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By J. Mizrahi, A. M. Baniel, A. Mitzmager, S. Star

This article gives an account of the latest developments in the use of TBE for sink-float separation of silicate minerals. A number of minerals for which the process has been tested and found suitable are reviewed. Specific examples are discussed in relation to the particular problems of sink-float separation and recovery of TBE as compared with non-silicate minerals. The economic aspects are outlined. Silica and silicates comprise the most common and abundant group of minerals, and since they are present in variable amounts in most ores, they constitute an appropriate subject for the review and discussion of the recent developments in the use of TBE for mineral concentration. The silicates considered as a group have an extremely wide range of chemical and physical properties. Some of these properties, which are common to all minerals, are of importance to concentration by TBE and are discussed in some detail in this paper, as well as the development of methods and apparatus for concentration and recovery of TBE and several examples of concentration of silicates. PROPERTIES OF MINERALS WITH RESPECT TO CONCENTRATION BY TBE The properties considered as most important to concentration by TBE are specific gravity, structure, surface and shape. The specific gravity of a mineral is a fundamental property and is constant between very close limits for the same species of different sources if particles are pure and free from cavities or cracks. In many species, however, solid inclusions and changes in chemical composition due to replacement of elements cause variations in the specific gravity. The plagio-clase series of feldspars between albite and anorthite illustrate this point (specific gravity from 2.60 to 2.77). Fig. 1 shows the specific gravity distribution of some of the common silicate minerals.' The highest specific gravity is about 4.7 (zircon) and the lowest is 2.0 (sepiolite), with most of them ranging between 2.6 and 3.5. Although most of the silicates given in Fig. 1 are found as constituents of rocks, those generally considered as rock making minerals are comparatively few. They include quartz, feldspars, nephelite, sodalite, leucite, mica, pyroxenes, amphiboles, chrysolite, kaolin, talc and serpentine. These minerals may appear in igneous rocks as coarse crystals in granites, syenites and diorites or as very fine grained dispersions in basalt and felsite. When the latter rocks occur in an ore, their specific gravities depend on the minerals present and structure. The same is true for the sedimentary and metamorphic rocks (sandstones, shales, gneiss, slate, schists). A comparison of specific gravities for the minerals listed in Fig. 1 with that of TBE (see Table I) shows that the important rock-forming minerals, with the exception of pyroxenes, amphiboles and chrysolite (olivine), lie in the specific gravity range of less than 2.96 and can therefore be separated by TBE. The ore structure is important both in determining the apparent specific gravity and the efficiency of TBE recovery. The structure can be compact (as in

Jan 1, 1963

By James F. O'Neill

Brown iron ore deposits in Quitman County , Ga . , were investigated by the Federal Bureau of Mines in cooperation with the State of Georgia , Department of Commerce , and the University of Alabama . Ninety- one holes were drilled , having an aggregate footage of 2,188 feet ; seventy- one holes penetrated 248 feet of iron mineralization . Average thickness of the ore zone was 3.5 feet under an average thickness of 14.7 feet of overburden . The drilling developed inferred reserves containing nearly 30 million long tons of crude ore with an average analysis of 28 percent iron plus minor quantities of manganese . Test work done by the Bureau on the crude ore samples indicated that they would upgrade by current log washer practice , with the use of a 1 /8 - inch screen , and yield 4.4 million dry long tons of concentrate with an average analysis of 52.1 percent iron plus manganese . The weight recovery obtained was 14.7 percent . Research studies made by the Bureau showed that the weight recovery would be increased by changing the screen size without any appreciable sacrifice of grade . The average weight recovery was increased to 18 percent with a 10 - mesh screen and 22.8 percent with a 20 - mesh screen . Screen tests studies indicated that there was no appreciable interlocking of the iron and manganese minerals and the clay and silica waste particles of the materials retained on a 200- mesh screen . Clay was prominent in micron - size slimes . Silica was deleterious in the minus 20 - mesh size .

