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By Kent R. Van Horn, W. P. Sykes

Since Honda and Murakamil in 1918 proposed their constitutional diagram of the carbon-free iron-tungsten system, considerable effort has been expended by several investigators in attempts to define more positively the structural features of the alloys. The existence of an intermediate phase corresponding to the formula Fe3W2 (68.7 per cent W) was proposed from evidence of a purely metallographic nature by one of the present authors2 in 1926. Since that time the identity of this phase has been confirmed by Arnfelt3 and by Takeda,4 both of whom employed X-ray methods as well as the microscope and the chemical analysis of isolated microconstituents. According to Arnfelt, Fe3W2, as crystallized from the iron-rich melts at a temperature above 1450° C., contains by analysis 68.7 per cent W. The lattice of this phase is characterized by trigonal symmetry. Arnfelt, moreover, proposed a second intermediate phase formed at some temperature between 1450" and 1000" C. by a peritectoid reaction involving Fe3W2 and the iron-rich solid solution. A melt containing 25 per cent W was cooled to 1000" C. and heated for 100 hr. The precipitated tungsten-rich constituent was separated and found by analysis to contain 62.6 per cent W. This composition agrees closely with that represented by the formula Fe2W (62.2 per cent W). Diffraction patterns from the concentrated precipitate showed a hexagonal unit cell. Takeda confirmed the data of Arnfelt regarding Fe3W2 but was unable to detect Arnfelt's second intermediate phase. While Takeda failed to describe in detail the treatments employed, he stated that in alloys containing 40 per cent W which were quenched after heating at various temperatures between 1200" and 1450" C. no evidence of the second phase (Fe2W) was observed 'either in the microstructure or in the diffraction patterns of isolated residues. He therefore considered the existence of this low-temperature hexagonal compound as disproved.

Jan 1, 1933

By Daniel Mesquita Duarte

A configuração física de equipamento do sistema de desenfornamento do laminador Morgan na unidade Resende, que é preparado para laminação em dois veios, torna o controle de GAP entre barras muito complexo. O sistema de controle original era suscetível a variações, acarretando na limitação do GAP mínimo na entrada do laminador em cinco segundos. Tendo como base as fontes de variação do projeto original, foi desenvolvido um novo sistema de controle que reduziu as variações em até 1700 %, reduzindo o GAP mínimo de cinco para dois segundos. No que tange à questão do GAP mínimo, o novo sistema de controle garante uma tolerância de 0,1 segundo. Este novo sistema pode ser dividido em duas partes: o controle e correção do GAP entre o forno e a primeira gaiola, e a correção de GAP no trem desbastador.

Jul 30, 2018

By John D. Ridge

For mining geologists, the most important trends during 1962 have been the increased concentration of the exploratory activities of American mining companies in the United States and Canada and the greater use of the combined techniques of geology, geophysics and geochemistry in searches over larger areas for wider varieties of metals and minerals. The principal reasons for these changes in approach have been the deterioration of the political-economic climate in many areas of the globe of equal or greater geologic promise and the realization that modern exploration is most efficiently and economically conducted through the use of all available means of detecting ores in areas sufficiently large to raise to a maximum the chances of success. The attitude of certain major U.S. metal-producing companies can be shown by the officially ex- pressed positions of their principal officers. Early in 1962, Clyde E. Weed, Chairman of the Board of Anaconda, remarked that "because of unsettled conditions and disruptive influences in many of the copper-producing areas of the world, it is imperative that domestic copper-producing capacity be improved and made as efficient as possible in order to meet consumer demands at reasonably stable prices." In November, Robert G. Page, President of Phelps Dodge, pointed out that his company is not only concentrating most of its exploratory effort on this continent but is also increasing the number of metals for which it is searching. Frank R. Milliken, President of Kennecott, recently said that "most of our exploration money is going into the northern part of the Western Hemisphere."

Jan 2, 1963

By C. B. Yu

The ore comprise of chalcopyrite, valleriite, pyrite, pyrrhotite and so on. Serpentine and talc are chief gangues. Copper phase of the tail shows that mostly valleriite be losed in tail, 70% mineral of copper is valleriite in tail, so severity reduce the recovery of copper. The traditional flow-sheet in acidity mine pulp to flotat the valleriite, but copper-sulphur separated in high alkaline pulp, so the valleriite be losed else. Explores the characters of the valleriite?s surface, studys on the flow-sheet of flotat valleriite and copper-sulphur separated. In neutral mine pulp, adopt of cationic collector to flotat valleriite, adopt of hyposulphite to depressant pyrite in low alkaline pulp can advance the recovery of copper to 5.06%.

