewan, Canada" dated October 30, 2018 with an effective date of September 24, 2018. A copy of this report is available on Denison's website and under its profile on SEDAR at www.sedar.com and on EDGAR at www.sec.gov/edgar.shtml.

Jan 1, 2020

Bowdil Co. Bucyrus-Erie Co. Coal Age Coal Mining Cobre Tire Dresser Construction FMC Corp. T. J. Gundlach Machine Co. Ingersoll-Rand Joy Mfg. Co. K&P Sales Engineers, Inc. Kennametal Lively Mfg. Co. Long Airdox Co. MSA McLanahan Corp. National Mine Service Co. Page Engineering Co. Plateau Supply, Inc. Pyramid Parts Scandura, Inc. TIC Utah International Utah Power & Light Co. Western Energy Co.

Jan 1, 1986

By Satu Jyrkönen

A single-particle laminar-flow technique was used to study oxidation of four synthetic nickel mattes, which were screened into three size fractions, Experimental conditions were: reaction gas from N2 - 21 to 75 vol-% O2; gas preheating temperatures ranging from 500 to I 100'C. The four mattes were synthesized so that Ni/Cu ratios of I and 10 were obtained with high and low iron contents. Chemical analysis of the particles was used to determine the oxidation degree of the materials, and optical and scanning electron microscopy were used to detect their morphology, internal composition and structure. The best sulfur removal from the synthetic nickel mattes was achieved under the most oxidizing conditions with the finest size fraction. The matte with Ni/Cu = 1 and high iron content was found to be most reactive. The least reactive matte was with Ni/Cu = 10 and low iron content; the coarse fraction particles did not react at all under the conditions studied.

Jan 1, 1996

By John C. Gagliardi

The size and complexity of modern surface haulage trucks has resulted in an increased reliance upon sensors and electronic-based instrumentation for safe and efficient operation. Design engineers need accurate information about the equipment vibration environment to efficiently and effectively build components for installation on mobile mining equipment capable of withstanding the mine environment. Examples of such components include backup alarms, communication equipment, microprocessor-based controllers, and a wide variety of sensors. Unfortunately, this information is not available to the majority of both original equipment and aftermarket equipment manufacturers. To address this problem, the U.S. Bureau of Mines performed field vibration measurements on a variety of surface mining haulage trucks. The vibration measurements were then analyzed and test specifications were developed in the form of envelopes. In conjunction with test specifications, recommendations to aid manufacturers in implementing a vibration environment test program have been included with an illustrative example.

Jan 1, 2010

By V. G. Papangelakis, G. A. Moldoveanu

"Rare earths adsorbed on clay minerals are easily recovered via ion exchange during leaching with inorganic monovalent salt solutions. The leaching efficiency of various salts at 0.5M and 25°C was investigated as a function of cation type and salt system (sulphates vs. chlorides). (NH4)2SO4 was identified as the lixiviant of choice and a procedure was established to investigate the influence of lixiviant concentration, temperature, pH and agitation on desorption kinetics and REE extraction levels. It was determined that the kinetics were fast and the optimum leaching conditions (for >80% total REE extraction) required pH below 5 and moderate temperatures (<50°C). INTRODUCTIONRare earth elements (REE) are at the core of numerous advanced applications due to their various uses in high strength permanent magnets, lasers, automotive catalytic converters, fiber optics/superconductors, and electronic devices (as phosphors in TVs and display screens for computers and cell phones). Because of the ongoing development of new technologies, there is an increased demand for REE in the international market, with emphasis on identifying new resources to insure an adequate supply for present and future use. World production of rare earths is dominated by China, the United States and Australia; however, in terms of resources, China dominates the world potential with reserves estimated to be over 90% of the total (Chen, 2011).The main commercially significant REE sources, as reviewed by O’Driscoll (1991) are bastnasite (carbonate) and monazite (phosphate) minerals, containing up to 70% wt. rare earth oxides (REO). In spite of being high grade, these ores are associated with elevated recovery costs due to difficulty in mining, separation and beneficiation. Moreover, aggressive conditions are required to solubilize the REE from the mineral, such as leaching with hot, concentrated acids or baking in 70% NaOH (Gupta & Krishnamurti, 2005)."

Jan 1, 2012

By Martin Hertzberg

In this Bureau of Mines study, an equation is derived for the limit burning velocity for divergent, spherical propagation from an ignition kernel of radius, r: (Su)e = ( ) . For flame propagation into a preexisting, stretching velocity gradient of magnitude dv/dx, the limit velocity is (Su)e = (a dv/dx)1/2. These formulations are shown to be equivalent to the fluid dynamic concepts of Damkoh1er, Kar10-vitz, and Markstein. Existing data for the b10woff limits of flames are shown to give excellent agreement with those concepts provided that proper account is taken of two dilution effects: composition dilution caused by entrainment and velocity gradient dilution caused by flow expansion. Approximate flow-field solutions are also derived for the unburned gas motion above an upward propagating, spherical flame kernel in buoyancy-induced flows. It is shown that;, the upward hemisphere propagates toward a stagnation plane in a counterflow configuration involving the balance between the combustion force, which accelerates the cold gas upward, and the buoyancy force that accelerates the cold gas downward. The position of the stagnation plane above the upward propagating hemisphere is related to the ratio of the buoyant velocity, vb, to the burning velocity, Suo Extinction of the upward propagating wave occurs by flame stretch in that counterflow configuration when n = Vb/Su begins to exceed the expansion ratio, Pu/Pb&apos; and the wave is blown off by its own buoyancy-induced flow field.

