Search Documents

By Peter Altounyan

The rate of decay of the energy from a hammer blow to a coal mine roof is related to the size and nature of the contacts between the rock being struck and its surroundings The use of this principle as a basis for testing roof condition in South African coal mines has been investigated under a SIMRAC funded project, with the objective of reducing the number of roof falls. ( I ) A prototype instrument having a simple numeric display related to the energy decay rate (the Acoustic Energy Meter) was constructed and used to carry out surveys at mines covering the range of coal mine roof geology and condition. The equipment was simple to use and provided excellent discrimination between visually intact roof and less stable conditions, once the normal/abnormal threshold had been established for a given site. Areas of potential roof failure were identified close to roof slips and igneous dykes, and confirmed in areas of visible deterioration. Directional stress effects on roof condition were also identified at some sites, with consistent differences in readings obtained depending on the direction of drivage. Repeat surveys also indicated areas where roof conditions were deteriorating with time. Based on the success of the prototype, a hand held version of the instrument. has been developed to a specification from Anglo Coal. This incorporates a simple 'traffic light' green / amber/ red display, making the device suitable for routine use by mine operatives This version is now undergoing trials at an Anglo Coal mine. It is concluded that the Acoustic Energy Meter shows great potential as a test instrument providing output which relates to the stability of the immediate roof.

Jan 1, 2000

By D. L. H. Bulbring

The removal of a cylindrical core from thick-wall sections for creep analysis by the relatively new Weldcore® process represents a very exciting methodology for obtaining more representative creep damage data from large engineering structures. The cylindrical core that is removed, representing about 60% of the wall thickness, leaves a substantial removal site that needs to be repaired. This paper presents data pertaining to taper Friction Hydro Pillar Processing as an alternative repair technique for filling the core removal site. Process parameters were evaluated with special attention being paid to the effect of downward force on process response variables, weld defects, and mechanical properties of 10CrMo910 steel. Process temperature and torque response as well as total process energy input were also considered. This paper also assesses the static and dynamic performance of this repair technique. The influence of a varying downward force and the occurrence and position of discontinuities were quantified. Downward force was shown to have the most notable effect on weld joint dynamic performance and was found to be related to the process temperatures achieved in close proximity to the weld interface.

Jan 1, 2013

By D. Blackwell, W. R. Reed, G. Ross, S. Peters, M. Shahan

Dust collectors for roof bolting machines generally use a dry box to collect the roof bolting material. Recently, an underground mining operation converted a dry box dust collector to a wet box dust collector with a unique exception from MSHA for testing purposes. Water is routed to the roof bolter from the main water line of the continuous miner. The wet box utilizes a water spray to wet the incoming material. Testing was conducted comparing the two different collector types. Respirable dust concentrations surrounding the roof bolter with the different collection boxes were similar. The main difference in respirable dust concentrations occurred when cleaning the dust boxes. The average respirable dust concentration during cleaning of the wet box was 0.475 mg/m3, and during the cleaning of the dry box the average respirable dust concentration was 1.188 mg/m3. The silica content of the roof material was high, ranging from 28.9% to 52.7% during this study. The results from this study indicate that using the wet box as a collector reduced exposure to respirable dust up to 60%when cleaning the collector boxes. INTRODUCTION Currently, the dry vacuum dust collection system is the standard dust collector on roof bolters in underground coal mining. It has been proven to be an effective dust control to prevent roof bolter operators’ overexposure to coal mine respirable silica dust during roof bolting operations [Potts eta l, 2011 and Colinet, 2013]. The dry collection system works as follows: drill cuttings are vacuumed into the precleaner. The precleaner dumps oversized material onto the mine floor while undersized material enters the dust box via vacuum airflow produced by a blower. The cuttings entering the dust box are either deposited on the floor of the dust box or into a dust collector bag. The vacuum airflow leaves the dust box through a final filter which removes any small particles from the airflow. Figure 1 shows the internal view of two dry collection system boxes; one that does not use the dust collector bags and another that uses the dust collector bags. Dust collectors that use dust collector bags to contain material inside the dust collector box have been shown to provide better protection to roof bolter operators than dust collectors that do not use the bags [Listak and Beck 2008]. The dry collectors are very efficient at reducing respirable coal mine dust exposure from roof bolting activities. Recently, Blue Mountain Energy’s Deserado underground coal mining operation, outside Rangely, CO, made a modification to the dry collector system to convert it to a wet collector system with a unique exception from the Mine Safety and Health Administration (MSHA) for testing purposes. The wet collector system still uses a vacuum system to pull material from the vertical roof bolt hole, but incorporates a water spray nozzle located inside the dust box to wet the incoming material. The flow through the nozzle ranges from 1.9–7.6 lpm (0.5–2.0 gpm) at 0.69 MPa (100 psi). The conversion to the wet collector system removes the precleaner and the cyclones inside the dust box. The wet material (sludge) then empties through a specialized valve in the bottom of the box. The final filter is still used to prevent respirable dust from leaving the dust box through the exhaust. During operation, the wet collector dust box is opened and hosed clean after roof bolting every place. After every two entries the final filter is changed out. Figure 2 shows the inside of the wet collector box.