Jan 1, 1965

By A Dennis, T Hunter, R Coleman

For metallurgical plant design, it is necessary to progress through successive phases of test work, piloting and process development before involving all the other engineering disciplines and “freezing” the process design criteria and flow sheet. This process usually relies upon the experience, skills and personal preferences of various technology providers, study and engineering entities, test work and metallurgical laboratories and, most importantly, the owner’s team and its operators. Current industry trends include lower grades, more complex orebodies, geometallurgy in defining orebody variation and design envelopes, more common “hybrid” plant processes and the market demands for more reliable, timely and predictable early plant performance.This paper will discuss interaction of these trends and provide guidelines for the level of detail and technical complexity required for a number of different “typical” examples. The paper will pay particular attention to the study definition level translated into the required detail and certainty needed by the overall process “owner” and original equipment manufacturer (OEM) equipment suppliers to ensure the best real plant performance. Some recent case studies will be discussed. In many projects, at a late stage of project definition, it has become common practice to undertake a “value engineering” phase. Although it could be argued that this should be undertaken earlier, it is largely driven by an overall need to reduce capex and “optimise” the perceived “fat” built into the project during the detailed design process. This value engineering can be very counterproductive to project timing and operational performance and warrants discussion.The paper is intended to promote discussion on a topic of wide interest. The authors’ diverse backgrounds and experiences are integral to the views in this paper.CITATION:Dennis, A, Coleman, R and Hunter, T, 2017. Critical process design considerations from test work to operations, in Proceedings MetPlant 2017, pp 12–30 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Sep 11, 2017

I. Book review Legal and institutional arrangements in minerals development. Edited proceedings of a workshop organized jointly by the VN. Department of Technical Co-operation for Development and the German Foundation for International Development (DSE), held in Berlin in August 1980. London, Mining Journal Books, 1982. Soft, 228 X 149 mm, xi + 223 pp. Approx. R30 + GST. Reviewer: M. J. Martinson 2. New books Strength of metals and alloys (IOSMA 6). R. C. Gifkins (Editor). New York, Pergamon, 1982. Approx. 1200 pp. 3 vols. V.S. $220. Deformation-mechanism maps. The plasticity and creep of metals and ceramics. H. J. Frost and M. F. Ashby. New York, Pergamon, 1982. Approx. 250 pp. V.S. $60. Pressure diecasting, Part 2. The technology of the casting and the die. D. F. Allsop and D. Kennedy. New York, Pergamon, 1982. $ V.S. 27.50.

Jan 1, 1982

By William Lodding

That grinding may change a crystalline material both in a physical and in a chemical sense has been shown by a number of authors in recent years. Thus Mackenzie (1) and Bartha (2) reported the effects of careful grinding on muscovite, quartz, gypsum, dolomite, etc. Increase in specific surface produced by grinding implies increase in total energy of a system. Newly produced surfaces are chemically more reactive; dislocations may be introduced during grinding, and existing strain may be released by the same process, as shown by Holt et el. (3) All these changes are easily detected by thermal analysis, but it is not easy to separate the multiplicity of effects registered and to arrive at quantitative interpretations. This paper is an attempt to analyze by the use of thermal analysis some effects produced in grinding. In differential thermal analysis (DTA) one measures all thermal changes occurring in a substance during heating or cooling. Chemical changes, such as decompositions, synthesis, oxidation, reduction, etc., and physical changes such as phase transformations, changes in specific surface and in thermal conductivity, strain release, etc. By thermo gradmetric analysis (TGA) on the other hand only chemical changes involving weight loss or gain are recorded. Similarly gas evolution analysis (GEA) will register only reactions involving gas evolution, including water vapor, and oxidation-reduction. By performing two or all three of these thermal methods of thermal analysis simultaneously and on the same specimen one can separate the different effects registered and by difference evaluate their magnitude.

Jan 1, 1966

By R. B. Elver

The St Lawrence Seaway, a deep-water canal system between Montreal and Lake Ontario, was opened for navigation on April 25, 1959. Prior to the opening of the new Seaway, small boats known as canalers and a few deep-sea carriers, primarily from Norway since World War II, were the only ships able to journey past Montreal into Lake Ontario through the old Canadian St. Lawrence canal system. Thus it was necessary for many tons of bulk and general cargo to be shipped all-rail to and from Atlantic ports or to be transhipped to and from canalers. With the opening of the new Seaway, large Great Lakes bulk carriers and a much larger percentage of the world's shipping fleet are now able to sail directly from the sea to the heart of industrial North America. In this paper, the historical events leading up to the construction of the Seaway and the physical nature of the Great Lakes transportation system are briefly reviewed. Following this, an attempt is made to evaluate the effects of the new Seaway on Canada's mineral industry. Because the Seaway has been in operation for only one season, this paper must be considered only an interim report. Because of the importance of the Seaway to iron ore, this commodity will be dealt with in detail, although the effect on other mineral commodities such as coal, petroleum, nonferrous ores, iron and steel will be mentioned. At this time the author wishes to thank the various company and government officials who provided both factual information and critical opinions.

