Search Documents

By James E. Adler, Timothy C. Richmond

The Stillwater District is located in south central Montana approximately 75 miles southwest of Billings, the state's largest city. It lies along the northeast front of the Beartooth Mountains and is within the boundaries of the Custer and Galatin National Forests. The first white visitors in the district were the early trappers, who were soon followed by the prospectors. These early prospectors were drawn to the area by gold and silver discoveries at Cooke City in 1870 as well as by the large gossan formation in Verdigris Creek near the west bank of the Stillwater River and by several scattered smaller gossan exposures throughout the area. The first patented mining claims were recorded in September, 1886.

Jan 3, 1974

By G. Rinelli, A. M. Marabini

A wide-ranging series of experiments has been carried out on value minerals (sphalerite, smithsonite and hematite) and gangue minerals (quartz and calcite) to assess the properties of various commercially available vegetable and synthetic tannins as dispersants for these minerals in a finely ground state (<5 microns). Experiments to determine the dispersing power of each reagents on every mineral have been performed through sedimentation tests run first in water and afterwards in the presence of a collector having specific action on the mineral concerned. The tests have been extended to a wide range of dispersant concentrations, maintaining the pH and collector concentrations at the levels known to be the best for the flotation of the various minerals. By comparing the results obtained on each mineral, conclusions have been drawn on the possibility of using different classes of vegetable and synthetic tannins in the selective flotation of fine particles. These results have been related to the structure of the tanning compounds and to the surface properties of the minerals.

Jan 1, 1980

ALTHOUGH the open-hearth charge contributes CO, C02, H2, A and water vapor to the combustion gases and absorbs oxygen from them, in the main the thermal effects in the melting charge and molten bath can be considered independently of those in fuel combustion; the latter then is regarded simply as the source of the net heat required to finish a heat of steel. First of all, it should be remembered that a large percentage of the heat supplied to the bath is furnished by oxidation of the various elements in the charge itself. If this charge consisted of 80 to 100 per cent of hot metal and the oxidation were accomplished by blowing in air or oxygen, as in the bessemer converter, the net heat absorption would be negative; that is, the bath would contribute part of the heat required to keep the melting chamber hot, in addition to that contained in the finished steel and slag. In actual open-hearth practices, probably the nearest approach to this is in the duplex furnace, charged with bessemer-blown metal and some hot metal, where very little heat is required to complete the refining and nearly all the heat energy from fuel combustion is used to keep the roof and walls of the melting chamber up to around 2900 to 3000 F (1600 to 1650 C), so that the bath will not cool off during the refining. The other extreme is with all-cold charges containing around 80 per cent steel scrap and 20 per cent cast iron or cold pig iron, in which case a very large proportion of the heat in the bath at tap is supplied from the fuel combustion. THERMAL EFFECTS IN MELTING In a typical heat, the fuel furnishes about four million British thermal units per ton of steel produced. The heat required, for the metallurgical processes is not easily defined in useful manner but it ranges downward from about one million Btu, depending not only on the charge but on the manner of calculation. In, any event, this requirement appears. small in comparison with the

