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By Eldon L. Abbott, Rebecca K. Bolan

The Florida Department of Transportation, Florida’s Turnpike Enterprise is studying the feasibility of a 1128 meter (3,700 foot) vehicular tunnel to provide direct access for Port of Miami traffic to/from I-395, I-95, SR-836 (Dolphin Expressway) and Miami International Airport. Both Bored and Immersed Tube tunnels were evaluated and re-evaluated for constructing two, two-lane, 11.9 meter (39-foot) diameter tunnels beneath the Main Shipping Channel lying between Watson Island and the Port of Miami on Dodge Island in Biscayne Bay, Miami, Florida, USA. Bedrock Geology of South Florida is predominately very permeable, vuggy limestone with sand seams and occasional voids. Groundwater inflows in deep cut-and-cover excavations, tunnel buoyancy, grouting, maintenance of Port operations and potential/possible environmental impacts to Biscayne Bay were significant issues.

Jan 1, 2005

By D. Grabowski, Z. Pokryszka

A study carried out in the iron basin of Lorraine (North-East of France) highlighted the existence of under-oxygenated and noxious gas emissions (carbon dioxide, radon…) in vast built-up areas related to former mine workings. Site investigations showed that the gas flow was mainly due to natural thermal air circulation between old mines and external atmosphere. The main hazards associated with this flow of gas and its potential accumulation in confined volumes in buildings are asphyxiation and intoxication. A further study is in progress in order to better understand the origin of the gas generation within the old iron mine workings. Following the first hypothesis, the carbon dioxide emission is mainly due to the specific hydro-geo-chemical process associating the pyrite oxidation with the acid dissolution of carbonates. KEY-WORDS : gas, emission, iron mine, pyrite.

Jan 1, 2003

By Larry Stearns, Lori Tiefenthaler

Remediation of contaminated soil represents a significant market for application of Deep Soil Mixing (DSM). Eighty-one percent of U.S. Environmental Protection Agency (EPA) Superfund Program’s site remedies have involved contaminated soil. Contaminated soil is frequently treated by In-situ Solidification/Stabilization (ISS). ISS treatment of contaminated soil involves mixing binding agents into soil using DSM techniques. DSM is a core business for many DFI members. Members may improve and broaden their services to clients by learning about the recent ISS treatment of contaminated soil at a Superfund site. ISS treatment is part of the EPA-selected remedy for a Superfund Site in the metro New York City area. The property has seen heavy industrial use for more than a century. Soil at the site is contaminated with a variety of volatile organic compounds (VOCs), polycyclic aromatic hydrocarbons (PAHs) including coal tars and heavy metals, principally arsenic and lead. Beginning in 2017 and continuing through 2018, approximately 150,000 cubic yards (115,000 cubic meters) of soil will be treated by ISS at the case study site. Portland cement and slag cement are mixed into the soil by DSM techniques using GPS guided excavators to immobilize the hazardous constituents within the treated soil. ISS treatment by DSM will contribute to redevelopment of this valuable property. This paper will describe ISS constructability and performance, case study grout mix design with geotechnical results for strength and permeability, and deep soil mixing techniques. INTRODUCTION In-situ solidification and stabilization (ISS) is a deep soil mixing (DSM) technique applied in the environmental remediation field to physically encapsulate, or chemically bind, contaminates of concern such that the impacts to human health and the environment are mitigated. Common remediation applications of ISS include mixing cementitious reagents into contaminated soils to form a monolithic mass with desired performance characteristics, and the installation of vertical subsurface walls designed to control groundwater movement. A key characteristic of ISS is that the contaminated soils are treated in their existing location at the project site and then are left in place after treatment. Typical performance characteristics of the ISS treated soils include improved unconfined compressive strength (UCS), reduced hydraulic conductivity (HC), and reduced leaching potential of soil contaminants. Increased shear resistance of the treated soil may also be a performance requirement where seismic loading is a concern.

