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By Lucien Weber

In the Shanghai area, the soil conditions are such that bearing piles have become an essential foundation part of the new highrise buildings. In order to reduce the settlements under the high working loads of about 2300 kN/pile, the Chinese building authorities require the pile tip to penetrate into the compact sand layer, situated at approx. 60-70 m depth. No H-piles have yet been tested under these conditions in Shanghai. This paper describes the driving of 8 H-bearing piles with 4 different shapes and with lengths varying from 45 to 75 m. Dynamic measurements are performed during driving and after a wait time of approx. 40 hours in order to assess the change in bearing capacity in function of time and in order to get an idea about the resistance distribution along the piles by using a stress wave analysis program (CAPWAP). One pile is equipped with channels between the flanges for executing verticality measurements with an inclinometer. However, this test has not yet been performed. One month after driving, two piles of 75 m length are statically loaded both in vertical and in horizontal directions.

Jan 1, 1987

By Mike Sapiro

"Heath Steele Mines is a base metal producer situated near Newcastle, N.B. presently treating 3500 TPD of complex Cu-Pb-Zn ore. The ore consists of massive fine grained sulfides averaging I. 1% Cu, 1.6% Pb and 4.5% Zn.The original mill started in 1956 at 750 TPD and was successively expanded through 1500 to 3000 TPD in 1969. In 1972 an expansion to 4000 TPD was initiated. It was planned to obtain the maximum benefit from equipment and manpower by adding some process equipment, instrumentation, an on stream analyser, and a process control system. The benefits from this approach could be greater than normally expected, because of the complex metallurgy of this ore.IntroductionThe crushing plant is of conventional design with two 5 ½ ft, Symons cone crushers with the crushed ore screened to -7/8 inch on a 61 x 16 1 Al I is Chalmers vibrating screen and stored in four 1000 Ion bins. There are two para I lei grinding circuits, each one consisting of the following: one Rod Mill in open circuit, one Ball Mill in closed circuit with two 20"" Krebs cyclones, and one Ball Mill in closed circuit with three 15"" Krebs cyclones, Al I the Mills are 9' x 121 Al I is Chalmers Mills. The secondary cyclone overflow from each grinding circuit is thickened and combined to form flotation feed. The final product is 65% - 400 Mesh. Two regrind mills have been installed as part of the expansion."

Jan 1, 1977

By Klaus Tietz, Hamish Adam, John Selby, Ian Glazier, Brian Sinfield

"Room-temperature tunable diode laser (TDL) analyzers are gaining in acceptance for highly critical safety monitoring applications in a variety of industries. This paper describes the testing, evaluation and deployment of a laser-based hydrogen cyanide monitoring system at the Campbell Complex of Goldcorp’s Red Lake Gold Mines in Balmertown, Ontario, Canada.A trial, single channel installation was followed by a staged multi-channel installation. Unexpected technical issues with the multi-channel installation were addressed and resolved.INTRODUCTIONLaser-based gas detection has several advantages over existing gas detection techniques (Ballangrud, 1993; Silver, 1992; Bomse, 1995; Table 1). For practical purposes, lasers generate light at a single wavelength. Room temperature tunable diode lasers (TDL) emit light in the near infrared (NIR) part of the electro-magnetic spectrum. Many gases of interest, including HCN, NH3 and others, absorb energy in the near infrared (NIR). Each gas has a unique absorption signature, or spectrum, made up of a large number of individual “absorption lines”. A TDL can be tuned to select a single absorption line of a target gas, which does not overlap with absorption lines from any other gases. Therefore, laser gas sensing is selective and does not suffer from interference from other gases. The single-wavelength nature of laser light also means that laser gas analysers have a linear response over a wide dynamic range.Tunable Diode Lasers (TDL) generate only a few mW of power. However, all this power is concentrated at one wavelength, the wavelength where gas absorption occurs, resulting in high signal-to-noise ratios and short response times, typically of about 1 or 2 seconds (Ballangrud, 1993). This also means that long path lengths can be used, enabling accurate measurements of very low concentrations, even with weakly absorbing gases. Tunable Diode Lasers provide all the advantages of other semiconductor devices: they are small, solid-state devices, operate at room temperature, and have long-term reliability (over 15 years). Currently, they can be obtained for any wavelength throughout the NIR (700nm to 2000nm). Because many gases absorb in the NIR, the technique is widely applicable."