Jan 1, 1964

By Kenneth F. Whinery, John M. Campbell

Basically, the Buckley-Leverett theory involves two systems which are similar in nature but are differentiated by time. These systems may be described by the fractional flow and frontal advance equations which essentially characterize the mechanics of oil movement while being expelled from the reservoir. The fractional flow equation originally developed by Leverettl may be expressed in the more usable form The development of this equation is based on Darcy&apos;s law describing fluid flow through porous media and applies to the flow at only one point (it is a point function). For simplification, the fractional flow equation is written in the above form because the capillary forces always increase the fractional flow of the displacing phase regardless of the direction of flow or the displacing phase. If, for simplicity, the effects due to gravity and capillary pressure differences are neglected, the fraction of the displacing fluid, f, at any point in the flowing stream is related to the properties of the system by 1 Thus, it is seen that in the absence of capillary and gravitational effects, fd for a given sand and fluids varies only with saturation and pressure. The magnitude of the viscosity ratio, —a has an effective range (range of about 30) in the system where gas is displacing oil and a much smaller range for water displacing oil. In order to make the fractional flow equation more versatile, it is necessary to connect the fractional flow at a given point and saturation with time. This problem was approached by Buckley and Leverett" who developed the frontal advance equation, Eq. 3 states that the rate of advance of a plane that has a fixed saturation, Sd, is proportional to the change in composition of the flow stream caused by a small change in the saturation of the displacing fluid. It is, essentially, a transformation of a material balance equation representing the net rate of accumulation of the displacing phase within a homogeneous sand block. This accumulation is proportional to the difference between the rate at which the displacing fluid enters the sand and that at which it leaves. Eq. 3 describes the velocity with which a plane of constant displacing phase saturation advances through a porous system. Buckley and Leverett," Babson,&apos; Kern," Welge, and others have adequately discussed the basic mechanism and application of the fractional flow and frontal advance equations. APPLICATIONS OF THE FRONTAL ADVANCE THEORY TO PETROLEUM RECOVERY Two general applications of the Buckley-Leverett frontal advance theory involve the system in which the oil is being displaced by an expanding gas cap overlying the oil zone and that in which the oil is being displaced by water. Displacement by Gas in the Presence of an Immobile Water Saturation A system in which gas is the displacing phase may be thought of as having two forces effecting the displacement process. These forces are the gravitational force and that force exerted by the displacing gas. The gravitational effects control the displacing efficiency of the gas. The gravitational effect will be less at higher rates of flow, thereby reducing the effectiveness of the displacement of the oil by the gas. The more efficient displacements occur at flow rates which are less than the gravity free fall rate. Capillary forces can be neglected without materially changing the magnitude of the gas saturation. The Mile Six pool is used herein to illustrate the calculating procedures in evaluating gas drive-gravity drainage field perfomlance. These calculations represent the determination of the gas-oil contact when the distribution of the hydrocarbon pore volume is considered. Two methods

By Oscar Weiss

STILFONTEIN and surrounding areas gave negative results in all prospecting attempts since about 1904 when Goerz and Co., a forerunner of Union Corporation Ltd., first drilled in the region and on the farm Stilfontein. Subsequent efforts by African and European Investments Co. and Anglo American Corp. from 1934-37 were completely unsuccessful. Holes drilled by these companies on the farms Rietfontein, Hessie, and Palmietfontein were stopped in the Lower Witwatersrand system without finding payable reefs.

Jan 10, 1951

By M. E. Lombardi

The cost of maintaining the production of an operating oil company is one of the most important, as well as one of the most difficult to estimate, of the various items which go to make up the total cost of producing oil. In the opinion of many operators the cost of drilling and developing new wells, whose, production takes the place of the loss in production through decreased yield of the old wells, is considered an operating expense, for the reason that the total income-producing power of the property is not increased. The cost of these new wells may be added directly to production expense, or it may be charged to capital account, and this account depreciated to the same extent. In either case, after an oil company is on a satisfactory income-producing basis, the money for drilling new wells to maintain production must be taken from the income of the company. Three factors determine the cost of maintaining production: First, the rate of decline in yield of the wells; second, the cost of drilling and equipping new wells in terms of their production; third, the decrease in initial production of new wells as the property is drilled and gas pressure taken off the sands, etc. In order to check theoretical figures for the cost of maintaining production the writer, with the assistance of Reed Bush and Fred Tough, has compiled the following figures. It is necessary first of all to choose a&apos; period of time during which production for the field or territory studied remains fairly constant. The longer the period of time over which this condition prevails, the better. It is also necessary to eliminate or allow for any extraneous condition which may have affected the production returns, such as the shutting down of a large number of wells, the bringing in of a well of exceptionally large yield, the opening up of virgin territory where the flush yield is greater than will be had from new wells in after years, etc. All these conditions are exemplified most simply in the case of the Coalinga field, and perhaps these figures are more truly prophetic than the two other cases given. In applying these figures to the future it is well to assume that the average yield of new wells will constantly de-

