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By Winston W. Spencer

ALTHOUGH by far the largest A consumer of platinum metals in the world, the United States until recently has been in- significant as a producer. Writing in the "Minerals Yearbook" for 1939, H. W. Davis states that 1938 probably marked the beginning of an- other period of transition in the world production of the platinum metals. In that year, he says, their production in the United States jumped to 49,380 oz., or fourth in the rank of world output. In the ten-year period 1925 to 1934 United States output ,averaged only 8300 oz. Practically all of this sudden in- crease in production is attributable to the introduction of mechanized equipment at the placer deposits in the Goodnews Bay district of Alaska. This district adjoins the Bering Sea and Kuskokwim Bay (accented on the first syllable), and is approximately 120 miles south of the mouth of the Kuskokwim River. The nearest village and post office is Platinum, which lies about eleven miles north- east of the Goodnews Bay Mining Company's camp. A good gravel road connects the mine camp and the village.

Jan 1, 1940

By Alexander Anderson

TABLES showing the drift and inclination of wells surveyed in the years 1924 to 28' and in the year 1929' have already been published. Each of these tables included a little over 1,000,000 ft. of rotary hole. In the year 1930 the table -shown-in . Fig. 1, comprising, the results of surveys .of 1,030,344 ft. of hole and representing 11,642 individual survey readings, was compiled. For that purpose we selected 'I only wells that had been drilled in California during that year. The footage of Fig. 1 differs from the two earlier tables in that the wells were all drilled in the year 1930. In the earlier tables, the footage shown was surveyed in the years designated, but some of the wells were drilled in earlier years.

Jan 1, 1931

By John Dasher

Extrapolation is a useful technique, but it can be overdone. Seldom is it justified to study over a range of 1 to 6 and extrapolate the results to 150,000. It is especially dangerous if the extrapolation is based on a false assumption. The authors assume settlers scale-up by residence time rather than by area, admit their result (a settler depth of 7 m) is "unreasonable" and suggest longer, wider, shallower settlers might be better. Various authors have noted for a copper-LIX system a total flow basis of 2 gpm per sq ft for sizing settlers. The results of this are compared with those in the paper in [Table 7]. The authors note that flooding of their settlers was never approached. Thus the smallest unit calculated is understandably twice too big. The largest however, is 5% of the required size. I note that the figures in [Table 6] for 1/min/cm2 are based on plan area rather than cross section as titled and are wrong by l0 4. A flow of 2050 1/min/cm2 is about Mach I. It is also 10 5/3 or 46.5 times that of the little one, although the abstract says the design was based on constant flow rate per unit cross section.

Jan 1, 1977

By S. L. Hoyt

ABOUT three years ago eight standard steels were prepared for the cooperative investigation of methods for oxygen analysis, sponsored by the Iron and Steel Division of the American Institute of Mining and Metallurgical Engineers and by the National Bureau of Standards. A preliminary report of the results was made at the annual meeting of the A.I.M.E. in February, 1936. ? This report showed the reliability of vacuum-fusion methods and further brought out certain advantages of the fractional vacuum-fusion method. The results obtained by the authors with the latter method will be discussed here, with some com-ments on the procedure for those who are interested in determinations of gases in steel. Some additional comments are offered on the use of the polarizing microscope for identifying the inclusions in the steel to check and amplify the findings of the fractional vacuum-fusion analysis. For details of the fractional method, see the paper by L. Reeve1.