Jan 1, 2011

By V P. Elpatyevskaya, V S. Arzhanova

Main geochemical problems concerning the environment and mining industry interrelation are connected with the transformation of natural water chemistry by mining wastes. The investigation of many mines in Primorye, the southern part of the Russian Far East, showed that their mining waters have high concentrations of heavy metals and aluminium. Water acidity is primarily connected with the amount of acid-forming sulphide minerals in ores and also depends on the neutralising capacity of rocks. Considerable quantity of metals occur in the waters in dissolved form. Metal concentrations in mining waters exceeds the natural levels by two to five orders of magnitude and can't be reduced to the background levels even after multiple dilution. It is necessary to develop and put into practice new technologies so that to reduce the geochemical impact upon the environment.

Jan 1, 1995

By T. S. Golosinski

Introduction Typical dragline rigging includes several sets of ropes: hoist ropes, drag ropes, dump ropes and boom suspension ropes. The drag and hoist ropes contribute most to the dragline operating cost. Both work in very difficult conditions and wear out rapidly. As a result, frequent rope changes are required resulting in substantial cost and productive time loss. Although performance of rigging has a profound impact on dragline efficiency, there are no common, industry accepted standards related to its selection, operation and maintenance. Little information on the subject is available and the practice differs widely throughout the industry. The performance of drag and hoist ropes depends on: •rope construction that should closely match requirements of the specific application, rope operating conditions and its maintenance and • correct definition and application of the rope discard criteria so that full advantage of the rope can be taken without endangering safety of its operation. This paper reviews the present practice related to all these factors. Its findings are based on the wide survey of the present industrial practice. Field survey In total, 33 North American dragline applications were surveyed of which 17 were Bucyrus-Erie machines, 10 were Marion and six were Page (now P&H). Most of the draglines were stripping overburden in coal mines, but the survey also included some unique applications such as phosphate mining in Florida and oil sand mining in Alberta. Hoist drive power of the surveyed machines varied from 300 to 7775 kW (400 to 10,400 hp). Drag drives varied from 300 to 5815 kW (400 to 7800 hp). Boom lengths varied from 37 to 110 m (120 to 360 ft). Bucket sizes varied from 5 to 96 m3 (6 to 115 cu yd). The hoist and drag ropes installed on the surveyed machines were supplied by 10 rope manufacturers and differed widely in type and construction. Most common rope strand constructions included standard strands, Seale, Warrington, Warrington-Seale and Filler-Seale. Results of the survey [ ] Working conditions Working conditions of hoist and drag ropes are quite different. The first cope primarily with bending on rope drums, point sheaves and deflection sheaves, and with tension force imposed by the bucket and its load. The drag ropes are exposed to severe abrasion at the pit crest, and to severe bending and crushing at fairleads, all while coping with tension forces imposed by resistance of the bucket to dragging. Bending of drag ropes at house rollers and at rope drums is of minor importance for their performance. Differences in working conditions result in different wear patterns, which make it feasible to install discarded hoist ropes to further serve as drag ropes. The hoist ropes wear primarily due to fatigue breaks of wires, while the drag ropes are subject to severe abrasion of outside wires, rope deformation and internal wire-strand breaking. The last is often indicated by the reduction of rope diameter. The summary of working conditions for the surveyed draglines is shown in Table 1. For simplicity, Table 1 does not include the data on rope bending at the fairleads, nor at the deflection rollers and house rollers. Similarly, Table 1 does not include the data on drag rope bending (other than that on the rope drum), as its influence on rope life is insignificant in view of severe abrasion and internal wear taking place elsewhere. The following abbreviations are used in Table 1: [D - diameter of rope drum. DP - diameter of boom point sheaves. d - rope diameter x - mean value of the measured parameter. s - standard deviation of x B/d - average bending ratio of ropes B/d =(D+ DP)/2d n - operational safety factor of the rope (rope stength) x (number of ropes) n(bucket load + bucket weight)] In terms of D/d ratio, the working conditions of hoist and drag ropes are similar to that in other related industrial applications. However, the safety factors of the dragline ropes are lower, which requires them to carry relatively large tension forces. The last explains the fact that the life of dragline ropes is low when compared to other industrial rope

