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By Min Chen, Qinghua Liang, Weishan Yan, Yuan Feng, Shigang Wang

Various coal mine robots (CMRs) and unmanned aerial vehicles (UAVs) are implemented to explore unknown mines for improving the safety and efficiency of mining. It is challenging for CMRs and UAVs to achieve accurate positioning due to the absence of GPS, poor lighting conditions, and similar geometric features in complex mine scenes. LiDAR-based localization and mapping methods are admittedly more accurate than others, while long-time running in large-scale scenarios will also introduce non-negligible cumulative errors. This study presents a semantic-aided LiDAR simultaneous localization and mapping (SLAM) with loop closure, which leverages the uniqueness of mine intersection structure to establish stable semantic loop closure. Specifically, we propose a semantic intersection descriptor of translation and rotation invariance, which encodes 3D point clouds of the same intersection from different positions and viewpoints into a unified image. By using the semantic descriptor, we can construct a constant loop constraint when the same intersection is revisited from different directions to reduce cumulative drift. We provide experimental validation using large datasets collected in two large underground mines, namely, a simulated Edgar mine deployed in ROS Gazebo and a public underground mine dataset provided by ETH. Experimental results show that the proposed method has higher localization accuracy and outperforms the existing LiDAR-based SLAM strategies.

Aug 10, 2023

Mine drainage and mine reclamation are topics of major interest to the mining industry, federal and local governments, and the general public. This publication and its companion three volumes are the proceedings of a conference held in Pittsburgh, Pennsylvania, April 24-29, 1994. There were twelve sessions (69 papers) that dealt with mine drainage, including modeling, geochemistry, prediction, treatment, control strategies, characterization, hydrology, and case studies. These sessions comprise volumes 1 and 2. The six sessions (34 papers) that dealt with reclamation and revegetation of disturbed lands are included in volume 3. Volume 4 includes the six sessions (34 papers) that dealt with such topical issues as fires at abandoned mine sites, subsidence, hydrology, mine wastes, and policy. Poster session presentations are represented by 49 papers and 92 abstracts that have been placed in the back of volumes 2, 3, and 4, consistent with the subject of that volume.

Jan 1, 1994

By W. P. Campbell

Foreword At the outset, it should be stated that this paper does not pretend to present a panacea for the ills that 'frozen' wells are heir to, but rather is an attempt to bring to the attention of those whose special concern it is, a little theory and some facts, which have been brought to light recently, in connection with the problem of 'freezing' as it applies to naphtha-producing wells in the Turner Valley field, and to draw some conclusions that follow from the facts discovered. It should also be stated that the investigation is not to be regarded as in any sense complete, but in progress. Doubtless new facts will be brought to light from time to time which may modify present ideas on the subject, but whether favourable or contrary, these will be welcomed, as the purpose of the Department is to secure as complete information as possible of the factors contributing to 'freezing', since this must be the first step to an intelligent attempt to remedy or prevent its occurrence, if such can be done. It is possible, too, that the cause or causes of freezing may not be the same in all cases, but whether this be so or not will have to be determined later as new information comes to hand. Introduction One of the worries which must constantly confront the operators of gas-naphtha producing wells in Turner Valley-although all, fortunately, have not met with it-is the possibility of the occurrence of what is commonly called 'freezing' (going off production).

Jan 1, 1930

Introduction Aggregate mining impacts on water resources are a source of concern to local governments. To evaluate those impacts, the Minnesota Department of Natural Resources conducted a four-year study at three gravel pits (two alluvial and one beach-ridge) and five quarries (flat-lying Paleozoic limestone). This research provides the first comprehensive look at aggregate mining impacts on ground-water systems in Minnesota. The results will be used by government officials making permitting decisions about aggregate operations and by responsible owners of aggregate mines as they plan their operations to avoid conflicts with neighbors and with resources dependent on ground water and surface water. Natural aggregate (crushed stone, sand, and gravel) is a vital part of our economic infrastructure in Minnesota. Aggregate is used for road and bridge construction and in a variety of building materials. In 2003, the value of construction sand and gravel and crushed stone in Minnesota was approximately $245,000,000. As Minnesota’s economy continues to expand, the demand for aggregate will continue to grow. Sand and gravel pits are located in every county in Minnesota. In 1990, the Minnesota Department of Natural Resources, Division of Minerals (DNR Minerals), estimated the number of active and inactive operations at 1500 with the view that this number was likely too low. Quarries for mining limestone, dolomite, sandstone, and hard rock (granite and quartzite) are found in 34 counties. A 1990 DNR Minerals inventory found 165 active operations, 88 percent of which were limestone quarries (Nelson and others, 1990). That same inventory counted 1,367 inactive operations, 70 percent of which were limestone quarries. Aggregate mining is an extractive use of resources: mining alters the landscape and its natural hydrologic system. When a new pit or quarry is proposed or when an existing operation needs to expand, local governments and citizens typically have many questions about the impacts mining might have. Local governments, which are responsible for reviewing these operations, rarely have the budgets to hire experts to evaluate potential impacts of quarry and gravel pit proposals. The Minnesota Legislature’s Aggregate Resources Task Force identified that local government units (LGUs) often lack the expertise to assess ground-water models (Southwick and others, 2000).