Jan 1, 1937

By T. L. Fritzlen

Extrusion of aluminum alloys in this country is performed mainly by direct extrusion, therefore this paper is confined only to factors affecting the rate of extrusion by this method. Many factors affect the rate of extrusion of aluminum alloys. It is the purpose of this paper to present a discussion on the factors that are subject to technical control. Most of them are closely related, so that a clear-cut distinction between them is rather difficult. However, an attempt will be made to evaluate the effect of each factor separately, as far as possible. The most important factors only will be considered, and these will be discussed in detail under three general headings: (I) characteristics of the equipment, (2) size and structure of the ingot, and (3) temperature of ingot, cylinder, and other parts. It is a well established fact1 that the pressure and the speed of extrusion are related and are exponential functions of one another. Therefore, whenever a certain condition tends, for instance, to increase the pressure required for extrusion, it will reduce the extrusion speed if the pressure is maintained constant. For this reason, in this paper the effect of various conditions is expressed either in regard to their effect on the pressure required or the extrusion speed. Another established fact is the relation- ship between the temperature of the material being extruded and the pressure required to extrude. According to Schi-shokin,= this relationship is of the exponential type, and as the temperature is increased the pressure required is decreased. It would seem from the preceding that the greatest rates of extrusion can be obtained by the use of higher temperatures. However, as is well known, other factors intervene to limit the rate of extrusion of aluminum alloys when increasing the temperature. These factors will be discussed in detail later. Characteristics of the Equipment The capacity of the press determines * the maximum unitary pressure that can be applied for any given cylinder diameter. Pressures used for extrusion of aluminum alloys range from approximately 50,000 lb. per sq. in. to 150,000 lb. per sq. in., dependent upon the alloy and the size of the shape extruded. Higher pressures could be used to advantage, but existing steels limit pressures employed in the production of extrusions. Numerous mechanical characteristics of the extrusion press affect extrusion rate. The most important characteristics of the press itself are: (I) sensitivity of the main pressure valve and accuracy of pressure gauges, (2) accuracy of equipment to heat the cylinder uniformly and to control cylinder temperature, and (3) accuracy of means of measuring the speed of extrusion. The variables subject to control during the extrusion operation are pressure, temperature, and speed, and it is evident that the preceding characteristics

Jan 1, 1946

By T. L. Fritzlen

Extrusion of aluminum alloys in this country is performed mainly by direct extrusion, therefore this paper is confined only to factors affecting the rate of extrusion by this method. Many factors affect the rate of extrusion of aluminum alloys. It is the purpose of this paper to present a discussion on the factors that are subject to technical control. Most of them are closely related, so that a clear-cut distinction between them is rather difficult. However, an attempt will be made to evaluate the effect of each factor separately, as far as possible. The most important factors only will be considered, and these will be discussed in detail under three general headings: (I) characteristics of the equipment, (2) size and structure of the ingot, and (3) temperature of ingot, cylinder, and other parts. It is a well established fact1 that the pressure and the speed of extrusion are related and are exponential functions of one another. Therefore, whenever a certain condition tends, for instance, to increase the pressure required for extrusion, it will reduce the extrusion speed if the pressure is maintained constant. For this reason, in this paper the effect of various conditions is expressed either in regard to their effect on the pressure required or the extrusion speed. Another established fact is the relation- ship between the temperature of the material being extruded and the pressure required to extrude. According to Schi-shokin,= this relationship is of the exponential type, and as the temperature is increased the pressure required is decreased. It would seem from the preceding that the greatest rates of extrusion can be obtained by the use of higher temperatures. However, as is well known, other factors intervene to limit the rate of extrusion of aluminum alloys when increasing the temperature. These factors will be discussed in detail later. Characteristics of the Equipment The capacity of the press determines * the maximum unitary pressure that can be applied for any given cylinder diameter. Pressures used for extrusion of aluminum alloys range from approximately 50,000 lb. per sq. in. to 150,000 lb. per sq. in., dependent upon the alloy and the size of the shape extruded. Higher pressures could be used to advantage, but existing steels limit pressures employed in the production of extrusions. Numerous mechanical characteristics of the extrusion press affect extrusion rate. The most important characteristics of the press itself are: (I) sensitivity of the main pressure valve and accuracy of pressure gauges, (2) accuracy of equipment to heat the cylinder uniformly and to control cylinder temperature, and (3) accuracy of means of measuring the speed of extrusion. The variables subject to control during the extrusion operation are pressure, temperature, and speed, and it is evident that the preceding characteristics