Jan 1, 1995

By Axel Preusse

Mining subsidence plays an increasing important role in the Chinese hard coal mining. Reasons for this are a substantial rise of production during the last decade, a dense settlement in many mining regions, the increasing emergence of private residential property as well as a grown environmental awareness. German companies and research institutions hold an over more than 150 years existing know-how in all subjects of mining subsidence engineering. Due to partially comparable preconditions regarding mining depth, mining methods and geological conditions, a close co-operation between German and Chinese mining subsidence engineering experts has been in existence for some years. This German-chinese co-operation is introduced in this paper.

Jan 1, 2007

By John E. Rourke, O&apos

This paper describes some of the results of a project for the design and demonstration of subsidence monitoring systems for underground coal mines. The project was designed to test monitoring systems described in an earlier feasibility report (O'Rourke and others, 1979). General objectives of the project were to develop reliable cost- effective monitoring systems for use above caving- type mining operations, over supported mines, and in urban undermined areas. Topics selected for discussion in this paper include a description of the instrumentation systems, the site conditions, problems of installation, resulting recommendations and an over- view of subsidence performance data obtained. There were some particularly difficult problems of installation to overcome at this site. Some of these could be experienced at any surface or under- ground project, others are probably more directly related to Western coal fields. Almost any subsidence monitoring program may face the following difficulties:

Jan 1, 1982

By David Smith

Construction of a new transportation link frequently requires crossing under an existing highway or railroad. Although traffic diversions may permit a cut and cover structure to be built, ‘zero impact’ tunnel solutions are becoming increasingly popular. The vertical clearance between the new tunnel structure and the existing highway or tracks may be very low; sometimes less than two meters. This leaves little room for error since any ground loss can rapidly translate into surface settlement. Problems can be avoided by maintaining the stability of the tunnel face and by minimizing ground movement around the tunnel lining. This paper examines construction methods that have been used to construct short tunnels with shallow cover, and highlights factors to be considered for future projects.

Jan 1, 2005

By Tim O’Neil

Dressed in black tie and Victorian attire, some 200 people came to Leadville, CO, for a September weekend featuring a National Mining Hall of Fame and Museum (NMHF&M) induction banquet and a scenic mountain train trip to Fremont Pass and the Climax Mine. The 18th annual induction banquet on Sept. 17 began with cocktails and a open house. It was a chance for visitors to tour the National Mining Museum including the new Hennebach Wing, opened in February. The new wing is named in honor of Ralph Hennebach, retired chairman of Asarco. Formerly Leadville Junior High School, the Hennebach Wing encompasses more than1,440 m2 (15,500 sq ft) of floor space in two stories. One prominent feature is a 1923 Wills Sainte Claire touring sedan. Climax Molybdenum donated this first all-molybdenum steel motorcar. Docents were available throughout the museum to give banquet attendees directions and answer questions.