Jan 1, 1916

By James H. Bechtold

The yield strength of annealed tungsten was found to have a strain rate exponent 12 times as great as that of low carbon steel. The effects of temperature and strain rate could be correlated through the Zener-Hollomon parameter with a heat of activation associated with yielding of 32,000 cal per g-atom. This heat of activation is independent of strain although both the temperature and strain rate dependence of the yield strength vary with strain. MOST metals have mechanical properties that are relatively insensitive to strain rate, especially at temperatures below that at which creep is important. In iron and molybdenum," however, relatively large strain rate effects are observed in the temperature range where the rapid increase in yield strength occurs which leads to the ductile to brittle transition. In this temperature range Zener and Hollomon&apos; have suggested that the effects of strain rate and temperature T on the yield strength could be correlated through a single parameter, P, in the following manner where Q is a heat of activation characteristic of the metal and associated with some unspecified relaxation process. They also observed that if the temperature is restricted to a relatively narrow range— below room temperature for steel—that the logarithm of the yield strength could be expressed as a linear function of the logarithm of P. From this relation the logarithm of stress should be a linear function of the logarithm of the strain rate at constant temperature: where r will be referred to herein as the strain rate exponent. At a constant strain rate the logarithm of stress should be a linear function of l/T, ay(e = C) ~ eT [4] where q = Qr [5] and is referred to herein as the temperature exponent. These equations have been found to relate the effects of temperature and strain rate on the yield strength of molybdenum in the temperature range wherein the ductile to brittle transition occurs, —75° to +150°C.2 Bechtold and Shewmon3 have shown recently that the ductile to brittle transition in annealed tungsten occurs in the temperature range +150° to +350°C. In this temperature range the yield strength in-

Jan 1, 1957

By David Schroeder, John Chipman

Jan 1, 1964

By FLOYD T. TAYLOR

IN 1833, less than one hundred years ago, Michael Faraday discovered and stated the laws of electrolysis. His discovery formed the foundation of a new use of metals which has now reached a variety of application not ordinarily appreciated. Furthermore, things can be done with electro-deposited coatings which have thus far defied other methods. Some of the uses of electro-deposited coatings are interesting. The tonnage of metals already finding an outlet through such a channel is considerable. In general electro-deposits have two characteristics: ornament plus utility; utility plus ornament. Both these factors are usually found associated in electro- deposits. Ornament plus utility was probably the first use. For example, the silver-plating of tableware, having its real birth in Birmingham, England, about 1844. However, this same ornament plus utility retarded the development of electro-plating, because in the beginning, electro-plated articles were branded with the odium of imitation and shunned accordingly. The gold brick of the swindler may be an exception to this statement.

Jan 1, 1929

By Thomas W. Mitcham

NUMEROUS ore deposits remain to be discovered. Many exposures of favorable host rock bodies within mineral provinces have not been adequately scrutinized geologically-the ore potential in buried portions of such rock bodies is enormous. Inasmuch as the more obvious deposits have been found, exploration has become more scientific and more expensive. Yet discovery continues to be very rewarding if exploration is intelligently approached. Although a number of exceptions can be cited, systematic geological exploration for ore on a significant scale has developed during the last two decades. So rapid has been the development of systematic exploration that a comparison of modern programs with those as recent as 1940, would suggest that many large mining companies and various Government agencies were hardly in the exploration business at that time. What is modern ore exploration? What major factors affect its success-economic discovery?