Jan 1, 2014

By R. J. Craig

Introduction All mining operations produce rock dust. Inhalation of rock dust, particularly if it has a high silica content, causes silicosis. Silicosis is, therefore, recognized as a hazard of the mining industry and has been made compensable throughout most of Canada. Most of the dust in any mining operation is caused by rock drilling and blasting operations and the movement and transportation of broken rock. Dust from blasting cannot be eliminated, but it can be controlled by means of increased ventilation, the use of water sprays, and the control of blasting hours. Dust from ore movement can be reduced by keeping the broken rock in a moist condition at all times. The dust from the rock drilling operation has been found to be the most difficult to control. Concentrations of dust caused by rock drills in stopes can usually be reduced to the safe minimum of 300 particles per cubic centimeter (p.p.c.c.) by diluting the air with increased ventilation. In development headings, where the machines are more confined, this is not always practicable. Therefore, the dust must be eliminated at its source. This paper deals with the reduction of dust from Leyner machines by adopting improved designs.

Jan 1, 1947

By A. Lawson

"Continued and expanded use of underground diesel-powered equipment is considered desirable in order to achieve necessary production capability, particularly when coal becomes increasingly in demand as an energy source. Although diesel engines are derated for underground use, concern has been expressed in many quarters regarding the health effects of worker exposure to diesel-generated particulate and NOx emissions. This concern will increase as Canadian diesel fuel quality becomes heavier and with higher sulphur content. This could result in a requirement to increase ventilation rates by 50%.This paper describes the results of studies of various approaches designed to reduce diesel emissions. Two major approaches have been followed: fuel modification, and emission control hardware development. The results of progress in the development of these approaches will be described.Fuel modification includes the application of water/diesel and methanol/diesel fuel emulsions to the engine. Details of the techniques employed in this approach will be described, together with the effects on diesel emissions. (The paper is concerned with the emission aspects only, not the possible major engine modifications and/ or substitute materials of construction for 100070 methanol.) Use of methanol has the added advantage of acting as a diesel fuel substitute and extender, and there are expectations that underground diesel engines could eventually operate on close to 100% methanol fuel, thereby eliminating particulate emissions. The results of emission control hardware development will also be presented and will include the effects of catalysts, water scrubbers, exhaust filters and exhaust gas recirculation techniques on emissions. A combined systems approach employing a number of these components appears to be the most viable method of controlling the complete array of diesel emissions.This work should culminate in a better understanding of the costs involved in employing fuel modification or emission control hardware relative to the costs of increased ventilation which mpy be necessary to maintain a safe working environment for the underground worker."

Jan 1, 1981

By K. L. Ford, D. R. Lentz, J. H. Rickard, R. P. Taylor

Abstract - Coupled gamma-ray spectrometric and lithogeochemical studies throughout the Heath Steele Mines area, Bathurst Camp, New Brunswick, indicate that primary and secondary geochemical differences exist between the stratigraphic footwall and hangingwall crystal tuff units which host the massive sulfide deposits. Of particular interest is Th, and to a lesser extent, Zr and Y, which are more concentrated in the hangingwall than the footwall crystal tuffs, whereas the opposite is true for TiO2. This expands on earlier lithogeochemical-chemostratigraphic results concentrated in the eastern part of the Heath Steele belt that led to revision of the local stratigraphy, and necessitated a structural re-interpretation of the area with implications for exploration. Although K depletion (decreased K and K/Th) is typical of chloritized footwall zones of chloritization, these features were not fully apparent here due to the recessive nature of these altered zones. In situ radiometric analysis using a portable gamma-ray spectrometer is a rapid, inexpensive analytical technique for chemostratigraphic characterization of rock units within volcanogenic massive sulfide deposit settings, provided there is a contrast in the distribution of natural radioelements, particularly Th and K.