Jan 1, 2007

By Peter B. Knuckey

1, Introduction Location Kalengwa mine is located in the North Western Province of Zambia, 402 kilometre by unpaved road to the west of Kitwe, which is roughly in the centre of the Zambian Copperbelt, well known as one of the world's centres of copper mining. Its position is illustrated on the map of Africa in Figure 1 and on the map of Zambia in Figure 2. It is a mine of Roan Consolidated Mines Limited whose other properties, Mufulira, Luanshya, Chambishi and Chibuluma Mines, are all located on the Copperbelt. It is managed by the Chibuluma Division of the company. The rate of production from Kalengwa will vary from 12 000 to 17 000 tonnes of saleable copper a year over the next six years. Kalengwa did not exist as a place until the first prospecting parties and later the mine became established and the early working population was recruited entirely from small villages in the surrounding area as much as thirty miles away. The mining area consists of fourteen mining locations amounting to 3.35 square kilometres and the land may be used for any purpose connected with mining, including housing, wood cutting and other utilities. The whole area is, except for minor undulations, a fairly flat plateau with main rivers running from north to south and flood basins known as "dambos" located in a general east west direction. Vegetation is, with the exception of the grassy dambos, temperate forest with relatively light undergrowth. Game of great variety is prolific, as is the associated tsetse fly.

Jan 1, 1971

By J Koshy, M Ralph, P Foley

Mining in the state of Western Australia (WA) formally commenced in the 1840s, and over the ensuing 180 years has evolved to be the epicentre of the Australian mining industry and a significant contributor to the national economy. The lithology of WA is replete with mineralisation that hosts uranium and ‘critical minerals’ required for the global renewable energy sector. The state’s first uranium mine is under development, and high levels of activity are occurring in the state’s nascent critical minerals sector, with 168 WA-based companies pursuing rare earth-bearing minerals, 51 of which are actively drilling on their tenements. WA’s mineral deposits typically contain levels of the naturally occurring radionuclides (NORs) thorium-232 and uranium-238 that are elevated above the global crustal average. Workers are exposed to NORs during the mining and mineral extraction processes, and radiation doses that exceed applicable exposure standards may eventuate. The research traces the history of worker radiation doses from 1977 to 2020, finding the maximum dose was 163.4 mSv, more than eight times the current derived annual dose limit. Whilst 93.5 per cent of all workers received doses of less than 5.0 mSv per annum, the potential for elevated doses is ever-present as witnessed by 10.3 mSv reported in 2009/2010. The increase in activity coincides with a revision of the dose coefficients (DCs) associated with the intake of radionuclides. The research evaluates the revised DCs and forecasts doses from inhalation of radioactive dusts will nearly double, and lead to workers receiving doses exceeding 5 mSv for the first time since 2009/2010. The research finds that the current regulatory framework is fit-for-purpose. However, inter-agency relationships, and the capacity of the regulator to effectively regulate the current and future number of mining operations is questioned. The mining industry is vulnerable to capability and capacity constraints – but has failed to respond to issues in relation to competent radiation safety officers first raised by the Winn Inquiry (Winn, Mathews and Tough, 1984). Disconcertingly, monitoring of worker exposures to NORs reached a nadir in 2021, raising questions as to the veracity of worker doses reported to the regulatory agency. The research recommends personal dust sampling be prioritised.

Apr 16, 2024

The Black Hills Mineral Atlas briefly summarizes all pertinent date available on the mines and mineral deposits in the Black Hills that have been explored, developed, mined, or located. The purpose of the atlas is threefold: First, from available date the general potentialities of the Black Hills region can be determined, although it is not possible to calculate actual ore reserves; second, it will provide the necessary basic information regarding a given property or commodity for further detailed study; and third, the compilation is a comprehensive directory of Black Hills deposits.