Jan 1, 2018

By James F. Archibald

Research has been conducted for the Workplace Safety and Insurance Board of Ontario (WSIB) to characterize thin, spray-on lining materials (TSLs), as well as combinations of TSLs and conventional spray supports, and to assess their capacity for inhibiting damage created by mining-induced rockbursts. This study has been performed to assess the capabilities of such support systems for preventing rock and support material damage that often results due to rockbursting. A variety of TSLs and other spray support media were subjected to the effects of simulated rockbursting, through use of explosive detonation trials, to evaluate their damage mitigation capacity. Results have validated that TSLs and variant layer combinations may be as effective as or better than conventional support materials for mitigating rockburst or like damage in highly stressed mine environments. In civil engineering construction, and typically in underground tunneling operations where concrete linings are applied, liner deterioration is a continuing and pervasive problem that often requires expensive and time-consuming rehabilitation effort. The ability of TSLs to provide effective concrete structural reinforcement while providing sustainable resistance against underground or restricted environmental hazards, as with fires or dynamic failure events, may permit wider use of TSLs than is currently foreseen by the mining industry. Significant benefits for use of TSL materials in concrete liner rehabilitation and for concrete material protection have been assessed.

May 1, 2006

By P. A. Kennedy

An environmental assessment or impact statement for onshore waste disposal under the Notional Environmental Policy Act is expected to occur with the development of commercial deep seabed mining. An environmental assessment was conducted in order that testing and refinement of nodule waste disposal techniques can he completed prior to 1988, when commercial seabed mining can begin under U.S. legislation. Within this study three classes of process and four classes of waste disposal technique were identified, and five sites were selected as representative of first-generation nodule operations. Each realistic site/process/disposal technique combination was compared against potential effects to determine important characteristics of the rejects and the sites. Regulatory requirements were also considered at each site to identify important issues and their effect on the permitting process. Principal conclusions in the report are the following: (1) uncertainties exist in the regulatory regimes for hydrometallurgical process tailings, primarily regarding classification as hazardous waste; (2) slogs from nodule processing are expected to be inert and relatively easy to dispose of at all sites; and (3) additional physical and chemical information on properties of rejects from all processes is necessary to predict environmental effects.

Jan 1, 1982

By Mehmet F. Tauer, Pierre Trudel

"The metamorphosed mineralized Archean Bourlamaque batholith, dated at 2710 +-54 Ma, is a homogeneous body, composed mainly of quartz diorite; it is cut by late dioritic, mafic and aplitic dykes, and contains metasomatized ultramafic xenoliths. A geochemical investigation confirms the calc-alkaline affinity of the batholith, and the REE profiles are similar (Lal Yb = 3.9 to 8.1) to those of the intermediate to felsic metavolcanic rocks at Val d'Or into which the batholith was intruded and to those of the calc-alkaline members of the Blake River Group at Rouyn.Gold distribution within the batholith is heterogeneous and anomalous. Although the background Au content of the batholith is estimated to be 3.2 ppb Au by RNAA , the estimated median gold content of the batholith is 10 pp b (with P84 =32 and PI 6=3.1 ppb), much higher than that of ""normal"" granites (I to 5 ppb A u). The gold mineralization exhibits a close relationship with shear zones (e.g. Belmoral Mine) or with diorite dykes (e.g. Sullivan, Perron and Courvan mines).The following sequence of geological events is proposed: (I) pretectonic emplacement of the batholith, which is cogenetic with its volcanic host rocks; (2) regional metam orphism and deformation with localized shearing; and (3) hydrothermal alteration and quartz veining. We conclude that: (1) the Bourlamaque batholith is a gold-enriched intrusion, and (2) the determination of average gold content may be an effective method f or distinguishing ""sterile"" intrusions from those with potentials for gold mineralization.RESUMELe batholite archéen minéralise de Bourlamaque, daté de 2710+-54 Ma, est une intrusion homogène, constituée principalement de diorite quartzique, qui a été recoupée par des dykes tardifs de diorite, d'aplite et de composition mafique. Il contient aussi des enclaves de roches ultramafiques metasomatisees. L 'étude géochimique confirme le caractère calco-alcalin du bath olite et les profits des ETR sont semblables (La/ Yb=3.9 a8.1) a ceux des volcanites intermédiaires afe tsiques de la région de Val d'Or dans lesquelles le batholite fait intrusion et à ceux des unites calco-alcalines du Groupe de Blake Ri ver a Rouyn. La distribution de Au dans le batholite est à la fois anomale et hétérogène. Bien que le bruit de fond du batholite ait été estime à 3.2 ppb A u par AANR, sa médiane a été estimée a10 ppb Au (avec P84=32 et PI6= 3.1 ppb) , ce qui est nettement plus élevé que la valeur des roches granitoides ""normales"" donnée dans la littérature (1 a 5 ppb A u). Dans la batholite, la minéralisation aurifère est intimement associée aux zones de cisaillement (e.g. mine Belmoral) au aux dykes de diorite (e.g. mines Sullivan, Perron et Courvan).La séquence des évènements géologiques suivante est proposée: (1) emplacement pre-tectonique du batholite, lequel est cogenetique avec les roches volcaniques encaissantes; (2) deformation et metamorphisme regional avec des cisaillements tectoniques locaux; et (3) altération hydrothermale et développement des veines de quartz. Nous concluons que: (1) le batho lite de Bourlamaque est une intrusion enrichie en Au; (2) la determination de la teneur en Au peu être une méthode efficace pour distinguer les intrusions stériles de celles qui possèderaient un pot entiel pour des minéralisation s aurifères."