Jan 1, 1984

By M. W. Von Bernewitz

AN important regional meeting of the American Institute of Mining and Metallurgical Engineers was held, at Salt Lake City on Aug. 22 to 26, jointly with the fifth annual meeting of the Western Division of the American Mining Congress. The whole meeting was marked by enthusiasm, keen attention to the subjects under discussion, and many renewals of personal contacts. The trips to the various plants were well attended and the local press paid much attention to the meeting. The A. I. M. E. sessions began Aug. 23, with a non-technical morning session. J. 0. Elton, manager for the International Smelting Co., presided. The purpose of this session was to present in a non-technical manner the relation of flotation to mining, smelting, and the State. Ernest Gayford, metallurgist with the General En-gineering Co. of Salt Lake City, gave the definitions of flotation as suggested by Rickard, the dictionary, Weinig, and Taggart. The active agent in flotation is the air bubble, and the two prime requisites are the formation of bubbles and the creation of selective action of the bubbles for metallic particles instead of for gangue particles. Broadly, all the sulfides are floatable minerals, but the oxides, carbonates, silicates and sulfates are not. As far as Utah is concerned, flotation has been one of the greatest means of conserving its natural re-sources, because it has converted millions of tons of waste rock into pay ore; it is recovering millions of pounds of metal formerly lost in tailings; it has con-verted the zinc from a liability into an asset; and has kept thousands of men at work and distributed millions in dividends for the benefit of the State. As to the future of flotation, Mr. Gayford can con-ceive that the next 5 or 10 years may see as much, if not more, advance than was made in the preceding period. The big problem is dressing oxides, carbonates, silicates, and sulfates, and simplification of the number of reagents, also the separation of different gangue min-erals from one another.

Jan 10, 1927

By Leandro Gusmão da Silva

Neste trabalho, foram estudados os efeitos da irradiação de uma superfície polida do aço inoxidável tipo ASTM F138 com laser de pulsos ultracurtos. As irradiações foram realizadas variando-se a velocidade de varredura do laser, ou seja, a taxa de sobreposição espacial de pulsos. Foi observado que após a irradiação houve uma visível mudança na coloração da amostra. Também foi verificado que com o aumento da taxa de sobreposição de pulsos a superfície tendeu a tornar-se preta, ou seja, absorvedora de luz. Com essa técnica, pode-se realizar marcações com alto contraste sem que haja formação de camadas de óxidos, nitretos ou alterações microestruturais no metal, o que é importante para um material com a precisão que um implante exige.

Aug 17, 2017

By Douglas Luciano da Silva Oliveira

Em uma linha de decapagem contínua, o tempo de parada da entrada para realização da solda é um dos fatores que mais afeta a produtividade. Estratificando-se o tempo total dessa parada, parte significativa é composta pelo tempo de centelhamento, que é um dos parâmetros fundamentais da soldagem a topo por centelhamento. Adicionalmente, a energia elétrica e o gás natural, consumidos durante o processo de soldagem, contribuem para onerar o custo de transformação da BQD. A fim de reduzir esse tempo e os custos de transformação, avaliou-se, através de análise metalográfica, ensaios de embutimento e dureza, a qualidade de juntas soldas com tempos reduzidos e sem o uso do sistema de depleção de oxigênio, para aços de baixo carbono, de acordo com referências da literatura. Com base nos resultados obtidos, foi possível reduzir o tempo médio de solda em 5s em materiais com espessuras superiores a 2,50mm e eliminar a necessidade do uso de gás natural em todos os aços da GRADE 0, o que representa em torno de 76% das bobinas produzidas nas LDCs.

Aug 8, 2018

By William Marsh Baldwin

TWO of the most useful and important equations available to the metallurgist for the study of plastic deformation of metals are the Huber-von Mises-Henckyl-~ and the St. Venant7-10 equations. Huber-von Mises-Hengky Equation The Huber-von Mises-Hencky equation answers the question: When does plastic flow occur in metal that is subjected to a multi-axial stress? It occurs, according to this equation, when the three principal stresses,t UI, u2, and u3 satisfy the equation: (<ri - <r2)2 + (<r2 - <rsY + (ff! - <r3)* = 2Ki [i] Here K is the yield strength of the material as determined in an ordinary tensile test. If the quantities ul, 52, andas are assigned to the coordinates of a Cartesian three-dimensional system, this expression describes a cylinder whose axis of symmetry is inclined at equal angles to the three coordinate axes4s6 (Fig. I). The radius of this cylinder is .\/%K. For the purpose of simplicity, it is sometimes advantageous to ascribe the values al/K = sl, az/K = s2, UD/K = SJ to the three coordinate axes instead of the principal stress alone. In this case, Eq. I becomes (*i - s*)1 + (s2 - S3)2 + (si - SiY = 2 [2] and the radius of the cylinder becomes \/%. In the latter method of representation, a point lying inside the cylinder indicates that the metal will react elasti-cally, whereas a point lying on the cylindrical surface indicates that the metal will behave plastically. Some of the geometric features of this cylinder are worthy of study. Let us inquire first as to what interpretation may be placed upon what we will choose to call the "circles of latitude" of the cylinder (L in Fig. I) and the "meridians" of the cylinder (M in Fig. I). Circles of Latitude Circles of latitude are formed by allowing a plane, passing perpendicular to the cylinder axis, to intersect with the cylinder. Any point, P, on this circle is presumed to have the coordinates sl, SZ, and s3. The coordinates of the point resulting from the intersection of the plane and the cylinder axis will be a, a, and a (since the cylinder axis is equally inclined to the three coordinate axes). L?t US now pass a line through the point on the circle and the point on the axis.

Jan 1, 1946