Jan 1, 2019

By N Clarke, R Dineen, W Jones

The Mt Lyell copper mine in western Tasmania has discharged acid drainage (AD) into the Queen and King Rivers and Macquarie Harbour for over a century. Presently, dissolved copper loads of about 1000 tonnes per annum and dissolved aluminium loads of >2000 tonnes per annum are contained in the AD, which is derived from underground workings (~60 per cent) and historic waste rock dumps (~40 per cent). Flows vary from about 100 L/s during dry periods, to >400 L/s during the wet winter. The site is presently operated by Copper Mines of Tasmania (CMT) who are not responsible for the acid drainage generated from the mine site. Although western Tasmania is famous for its mining history, tourism and aquaculture have emerged as the new industries on the West Coast, with a major tourism railway (the Abt) recently opened along the banks of the Queen and King Rivers. The emergence of these industries in a æclean greenÆ Tasmania has resulted in a strong community and government push to remediate the acid drainage. Remediation investigations and efforts at Mt Lyell were initiated by the Department of Primary Industries, Water and Environment (DPIWE), previously known as DELM, in 1995, and have included the quantification of environmental impacts arising from the AD, and the investigation and costing of potential remediation options. A primary focus of the work has been to identify cost-neutral options which recover metals from the AD in a saleable form to help defray on going treatment costs. This paper summarises these activities in generally a chronological order, highlighting findings of the program that are potentially applicable to other acid drainage sites.

Jan 1, 2003

The following is a summary of some of the companies that were exhibiting their products and services at MINExpo INTERNATIONAL 2000. Atlas Copco develops, manufactures and markets rock drilling tools, tunneling and mining equipment, and surface and geotechnical drilling equipment. The company provides a line of drilling products, including production drilling rigs, rock reinforcement bolts and rock drills. Atlas Copco’s Boomer is a series of high-capacity drill rigs that provides economy, production capacity and reliability

Jan 1, 2000

The 105th Annual General Meeting of The South African Institute of Mining and Metallurgy was held in the J.C. Lemmer Auditorium, SA National Museum of Military History, 22Erlswold Way, Saxonwold, Johannesburg on Thursday, 8thAugust, 2002. Welcome The President extended a special welcome to the guests and representatives of our sister institutes and other associations. Also to recipients of awards, senior members of industry, Honorary Life Fellows, Past-presidents, our Members and other guests, among them the following: Mzolisi Diliza, Chief Executive, Chamber of Mines of South Africa Dawie van Wyk and Rod Tucker, Vice-presidents, The Geological Society of South Africa Vaughan Townsend, President, Institute of Certificated Mechanical and Electrical Engineers, South Africa Karel Landman, President, Institute of Mine Surveyors of South Africa Frik Grobbelaar, South African Colliery Managers? Association Pierre Ballot, President, South African Institute of Electrical Engineers Trueman Goba, President, South African Institution of Civil Engineers

Jan 1, 2002

By Ruth F. Brinkley

This report is the 18th of a series of reports originally issued annually, and more recently bienially, to acquaint the public with the work of the Federal Bureau of Mines in explosives technology. Part I reviews briefly the overall activities during fiscal years 1957 and 1958.4/ Part II presents in abstract form the publications prepared by the Bureau that appeared during the period.5/