Jan 1, 1989

By Michael S. Miller

In 1987 and 1988, at the request of the U.S. Bureau of Land Management, the U.S. Bureau of Mines studied the 3,100-acre Borah Peak Wilderness Study Area (10-047-004) and a 708-acre parcel adjacent to the north in order to evaluate their identified mineral resources. The study area is located in Custer County, ID, about 18 mi northwest from MacKay. The study area lies along the western foothills of the Lost River Range and is underlain by quartzite, sandstone, shale, argillite, dolostone, and limestone. The Lost River fault, a major active fault, lies along the length of the study area. Large alluvial fans spread out from valleys originating east of the study area.

Jan 1, 1989

By R. R. Rollins

Field data combined with theoretical derivations were used to design a surface mining operation using explosive casting. Calculated casting results varied from 44 to 65% depending on bench height. This model was then applied to field tests at an eastern, contour, coal stripping operation. Results from five experimental casting shots are summarized and compared to conventional mining methods. The overburden material removed by casting ranged from 35 to 65% with an average of 50%. Fragmentation was improved and it was demonstrated that this procedure is economically attractive with a resultant cost savings of $.59/m3 or $5.93/t of clean coal.

Jan 1, 1987

In its April 1991 issue, MINING ENGINEERING published a salary survey form asking for information relating to engineering and management jobs in the minerals industry. 1038 of these forms were filled out and returned, most of them being received in the magazine's offices at SME headquarters before the end of June 1991. An SME volunteer took on the task of tabulating and analyzing data from the forms, but the press of other business interfered with this work, and publication has been delayed until this issue of MINING ENGINEERING. Appreciation is extended to SME members who took the time to fill out and return the salary survey forms, and our apologies go to MINING ENGINEERING'S readers for the delay in publication. Of the total number of forms received, more than 97% were from SME members. The geographic distribution of the respondents closely mirrored that of SME membership as a whole, about 50% being from the Society's Western Region, 19% from the Central Region, and 23% from the Eastern Region. About 8% were from outside the US. Average salaries for each of the four geographic areas ranged between $55,000 and $60,000, with the highest average in Eastern Region (Fig. 1). Respondents were asked to answer a number of questions formulated to determine if there are significant differences in salaries based on the type of organization for which they work. As indicated by Table 1, salary averages at mining companies do not vary markedly with the size of the company: • Large companies, defined as those having more than $1 billion in annual sales, accounted for just over 16% of the returns. Their average salary was $61,840 per year.

Jan 1, 1992

By E. L. Garton

Michigan is becoming one of the important oil-producing States of the country. The amount of crude oil produced within its boundaries has increased from only 4,000 barrels in 19253/ to nearly 16 million barrels in 19935.4/ The Bureau of Mines method of crude-oil analysis and classification-indicates that the oils from the several producing fields are predominantly paraffin-intermediate-base, wax-bearing crudes. In general, they will yield 25 to 35 percent of highly paraffinic gasoline and about the t- me amount of kerosene and gas-oil combined, 7.2 to 15 percent of lubricating oil stock, and 20 percent of residuum with a carbon residue or about 6 to 7 percent. In addition, there appears to be some correlation between certain properties of the crude oils and both the geographical location and geological structure of the oil-producing areas within the State. These general conclusions are based on the analytical data presented in this report, which is one of a series of papers that record the general characteristics of crude oil from the many producing fields of the United States. This report discusses briefly the oil fields of Michigan and the characteristics of the crude oils produced from them. The analyses of 15 samples are given. These samples were obtained from 13 fields in 9 counties in the lower peninsula and represent crude oils produced from the Berea sandstone, Upper Traverse and Traverse limestones, and the