Jan 1, 1960

1. Book reviews Geophysical and geochemical techniques for exploration of hydrocarbons and minerals, edited by M. Sittig. (Reviewer: J. Keenan) Separation procedures in inorganic analysis. A practical handbook, by Roland S. Young. Charles Griffin, 1980. £23.00. (Reviewer: R. Murray-Smith) 2. Historical reprints Theinin~rs dictionary, by William Hooson. £14. Discovery of subterraneal treasure, by Gabriel Plattes. £12. Fodinae Regales (The Mines Royal), by Sir John Pettus. 3. De Beers' booklets Amborite - a remarkable new cutting material, by De Beers Industrial Diamond Division (P.O. Box 916, Johannesburg 2000). Booklet, 14 pp., free of charge. Natural and synthetic micron powders, by De Becrs Industrial Diamond Division (P.O. Box 916, Johannesburg 2000). Leaflet, 5 pp., free of charge. 4. New books Nickel in the environment, edited by J. O. Nriagu. New York, Wiley, 1980.928 pp. $65. Underwater minerals, by D. S. Cronan. London, Academic Press, 1980. 364 pp. $57.50. Data conversion integrated circuits, edited by D. Dooley. New York, Wiley, 1980.298 pp. $26.95 (cloth), $17.50 (paper). 5. NIM reports Report 2057 A mineralogical study of the Rooibokkop- Boschhoek copper deposit in the Marble Hall area. Report 2069 A utomatic setting of the distance between sample and detector in gamma-ray spectroscopy. Report 2070 The prereduction of chromites from the UG-2 Reef. Report 2075 The optimization of some of the conditions for analysis by spark-source mass spectrometry. Report 2082 A survey of the literature on gravity separation.

Jan 1, 1981

By Frank A. Peters

A series of evaluations is being made to determine the relative processing costs of producing metallurgical-grade alumina from low-grade aluminous materials. These evaluations include the estimated operating and capital costs as well as recommendations for additional research and development to improve the processes and to lower their costs. The design for each process is based on published work. The three processes considered in this evaluation are designed to leach alumina as aluminum sulfate from calcined clay with sulfuric acid and to remove the silica residue by filtration. The filtrate from leaching is then purified by one of the following methods: Removal of iron in electrolytic cells using mercury cathodes; removal of iron by chemical precipitation through the formation of an iron-manganese complex; or precipitation of the alumina from an aqueous-ethanol solution, leaving iron in solution. Both the operating and capital costs for these processes are higher than those for the Bayer process. For plants producing 1,000 tons of alumina a day, the estimated operating costs per ton of alumina are: Electrolytic iron-removal process........... $81.35 Chemical iron-.removal process............... 82.08 Ethanol purification process............... 86.17 The investment in mercury is not part of the operating cost since this cost is considered equivalent to catalyst cost which would not be shown. The estimated capital investments for 1,000- ton-per- day plants on a Marshall and Stevens chemical equipment index basis of 240.0 are: Electrolytic iron-removal process...... $116,775,500 Chemical iron-removal process............... 99,418,900 Ethanol purification process................ 94,210,200 These investments include the working capital but not the land for each of the processes. Included in the electrolytic iron-removal process is an investment of $4,859,400 for mercury. Investigation of other methods for removing iron, of the decomposition operation, and of the leaching operation could reduce these costs.

Jan 1, 1963

By C. R. Tang

The respirable dust real-time monitoring equipment export information is complex, and electromagnetic wave wireless transmission is affected largely under mine conditions. The respirable dust concentration information transmission method based on led light equipment is proposed. The respirable dust concentration data of the individual real-time monitoring equipment is encoded to fit the system transmission; the encoded signal is modulated onto the LED mine lamp; the light signal is transmitted by the spatial channel; the signal is received by the receiver to the photoelectric conversion to restore the respirable dust concentration data for subsequent processing. Simulation and verification experiments showed that the respirable dust concentration information transmission method based on led light equipment can achieve the LED miners? lamps visible light wireless data transmission.