Jan 1, 1961

By P. P. Sinha, D. N. Bhatia, B. R. Ghosh, R. K. Gupta

Medium carbon, low alloy, high-strength steels containing Ni, Cr, and Mo are used for the fabrication of various types of high-strength fasteners required for launch vehicle structures. Cold heading properties and response to hardening and tempering are the essential requirements of the material for fabrication and application, respectively. Combining these two requirements is essentially warranted in high-strength fastener-grade steels. Cold heading properties require ductility, which can be achieved through spheroidizing treatments. In the absence of a suitable spheroidizing cycle for medium carbon 3.8 Ni, 1.8 Cr, 0.3 Mo steel, experiments were carried out with a theoretical understanding of the alloy system. This paper presents the experiments and results obtained after a spheroidizing treatment, which was carried out to optimize the process. Hardness measurements were carried out and microstructural studies were conducted to assess the spheroidization process and to determine the optimal spheroidization parameters.

Jan 1, 2007

By C J. Kruger, E le Roux

Anglo American Platinum has adopted a strategy of Best Practice Principles (BPP) for sampling, mass measurement, analysis and metal accounting for more than a decade now. When new plants are designed, the most suitable sampling equipment and sampling protocols are implemented and material flows and plant layouts are designed around sampling strategies. A few years ago, a crushing plant for a high-grade matte stream was commissioned.The design called for the high-grade material to be crushed to 95 per cent passing 2 mm and the design allowed for a single cutter primary Vezin sampler, increments taken from a gravity flowing stream at regular intervals, whilst filling a tanker for the pneumatic offload at our base metal refinery. This was a single point of sampling and analysis that would measure the wanted output from our smelting complex and the input to our refineries. In addition, the design incorporated the functionality to collect increments in an ‘interleaved’ fashion from the Vezin sampler for internal precision checks.The metal accounting strategy for Anglo Platinum is the ongoing measurement of all inputs, outputs and stock levels for all our operations for platinum group metal (PGM) and base metal (BM) content. Included are yearly stocktakes, usually done on 1 February every year, across the smelters and refineries (at least the base metal refinery). A trend was developing in the accounting period immediately following the introduction of the new crushing and sampling facility, whereby the absolute difference between the physical stock and theoretical stock (PGMs predominantly) increased for the two respective sites on an ongoing basis. The smelter (sender) showed an increase in physical stock compared to the theoretical stock and the base metal refinery (receiver) showed that their theoretical stock increased against their physical stock. Because of this anomaly, an additional stocktake was held in September for the period in question and it was confirmed through the physical stock measurement results, that the PGM accounting problem was indeed pointing towards the evaluation of the high-grade matte stream.This paper showcases parts of the process that took place to explain the poor accountabilities for the respective sites. Previous results from the sampler ratification process (of the interleaved sampling design) were analysed again, a physical inspection was carried out on the sampling system again and the sampler performance was monitored (quality control parameters) for the period.From these investigations, it was found that airflows present inside the Vezin introduced the sampling bias and a change in sampling protocol was introduced as well as physical changes to the sampling equipment were made to eliminate the airflow and thus the bias conditions significantly. The accounting period which followed, after a phased upgrading process, showed that the accounting between our smelter and base metal refinery had been restored to within statistical limits (difference between physical and theoretical stock below five per cent relative to theoretical stock).CITATION:Kruger, C J and le Roux, E, 2017. Pitfalls in Vezin sampling for finely crushed materials, in Proceedings Eighth World Conference on Sampling and Blending , pp 151–158 (The Australasian Institute of Mining and Metallurgy: Melbourne).