Jan 1, 1937

To improve communications between mine workings and surface locations during emergency situations and for administrative purposes. The Approach: Development of a device for interconnecting phone systems which permits two-way communication between a public telephone and a mine pagerphone by authorized personnel. How It Works: The system, developed by personnel at the Bureau's Pittsburgh (Pa.) Mining and Safety Research Center, makes connections between the public phone line and mine pagerphone line. As shown in Fig. 1., incoming calls are sensed by the ring detector (4) and the system "answers" the call electronically. To reach the pagerphone system, the caller inserts an audible tone of fixed frequency through the microphone of his telephone. This tone is produced by a miniature, pocket-carried tone generator and is detected by a tone recognition circuit (5). When this hap-pens, relay, switching, and logic circuitry (6) closes the connections between the two phone systems. Simultaneously, a page activator (9) places a DC paging voltage on the mine phone line.

Jan 1, 1974

By Philip J. H. Ball

The new application and development of grout jacking processes has combined, over the last decade in particular, to provide a method by which the effects of new underground construction on superficial structures can be controlled to acceptable levels. This paper sets out the basic principles, processes and limitations of compensation grouting. It describes key elements of the philosophy and design and details the control systems required to perform satisfactorily. To illustrate the application, a case history is described for the construction of a shaft and tunnel within and beneath the prestigious structure of Harrods in London.

Jan 1, 2000

The National Institute for Occupational Safety and Health (NIOSH) conducted a study to determine the effectiveness of a filtered air delivery system to reduce respirable dust exposure to roof bolter operators in underground coal mines. When performing roof bolting operations, roof bolter operators may experience exposure to high levels of respirable dust during a working shift, especially when working downwind of the continuous mining machine. While drilling and installing roof bolts, this filtered air system supplies a clean curtain of air over the roof bolter operator by means of a plenum mounted beneath the canopy. This experimentally designed air curtain, adapted for roof bolting machines used in this study, is based upon previous design prototypes, computational fluid dynamics (CFD) simulations, and trial-and-error testing. Both prototype and final designs were tested in the full-scale mining galleries at the Office of Mine Safety and Health Research (OMSHR) in Pittsburgh before being taken underground for field testing. Test results of the system in both laboratory and field studies show reductions in operator exposure to respirable dust when the operator is positioned directly under the protected zone of the canopy.

Jan 1, 2012

By R. E. Simpson

Beginning in 1972, fully grouted resin bolts were used in underground mines. An estimated 20 million resin bolts will be installed in 1980 owing to their apparent support improvement in most roof-bolt applications. Inorganic cements were tested to replace the resin at a lower cost while retaining the advantages of a grouted bolt. Although other inorganic materials were considered, all but portland and gypsum cements were rejected for reasons of availability, performance, or cost. Portland and gypsum-type cements were tested by the Bureau of Mines to select a fast-hardening, low-cost material that would anchor a roof bolt adequately to meet safety standards. An alpha-gypsum cement, accelerated with potassium sulfate, was selected as the best material because it had adequate pull strength at a desired set time of less than 5 minutes and was readily available.

Jan 1, 1980

By George S. Rice

In response to numerous requests for information as to the status of internal-combustion mine locomotives of the Diesel type that use heavy or nonvolatile oil for fuel, with special reference to their safe use in coal mines, the United States Bureau of Mines is issuing this t port. Data were obtained on application of such locomotives to coal mining only in Belgium, France, Germany, and Great Britain. The locomotives are used in coal mining in other countries, as well as in potash, iron, and other kinds of mining, but their chief development has been in coal mining in Germany, France, and Belgium. Recently popular interest in the Diesel type of engine for motive purposes was aroused in this country by the successful application of Diesel engines to railroad locomotives hauling fast transcontinental trains, and, according to published statements, at a low cost of fuel per mile of run.