Jan 1, 1954

By A Valero, G M. Mudd

There is active debate and research around the most suitable indicators to assess the sustainability of mining. The most common approach is to report a range of data for a given mine site (or less preferably, a company total), such as inputs, outputs, benefits and potential costs. The most popular protocol in use (and growing rapidly) is the Global Reporting Initiative (GRI). However, these measures are numerous and still do not allow a single over-arching indicator to be developed. Other measures, such as known mineral resources over time, do not account for critical challenges such as declining ore grades, increasing wastes and poorer quality ores or more difficult mineralogy. By adopting a thermodynamic approach to sustainability, through the concept of æexergyÆ, it is possible to incorporate into a single measure the effective quality of mineral resources. Exergy involves the assessment of the minimum energy costs involved in producing a mineral resource with a specific chemical composition and concentration from common materials in the environment. The exergy of a mineral resource is evaluated from mineralogic composition, concentration (or ore grade) and, of course, quantity, by multiplying the unit exergies with the tonnes of the resource produced (or consumed). Since exergy is a thermodynamic quantity (ie energy or joules), it is additive across different minerals, such as iron ore to gold to copper or even oil and gas or coal û making it an ideal indicator to assess mineral resource sustainability at the industry scale rather than the individual mine scale. This paper briefly outlines the theoretical basis for exergy, and then presents a range of commodity case studies showing the application of exergy to the Australian mining industry. Overall, the usefulness of exergy is clearly demonstrated for use as a broad indicator of the sustainability of mineral resources at the national or even global scale.

Jan 1, 2009

By Cam Thomas

The initial application for reflectorless laser technology was for profiling rock faces to determine front row burden and improve flyrock control and airblast. Over the past fifteen years a number of laser systems have been developed for general ground modeling purposes and GPS offsets, but these advances have yet to gain common acceptance in construction, mining and quarry blasting. This paper will outline a number of applications for reflectorless laser technology, including the latest method for rock face profiling, mapping, and 3-D modeling to calculate available and excavated rock volumes. Drilling deviation measurements will be presented in conjunction with rock face profiling to demonstrate how this information can be used to improve blast results. In complicated excavations, the actual quantity of rock excavated for payment purposes and the amount of overbreak can be very controversial. Procedures to calculate these volumes using laser technology will be outlined and comparisons will be made between these results and traditional techniques.

Jan 1, 2003

By T. Kunitake, H. W. Paxton

The self-diffusion coefficient of chromium in various alloys in the iron-chromium system has been measured. A variation in Dofrom 10-4 for pure chromium to a maximum of 102 near 60 pct Cr appears with a range of activation energy from about 50 to 80 kcal per mol. The general pattern of behavior observed is not consistent with present theories of diffusion by a vacancy mechanism. Suggestions are made for further clarifying experiments. RECENT work on the self-diffusion of chromium,' ?-uranium2-4 and ß-zirconium,23, 26 has indicated that these elements have very low Do (10-3 to 10-4) compared to that conventionally expected for vacancy diffusion. Pound et al.5 have suggested that this may be due to ring diffusion being operative, and have proposed a model which gives Do of the correct order of magnitude. The essential difference between this model and Zener's earlier model6 is that whereas Zener assumes tight coupling between atoms in a ring to establish a vibrational frequency, Pound's model allows the atoms to vibrate essen- tially each in their own normal modes. The probability of each atom moving in the correct direction to cause a ring of n atoms to rotate by 2p/n must then be calculated as a "synchronal entropy" which may be -20 e.u. for a 4 atom ring. In iron, the latest determinations of self-diffusion yield Do in the range 18 to 522.7-9 The most accurate is probably that of Borg and Birchenall8 which is 118 ± 3. This value is not inconsistent with that expected for a vacancy mechanism. Since iron and chromium are very closely similar in size, are both transition metals, and their solution is thermodynamically ideal at temperatures of interest in diffusion, it appeared that a determination of self-diffusion coefficients, Do and Q as a function of composition would be of substantial interest to diffusion theory. The following measurements were made with this purpose in mind.