Jan 1, 1946

By R. E. Fryxell, E. C. Duderstadt, P. K. Conn

Permeation rates for nitrogen through are-cast tungsten were measured in the temperature range 1800° to 2600°C at nitrogen pressure differentials of 1.0 and 0.1 atm. Gas chromatography was used to measure the quantities of nitrogen which permeated through 0.26-and 0.53-mm-thick membranes. Permeation rates were proportional to the difference between the square roots of the nitrogen pressure on each side of the membrane and inversely proportional to membrane thickness, indicating that atomic nitrogen was the difjusing species and that diffusion was the rate-limiting step of the process. Permeation coefficients calculated from the rates may be represented by the equation: where P is expressed in the units cu cm (stP)-mm per 1/2 sq cm-min-atm"' and 70.0 * 0.8 is the activation energy in kcal per mole of permeating species. In a previous paper' permeation rates were reported for hydrogen and for oxygen through tungsten. The permeation cells used for the hydrogen measurements were suitable for measuring nitrogen permeation under similar conditions, so the study was extended to include nitrogen. Permeation rates of nitrogen through the polycrys-talline arc-cast tungsten membranes were measured in the temperature range 1800" to 2600°C using two membrane thicknesses and two nitrogen pressure differentials. Permeation coefficients were calculated and the activation energy of the process determined. THEORY For diatomic gases which dissociate prior to diffusion, the quantity of gas which permeates through a membrane or wall at an elevated temperature where bulk diffusion is the rate-limiting step of the process is given by the equation: where: q = total amount of gas permeating a membrane, P = temperature-dependent permeation coefficient, A = area of membrane, t = time, p1 = gas pressure of high-pressure side, p2 = gas pressure of low-pressure side, and d = thickness of membrane. When bulk diffusion is the rate-controlling step, and the solubility of the gas obeys Henry's law, a further relationship is that, for any given temperature and pressure, the permeation is the product of diffusivity and the amount in solution. The permeation coefficient, P, is temperature-dependent according to the equation: where: Po = permeation constant, Q = activation energy, R = gas constant, and T = absolute temperature. EXPERIMENTAL PROCEDURES Cell Design and Experimental Apparatus. Two of the permeation cells used for the previous measurements of hydrogen permeation are shown in Fig. 1. Each consisted of a cylindrical chamber divided into two parts by a permeation membrane fabricated from high-purity (>99.9 pct W) wrought tungsten sheet made from vacuum arc-cast tungsten. The membrane in one cell was 0.26 mm thick and the other was 0.53 mm. The fabrication of these cells was described previously.' The permeation cells were mounted vertically in a high-temperature tungsten resistance furnace and the membranes and the center portions heated to test temperatures. Temperatures were measured by sighting an optical pyrometer on the edge of the membrane through a small hole in a tungsten plate which was fastened to the side of the cell. This arrangement provided an approximate black-body condition and eliminated the need for emittance corrections. Appropriate corrections were made for the quartz window through which the temperatures were measured. Argon gas flowed through the 10-liter volume of the furnace at the rate of 4.7 liters per min. An impurity