May 9, 2017

By Wightman D, Hoyle M. W H, Peters W. S

The Radio Hill nickel-copper deposit is located 30 km south of Karratha. It is a new discovery in an area where similar mineralization had been previously discovered at Mt. Scholl and Ruth Well. Radio Hill is the first massive Ni-Cu sulphide deposit of economic significance to have been located in the Western Pilbara.Preliminary studies indicate that the sulphide mineralization occurs within gabbros, pyroxenites and peridotites of a basic igneous cumulate layered sequence. Primary sulphides have been subsequently remobilized and concentrated as stringer and massive mineralization. This is tentatively attributed to the intrusion of a further gabbroic body.The deposit appears to be of the gabbroic association type with a Ni:Cu ratio varying from 1:4 in the outer parts of the mineralized envelope to 1:0.9 towards the central zones. In drill core observations, chalcopyrite surrounding pyrrhotite was noted in many instances. Drilling has so far delineated a body developed over a strike length of 600 m and a horizontal width of up to 25 m. The mineralization plunges 20° to the southwest with a southerly dip varying from 75° in the west to about 20° - 30° in the east.The deposit is a leaf-shaped ore zone, plunging southwest from a vertical depth of 17 m in the north to 300 m in the south. The massive sulphides occur as lensoid masses within this zone. A geological resource of up to 2.5 million tonnes at 1.5 per cent Ni and l.4 per cent Cu is indicated.The predominant sulphides are pyrrhotite, chalcopyrite and pentlandite, with significant cobalt, platinum group metals and gold. Tellurides of Pd, Bi and Pb were detected by scanning electron microprobe within the pyrrhotite and other trace metals include Zn and native tin. Massive magnetite is sometimes associated with the massive pyrrhotite intersections.A test on one composite massive sulphide sample showed that pyrrhotite is present mainly as the non-magnetic hexagonal variety and only 10 per cent is present as magnetic monoclinic pyrrhotite.The deposit has no surface expression and its identification was based mainly Oil drilling targets generated by geophysical methods. No secondary minerals have been observed in association with the primary sulphides, even though the deposit is only 17 m below surface in the northern part.

Jan 1, 1987

By J. B. Clark

In multiphase ternary diffusion studies, plots of the variation bf the composition on the isotherm constitutes one of the most effective methods of presenting experimental results, especially if such plots are made in a manner which relates the composition path on the isotherm with the diffusion layer structure in the couple. Unfortunately, if different conventions for plotting are used serious misinterpretations occur readily, causing apparent disagreement between investigators who actually share the same viewpoint. A common convention for mapping these diffusion paths is needed at this time because with the increasing use of the electron-probe X-ray microanalyzer, a much greater number of ternary diffusion studies can be expected in the near future. In an effort to prevent unnecessary confusion in the future litera- ture, a convention for these plots is proposed, as outlined below. A hypothetical example of the use of these conventions is given in Fig. 1 where the path of composition through the diffusion structure of the 100 pct A/50 pct B, 50 pct C couple is plotted on the appropriate isotherm of the ABC system. The lower case letters relate the region in the diffusion layer structure to the appropriate composition on the ternary isotherm. 1) The diffusion path is plotted on the isothermal section corresponding to the diffusion temperature of the couple. 2) The terminal compositions of the plotted diffusion path are the initial compositions of the couple halves—provided infinite boundary conditions are maintained. If, in either couple half, infinite conditions are not maintained, then the path terminates at the composition of the exterior surface of the couple. If, at this surface, the composition varies with time or if the plotted path is time dependent, then the diffusion time should be noted beside the plotted path. 3) A solid line crossing a single phase field (e.g., line a-b in Fig. 1) denotes an existing layer of that phase in the diffused couple. 4) A dashed line crossing a two-phase field parallel to the tie lines (e.g., line g-h) represents an interface between the two phases with interfacial compositions designated by the ends of the tie-line. The line represents no spatial extent. 5) A solid line crossing a two-phase field so as to cut tie lines (e.g., line b-c or line j-k) represents a locally equilibrated columnar two-phase layer. The solid line should cut those tie lines which correspond to the lateral interfacial equilibria along the columnar

Jan 1, 1963

By W. Breytenbach

Traditionally, dithiocarbonates (xanthates) have been the preferred collectors for the flotation of platinum-bearing sulphides. However, collector development has led to trithiocarbonates (TTC), which have proven to be very effective bulk sulphide collectors. The interest in TTC flotation behaviour is currently focused on the interaction of these collectors with other collectors, specifically the dithicarbonates. Batch-flotation research has shown synergism to exist among dithiocarbonate, dithiophosphate and trithiocarbonate collectors. Increased sulphide recoveries, both for the first-minute and final concentrate, were realized using mixtures of these collectors relative to the standard.

Jan 1, 2003

These proceedings consist of an introduction and four descriptive papers. The first paper is an update on fire protection for large haulage vehicles, the second paper is concerned with improved visibility systems for large haul- age vehicles, the third paper is on improved ladders for large haulage vehicles, and the fourth paper is concerned with large haul-age vehicle operator training systems.