Jan 1, 1961

By R. F. Balazik

By March 2001, shrinking global markets, reduced consumer spending and declines in domestic manufacturing and industrial output ended the longest economic expansion in US history and pushed the nation’s economy into its first recession in a decade. Aggravated by the terrorist attacks of Sept. 11, the recession led to large reductions in the domestic production of processed mineral materials. Some of the most significant production declines in the US metals industry were registered by aluminum, copper and steel producers. They faced strong foreign competition, higher energy costs and lower prices for their products. However, homebuilding and other domestic construction sectors — major users of nonmetallic mineral products such as cement, brick, glass and stone — remained strong enough to help raise the output of industrial mineral materials slightly above previous year levels. A strong US dollar continued to weaken the competitive stance of US metal and nonmetallic mineral materials companies alike against foreign producers in markets at home and abroad.

Jan 1, 2002

By Don M. Coulter

"INTRODUCTION The Margerum bauxite district, in Colbert County, Ala. was investigated in December 1940 and in February 1943 by R. W. Smith of the Bureau of Mines .3/ A geologist of the Federal Geological Survey investigated and mapped the district in the fall of 1942.These preliminary investigations indicated bauxite showings over an area about a mile long by 2,000 feet wide. It was felt that the chances were good for finding one or more large deposits of low- to medium-grade bauxite. The location - within 35 miles of the alumina plant of the Reynolds Metals Co. atLister Hill, Ala. – made it especially attractive. A field office was established in Iuka, Miss., on May 19, 190,, and mineral agreements were executed with four landowners covering 1,146.6 cores.The drilling on the project was done under contract. The power drilling was supplemented by a labor crew that drilled hand-auger holes, where there was little or no gravel overburden, and sampled the old test pits.The Federal Geological Survey, after thorough study of the district, recommended 54 drill holes 4/ to delimit the known deposits and to search for possible extensions. After the drilling started, many of these locations eliminated, and others were changed upon the basis of information gathered from the holes as they were drilled."

Mar 1, 1948

By C. H. Mathewson

CONSIDERABLE progress has been made during the last few years in analyzing the action of plastic deformation in metallic crystals. This is due largely to the development of X-ray spectrographic methods for studying changes in the orientation of single crystals, or of conglomerates, as they occur during the process of plastic deformation, but partly to the widespread knowledge of suitable technique for preparing large (single or variously combined) crystals for direct crystallographic observation under stress or in various conditions of strain. These two methods of studying changes in the crystalline structure of metals may of course be used in conjunction with features of mutual support, but unfortunately the advantage of direct crystallographic observation is lost when we proceed to the study of severely cold-worked structures, owing to the occurrence of real or apparent crystalline discontinuities which become more and more complicated as the amount of plastic action increases. Furthermore, the X-ray methods do not appear to be adequate, at least in their present stage of development, to fix definitely the character of structural alteration in the parent crystal lattice by plastic deformation. The principal question at issue concerns the nature of the crystalline particles that remain after plastic deformation. These are generally known in our American metallurgical literature as crystalline fragments,' and they seem, indeed, to diffract as individuals causing the Hull pattern of a severely cold-worked metal to resemble the pattern of a fine powder,2 with certain features of preferred orientation among the particles deter- mined by the manner and intensity of cold working. We must freely concede that there are conceptions of lattice alteration, apart from that of simple fragmentation, which would account for an increasing number of lattice positions according to X-ray spectrographic observation as the degree of deformation increased.

Jan 1, 1927

By E. J. Gleim

This report describes a trip to Europe in the interest of safety in coal mines. It reviews the Eighth International Conference of Directors of Safety in Mines Re-search, which met in Dortmund-Derne, Germany, July 5-10, 1954, to discuss results of studies made in different countries to improve health and safety conditions under-ground. It also summarizes information on subjects of special interest in the United States gained by the writer in visits to mining experiment stations in Belgium, France, and England. The efforts being made to protect life and property underground were discussed, and ideas and experiences were interchanged freely, not only during the conference but also during visits to the several countries. Helpful information was obtained on many topics of interest, but time did not permit as thorough a discussion on some of them as might be desired.