Jan 1, 2005

By Roy L. Wilfong

The linear expansion of high-purity oxides of yttrium, cerium, samarium, europium, and dysprosium was determined by the interferometric method for the temperature range 25° to 1,000° C. Single-crystal magnesium oxide and single-crystal aluminum oxide were used as reference materials. The bulk density and crystal form of the nonreference materials also were determined. The coefficients of linear expansion in the range 25° to 1,000° C were found to be 8.10 x 10-6 for yttria, 12.10 x 10-6 for ceria, 10.81 x 10'6 for samaria (monoclinic), 10.35 x 10-6 for europia (monoclinic), and 8.13 x 10-6 for dysprosia, each given in centimeters per centimeter per degree Centigrade. A detailed investigation of the interferometric technique for measuring thermal expansion in this temperature range was made. The interferometer was found to be a precise tool but only when adequate precautions were taken. These precautions are described.

Jan 1, 1963

By Stephen D. Smith

This chapter summarizes data on crude nonfuel mineral production for the United States, its island possessions, and the Commonwealth of Puerto Rim. Also included are tables that show the principal nonfuel mineral commodities exported from and imported into the United States and that compare world and U.S. mineral production. The detailed data from which these tables were derived are contained in the individual commodity chapters of Volume I and in the State chapters of Volume II of this edition of the Minerals Yearbook. Although crude mineral production may be measured at any of several stages of extraction and processing, the stage of measurement used in this chapter is what is normally termed "mine output." It usually refers to minerals or ores in the form in which they are first extracted from the ground, but customarily includes the output from auxiliary processing at or near the mines.

Jan 1, 1988

By William R. Barton

Anthracite has been mined from the Narragansett Basin of Rode Island and Massachusetts sporadically, and with limited success, for more than 170 years. Beginning in 1974, interest in the coal of the Basin was renewed because of increasing prices and supply uncertainties involving petroleum products. During 1974-77 the Bureau of Mines analyzed 28 samples of Basin coals and conducted washing tests on 20 of them. Results, reported herein, indicate that the coals are low-sulfur, moderate- to high-ash anthracites and semianthracites, suitable for physical preparation to a product generally containing less than 10 percent ash. Additional exploration, sampling and testing will be required to permit appraisal of the potential value of the Narragansett Basin coal resources.

Jan 1, 1977

By S. J. Rodgers

This report presents the results of in-mine studies to determine the severity of dust sources in conventional mining operations. Three underground coal mines were surveyed using gravimetric samplers and GCA RAM-1 continuous dust monitors. Two additional mines were surveyed using only GCA RAM-1 monitors. Data on dust control methods were acquired during the survey, also. The results indicated that cutting/drilling and loading out were the dustiest operations during a conventional mining cycle. Roof bolting, shot firing and product transport were less severe dust sources.

Jan 1, 1983

By John H. Johnson

This report covers research which is directed toward the measurement and control of underground mine diesel emissions. The report consists of three separate reports presented as Sections 1, 2, and 3. Section 1 "Emissions Measurement Apparatus" (EMA 1) discusses the selection and evaluation of instruments and procedures to be used as part of a diesel tailpipe emissions dilution and measurement apparatus. The instruments selected for gaseous pollutants are the Energetics Science Inc.* E.S.I.) 2000 for CO, the E.S.I. 7000 for NO and N02, and the Fuji ZFP5 for C02. Particulate matter is presently measured with the Celesco 1013 Smoke Opacity Meter. The raw exhaust concentration of one of these constituents is used Lo calculate the dilution ratio. Either a modified high range E.S.I. 2000 CO instrument or a Daco Products Cobra C02 instrument can be used, but neither is totally satisfactory. The study also indicated that it may he possible to increase the sample collection time from 15 seconds to the total 30 seconds over which the engine can be loaded without increasing the probability of damaging the vehicle hydraulic systems. Section 2 "The Effect of Fuels, Catalysts and a Filter Trap on Drift Pollutant Concentrations" discusses research in the Mine Air Quality Laboratory. A Wagner ST5D LHD with a Deutz F8L714 engine was used to compare three exhaust aftertreatment devices and a muffler-only system. The effect of these four systems on CO, C02, NO and N02 and on total, soluble, sulfate, and solid particulate matter was measured in the drift and on the LHD. The filter trap successfully reduced particulate matter for both fuels without significantly increasing the concentrations of any of the other constituents. The PTX catalyst was effective in reducing CO, and soluble particulate, but significantly increased N02 and solid and sulfate particulate matter. The Oxy Cat catalyst tested didn't seem to he working on the gases, and it significantly increased sulfate, soluble arid solid particulate concentrations. Section 3 "Diesel/Coal Particulate Matter Characterization by Laser Raman Spectroscopy" covers basic research on a method for determining the percentage by weight of diesel particulate on a filter containing a diesel-coal mixture. Signal-averaged Raman spectra provide the necessary precision. The method developed is non-destructive and uses as-received filters requiring no sample manipulation. Particulate with diesel contents in the range of 10 to 50% by weight have been analyzed with accuracies better than 6%t of the mean value. A number of samples containing diesel-coal mixtures were characterized by the procedures developed and the results are analyzed in light of various spectral and other system variables including coal rank and form and diesel engine operating conditions.