Jan 1, 1998

By M. R. Hosseini

Among all gravity concentration methods, Shaking-table is the most effective one from the metallurgical point of view. In this study, Shaking-table was used for concentrating a manganese ore sample from Ghasem Abad area in Kerman, Iran. Experiments were designed by using L8Taguchi design with five variables and each variable in two levels. The influence of each variable and their interactions on the operation of the device was studied. The variables under investigation were: table slope, table frequency, water flowrate, feed rate, and particle size. The manganese concentrate grade and recovery were used as response variables. It was shown that water flowrate, table slope, feed rate, and particle size are the significant variable on concentrate grade; while, all the variables influence manganese recovery.

Jan 1, 2014

By R. L. Attridge

Namibia's newest mining enterprise, the Navachab Gold Mine, was officially opened by President Sam Nujomo during June 1990. The mine is a joint venture between Erongo Mining & Exploration Company Limited, Metal Mining Corporation of Canada, and Rand Mines Windhoek (Pty) Ltd. Erongo has a 70 per cent interest in the mine, while Metal Mining and Rand Mines hold 20 per cent and 10 per cent respectively. Anglo American Corporation and its associates hold two-thirds of Erongo shares and CDM (Pty) Ltd one-third. The Mine is managed by Erongo Mining & Exploration Company. The property is located some 10 km southwest of the town of Karibib and 170 km west-northwest of the Namibian capital of Windhoek (Fig. 1), the name of the Mine being taken from the farm on which the gold deposits were discovered. Navachab is an opencast operation and was brought into production in December 1989 at a cost of around R84 milion-RS,2 million under budget. The plant is designed to treat 840 kt annually at an average gold grade of 2,6 g/t. This wil produce 1900 kg of gold per year, which at today's prices will earn Namibia more than R60 million in foreign exchange.

Jan 1, 1991

By John H. Nicholls

In this paper, Imperial Oil Limited reports briefly on the drilling by contract rigs of twenty-nine slim holes in the Virden, Smiley, and Souris Valley areas. The investigations showed that slim-hole penetration rates, as a result of careful control of drilling variables, can approach those achieved with 7 7/8-inch bits. It is concluded that slim-hole drilling is acceptable for development or exploratory work. Imperial also reports on the completion techniques and equipment that have been developed on twenty-seven tubingless 2 1/2-inch casing completions. Indications are that the method is economically desirable where excessive gas or water production is not anticipated.

Jan 1, 1958

Pictured on these pages are the eight RMCMI Scholarship Award Winners for the 1989-1990 year followed by a brief profile. All winners, except Emmet Roache from New Mexico, were present as guests of the Institute at the June convention in Steamboat Springs, Colorado to receive recognition at the Welcome Session Monday, June 25, 1990. Each state vice president served as the host for the collegiate winner. In addition to receiving a plaque from the Scholarship Chairman, Dr. Donald Gentry, each winner receives $750 tuition credit for the coming academic year. As this is a continuing award, the winners from the previous year will receive another $750 for tuition credit in their senior year if they have maintained good academic standing and are recommended by their university. Criteria for these awards to be made in the spring annually is (1) That the award be made to a sophomore student and used as tuition during the junior year. (2) That the recipient be both a U.S. citizen and a resident of the state involved. (3) That the recipient have good academic standing, be pursuing a degree in a mining related field and have an expressed interest in Western coal as a possible career path. The scholarship program includes curricula other than those in the mining departments, but in the engineering disciplines, such as geology, mineral processing and metallurgy. Contributions to this worthy project are tax deductible to each individual RMCMI member or his firm. Through annual donations of $100 or more, the Patrons of the Institute fund the scholarship program, and the various vice presidents contribute the travel expenses to conventions for these outstanding young collegiates. Donations to this worthwhile program may be made payable to RMCMI Scholarship and mailed to the RMCMI Office, 3000 Youngfield Street, Suite 324, Lakewood, CO 80215. Profiles of the 1990 Scholarship Winners follow. [ ] Mildred Benally University of Arizona Tuscan, Arizona Mildred has attended San Juan College in New Mexico, and will graduate from the University of Arizona in May, 1991. Upon completion of her, schooling she hopes to pursue a career in the coal mining industry. In preparation for her goal, her work experience includes being a lab technician, a mining engineer intern, and a lab technician assistant; she also is very skilled in various computer applications. She has been a member of SME-AIME, and secretary to the U of A Student Chapter, and recipient of the SME Coal Division Scholarship and past recipient of the Navajo Tribal Scholarship. [ ] Joshua Olmsted Colorado School of Mines Golden, Colorado Josh is a sophomore majoring in mining engineering at the Colorado School of Mines. He is an outstanding student as well as an accomplished athlete. Josh was on the Academic Honor Roll 1988-1989 and has been awarded an athletic scholarship. He plays varsity soccer and intramural basketball.