Jan 1, 1969

By C. E. Coleman, D. Hardie, A. E. Wraith

A photoguaplric method of measuring crack velocities has been applied to an examilzation of- the effect of hydrogen on the impact properties of zirconium. Results indicate that the crack in hydrided zirconit travels at about 26 m per sec whereas that in the uacuum -annealed is dependent on the speed of the hammer. RECENT work on the effect of hydrogen on zirconium reveals that when hydrided zirconium is tested in slow bending the crack producing failure can be unstable. The mode of fracture seems to involve the crack linking up broken hydrides by a ductile mechanism in the zirconium matrix.2" In order to compare the fracture of zirconium with that of other metals which show unstable crack propagation, notably steel, the rate of the crack spread must be known. As the methods previously used for measuring crack growth are either unsuitable for the present work5-'' or very costly," a simple technique has been devised in which the maximum crack velocity is derived from a series of crack position-time measurements. EXPERIMENTAL PROCEDURE The experimental arrangement is shown schematically in Fig. 1. The flash unit12 was triggered when the Charpy hammer touched the specimen and the 6-psec flash of the lamp delayed by a preselected time interval in the range 100psec to 10 msec. The camera was left on open shutter during the test. From direct measurement on a calibrated photographic print, Fig. 2, the position of the crack and the specimen was found at a known time after impact and, from a series of such tests using an appropriate range of flash-delay times, the crack velocity was estimated. Preliminary experiments were carried out on mild steel above and below its transition temperature. Vacuum-annealed zirconium, and zirconium hydrided to 100 ppm H were then tested at 20" and 150°C. For comparison, Zr-2.6 pct Nb alloy (in the 0 + transformed /3 condition), vacuum-annealed or hydrided to 100 ppm H, was tested at 20 C. The chemical analyses of these materials are given in Table I. For the high-temperature tests a fine chromel-alumel thermocouple was spot-welded onto each specimen close to the notch. The test piece was heated up to 200°C to allow enough time for preparing the apparatus while the specimen cooled to the testing tem- perature. It was assumed that the specimen cooled uniformly. The accuracy of the flash-delay time was better than i2 pct i 5 psec. The crack length was taken as its maximum distance traveled normal to the length axis of the specimen. Errors in these measurements arise as a result of the uncertainty in the location of the crack tip and the difficulty in defining the exact position of the crack starting point. The latter was due to the bonding and large amounts of deformation at the hammer contact point, especially in the vacuum-annealed specimens tested at 150°C. The maximum error in the measurements was however estimated to be about 5 pct. DISCUSSION OF RESULTS From the trial experiments using mild steel above its transition temperature it can be seen from the plot of crack length against time after impact, Fig. 3. that a reasonable estimate of the maximum crack velocity at the surface of the specimen may be made. Other features of note are the initiation time before the crack is first seen and the slowing down period

Jan 1, 1967

By P. H. Metzger, D. W. Fuerstenau

The activation of sphalerite was found to occur at a much lower rate with Pb++ then with Cut++ or Ag+. To prevent activation with Pb++, the ratio [m in solution must approximate 103. An example is given illustrating how this condition is met in practice through the addition of zinc sulfate and soda ash. In selective lead-zinc flotation, the mill operator, especially the one who is concentrating a partially oxidized ore, often must add zinc sulfate and/or soda ash for effective depression of the sphalerite. In the present paper the authors show how this practice prevents the activation of sphalerite in the presence of Pb++. A number of years ago Gaudin (1) postulated that Zn++ might control the activation of sphalerite with Pb++ through competitive adsorption. However, recent experimentation has shown the activation of sphalerite with Ag+ and Cut++ to be a chemical reaction in which silver or copper ions replace zinc in the sphalerite lattice through the formation of a more insoluble sul-fide (2,3,4) Thus, if activation with Pb++ is similar to that with Ag+ or Cu t+, zinc salts should control the activation of sphalerite not through competitive adsorption but because the ratio of [zn++/Pb++] in solution regulates the extent of the chemical exchange between Zn++ and Pb++ in the solid phase. The objective of this investigation has been to study the kinetics and equilibrium conditions for the uptake of Pb++ by sphalerite and to investigate the prevention of lead activation with zinc salts. BASIC PRINCIPLES Sphalerite activation has been shown to be a replacement reaction wherein a less soluble compound is formed at the expense of the more soluble zinc sul-fide (2,3,4) For example, if sphalerite is placed in an aqueous silver nitrate solution, ZnS gives to the solution more S= than can exist together with Ag+, and hence the following reaction takes place: ZnS + 2 Ag+? Ag2 S + Zn ++; k = [zn ++]/[Ag ++]2 = 10 26 (1) Therefore, ZnS will dissolve in the presence of Ag+ and activation of sphalerite with Ag+ will proceed after monolayer coverage by solid state diffusion until equilibrium conditions are reached in the system (2, 4) Because of the large difference in the solubility of ZnS and Ag2S, zinc salts cannot affect the reaction unless a complexing agent, such as cyanide ions, is present to complex Ag+ more tightly than Zn++ . By complexing Ag+ and Zn++ in solution, the uptake of Ag+ by sphalerite can be regulated by controlling the ratio m. . Experimentally (2) it was found that the activation of sphalerite by Ag+ could be prevented through the addition of NaCN if this ratio reached a value of approximately 10 26. The mechanism of sphalerite activation with copper salts is given by the following reactions: ZnS + Cu ++ ? CuS + Zn + + ; (2) k = [Zn++]/[Cu++] = 10 11 ZnS + Cu + ? Cu2S+ Zn++; (3) Experimentally Mao (3) found that the activation of sphalerite with Cu++ or Cu + was prevented if the ratios expressed in Equations 2 and 3 were approximately l09 and l022, respectively, with cyanide ions as the deactivator. Although zinc salts do not affect the activation of sphalerite with silver or copper ions in the absence of a complexing agent, activation with lead ions theoretically can be controlled by the addition of zinc salts because of the relatively small differences between the solubility of ZnS and PbS (5). Equilibrium