Jan 1, 1936

By J L. Maule, S J. Mathews, K A. Rodgers

Gold and Silver bearing epithermal veins of the Golden Cross deposit are hosted in Miocene and Pliocene calc-alkaline volcanics occurring 8 km northwest of Waihi at the southern extent of the Coromandel Peninsula, North Island, New Zealand. Veining occurred during a period of hydrothermal activity that began early to late Pliocene, and possibly continued into the Pleistocene.   Field relations and petrographic relationships reveal that multiple generations of FeS2 occur in the Golden Cross region, with FeS2 occurring in all nine rock types recognised at Golden Cross. The variability of FeS2 morphology was investigated by preparation of high purity FeS2 separates, and grain counting. Marcasite is the dominant FeS2 phase at Golden Cross, and along with pyrite is shown to have a systematic habit variation. Pyrite shows a sequence from cubes through octahedra to pyritohedra to dendritic growth. This pyrite sequence conforms to an experimentally determined sequence. The parallel sequence for marcasite at Golden Cross is from tabular through bladed aggregates to euhedral miscellaneous marcasite morphologies. The FeS2 sequences observed are believed to be due to increasing temperature, and perhaps also increasing FeS2-oversaturation and fluid flow.

Jan 1, 1994

By Zhang Hanbo, Niu Liping, Zhang Zhiqi, He Jicheng, Dou Zhihe

"Rutile, ilmenite and Al-Ca complex reducer were used to prepare high titanium ferrous alloy by enhanced reduction-SHS method. The effects of the complex reducer compositions and slag types on the enhanced reduction-SHS process were investigated. The high titanium ferrous alloys were characterized by XRD and SEM. The results indicate that the high titanium ferrous alloys consist mainly of TiFe2, AlTi3 and Al2O3. The oxide inclusions exist resulting in directly the high oxygen content and micro-structural defects in the alloys. The titanium and oxygen contents decrease, but the aluminum content in the alloy increases while the mass ratio of calcium in the Al-Ca complex reducers increases. When the mass ratio of Al/Ca in the Al-Ca complex reducer is 6:1, titanium, oxygen and aluminum contents are 63.75%, 3.01% and 10.72% respectively. When the mass ratio of Al/Ca is 5:1 titanium content is 55.00% nearly and aluminum content is higher than 14.00%, but oxygen content is lower than 2.0%.1. IntroductionThe high titanium ferroalloys with 65%~75% titanium have the advantages of low melting point and high titanium content. They are widely used in special steel refining, while they are also a kind of very important quality orientation alloys in the rage of aviation and aerospace. At present, the methods of preparing high titanium ferroalloy include vacuum remelting and thermit reduction. The alloys prepared by the vacuum remelting method have good qualities and low oxygen content, so it is widely used in Russia, Western Europe and other developed countries. In China, there are abundant rutile resources, but waste titanium is lack, therefore, the preparation method is the thermit reduction. But there are many quality defects in the high ferrotitanium alloy, including high oxygen content, unstable quality and so on. In order to improve the qualities of the high titanium ferroalloy, especially to reduce oxygen content, the domestic and overseas have done a lot of further researches. For example, Sichuan E-mei ferroalloy plant and Beijing Nonferrous Metal Research Institute have prepared high titanium ferrous with 73.77% titanium with natural rutile, but the oxygen content is high. Through controlling the quality of raw material, they obtained the better qualities, but the oxygen content is still very high. South Africa Mintek company have prepared high titanium ferrous alloy with low nitrate by plasma heating under the isolation air conditions, but they couldn’t also remove effectively oxygen in the alloy. The oxygen exists in the form of Al2O3 and titanium protoxide. So it can be speculated that except TiO2 not being fully reduced, the no-sufficient alloy-slag separation is the direct reason resulting in high oxygen and poor microstructure. In view of present technical difficulties during preparing high titanium ferroalloy by thermit reduction, this paper proposed a new method of preparing high titanium ferrous with low oxygen by enhanced reduction-SHS with Al-Ca complex reducer. Ca in Al-Ca complex reducer has stronger reductive ability, it can effectively strengthen the reductive degree of TiO2. The slagging agent CaO CaF2 and MgO can effectively reduce the viscosity of Al2O3 slag to improve its liquidities to strengthen alloy-slag separation effects so that to remove inclusions and oxygen. In this paper, effects of slagging agent type on the reduction and the qualities of high-titanium ferroalloy were studied."