Jan 2, 1955

By J. Gurland

A method of measuring the degree of contact between grains of 1 phase in multiphase alloys is derived. It is shown that the number and the areas of contacts between grains can be determined by metallographic analysis. Relations between the area of contact, the dihedral angle, and the mean free path of spherical grains are developed. It is often desirable to interpret the mechanical behavior of alloys in terms of structural features observed under the microscope. A quantitative description of microstructures of multi-phase alloys requires consideration of geometrical and topological factors such as the amount, size, and shape of grains and the continuity of the constituent phases. The number and dimensions of grains may be metallographically determined by applying the methods described by Smith and Guttman1 and by Fullman2 in their papers on the measurement of particle size and internal boundaries in opaque bodies. The present work intends to show that the same methods can be used to evaluate some of the parameters of phase continuity; namely, contiguity, number of contacts, and areas of contact of grains of 1 phase. Application of these concepts may be found in such problems as the calculation of electrical conductivity of 2-phase alloys, or the evaluation of the length of fracture path through grains of a brittle phase more or less dispersed in a matrix. I. DEFINITION The following definitions and derivations are based on 2-phase alloys, of which the units of the microstructure are grains. Contiguity is defined as the average fraction of surface area shared by 1 grain of a phase with all neighboring grains of the same phase. In a 2-phase alloy of constituents A and B, the contiguity of phase B is given by: where Cb is the contiguity of phase B aBß is the average area of contact between a grain of phase B and adjacent grains of phase B, aAB is the average area of contact between a grain of phase B and adjacent grains of phase A. The contiguity is a measure of the average degree of contact between grains of phase B in the 2-phase mixture. The ratio varies from 0 to 1 as the distribution of phase B changes from a completely dispersed to a fully agglomerated structure. Smith and Guttman1 have shown that the relative areas of 2 kinds of interfaces in a volume are directly proportional to the number of interfaces of each type intersected by a random line. The lines can be drawn on metallographically prepared surfaces as long as these are random sections through the sample. The contiguity ratio of phase B then becomes: Cb = 2NBB/NAB + 2N BB [2] where: NBB is the number of interfaces between grains of phase B intersected per unit length of random line. Nab is the number of interfaces between grains of phase B and grains of phase A intersected per unit length of random line. The factor 2 arises in Eq. [2] because each interface B-B is associated with 2 grains of B-phase, whereas the interface A-B involves only 1 grain of B-phase. The calculations of contiguity do not require any assumption as to volume fraction, particle size, or particle shape. Fullman2 gives an expression for the determination of the mean free path between particles. The mean free path PB between grains of phase A, i.e., through grains or agglomerates of phase B, may be found from the relationship: PB =2fB/NAB [3] where fB is the volume fraction of phase B. The calculation of the mean free path is independent of grain shape and grain size distribution. The calculation of the number of contacts and of contact area requires assumptions of grain shape, grain size, and contact shape. In the case of uni-

Jan 1, 1959

By Louis D. Huntoon

AFTER the completion, in 1905, of the Hammond Mining and Metallurgical Laboratory of the Sheffield Scientific School, Yale University, it became necessary to secure and assay a large assortment of ore-samples, and to arrange the results in such a manner as to admit of use with the least amount of work on the part of the instructor. At first, pulp-samples, together with their respective assays, were secured from the mines, smelters, and public assayers, but this practice did not prove satisfactory. It was not only difficult to secure a sufficiently large supply of material, but it was also impossible to secure the proper assortment required for instructing students. It involved considerable work for the donors to select the samples and furnish a record of the assays, and also for the instructors to examine each pulp and determine its character. Some of the samples did not contain a sufficient quantity of pulp for the student to check his work in case his first assay did not correspond to the record. In order to increase the number of samples and to vary the character of the material, pulp-samples were later mixed with barren rock and with sulphides, but this method also was unsatisfactory and has been discontinued. At present., small lots of ore are secured by gift or purchase from engineers, public assayers, and the managers of mines, mills, and smelters. These lots weigh from 10 to 100 lb. each, and are rarely finer than 0.25 in. in size. The larger samples permit of a careful study by the instructor in order to determine the best method of assaying to be followed. In universities in which assaying is taught the record of the samples should fulfill the following requirements