Aug 1, 2013

By M J. Nugus

The Geita gold mines in north-western Tanzania have produced 5 Moz of gold from an estimated endowment of 15 Moz. They are generally classified as typical Archaean orogenic banded iron formations (BIF)-hosted gold deposits in banded iron formations as described by Goldfarb, Groves and Gardoll (2001); Neall and Phillips (1987); Phillips and Powell (1993) and Neall (1987). The controls on gold mineralisation have been reassessed to conclude that Nyankanga, and we conclude that Nyankanga, the largest deposits within the group, developed during a dynamic and protracted deformation history intimately associated with several stages of hydrothermal fluid flow and alteration. The fluid-induced fractures associated with gold mineralisation are primarily manifested as submillimetre to metre-scale fractures and breccias developed preferentially in rocks that have been previously deformed and altered by silicification or seafloor metasomatism. This realisation detracts from the exploration and mining strategies that would solely concentrate on fluid pathways and associated wallrock alteration and veining solely within the BIFs as hosts for economic gold mineralisation.

Aug 22, 2011

By Paulo Couceiro, Juan Navarro

The impact of rock blasting fragmentation and heave on digging performance in open-pit mining operations is usually the first true indicator of blasting outcomes. Within the typical excavation cycle, the bucket loading time or instantaneous digging rate are the ones that present the strongest correlation with rock fragmentation size distribution, swelling, and shape of the muckpile, a part of rock mass hardness, equipment size, power, and others. As the efficiency of unit operations becomes increasingly important for long-term mining strategies, cost-effective approaches are needed to increase mine productivity. In this line, the performance of downstream operations, such as digging, hauling, and comminution, may be affected by the energy input in blasting. This requires a better understanding of the explosive’s energy role in such unit operations in order to drive consistent improvements. Therefore, this paper examines the impact of the explosive’s energy distribution on shovel diggability from production shots carried out with different explosives in an open pit gold mine, with the aim of modelling the interface between blasting and excavation.

Jan 21, 2025

By Juan L. Luque Lanza

Durante las fases de minado como la exploración, desarrollo, preparación y explotación de una zona mineralizada, surgió la necesidad de clasificar geomecánicamente el terreno a través del uso los conceptos básicos de la mecánica de rocas y la integración de dicha disciplina al planeamiento del minado de una mina subterránea. Por ello, el presente texto describe el proceso de esta metodología que consiste en la clasificación del terreno según los grupos de similar comportamiento y la elaboración de planos geomecánicos, con la finalidad de encontrar la relación existente entre el tiempo límite y el espacio activo para una excavación subterránea, diseño y cámaras pilares en la mina subterránea de Yauricocha.

Aug 26, 1988

By E. C. Perkins

Preliminary experiments are reported utilizing bacteria to leach manganese from a variety of domestic low grade manganiferous materials. In two large leaches manganese extraction ranged from 71.7 to 92.5 percent, and the products analyzed over 48 percent manganese. Nutrient requirements and leaching time experiments were made. The mechanism of leaching is not understood, but is different than the mechanism encountered in the microorganism accelerated leaching of copper in the presence of sulfide minerals.

Jan 1, 1962

By D. J. Esdale, D. F. Pridmore, F. W. Lindman, J. H. Coggon

Almost all the presently viable nickel reserves in the Yilgarn Block contain nickel in a sulphide phase. Both volcanic peridotite- associated (VPA) deposits and intrusive dunite-associated (IDA) deposits are characterized by massive, matrix and disseminated sulphides (typically, pyrrhotite, pentlandite, pyrite, chalcopyrite, magnetite and other spinels), though in the IDA deposits the volume of disseminated sulphides is far greater than that in the VPA deposits. Potentially all geophysical techniques have application in the direct detection of these deposits'gravity for the detection of the dense massive and matrix ore; magnetics for the detection of magnetite and pyrrhotite in the ores; electromagnetics for the detection of the massive and matrix ore; and induced polarization for the detection of disseminated and to some extent matrix and massive ore. In practice the application of geophysical techniques is limited to a varying extent by (1) the relatively small size of an economic accumulation of sulphides, particularly the VPA deposits, (2) the extreme depth of weathering and lack of outcrop on the Yilgarn Block and (3) the abundance of geological noise or anomalous responses caused by sources other than economic mineralization.