Jan 1, 2012

By Sara Jane Boles

In recent years the interest in rare-earth compounds as refractory materials has exceeded the available literature on the subject. While some basic properties, such as density and melting point, of the more readily available rare-earth compounds have been reported in the literature, relatively few papers can be found that deal comprehensively and primarily with high-temperature refractory properties and applications of rare-earth oxides, carbides, sulfides, and nitrides. Therefore, this bibliography has been pre-pared for the use of the ceramic industry as a guide for locating and utilizing the scattered and frequently fragmentary information available. The term "rare earths", as applied in the literature search for this bibliography, is understood to include the following elements: cerium, dysprosium, erbium, europium, gadolinium, holmium, lanthanum, lutetium, neodymium, praseodymium, samarium, terbium, thorium, thulium, uranium, and ytterbium. (On the periodic chart, these elements appear as numbers 57 through 60, 62 through 71, 90, and 92.) It is emphasized that many of the abstracts included are from papers in which the rare-earth compound or compounds are treated along with several other ceramic materials, are mentioned only secondarily, with primary interest placed on a more commonly used refractory material, or are used as part of a mixture of materials formed experimentally and reported on in the paper. As the better known rare-earth materials, such as the oxides of uranium, thorium, and cerium, appear more frequently in the literature, they also appear more frequently in this collection. Articles abstracted include only information on the basic properties that are of interest to the refractories investigator. References to crystal lattices and related topics are generally excluded from this publication. The temperature 1,500° C. has been set arbitrarily as the lower limit for reported data on thermal properties. However, because of the scarcity of information, some reports are included in which data are limited to those obtained at lower temperatures. Many of the articles abstracted include lists of references that will be of additional assistance in pursuing specific lines of investigation.

Jan 1, 1962

By J. M. Riley

This report summarizes Bureau of Mines experiments in purifying sulfate leach liquors, which were prepared from low-tenor beryl concentrates by modifying the Degussa process. The leach liquor was prepared from a beryl concentrate containing 2.7 percent BeO by (1) sintering the beryl concentrate with limestone in a rotary kiln at about 1,150° C. and by (2) treating the sinter first with sulfuric acid and then with water to form and extract beryllium sulfate. About 80 percent of the beryllium was dissolved. The resulting leach liquor contained 2.4 grams of BeO, 20 grams of Al203, and 6 grams of Fe203 per liter. The laboratory solution contained much more aluminum and iron than a solution derived from treating 10 percent BeO concentrate, which is the standard raw material used by industry. Tests were made to determine the behavior of the solution toward alum purification and limestone neutralization both of which were employed industrially in conventional Degussa procedure.

Jan 1, 1962

By W. C. Winegard, A. Galibois, C. J. Beingessner

The effects of solutes on the distribution of two-dimensional configurations of grains in zone-refined tin have been studied. When solutes with partition coefficients (ko) greater than unity are added, three-sided pains become more prevalent and the growth law changes. It is shown by electron-Probe micro-analysis that a solute buildup occurs ahead of a moving grain boundary when ko > 1. It has been found recently1, 2 that solutes with partition coefficients greater than unity have a larger retarding effect on grain growth than solutes with k, less than unity. ko is defined as the ratio of the concentration of solute in the solid to the concentration of solute in the liquid with which the solid is in equilibrium. Niessen and winegard2 have suggested that this effect is probably due to the complex shape changes which occur during the process of grain growth and that no theory based on single boundary motion3-5 can explain the results. They suggested that the dissociation of the unstable fourfold junction was delayed in alloys where ko was greater than 1 because the boundaries at the junction had to move into a region of high solute concentration. If indeed this mechanism were correct, it was felt that not only would the dissociation of fourfold junctions be affected by the solute buildup ahead of the boundaries, but the collapse of three-sided grains would be impaired. These combined effects would naturally lead to a modification in the distribution of the number of sides per grain seen on a two-dimensional section. The present investigation was undertaken to test these hypotheses by examining the grain-growth process in detail. EXPERIMENTS The Distribution of Grain Configurations in Zone-Refined Tin as Seen on a Two-Dimensional Section. Following the method of Bolling and Winegard,6 zone-refined tin was cast into button-shaped specimens and, subsequently, plastically deformed under a drop hammer at room temperature. The resulting flat coin-shaped samples were annealed at 200°C, some for 50 sec and others for 100 sec. The specimens were then examined to determine the distribution of the number of sides per grain, i.e., the num- ber of crystals adjacent to any particular grain in the section. For simplicity, the grains were classified as three-sided, four-sided, and so forth; this concept is schematically illustrated in Fig. 1. As indicated by smith,' it was necessary to examine every grain within an enclosed area to obtain a proper distribution of the relative frequency of each type. The distributions for the two annealing times are illustrated in Fig. 2. The total number of grains examined is also indicated on the figure. It is evi-

Jan 1, 1965