Nov 1, 1909

By Ralph H. Sweetser

Carbon in pig iron is not only essential but, ordinarily, it is the most abundant metalloid present; iron without carbon could not be pig iron. Carbon in pig iron has been accepted, but seldom specified. How it gets into the pig iron as it is being smelted in the blast furnace, and why just about so much of it enters into the pig iron in certain blast furnaces, and more of it,; or less of it, enters the pig iron in other blast furnaces, or in the same blast furnace under varying conditions, are problems that have not yet been satisfactorily solved. During my own practical blast-furnace experience, I collected analyses of pig iron, including the graphitic and combined carbon, and recorded them in reference to the percentage of silicon present, having in mind the generally accepted explanation that "silicon drove out the carbon." To this actual experience, I have added some analyses given to me by J. B. Rogers, who was superintendent of the blast furnaces of the Ashland Iron & Mining Co., Ashland, Ky., and was making "silvery iron" at the time. These analyses are shown in Table 1. The analyses do not tell the whole story, but they show that with Pocahontas beehive coke, the total carbon was generally high. The data relating to the composition of the slag are lacking but my own customary practice was to have a rather basic slag. During my experience in making pig iron for the Bessemer and open-hearth departments, there were times when the steel men would complain about some mysterious quality in the pig iron that caused bad steel, in spite of the fact that the percentages of silicon, sulfur, phosphorus and manganese were within the specifications. Many reasons were advanced for this undetermined "poison" in the pig iron, but the favorite one offered by the steel men was that the blast-furnace man had "oxidized" the pig iron at the tuyeres in his eagerness to get big production and low cost. To these complaints of the users of steel-making pig irons were added those of the gray iron-foundry men and the malleable iron men. These groups are unaninlous in their conclusions that the trouble lies with the blast-furnace men; but there is not yet any harmonious conclusion as to the exact cause and remedy.

Jan 1, 1927

By John T. Galey

An intensified search for gas, because of the shortage in the area, led to the completion of 482 wells in southwestern Pennsylvania during 1944. This number was 27 more than the number in 1943, but 118 of the wells were nonproductive. Shallow Development Oil The initial production of the 25 producers completed was slightly less than was obtained from four wells above last yearJs total. The largest well, 20 bbl., was found in the Big Injun (Miss.) sand in Morris township, Washington County, at a depth of 2085 ft. It is currently producing about 3 bbl. per day. Outside the main producing area, a well drilled in Nicholson township, Fayette County, obtained 15 bbl. per day from 1864 to 1866 ft. in the Gantz (U. Dev.) sand. The Federal subsidy of 75¢ per barrel, effective , 1, 1944, which increased to $3.40 the current pipe-line price in this area, seems to have been insufficient stimulus to materially increase drilling for oil, although more repressuring operations are contemplated. Gas The volume of initial open flow of gas developed is off slightly over 10 million cu. ft. from 36 more wells than were completed a year ago, and the average rock pressure of this new gas is more than 100 lb. less than that obtained a year ago. Apparently the best find of this year was reported in Patton township, Allegheny County, where an initial volume of over 4 million cu. ft, was encountered in the Speechley (U. Dev.) sand at a depth of from 3293 to 3303 ft. The rock pressure there, 1190 lb. per sq. in., is nearly virgin. However, this area is fairly well delimited by dry holes and docs not seem nearly so promising from the standpoint of reserves as the Armbrust area, which was discovered several Years ago. In the patton township locality another fair well with 1303 M cu. ft. open flow and 400 lb. Per 59. in. rock pressure completed in the Hundred-Foot (U. Dev.) sand at a a depth of 2125 feet. Armstrong County, as usual, leads in number of producing wells completed with lowest percentage of failures but ranks only fou th in volume of production developed. Only two wells here had more than one million cubic feet capacity, but the rock pessure was under 200 Ib. Per sq. inch. In Fayette County, where the largest portion of new gas was found, activity appears to be shifting eastward. In Luzerne township, four producers having a total combined initial open flow in excess of 10 million cu, ft, were found in the Big Injun (Miss.) sand. The best well was found also in the same area in the Speechley sand (U. Dev.) at a depth of 3460 ft. This was a 2500-M CU. ft. well in Georges township. Several wells of more than a million cubic feet capacity were found in Jackson, Washington, Wayne and Whitley townships, Greene County. None of these, however, was in a new pool.