Jan 1, 1984

By A. H. Lang

"The great interest taken in uranium in Canada during the past few years has resulted in the discovery of a very large number of occurrences, and in much research that has added to the knowledge of the mineralogy and geology of uranium deposits. The object of this paper is to present that information in condensed form. Some of it has been published before, but the writer has been asked to bring it together and to add more recent, unpublished data. The paper therefore contains short accounts of the mineralogy of uranium and of the types and distribution of occurrences; brief regional descriptions, including information on some of the characteristic deposits; and conclusions regarding prospecting and development possibilities.The writer has access to much confidential information supplied in compliance with regulations of the Atomic Energy Control Board. He has used this only for making broad generalizations that could not affect individual interests, and only where the owners of properties have agreed to its use.Much of the information on mineralogy and geology is derived from the work of others. The writer is particularly indebted to M. H. Haycock and S. Kaiman of the Mines Branch; H. V. Ellsworth, S. C. Robinson, E. J. Brooker, H. R. Steacy, W. E. Hale, and A. M. Christie of the Geological Survey; and E.W. Nuffield, J. S. Stevenson, and other officers of provincial Departments of Mines. For information and many courtesies he is greatly indebted to so many officers of Eldorado. Mining and Refining (1944), Limited, and owners and staffs of private properties, that it is impossible to mention them individually."

Jan 1, 1950

By B. G. Kelley

The MIDREX® Direct Reduction Process was developed during the 1960s by the Midland-Ross Corporation, which had pioneered shaft furnace technology and stoichiometric gas reforming for use in processing minerals. In 1969, the first MIDREX® Direct Reduction Plant was built in Portland, OR. Since then, 49 additional modules have been sold in 18 countries. For the last ten years, over 60 percent of the world's direct reduced iron has been produced in MIDREX Plants. During the quarter century since commercialization, many technical improvements have been made, including larger shaft furnaces, in-situ reforming, greater heat recovery, improved catalysts, and hot briquetting. Midrex continues to enhance the technology in the areas of economy-of-scale, energy efficiency, alternate fuels, and raw material flexibility.

Jan 1, 1998

By Volkan Arslan

This study aimed to remove the contaminants in quartz sand by using an eco-friendly method and to obtain high-purity quartz. For this purpose, ultrasound-assisted acid leaching was applied. Equal amounts of a mixture of diluted hydrochloric and oxalic acids were used as the solvent. Response surface methodology (RSM) was used for optimizing, modeling, and predicting the experimental parameters. The correlation coefficient ( R2) of the proposed quadratic model for the relationship between iron removal yield and test parameters was calculated as 0.9731 and it was determined that the predicted and actual values were compatible. Finally, optimization experiments were made and optimum experiment conditions were revised and determined as 83.38 °C of leaching temperature, 196.35 min of leaching time, 2.86 M of acid concentration, and 202.24 W of ultrasound power. Under the optimum conditions determined after optimization, the highest yield of iron removal was determined as 95.08%. Under the optimal parameters, the SiO2 content of the concentrates increased from 97.841 to 99.907% and the Fe2O3 content reduced from 0.225 to 0.011%.

Jul 12, 2021

By K. Terhaar

The objective was to determine operating protocols for a lead and silver column flotation cleaner, being considered for installation at Sunshine Mining & Refining Co.'s Kellogg mill in Northern Idaho. In this column, tetrahedrite and galena were floated, and pyrite and other gangue minerals, including siderite and silica, were depressed. The procedure was to develop a dynamic simulation using a linear transfer function approach. The transfer function related cause and effect variables such as the influence of collector and depressant dosages on recovery and grades. Bench-scale flotation tests followed by pilot column testing provided the data used to develop a linear transfer function. The transfer function was derived using a spreadsheet. This model was applied to simulate how the flotation column could be made to respond to disturbances in feed grade. The results were that xanthate, zinc sulfate, and sodium cyanide were found to be suitable controls for grade and recovery. Simulations showed the best sequence of manipulations of these reagents, and these sequences were useful for future operator training. The conclusion was that linear transfer functions were able to simulate lead and silver recovery, develop scenarios for operator training, and provide a foundation for future on-line control.