Jan 1, 1990

By Robert Hochscheid

A patent issued to J.N.J. Leeman (1957) described the change in performance that takes place when a cyclone is installed in the horizontal position rather than the vertical position. Although this patent was directed more toward improvements that could be realized in the heavy medium cleaning of coal, it contained specific references to reducing the quantity of fine solids that would report in the underflow, and an example for fine sand classification is also included. The three cyclone installations for which data is given in this paper demonstrate that horizontal mounting of large cyclones can improve classification efficiency, eliminate some operational difficulties, and reduce cyclone maintenance requirements in closed circuit grinding installations. Cyclone Experience at Serrana S.A. Each of four grinding circuits at the Serrana S.A. de Mineracao Apatite flotation plant in Brazil have a 2.7 X 4.6 meter (9 X 15 foot) rod mill and each originally operated in closed circuit with two vertically mounted Model D20B (500m nominal diameter) Krebs Cyclones. New feed size is 25mm. The Apatite is liberated at a relatively coarse 35 to 28 mesh grind, but the 500mm cyclones had to be fed at 66 pct. solids in order to obtain an overflow analyzing 12 pct. coarser than 42 mesh. Because dilution water in the cyclone feed had to be limited, classification was inefficient, and there were other significant circuit difficulties as summarized in a recent article by C. A. Busnardo (1984):

Jan 1, 1985

By Jeffrey Shawn Peterson

The testing procedures of the u.s. Mine Safety and Health Administration specify that intrinsic safety acceptance tests be conducted using a standard tungsten-cadmium electrode configuration in the break-flash apparatus. However, in realistic mining environments, other materials may be more likely sources of sparking. Information defining the probability of spark ignition between common materials such as aluminum, brass, copper, lead, tin, cold-rolled steel, and stainless steel is of more practical value in determining ignition hazards. The U.S. Bureau of Mines has completed an investigation of the influence of material on the ignition probability using the breakflash apparatus. By comparing ignition currents or ignition voltages corresponding to a probability of one ignition per thousand sparks to those found previously for cadmium, a margin of safety may be estimated for each material. This report presents the results of an investigation into the influence of disk electrode material on the probability of ignition.

Jan 1, 2010

By Carl G. Hogberg

To the casual observer there is probably no simpler appearing operation in the mineral industry than a limestone quarry. It might seem that the entire operation - from the drilling, blasting, and loading of the stone, its transport to a mill for crushing, washing and sizing, to loading into boats, railroad cars, or trucks for delivery to customers - can be comprehended at a glance. But no first impression could be more misleading. It is one of the purposes of this presentation to sketch the broad outlines of the extensive limestone industry in the United States which, measured in terms of volume of production since the end of World War II, has grown almost 300 per cent to a national level in 1957 of 384 million net tons.1 Another objective will be to discuss in more detail this industry in the State of Michigan. For this latter purpose, the Michigan Limestone Division plants at Calcite and at Cedarville will be used as examples. These descriptions will, we believe, show that the limestone business has complexities to match its size.

Jan 1, 1962

By R. M. Santmyers

Caesium, rubidium, and lithium are sometimes described as the minor or rarer alkali metals. They generally occur together in nature, although, lithium is distributed more widely and is far more abundant than either of the other two. The chemical, and even the physical, properties of these three elements can best be considered In conjunction with the more familiar members of the alkali group, sodium and potassium. The five elements lithium, sodium, potassium, rubidium, and caesium show an interesting gradation properties from member to member with the increase in atomic weights. All are silvery white and soft enough to be cut with a knife. They tarnish rapidly in air and decompose water at ordinary temperatures. The lowest temperature at which the action of the several metals on water can be de¬tected is -98°C. for sodium, -105°C, for potassium, 108°C. for rubidium, and -116°C. for caesium. The chemical activity appears to increase steadily from