Jan 1, 1945

By Howard A. Smith

Of late considerable experimental and theoretical interest has been shown in the rates of transformation from a single phase, usually a supercooled solid solution, into one or more phases. Such reactions may involve both diffusion and transformation of the major constituent, as in iron alloys, or it may simply involve diffusion, as in superstructure formation and in age-hardening systems. Most of the work has been confined to ferrous alloy1-9† although two investigations have been made on copper alloys10*". That such work may be of considerable practical importance has been demonstrated by Bain12, by the workers at the Kaiser Wilhelm Institut fur Eisen-for~chung&apos;13, 14, and by the everyday use of precipitation and age-hardening principles15. Experiments in this country have generally followed Davenport and Bain&apos;s technique of rapid supercooling followed by isothermal treatment. In Germany16, 17 the work has been extended to the study of the influence of accurately controlled and measured rates of cooling. The work on steel indicates that there are two subcritical temperature ranges where reaction starts sooner after quenching and proceeds at a more rapid rate than at other temperatures. At suberitical temperatures above Ar" (temperature of martensite formation) where reaction is dependent upon atomic migration there is a period of time of which the length depends upon the alloy content and the temperature, before which no reaction has been detected. Davenport and Bain&apos; find that different sorts of atoms in solid solution in gamma iron affect the length of this " prereaction" period differently, manganese probably being the most effective in lengthening it. It is very difficult to believe that nothing occurs within these "prereaction" regions, for if this were so there is no reason why any reaction at all should be observed. In the light of experimental facts and theoretical considerations it is certainly

Jan 1, 1935

By Howard A. Smith

Of late considerable experimental and theoretical interest has been shown in the rates of transformation from a single phase, usually a supercooled solid solution, into one or more phases. Such reactions may involve both diffusion and transformation of the major constituent, as in iron alloys, or it may simply involve diffusion, as in superstructure formation and in age-hardening systems. Most of the work has been confined to ferrous alloy1-9† although two investigations have been made on copper alloys10*". That such work may be of considerable practical importance has been demonstrated by Bain12, by the workers at the Kaiser Wilhelm Institut fur Eisen-for~chung&apos;13, 14, and by the everyday use of precipitation and age-hardening principles15. Experiments in this country have generally followed Davenport and Bain&apos;s technique of rapid supercooling followed by isothermal treatment. In Germany16, 17 the work has been extended to the study of the influence of accurately controlled and measured rates of cooling. The work on steel indicates that there are two subcritical temperature ranges where reaction starts sooner after quenching and proceeds at a more rapid rate than at other temperatures. At suberitical temperatures above Ar" (temperature of martensite formation) where reaction is dependent upon atomic migration there is a period of time of which the length depends upon the alloy content and the temperature, before which no reaction has been detected. Davenport and Bain&apos; find that different sorts of atoms in solid solution in gamma iron affect the length of this " prereaction" period differently, manganese probably being the most effective in lengthening it. It is very difficult to believe that nothing occurs within these "prereaction" regions, for if this were so there is no reason why any reaction at all should be observed. In the light of experimental facts and theoretical considerations it is certainly