Jan 1, 1980

By Harry E. Tuff

"This paper is based data obtained by the Bureau of Mines from some of the principal mine operators in Pennsylvania, in the course of a study conducted in cooperation with the U. S. Forest Service, with regard to economies that might be effected in the selection storage, and preparations of timber particularly treatment with preservative to prolong its life.The Pennsylvania anthracite region, considered as a single mining district is by far the largest user of mine timber of any mining district, either coal or metal, in the United States, and the bituminous districts of Pennsylvania rank second. The present annual consumption of mine timber by the coal-mining industry of Pennsylvania probably exceeds 100,000,000 cubic feet annually.In 1919, Pennsylvania produced, in round figures, 145,300,000 tons of bituminous coal, 86,200,000 tons of anthracite, and 5,400,000 tons of iron ores. If it be assumed that the bituminous coal mines required 0.33 cubic feet, anthracite mines 0.7, and iron mines 0.9 cubic feet per ton mined the timber requirements were bituminous. 47,950,000; anthracite, 60,340,000; iron mines, 4,860,000 or a total of over 113,000,000 cubic feet.The average cost of round mine timber in the anthracite region in 1905, was, according to the U. S. Forest Service, 6.6 cents per cubic foot, and $15.00 per 1000 board feet for sawed timber. The present cost Las advanced to 27.5 cents per cubic foot for round timber, delivered to the mine, of which cost 57.4, represents freight charges."

Nov 1, 1923

By L. M. Sekhukhune

The atmospheric leaching of copper-bearing matte by acidic ferric chloride solution was studied at the laboratory scale. The aim was to achieve maximum copper and nickel recovery by investigating the mechanisms of leaching, as well as identifying the effect of temperature, and concentration of ferric chloride and oxygen. Djurleite (Cu1.96S), hazelwoodite (Ni3S2), and Ni alloy were the primary phases detected in the matte. The quantitative composition of the matte was Cu 31%, Ni 50%, S 13%. Fe and Co constituted 2%, with platinum group metals (PGMs) accounting for 0.5%. A maximum nickel extraction of 98% was achieved using two-stage oxidative leaching at 90°C and 11 g/L Fe3+ as compared to 65% under non-oxidative conditions. A copper extraction of 99% was achieved in the first 45 minutes using two-stage non-oxidative leaching, and copper was recovered from solution by cementation. Three processes took place simultaneously throughout the leaching process, namely: dissolution, cementation/ metathesis, and oxidation. The leaching process was found to be diffusioncontrolled.

Jan 1, 2014

By I. Gaballah

Cadmium is toxic to plant, animals and humans. The council directive of the European Communities No 8315 13lEEC has fixed an upper limit of 200 ppb for the release of cadmium in industrial effluents. The conventional method of neutralization/prccipitation ( NIP ) is inefficient to reach this limit. The objective of this study is to test the efficiency of the trees modified bark to remove cadmium cations from industrial effluents after the conventional treatment by NIP. Laboratory scale tests with synthetic solutions show that the cadmium removal depends upon pH and initial concentration. About 99.9 %, 99 % and 96 % of the metal are removed from synthetic solutions containing 10, 100 and 1000 ppm respectively. Pilot plant trials ( 1 m3 ) with an industrial effluent bearing about 500 ppb of cadmium lead to the almost complete elimination of the cadmium ( final concentration is lower than the analytical detection limits < 20 ppb ).

Jan 1, 1994

By J. L. Kohler

This final report on Bureau of Mines Contract J0348005 presents the results of an investigation into the development of a Management Information System (MIS) for underground coal mines. The motivation for the research is the unrealized potential for increasing safety and productivity of the well developed mine monitoring system technology. The intent of this project was to examine the information issues, various design aspects of an integrated monitoring/MIS, and associated application concerns, such as the impact of this technology on safety. The work performed on this contract used mine ventilation as a prototypical example. The report is presented in five chapters and six appendices. In addition to the introduction and conclusions chapters, one chapter deals with ventilation MIS system requirements; another with the formulation of a knowledge-based expert system (KBES) structure to implement the integrated ventilation monitoring/MIS system, and one on the health and safety implications of the system. The appendices present details of the KBES system application with an example using a mine ventilation simulator (PSU/MVS). An important conclusion is that a KBES formulation of an integrated monitoring/ MIS for coal mine management is feasible and desirable.