Jan 1, 1982

By E. M. Norris

Phosphate deposits are distributed widely over the earth's surface. Of the known areas of deposit, eight fields are of particular interest because of their vast reserves of high grade phosphatic material and the volume of their production that goes to the world's great consuming areas. These fields, in the order of their present economic importance, are situated respectively in Florida, French Morocco, Kola Peninsula of U.S.S.R., Tunisia and Algeria, Tennessee, Montana-Idaho-Wyoming-Utah, Ocean and Naru Islands in the Gilbert group, and in Egypt. The Rocky Mountain deposits have a comparatively low ranking in the phosphate trade of today, but this field contains one of the largest known reserves of phosphatic material, associated with which are recoverable trace minerals, which are of increasing importance in our national economy. The first discoveries of phosphate rock in the western states were recorded in Cache1 and Rich2 counties in Utah, respectively in 1889 and 1897. Mining operations were begun on these deposits near Montpelier, Idaho, in 1906. During the latter year geological studies of the phosphate beds were started by Weeks and Ferrier of the U. S. Geological Survey. These studies have been continued to the present day by a distinguished roster of the Survey's technicians. As a result of this systematic exploratory program, the Survey has published a series of bulletins, papers, and maps, which provide the mining public with a comprehensive study of the exposed

Jan 1, 1949

By C. Wen

In Huoqiu region of Anhui Province, Fe2O3 occurs mainly in the form of specularite. Besides quartz, the gangue minerals include iron-bearing silicates such as chlorite and sericite which account for about 10% of the total gangue. The separation effect of conventional collectors is poor in the flotation of the minerals, that is, the average grade of iron concentrates is only 60-62%. Using the developed amphoteric collector can successfully realize not only the separation of specularite from various gangue minerals with results of iron concentrate grade above 65% and iron recovery of above 80% but also low temperature flotation at 15°C.

Jan 1, 2012

In eastern China, most of the copper skarn deposits occur in folded troughs which are controlled by the EW-trending faulted fold systems (the Pal-Asian geotectonic domain), and the NNE-trending rift or fault zones (the Marginal-Pacific geotectonic domain), particularly the later. From the north to the south, there are four troughs hosting the main copper skarn deposits in eastern China: the Yanliao Trough, the Yangzi River Trough, The Qiantang-Yuanshui Trough and the Zichen Trough. There are more than 30 copper skarn deposits in eastern China, and ore reserves of each deposit are between 30 to 100 Mt with average grades over 1% Cu.    Most of the large copper skarn deposit-related intrusions are Mesozoic in age (170 to 100 Ma) and were emplaced during the Yanshanian Movement. Outwards from the intrusion bodies, both the skarn alteration and mineralisation show certain patterns of zonation. Mineral assemblages indicate a relatively high oxidisation state during metasomatic alteration and mineralisation. Sulphur isotopic work indicates that most d34S values of the sulphides are between ~4 to 3ë suggesting a common magmatic sulphur source. Fluid inclusion and oxygen isotopic studies suggest that early-stage fluid shows magma-related fluid characteristics although meteoric water was involved during late-stage alteration.