Jan 1, 1930

By D Craw

The Macraes gold deposit is located in a low angle NE dipping (~15¦) shear zone, the Hyde Macraes Shear Zone (HMSZ) cutting greenschist facies metasediments of the Otago Schist. The shear zone is host to large volumes of mineralised schist and relatively sparse quartz veins. Early in the development of this through going shear the schist experienced an episode of hydro fracturing and fluid redistribution. As a result, presently exposed schists within the Intrashear sequence are pervaded by localised swarms of quartz filled pure extension and extensional shear fractures hosting goldscheelite mineralization. The swarms comprise networks or æstockworksÆ of veins that strike NE, are subvertical and form subperpendicular to the shear zone fabric. Vein frequency across strike is typically ~1 m-1, with most veins five to ten centimetres thick and vertically continuous for up to ~20 m. Many of the veins show delicately banded internal textures that are parallel to the vein margins. These bands/lamina indicate incremental growth and are defined by a variation in grain size or alternatively by thin slivers of wallrock schist, though typically uncommon. The majority of veins are overprinted by a weak plastic deformation, although primary structures are largely preserved. This deformation has produced subgrain structures, migration of grain boundaries with sutured margins and undulose extinction of grains. These microstructural observations possibly indicate that temperatures were around 300¦C during stockwork vein formation. In general, the mode of brittle failure that developed the stockwork veins can be directly related to lithological variation. The geometry of stockwork veins indicate that local vertical shortening and extension occurred in the Intrashear sequence of the HMSZ synkinematically with thrusting. Localised extension was mainly parallel to the structural trend; that is, it took place perpendicular to the direction of inferred thrusting. The development of lateral ramps most likely gave rise to extension in parts of the shear zone during continuous shortening to form swarms of stockwork veins.

Jan 1, 2004

By K. N. Subramanian

Previously reported work on total oxidative leaching of chalcopyrite concentrates ha s shown that high copper extractions are obtained at 210°C and 0.4 MPa oxygen pressure. A simple integrated flow sheet using pressure leaching, solution treatment involving precipitation with a calcium base, and electrowinning to produce wire-bar-quality copper is described. Reagent and energy requirements developed from this work indicate that the process could be attractive for small operations where a smelting-refining complex cannot be justified.

Jan 1, 1978

By Jogeshwar P. Singh, Mohamed Ashour

The Soil-Foundation-Structure-Interaction (SFSI) problem involves Kinematic Soil- Foundation Interaction occurring during large (cyclic and permanent) ground deformations as well as Inertial Foundation-Structure Interaction occurring during shaking all of which take place while the soil and possibly structural properties degrade with time. The design of the deep foundations for liquefaction induced lateral spread loads include estimation of passive pressure applied by the liquefied material as well as the amount of anticipated displacement. Coupled analyses for SFSI problems that account for liquefaction induced lateral spread and their interaction with the deep foundation system can be performed using sophisticated numerical modeling techniques based on finite element and/or finite difference methods using computer programs such as FLAC or OPENSEES. Such complete SFSI analyses are very tedious and expensive and not feasible for most projects. In 2011, California Department of Transportation (Caltrans) released guidelines for foundation loading and deformation due to liquefaction induced lateral spreading. This simpler prescriptive approach combines empirical and analytical methods through decoupled analyses using computer programs such as LPILE and SLOPE-W together with liquefaction induced lateral spread estimates based on published empirical equations. Pile group effects and pile caps are accounted for using a concept of super-pile. In this paper, we discuss the solution of the same lateral spreading related SFSI problem using computer program CGI-DFSAP (CGI-Deep Foundation System Analysis Program) based on the strain wedge theory that can account for liquefaction, lateral spreading, pile groups, pile caps and nonlinear behavior of piles in a more coupled manner to analyze the foundation system under the lateral spread loadings. CGI-DFSAP can be used to analyze piles in sloping ground conditions as well as piles beneath the abutments near a free-face slope. We have included Strain Wedge Model (SWM) solutions using CGI-DFSAP of several field and laboratory case studies of lateral spreading related to pile foundations. Finally, we have also included the SWM solution of one of the Caltrans (2011) example problems.