Jan 1, 1961

By Homer Griffield Turner

The nature and comparative features of anthracite and bituminous coals have been discussed by the writer in two previous papers.' Although this paper is offered as a further contribution to the subject, it seems desirable at the outset to repeat some of the descriptive matter of the early works in order to show the actual connection between various constituents of both coals and the new photomicrographs and other physical and chemical properties. Structure of Anthracite and Bituminous Coals A lump of bituminous coal (Fig. 1) is readily seen to be composed of layers differing from one another in texture, luster and thickness. There are, in general, three kinds of layers, although only two are usually seen. One is deep black, very compact, and has a bright luster; another is grayish black, has a duller luster and is less compact; the third is black, dull and porous in appearance, but because of its thinness is not often seen except on parting surfaces. This last material is charcoal. American students of coal morphology use the names anthraxylon, attritus, and fusain to designate these three constituents of laminated coal. Anthraxylon refers to the brightest bands, attritus to the duller layers, and fusain to the charcoal. Close examination of a lump of bituminous coal shows the brightest deep black layers to be embedded in the duller grayish black laminae. These deep black layers are lens-shaped and vary in thickness from thin sheets to over half an inch. They are often so continuous through the lump that their tapering terminae are not noticeable. On careful examination the duller grayish black laminae (Fig. 7) are seen to contain many very thin sheets of this very bright black material. The charcoal

Jan 1, 1930

By L. Mair

A STUDY by J. R. Low, Jr.1 on the effect of quench aging on the Charpy-impact specimens of semikilled 1020 steel disclosed that a decrease in cooling rate from 1275°F raised the transition temperature. This was demonstrated in his investigation by controlling the cooling rate of impact specimens to duplicate that of a heavier plate and com- paring the properties with air-cooled specimens and quenched specimens. The transition temperature of the samples that had been cooled at a rate estimated to be similar to that of an air-cooled 3/4 in. plate was approximately 45ºF higher than the quenched samples. The transition temperature of the air-cooled series was between that of the slow-cooled and the quenched series. On the basis of this work, it appeared that the cooling rate of plates after rolling in a hot mill would have a bearing on the brittle fracture of the