Jan 1, 1995

By Rudolph P. Frizzi

Quality control is essential for augered cast-in-place (ACIP) piles (also known as continuous flight auger (CFA) piles outside the United States) and augered displacement (AD) piles since the pile is constructed below the ground surface out of the direct sight of the personnel constructing and inspecting the pile. ACIP piles are being successfully constructed to support high-rise structures, arenas and stadiums, mass transit systems, and power and industrial facilities. The use of AD pile technology is also gaining ground in the United States, typically utilizing proprietary systems such as Omega (currently utilzed by Richard Goettle Inc., and LG Barcus and Sons, Inc.), Berkel, and DeWal (currently utilized by Morris-Shea). Different types of ACIP/AD pile installation equipment are shown in Figures 1 and 2. ACIP piles are installed into granular and cohesive soils, and soft rock to lengths currently approaching 130 ft (39.5 m), with diameters up to 24 to 36 inches (610 to 915 mm), and sustaining design loads approaching 900 kips (4000 kN). Current AD pile installation equipment in the United States is capable of installing up to 79-ft-long (24 m) piles with diameters ranging from 12 to 18 inches (305 mm to 460 mm).

Jan 1, 2002

This report summarizes the results of the Narragansett Win Projec't's activities during the U.S. Bureau of Mines (BOM) Phase 1, which was transitional from and which followed the National Science Foundation (NSF) Phase which initiated the investigation of New England's potential roil resource. The 960 sq. mile basin is structural and topographic lowland containing 12,000 to 20,000 ft. of terrigenous clastic sediments of late Pennsylvanian age, and which rests on an upper Precambrian and Cambrian basement. The Rhode Island Formation, which is the coal-bearing unit, comprising the bulk of the Pennsylvanian rocks consists, in order of decreasing abundance, of sandstone, conglomerate, silts tone, shale, and coal. In the NSF Phase, 24 drill-holes yielded 17,900 ft, of core; in the BOM Phase I study, 4 drillholes yielded 2,100 ft. of core. Anthracite and semi-anthracite was encountered in beds Up to 30 ft. thick in widely spaced parts of the Basin. The coal, typically very low in sulfur, and a high ash anthracite, won mined in substantial volumes from 1808 to 1959 from shaft and open lit in Portsmouth and Cranston, R.I., and in lesser volumes in Mansfield, Mass. Currently coal is now being mined in Plainville, Mass. as a fuel in the manufacturing of light-weight aggregate from the same quarry that serves as the source of the rock being processed. The structurally complex Narragansett Basin is now known to have a greater extent than earlier since recent drilling by others (Chapter 2) has confirmed our interpretation that the Basin extended offshore south A Boston. The, Basin also extends into Rhode Island Sound to the south. The geological structure is more complex in the southern part of the Basin than in the northern part. Three episodes of folding have been documented on Aquidneck Island and four episodes of faulting have been demonstrated for the Basin as a whole. Relatively less well exposed rock in the northern part of the Basin, increases the difficulty of recognizing and correlating structural episodes in the northern part of the Basin. The Basin his hewn subdivided into six structural domains which appear to have distinctive structural, metamorphic, paleontological and sedimentological differences that mw assist in isolating important events in the evolution of the Basin and its component parts. The tentative structural model recently developed in POP Phase I has important implications for exploration and mining. In the first and second folding stages the coal is mobilized and thickened in the crests and troughs of folds whose axes are horizontal to subhorizontal. While conventional coal exploration and mining methods are not applicable, great thickening in the crests and troughs of large scale structures, which can he defined by geology, geophysics and drilling, may provide compensating advantages. Bedrock over most of the Basin is 0-50 ft., but thicknesses of glacial deposits up to 150 ft. are present locally. Pro-Pleistocene topographic trends are controlled by structure and rock hardness; Pleistocene deposits aligned to the S. F. are superimposed on earlier trends. The southern part