Jan 1, 1935

By Neville J. Price

In order that the reader may not be misled, I feel it necessary to comment upon the title of this paper. "Laws of Rock Behavior," one may take as being part of the all-embracing "Law of Nature" and this, according to the Oxford Dictionary, relates to the principles of conduct recognized as being pleasing to God. I feel it would be presumptuous to erect a code of rock behavior on this basis, so turn to a secondary definition, namely that a "Law" is that which is intrinsically reasonable. It is extremely unlikely that any group of geologists, or workers in rock mechanics would be in complete agreement about what could be taken to be "intrinsically reasonable." Therefore, this paper does not present any deified utterances, but rather deals with a few aspects of rock behavior which I consider to be intrinsically reasonable and with which I hope the reader will concur. The mode of behavior of rocks in the Earth&apos;s crust covers the range from wholly brittle to completely ductile ; with a deformation time scale which may be measured in milliseconds, for some events such as meteoritic impact, or in millions of years for the tectonic deformation involved in mountain building. A complete survey is, of course, outside the scope of an introductory paper, so I must be both brief and selective in my treatment. Any attempt to establish the mode of rock behavior in the Earth&apos;s crust should take into account data and relationships established in laboratory experiments and correlate these with field evidence. Consequently, the first section of this paper presents a brief discussion of the experimental aspects of rock mechanics which are pertinent to the subsequent discussion.

Jan 1, 1970

By Lyman Johnson

Single crystals qf copper in "single slip" orientatiorzs have been deformed in compression. During defortnation all of the independent deformation parameters have been measured. These parameters consist of thefive strain components and three components descrihing the lattice rotation. By a finite strain analysis these pararmeters , forrming a deformation gradient martrix, are related to the amounts of slip on each of the twelve slip systems. The results show that the amount of secondary slip is about equal to the amount of primary slip. This is an order of magnitude larger than has been believed previoutsly. ACCORDING to early theory and experiments, when a single crystal of a fcc metal is deformed in tension or compression it should deform by slip on only one slip system until the stress axis reaches a symmetrical orientation.&apos; However. the observation of a large increase in the secondary dislocation density during ..single slip" makes it clear that some slip does occur on secondary systems. Knowledge of the amount and distribution of this secondary slip is essential to a complete understanding of the mechanisms of single-crystal deformation. Ahlers and Haasen 2 and Mitchell and Thornton1 have tried to detect the amount of secondary slip in single crystals of silver and copper, respectively. Each simultaneously measured the angle A, between the tensile axis and the primary slip direction and the length 1 of a gage section of the specimen after incremental amounts of deformation in tension. The measured A, was then compared with the theoretical single slip angle hp. given by sin Ap = j sin . hO where ?o was the initial angle between the tensile axis and the primary slip direction and lo was the initial gage length. In both sets of experiments a small but systematic difference between ?e and ?p was found. This difference must be due to the occurrence of secondary slip. However, as Mitchell and Thornton1 pointed out. nothing quantitative can be said about the amount and distribution of this secondary slip from the measurements that they made. The reason that no quantitative conclusions could be made is because no unique solution for the distribution of slip on the twelve fcc slip systems can be determined from only two measured deformation parameters such as A and 1. There are, in fact, eight independent macroscopic deformation parameters that can be measured when a single crystal undergoes a homogeneous deformation. Physically these can be thought of as the five finite strain components and the three angles describing the crystal lattice rotation. All eight of these parameters were measured by Taylor4,5 for aluminum deformed in tension and compression. At that time the concern was to show that slip occurs on {111 (110) systems in fcc metals, and the mathematics were not available to determine what slip distributions were compatible with the measurements. In this paper the mathematics6,7 are developed that allow the slip distribution to be determined from these measurable macroscopic deformation parameters. The analysis is applied to the measurements of the strain and lattice rotation of copper single crystals deformed in compression. The results show that the amount of secondary slip is an order of magnitude larger than had previously been thought. CRYSTALLOGRAPHIC DESCRIPTION OF A HOMOGENEOUS DEFORMATION The deformation of a solid body can be represented by a transformation matrix F that transforms the un-deformed state into the deformed state. Consider a vector X connecting two material points in the unde-formed material and the vector x connecting the same two material points after deformation, where both vectors are referred to the same set of Cartesian axes. The final vector x is related to the initial vector X by the equation: X = FS. [2] Eq. [2] can be considered as the equation defining F, which is called the deformation gradient matrix. Its components are: If the deformation is homogeneous, the transformation is linear and the components of F are constants. Using subscript notation, if P is the unit vector in the initial direction of a material line, the components of the unit vector p in the direction of the same material line after deformation are given by:

Jan 1, 1970

By CHARLES R. KETES

I. INTRODUCTORY. Lake Valley, New Mexico, has long been one of the most widely known mining districts of southwestern United States. For many years its silver-mines have been among the most famous of the country, visited by many mining men and geologists; yet little information regarding the origin of the ore-deposits and the influencing geologic conditions has found its way into print. With the recent revival of public attention, after a decade and a half of utter stagnation, to the mining of silver in the Southwest, special interest attaches to the genesis and geologic disposition of the ore-bodies which are so finely open to inspection in the Lake Valley district. Moreover, the local features here described are typical of the conditions existing over a much larger field. The fact that the ores are chiefly the chloride and the chloro-bromide of silver adds further interest. Data bearing upon the genesis of haloid ore-deposits are, at the present time, very much sought. Arid regions offer particularly favorable conditions for the formation of such ores. This New Mexican district appears to supply solutions to many problems concerning this class of ores, which have long vexed the student of ore-deposits. II. LOCATION AND HISTORY. The town of Lake Valley is situated in Sierra county, in the southwestern part of New Mexico, and 100 miles northwest of El Paso, as the crow flies.From a mining standpoint, the location of the place is itself suggestive, as it lies on the southeastern slope of the great quaquaversal arch of the Colorado plateau. The center of this vast dome is in north-central Arizona, and radii about 150 miles in length reach its foot in all directions. Around its basal margins runs the broad mineralized belt containing most of the great mines of the Southwest, which extends from south-central Colorado southward and southwestward through New Mexico, thence westward through Arizona, northwestward and northward through southeastern California and western Nevada, and, finally, eastward through Nevada and Utah into Colorado again. This great mineralized belt is important as geographically limiting profitable mining over the greater part of five States.

Jan 1, 1908

By Aug. J. Jr. Bowie

(Read at the Wilkes-Barre Meeting, May, 1877.) Brief Outline of the General Topography of the Gold Regions of California. THE topographical features of California, as demonstrated by the explorations of the State Geological Survey, are found to be exceedingly simple. Three equidistant parallel lines can be used in conveying a general idea of the physical geography of Central California. A straight or " main axial line," whose course would be north 31° west, passing through the culminating peaks of the Sierra for a distance of five hundred miles, can be assumed as the eastern boundary of the State. A second parallel drawn fifty-five miles west of the " main axial line" will skirt the western base of the Sierra Nevada, along the edge of the foot-hills. A third parallel run equidistant from the second will represent "as nearly as possible the western base of the Coast Ranges." These parallel lines divide the State into three belts, namely, the Sierra, the Great Valley of California, and the Coast Ranges. " This arrangement of the physical features holds good for a length of four hundred miles in the direction of the main axial line, comprising almost the whole of the agricultural and the greater part of the mining districts."* The section of the country which is of immediate interest to the miner is the western slope of the Sierras. These mountains, rising in a short distance from the Sacramento plains to elevations of over seven thousand feet, with occasional peaks ten and twelve thousand feet high, are cut by numerous deep and precipitous gorges or capons, through which drains the immense watershed of the Sierra, supplying the main rivers of the State and ultimately emptying into the Pacific Ocean. Between these capons, ridges or divides are formed, on top of * See vol. i, p. 5, Geological Survey of California. J. D. Whitney, State Geologist.

Jan 1, 1878