Jan 1, 1956

By Kerry Spickelmier

The only nickel smelter and the only active nickel mine in the United States is Glenbrook Nickel Co., a joint venture (50% each) of Cominco Resources International Ltd. and Cominco Ltd. In 1989, with the nickel price riding high between $2.30 and $2.70/kg ($5 and $6/lb), Glenbrook seized the opportunity to purchase and recommission a southwestern Oregon ferronickel smelter and the adjacent nickel-ore mine. This Douglas County site is only about 97 km (60 miles) due east of the Pacific Ocean, and California's border lies a similar distance to the south. Hanna Mining Co. had closed the operation in 1987. And the following year, the equipment had been largely stripped for salvage value. From November 1990 through August 1992, the mine supplied an average 5 kt/d (5500 wet stpd) of ore. Currently, with import ore supplying 40% of the smelter feed, the mine's daily tonnage averages 4.2 kt (4600 wet st). From November 1990 through August 1993, the mine has delivered 2.1 Mt (2.3 million st) of ore grading 1.22% nickel with an average moisture content of 26%. Buffaloed nickel? A nickel is not worth what it was in 1989 and neither is ferronickel, with recent prices hovering around $1.13/kg ($2.50/lb). To survive, Glenbrook has focused on increasing smelter production to lower its operating costs. And this strategy has triggered several bold moves: • a new, $30 million, port facility and • a 10-year importation contract for ore from New Caledonia, an island approximately 1000 km (625 miles) east of Australia. For a Glenbrook update, a May 25, 1993 visit was made to the company's Oregon operations - the mine and smelter near Riddle plus its new Coos Bay port facility. Unfortunately, as the rain came down that day, so did news of another temporary shutdown. The previous suspension had lasted from Dec. 20, 1992 until Feb. 22, 1993. Barely three months back to work on a wet May afternoon, more than 250 of Glenbrook's approximately 300 employees contemplated yet another shutdown, effective July 31, 1993.

Jan 1, 1993

By Robert McIvor

The following is a summary of the Robert H. Richards Lecture on “Learning and Good Fortune on the Road to Discovery” presented at the Mineral & Metallurgical Processing Division (MPD) Awards Plenary Session on Feb. 23, 2026 during the MINEXCHANGE 2026 SME Annual Conference & Expo in Salt Lake City, UT.

Mar 1, 2026

By Zsuzsanna Zborovszky

A circuit is considered intrinsically safe when any spark or thermal effect produced normally (that is, by operating the equipment in its correct operational manner to fulfill its purpose) or accidentally (caused by short circuit, earth fault, defective components, breaking the wiring, etc.) is incapable under prescribed test conditions of causing ignition of a prescribed gas mixture. The test conditions and gas mixture should be at least as hazardous as the true parameters of the environment where the circuit will be operated. According to present practices, the question of whether or not a circuit is intrinsically safe is decided upon experimentally. The circuit is inspected first for mechanical soundness and a survey is made to determine what faults should be considered as probable. Then the individual branches are connected, in sequence, to a test apparatus called 'breakflash" which acts as an opening, closing contact and thus draws sparks from the circuit. This test is repeated a given number of times in the presence of the prescribed gas mixture under specified conditions (electrode configurations, gas parameters, etc.). The equipment will be regarded as intrinsically safe if during testing no ignition has occurred.

Jan 1, 1972

By C. M. Campbell

IN 1902, a famous Canadian geologist made the following statement : ?'From what we know row of the iron-ore fields of the Province, we may feel that Ontario is assured of a great future as an iron-ore producing country. Judging from the extent of the territory over which the newly discovered ranges have been found, Ontario should in the not far distant future take her place as one of the chief iron producers in the world". In 1905, an official of the Department of Mines said: "In ten years Canada will have b:ecome a great metallurgical country. You will see an iron industry in this Dominion larger than in any country in the world. Canada will yet furnish the world with its iron supply. It will be the same with iron as with wheat. A decade from now Canada will outstrip all other countries in wheat growing. The production of iron at a cheaper rate than it can be made elsewhere will cause Canada to take a similar position as far as iron is concerned". In 1924, a former President of the Institute, in arguing his claim for inconceivable mineral wealth in this country, stated as a "certainty" that iron-ore deposits on the scale of the ones in Minnesota would be found "again and again" in the Canadian Precambrian. In 1930, a Minister of Mines announced that "The country surrounding Churchill holds large deposits of valuable iron and coal", and he stated that, at that place, 'We will have an industry in iron that will compare with Pittsburgh". These statements are definite promises, just as definite and important as the statement "I promise to pay" on a note, and they are not fulfilled by casually stating, as is the habit, that someday we will work our low-grade iron ores. Nor are they fulfilled by stating, as is often done, "Oh, So-and-So did not mean that ' . Due to their importance and to the prominent positions held by the men who made these statements, they were widely circulated throughout Canada. They were taken at their face value, and on the strength of them and many more of the same kind in regard to our other resources we have planned and built, at huge expense, provinces, governments, civil services, railways, and other equipment. The reserves that were to justify these expenditures have not appeared. There has not been a ton of iron ore mined in Canada for many years, and important commercial reserves are unknown. We have built the mill, but adequate ore is lacking.

Jan 1, 1937

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