of the Basin is mainly dominated by high grade Barrovian metamorphism and plutonism of Permian age, related to the Alleghanian Orogeny. About 300 sq. miles of the 960 sq. mile Basin has been affected. The remaining 660 sq. miles, in the chlorite and subchlorite zones of metamorphism are compatible with the presence of high quality anthracite and semi-anthracite. Illite crystallinity studies begun in the NSF Phase, have been carried out in the BOM Phase l with important results. About ME of the northern Basin is now known to be in the diagenetic (unmetamorphosed) or subchlorite zone and the remainder in the chlorite zone of metamorphism. Mite studies, probably best recording temperature effects, show a generally progressive increase from the NW corner of the Basin near Plainville, Mass. toward the south and southeast. Reflectivity and coal petrography studies, probably best recording pressure and effects related to shearing, indicate a generally opposite pattern. Thus these methods provide powerful tools for the ultimate solution of problems important to coal exploration for coals of higher combustible volatile content and exploitation of these. Due to the complex nature of the coal, chemical data may not he easily used to determine rank. The coals have been tectonically deformed and mineralized. This deformation plus thermal metamorphism have altered the coals, in some cases by producing natural coke. Brecciated coal is often coated with a secondary depositional carbon. The coals' hydroscopic nature and high ash contents are due to the deformed nature of the coal and the presence of this secondary carbon. The stratigraphy and sedimentology of the coal-bearing Rhode Island Formation is similar to described alluvial fan deposits. The non-geological studies al-low three conclusions to be made: 1. A substantial number of areas have been identified in the Narragansett Basin in which mining could be carried out without undue difficulty from a land use point of view. 2. Substantially more than two hundred instances of past or current- mining activities have been identified in the Basin. Many of those are in areas defined as geologically interesting, and may be advantageous From the point of view of future exploration. 3. The map synthesis technique developed for this contract is successful and may easily be adapted to future exploration in its current form and also in its expandable form dealing with unit measurements of one-tenth mile. We recommend that BOM Phase 2 exploration should accomplish the intent of the Congressional language in House Report No. 95-1251, to continue a substantial drilling and geophysics program: "The Committee expects the Bureau to continue studies involved in ascertaining the extent and quality of low sulfur coal reserves in the Narragansett Basin in New England including necessary drilling and geophysical studies. The knowledge of the extent of such deposits is of great importance to this 'energy pour' area".

Jan 1, 1979

By R. Barany

In this paper, closed expressions have been obtained for the frequency spectrum of a Born-Karman square lattice in terms of elliptic and hyperelliptic integrals. This work is part of continuing research by the Bureau of Mines with the thermodynamic properties of metals and minerals. Although other workers have obtained various types of approximations for the general case of the frequency spectrum of a square lattice, no one previously has obtained closed analytic expressions for this spectrum. To understand the optical and thermodynamic properties of crystals, several investigators have studied the distribution of frequencies of normal modes of vibration of the crystal lattice. Born and Karman3 laid the foundation for the theory of lattice dynamics and obtained detailed results for the case of a one-dimensional lattice. Blackman4 used numerical techniques to estimate the frequency distribution of a two-dimensional square lattice. Mbntroll5 analytically determined the frequency distribution of a square lattice for a particular value of the force constants. He also studied the more general problem and obtained some analytic approximations, using the method of moments. However, the calculations by this method were so difficult that it was not always practicable to carry them out. Van Hove6 and Montroll7 studied the nature of the singularities in the frequency spectrum of both a two and

Jan 1, 1962