Jan 1, 1955

Executive Committee, Board of Directors Augustus B Kinzel, Chairman, J L Glllson, Vice-Chairman, A W Thornton, Howard C Pyle, Grover J Holt Finance Committee, Board of Directors Andrew Fletcher, Chairman, J S Vanick, Gall F Moulton Investments Gail F Moulton, '60, Chairman, Henry Krumb, '59, J Loveloy, '61, C R Dodson, ex off as Treasurer, Andrew Fletcher, ex off as Chairman, Finance Com¬mittee Endowment Andrew Fletcher, Chairman, N G Alford, H DeWitt Smith, W J Coulter, J V N Dorr, R B Gilmore, J B Haffner, O H Johnson, D H McLaughlin, J R McMillan, L F Reinartz, C E Weed, Wilfred Sykes, J R Suman Honorary Memberships H DeWitt Smith, '59, Chairman, C E Reistle, Jr, '59, Grover J Holt, '59, L F Reinartz, '59, M L Haider, '60, D H McLaughlin, '61, John M Lovejoy, '62, Augustus B Kinzel, ex off as President

Jan 1, 1958

By F. R. Brotzen, D. L. Davidson

ALTHOUGH much effort has been devoted to the problem, the nature of plastic flow in bcc metals is still not fully understood. Some of the difficulties encountered stem from the scarcity of information on orientation effects and the uncertainty as to the glide system in these metals. In an attempt to provide some of this information, the present investigation was carried out, using zone-refined molybdenum single crystals deformed in tension and in direct shear. Considerable evidence exists to indicate that the primary slip system for molybdenum is (110) <111>.1,2 Figs. 1 and 2 indicate that this is, indeed, the case for direct shear at room temperature (see Ref. 3 for a description of the shear-testing equipment and procedure). Moreover, from Fig. 2, the shear stress on the (123) is lower than that on the (112). This would be the case if, as has been suggested,4,5 slip on these two planes is in reality com-

Jan 1, 1965

THE CHAIRMAN (F. K. COPELAND,* Chicago, Ill.).-At this particular time conditions existing in this, country, and elsewhere, make all questions of milling or smelting or mining, or anything else, absolutely secondary to the one question of labor. We have always devoted our attention largely to the efficiency of machinery, and to reductions in costs, etc., and have let this tremendous problem of our relation to labor more or less take its own chances. There has never been a time when those who are responsible for the operation of business of different kinds were as com-pletely at a loss as they are now, so that anything that can be brought out that relates to labor is, to my mind, of utmost importance. T. T. READ, Washington, D. C.-This formulation of a method of curtailing forces at the Copper Queen is a notable step in advance of our treatment of personnel in the mining industry. So far as I know, it is the

Jan 12, 1919

By J. F. Abel, F. T. Lee

Subsidence is controlled by a complex com¬bination of mining and geologic factors. For example, a compilation of worldwide data shows that, as the percentage of shale in the overlying rock mass decreases and the amount of sandstone increases, the angle of draw (and the area affected by subsidence) decreases. Limestone in the over¬burden appears to cause a more than twofold decrease in the angle of draw compared to a like amount of sandstone. Increased amounts of sandstone were accompanied by a greater surface subsidence relative to the mining height. The total thickness of overburden did not appear to influence the subsidence magnitude above super-critical panels. The greater the thickness extracted, the smaller percentage of that thickness shows up at the surface as subsidence. The greater the percent of the seam extracted, the greater the subsidence reaching the surface. The maximum subsidence above room-and-pillar panels de¬pends on the pillar height and minimum width as well as the other factors listed.

Jan 1, 1984

By E. Peters

As in other fields of Extractive Metallurgy, Hydrometallurgy is preoccupied with separation processes and with oxidation-reduction processes. The physical chemistry of each type of process can be described in terms of thermodynamic equilibria and in terms of reaction kinetics. Reaction kinetics are much more important at the low temperatures limiting hydrometallurgical processes than in com- parable pyrometallurgical operations and the number of cases in which the kinetics can be described by simple liquid-phase mass-transfer models are sharply limited. It is convenient to subdivide the applicable rate phenomena into processes in which (a) interface reactions control the rate,(b) mass transfer processes control the rate, (c) solid state process affect the rate, (d) thermodynamically predicted phase changes or molecular reactions fail to take place, (d) metastable substances or supersaturated phases persist, and (elchomogeneous reactions in solution affect the chemistry and the kinetics. Examples are drawn from the unit steps of leaching, cementation, hydrogen reduction, and electrowinning.