Jan 1, 1999

By Maynard H. Jameson

Earlier investigations of the potential-drop-ratio method of electrical prospecting have indicated that under suitable conditions this method is well adapted to the location of formation boundaries in stratified ground. A description of this development was given several years ago by H. Lundberg and Th. Zuschlag.l The curves published by these authors for the potential-drop-ratio variation above a horizontal contact indicated a definite relation of the position of the curve peak to the depth of the interface. The theory underlying this relation was subsequently studied by Z. Mitera in greater detail,' and the theoretical deductions were compared with the results of tank experiments. The investigations available at this writing were confined to studies of horizontal formation boundaries. It is the purpose of this paper to extend the scope of the previous work to the problem of dipping layers. Theory Consider the case of three media of different resistivities, whose interfaces are not parallel. If a point-source is located in one of these interfaces, its images do not lie in a straight line, but on the circumference of a circle whose center is at the hypothetical junction of the interfaces. R. F. Aldredgea determined the relation that exists between the degrees of dip of the two interfaces and the distances between the various images and the point for which the potential is to be found. As seen in Fig. I, three media of resistivities PO, p1, and p2 are involved, and the source I is located at the interface of the media Coo) and (p1). The perpendicular depth of the lower interface is h, 0 is the dip, R is the distance between source I and potential point P, and r is the distance between the images and that point. To distinguish between images lying above the ground interface and those below, the notation "odd" and "even" images will be employed; images below the ground interface will be termed "odd" and those above "even." The following relations govern the distances between either kind of images and the potential point: EvEn Odd Ta — R r1 - [rl] - [RS + 4h(h + R sin 01½ r, = [r] =. [R1 + 4h cos 0)2(h + -R sin 0)1½ ri - [r3] ={r3} [R* + 4h(4 cos2 0 - i)1 (h + R sin 0)l½ r4 = [r4] = [R2 + 4h(4 cos $ cos 30)1 (h + R sin 0)]½ r, — [r4] - [R2 + 4h(4 cos9 R cos 20 + cos 48)2 (h + R sin 01½ I RI + 4h[2 cos 30(4 cos2 0 - I)12 (h + R sin 8)1 ½ rn - [r4] - [R2 + 4hlf(cOs 0)18(h + R sin R)l½ As previously pointed out, the images of the source are on the circumference of a circle. If the angle of dip is 0, the angle measured from the horizontal to the first image is 28; to the second image it is 48, and so on. Since the limit of the reflecting interface is at its outcrop, the last possible

Jan 1, 1946

By Maynard H. Jameson

Earlier investigations of the potential-drop-ratio method of electrical prospecting have indicated that under suitable conditions this method is well adapted to the location of formation boundaries in stratified ground. A description of this development was given several years ago by H. Lundberg and Th. Zuschlag.l The curves published by these authors for the potential-drop-ratio variation above a horizontal contact indicated a definite relation of the position of the curve peak to the depth of the interface. The theory underlying this relation was subsequently studied by Z. Mitera in greater detail,' and the theoretical deductions were compared with the results of tank experiments. The investigations available at this writing were confined to studies of horizontal formation boundaries. It is the purpose of this paper to extend the scope of the previous work to the problem of dipping layers. Theory Consider the case of three media of different resistivities, whose interfaces are not parallel. If a point-source is located in one of these interfaces, its images do not lie in a straight line, but on the circumference of a circle whose center is at the hypothetical junction of the interfaces. R. F. Aldredgea determined the relation that exists between the degrees of dip of the two interfaces and the distances between the various images and the point for which the potential is to be found. As seen in Fig. I, three media of resistivities PO, p1, and p2 are involved, and the source I is located at the interface of the media Coo) and (p1). The perpendicular depth of the lower interface is h, 0 is the dip, R is the distance between source I and potential point P, and r is the distance between the images and that point. To distinguish between images lying above the ground interface and those below, the notation "odd" and "even" images will be employed; images below the ground interface will be termed "odd" and those above "even." The following relations govern the distances between either kind of images and the potential point: EvEn Odd Ta — R r1 - [rl] - [RS + 4h(h + R sin 01½ r, = [r] =. [R1 + 4h cos 0)2(h + -R sin 0)1½ ri - [r3] ={r3} [R* + 4h(4 cos2 0 - i)1 (h + R sin 0)l½ r4 = [r4] = [R2 + 4h(4 cos $ cos 30)1 (h + R sin 0)]½ r, — [r4] - [R2 + 4h(4 cos9 R cos 20 + cos 48)2 (h + R sin 01½ I RI + 4h[2 cos 30(4 cos2 0 - I)12 (h + R sin 8)1 ½ rn - [r4] - [R2 + 4hlf(cOs 0)18(h + R sin R)l½ As previously pointed out, the images of the source are on the circumference of a circle. If the angle of dip is 0, the angle measured from the horizontal to the first image is 28; to the second image it is 48, and so on. Since the limit of the reflecting interface is at its outcrop, the last possible

Jan 1, 1946