Jan 1, 2015

By C. W. Davis, L. R. Messer

THE name fuller's earth, which was derived from its early use in "fulling" or removing grease from woolen goods, is a term that is generally considered to designate mineral matter, containing hydrous aluminum silicates of the clay group, which has a high capacity for removing colors from oils, whether of animal, vegetable, or mineral origin. Fuller's earths are usually dried and may be "tempered" by heating or may be treated with water or reagents to improve their efficiency. For our purpose the term "acid-treated earths" will include those products from the partial decomposition of mineral water by acid which are equal to or more efficient than an untreated fuller's earth from Quincy, Fla., when used in bleaching mineral oil by the "contact" process. In general, the contact process for treating oils consists of heating and agitating a mixture of oil and finely divided adsorbent, the latter being subsequently removed by filtration. The term "adsorbent" is used because, although there has been a great deal of controversy over the mechanism of removal of impurities from oils by mineral matter, there is no doubt that adsorption, which involves the surface of the solid, plays a major part.' The properties that make fuller's earth useful in the treatment of petroleum products by "percolation1' and in the purification of edible oils by the contact process have long been studied, but the comparatively recent adaptation of the contact process to the bleaching of petroleum products has made desirable the further investigation of fuller's earth and other adsorbent earths.

Jan 1, 1929

By N. A. Gjostein

The formal descnption of the decay of an isolated scratch can be written in terms of an appropriate Fourier integral. With the application of certain approximations, this description leads to the second-moment analysis developed by King and Mullins. It is shown that the second-moment analysis does not adequately describe the behavior of a decaying, isolated scratch, and that it is difficult to obtain internally consistent values of the surface self-diffusion coefficient, D,,from this analysis. This inconsistency arises from contributions of higher-order moments to the decay process. Two new analytical methods, based on the Fourier integval representation of a scratch profile, have been developed for determining values of D, from the decay kinetics of isolated scratches. In the profile-matching method, a given initial profile is resolved into its Fourier components, the components are allowed to decay exponentially over an annealing time interval, At, and finally they are synthesized to form a decayed profile. The predicted profile is adjusted to fit the experimental profile by varying only the parameter, D,At; the contribution from volume diffusion is directly taken into account and the integrals involved in the Fourier analysis are evaluated by numerical integration on an electronic computer. In the kinetic method, the widths, W, of a series of predicted profiles are determined for various volume-diffusion contributions, and the results are plotted in the form W vs DSAt. For a fixed ratio of surface to volume diffusivities, R, these plots are linear; the slope of the lines increases as R decreases. A simi-lar analysis can be performed on the depths of the predicted profiles. In this case, plots of (l/df3 vs D,At are found to be nonlinear. The proper value of Ds is found by superimposing the data for the experimental widths and depths on Plots of this kind and adjusting Ds until a fit is obtained with the line having the appropriate value oj R. An analysis of the slopes of these plots for R —= (surface diffusion only) reveals that they do not give the correct value, 2276, for width tf second-moment standard profile. This finding allows one to modify the second-moment analysis in such a way as to obtain internally consistent values of Ds. ThERE are several processes, involving a flow of matter along a surface, due to gradients in curvature of the surface, that may be used to determine the surface self-diffusion coefficient, Ds. These processes are commonly known as 1) thermal grooving, 2) single and 3) multiple scratch decay, 4) blunting of field-emitter tips, and 5) sintering. In this series of papers, the first three of these processes are examined in detail in an attempt to subject the phenomenological theories governing these processes to a critical test and, furthermore, to make a critical comparison of the values of D, obtained from these techniques. Although the thermal grooving technique has been established'' as a reliable method for determining D, , this has not been the case for the process of scratch flattening. Mullins and coworkers374 have proposed phenomenological laws governing the growth of the width and the decay of the amplitude of an isolated scratch, but only in one study5 has the width-growth law been supported by experimental evidence. In paper I of this series detailed experimental evidence is presented that points up the deficiencies of the second-moment analysis; the origins of these deficiencies are also discussed. Following this development, some new analytical procedures, based on representing the scratch profile by Fourier integrals, are presented as a means of obtaining reliable values of D, from the kinetics of the scratch-flattening process. Further applications of the Fourier integral approach are reported in papers 11' and 111,~ where the method has been useful in interpreting the anisotropy of flattening rates of isolated scratches (paper 11) and in describing the multiple scratch decay process (paper 111). THEORY OF SCRATCH DECAY Following ~ullins" approach we consider an arbitrarily shaped scratch profile, Fig. 6, at some time, t. The profile is designated by a function z(x,t) which can be expressed in terms of a Fourier integral as follows:

Jan 1, 1967