Jan 1, 1973

By John W. Langley

In the summer of 1888 it was the fortune of the writer to present the subject of the desirability of establishing a set of samples of steel, which should be analyzed with extreme care, in order that they might become standards to which scientific and commercial analyses of iron and steel could be subsequently referred; also, that greater uniformity in the results of analyses might be brought about, since these standards would bear towards analytical methods somewhat the position which the original units of weight and length, the gramme and meter, or the pound and yard, preserved in Paris, London, and Washington, do to the mechanical arts. The plan met with hearty co-operation, with the result that com mittees were appointed in Sweden, Germany, France, England, and America, to receive the material and to see that the necessary au alyses were executed. In England, the British Association for the Advancement of Science appointed a committee, which subsequently published a plan

Jan 1, 1891

Herewith are transmitted the joint report of the Treasurer and Finance Committee for 1934 and the reports for the same year of the Chairmen of the following Committees: Admissions, Membership, Papers and Publications, Library, and MINING AND METALLURGY. TO these reports you are referred for details of the year&apos;s activities. Finances.-Income for 1934 from all sources totalled $134,967 com- pared with $121,689 in 1933. The increase is accounted for principally by four items: $6000 increase in initiation fees and dues of new members; $1800 in current dues; $4000 in "back" dues; and $2800 in the sale of publications, including TRANSACTIONS volumes and technical papers in the form of "separates." In passing, it may be remarked that income from back dues during 1935 will be less than in 1934, for the obvious reason that the total amount of dues in arrears has shrunk and consequently there is less to draw from. Income from

Jan 1, 1934

By Edward L. Wilson, Keshavan Nair, Ranbir S. Sandhu

In planning and designing of underground excavations and construction, it is of considerable importance that the stresses and displacements in the rock mass subjected to arbitrary sequences of unloading and loading be within allowable limits. For determination of the stress and displacement fields, the usual approach is to treat the rock as an elastic material and to apply the principles of the theory of elasticity. However, analytic solutions are available only for a limited class of problems of simple geometry and idealized material properties. Nonhomogeneity and anisotropy of material coupled with complex geometrical configuration and initial stress fields that are almost always preexistent in rock masses at great depths, render the problem intractable by analytical methods. Approximate solution techniques using numerical procedures have, therefore, to be resorted to. The finite element method as applied to plane stress analysis was introduced by Clough.1 It has developed into a powerful tool for the analysis of various field problems in structural and continuum mechanics. The method is well documented in the literature2-6 and, therefore, its historical development will not be discussed here. Wilson&apos;s analysis of the plane stress/strain problem has found extensive use in the area of soil and rock mechanics including stresses around underground openings; stresses and displacements in dams, foundations, etc.7-11 In his analysis of the axisymmetric solid,3 Wilson proposed a procedure to allow for certain cases of nonlinear material properties. In this chapter, the develop-

Jan 1, 1972

By Walter C, Smith

Metallic bismuth was known in the Middle Ages and the name is supposed to come from the German Wismut. The origin of the German name is uncertain. References to bismuth are found in the writings of Valentine, Paracelsus, and Agricola between 1450 and 1550. Early specimens of bismuth were very impure and often were confused with antimony, tin, and zinc. About the middle of the eighteenth century, J. H. Pott, C. J. Geoffroy, and Torbern Bergman succeeded in producing fairly pure bismuth and showed it to be an elementary metal similar in many respects to lead.

Jan 1, 1953