Jan 1, 1986

By Zhouhua Jinag

The attempt has been made to manufacture high nitrogen austenitic stainless steels by pressurized electro-slag remelting furnace with maximum nitrogen pressure of 7MPa. To obtain high nitrogen content in steels, the compound electrodes with different nitrogen sources (FeCrN, Si3N4) were prepared. Using the Si3N4 as the nitrogen alloying source, the silicon contents in ingots were prone to be out of the specification range, and the electric current fluctuated greatly and the surface qualities of the ingots were poor. The surface qualities of the ingots were improved using FeCrN as nitrogen alloying source. The sound and compact macrostructure ingot with the maximum nitrogen above 1.0wt% could be obtained. A series of high nitrogen austenitic stainless steels have been successfully developed by this method. The mechanical and pitting corrosion resistance properties of high nitrogen austenitic stainless steels were investigated. The results show that the steels exhibit excellent mechanical and pitting corrosion resistance properties.

Jan 1, 2009

By C. E. Van Orstrand

An intrusive body is a mass of igneous rock that has migrated upward, presumably from great depths. Great variations in form, composition and depth of burial occur. It is not proposed in this paper to go into all of the details of the problem. Instead, it mill be assumed here that the intrusive has the form and characteristics represented in Fig. I. According to W. 11. Emmons minerals are not deposited in appreciable quantities below the "dead line." Important amounts of ores of virtually all metals may be found around summit cupolas, but only gold, copper and zinc (in limited quantities) are usually associated with trough cupolas. Most students of ore deposits agree that temperature changes are largely instrumental in precipitating many ores in the "hood" and that the difference in temperature between the intrusive and that of the country rock may be the chief factor in determining the mineralogy of a deposit. A problem then of some interest is to correlate the principal physical features of the intrusive with the phenomena of heat conduction as evidenced by the cooling curves and the isothermal surfaces. Mathematical Theory In order to show the possible application of heat conduction to the interpretation of the processes of metalliferous deposition associated with intrusives, it will be as- sumed that the intrusive is a large par-allelopiped of dimensions, 2l, 2m, 2n. The equation that represents the flow of heat from the parallelopiped into country rock (v = o, 1 = o), which has the same thermal properties as the intrusive, is2,3 l-x v I FT 2 [2 2 — l-x m — y — m — y n — z In this equation, the origin, x = o, y = o, z = o, is at the center of the parallelopiped. v = temperature at point x, y, z, time 1. v, = initial temperature throughout the intrusive, 1 = o. k = coefficient of thermal diffusivity. a, ß, y are variables of integration. Put n = m in Eq. I, and we have v I [2/5 [2I-x 2 — l-x m — y 2 2 2 kt 2 20xt e-a2da ebrdß

Jan 1, 1946

By C. E. Van Orstrand

An intrusive body is a mass of igneous rock that has migrated upward, presumably from great depths. Great variations in form, composition and depth of burial occur. It is not proposed in this paper to go into all of the details of the problem. Instead, it mill be assumed here that the intrusive has the form and characteristics represented in Fig. I. According to W. 11. Emmons minerals are not deposited in appreciable quantities below the "dead line." Important amounts of ores of virtually all metals may be found around summit cupolas, but only gold, copper and zinc (in limited quantities) are usually associated with trough cupolas. Most students of ore deposits agree that temperature changes are largely instrumental in precipitating many ores in the "hood" and that the difference in temperature between the intrusive and that of the country rock may be the chief factor in determining the mineralogy of a deposit. A problem then of some interest is to correlate the principal physical features of the intrusive with the phenomena of heat conduction as evidenced by the cooling curves and the isothermal surfaces. Mathematical Theory In order to show the possible application of heat conduction to the interpretation of the processes of metalliferous deposition associated with intrusives, it will be as- sumed that the intrusive is a large par-allelopiped of dimensions, 2l, 2m, 2n. The equation that represents the flow of heat from the parallelopiped into country rock (v = o, 1 = o), which has the same thermal properties as the intrusive, is2,3 l-x v I FT 2 [2 2 — l-x m — y — m — y n — z In this equation, the origin, x = o, y = o, z = o, is at the center of the parallelopiped. v = temperature at point x, y, z, time 1. v, = initial temperature throughout the intrusive, 1 = o. k = coefficient of thermal diffusivity. a, ß, y are variables of integration. Put n = m in Eq. I, and we have v I [2/5 [2I-x 2 — l-x m — y 2 2 2 kt 2 20xt e-a2da ebrdß

Jan 1, 1946