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APPROXIMATELY 90 per cent of the steel that is melted and refined in the United States and poured into ingots is made in basic open-hearth furnaces, as shown in Table 1-1. The annual ingot capacity of the steel industry reported January 1,1950, by the American Iron and Steel Institute8* was 99,040,160 tons, of which the basic open-hearth process accounted for 85,896,580 tons, 86.7 per cent of the total. The capacity of the individual furnaces varies over a wide range, a large majority falling within limits of 50 to 200 tons (Fig 1-1). Most of the units constructed [ ] since 1942 are in the larger size groups, between 175 and 225 tons capacity.

Jan 1, 1951

APPROXIMATELY 90 per cent of the steel that is melted and refined in the United States and poured into ingots is made in basic open-hearth furnaces, as shown in Table 1-1. The annual ingot capacity of the steel industry reported January 1, 1950, by the American Iron and Steel Institute3* was 99,040,160 tons, of which the basic open-hearth process accounted for 85,896,580 tons, 86.7 per cent of the .total. The capacity of the individual furnaces varies over a wide range, a large majority falling within limits of 50 to 200 tons (Fig 1-1). Most of the units constructed [ ] since 1942 are in the larger size groups, between 175 and 225 tons capacity.

Jan 1, 1964

By P. Somasundaran, D. W. Fuerstenau

This article presents the results of an analysis of grinding of 1:1 mixtures of 4x8-mesh quartz and limestone in laboratory ball and rod mills. From these experiments, the amount of energy consumed in grinding each component of the mixture was determined. In the ball mill, limestone consumes slightly more energy than quartz in the initial stages of grinding, but as the grinding proceeds quartz begins to consume a slightly greater fraction of the energy. The postulate that the fraction of energy consumed by any material in a ball mill is proportional to its volume fraction has been shown to be approximately true. On the other hand, in a rod mill energy consumption by quartz and limestone is equal only in the initial stages of grinding, with energy consumption by quartz greatly exceeding that by limestone as rod milling proceeds. Preferential energy consumption in tumbling mills has been discussed in a number of papers. For example, from an analysis of the kinetics of comminu- tion in ball mills, Arbiter and Bhrany' obtained rate equations based on the postulate that only coarse particles are ground, indicating that fine particles are protected from the action of the balls by coarser particles. In rod mills this protective action is much more pronounced than in ball mills. Recent studies on the rod milling of limestone-quartz mixtures have shown that this protective action causes the mineral with the lowest grindability (quartz in this instance) to consume the greater fraction of energy. 2 However, in the ball milling of mixtures it has been postulated that the consumption of energy by one of the constituents is determined by its volume fraction within the mill. 3 Possibly this hypothesis may be a simplification of the ball milling of mixtures since the protective action suggested by Arbiter and Bhrany may result in some preferential energy consumption by one of the constituents of a mixture. The objective of this study has been to determine preferential energy consumption in laboratory ball and rod mills by analyzing size distributions of each material in the products obtained from grinding 1:l mixtures of quartz and limestone. MATERIALS AND METHOD The procedure for carrying out the tests on wet grinding quartz-limestone mixtures has already been described.'r3 In the present investigation, 1:l mix-

Jan 1, 1963

By A. P. Herring, S. F. Ravitz

Manganese dioxide reacts with sulfur dioxide solution in the absence of oxygen to form manganous ion and dithionate ion, together with a small amount of sulfate ion. The effects of SO, concentration, hydrogen ion concentration, stirring speed, and temperature on the rate of the reaction were studied. If it is assumed that undissociated SO2 molecules react rapidly with MnO, at active surface sites and that bisulfite ions react slowly, an equation can be derived that satisfactorily represents the observed reaction rates. For solutions in which the reaction with undissociated SO2 predominates, reaction rates and activation energies estimated from diffusion theory agree well with those found experimentally. Manganese dioxide dissolves readily in aqueous solutions of sulfur dioxide. The nature of the dissolution reaction was first investigated by Gay-Lussac and welter1 in 1819; they identified a new oxysulfur radical, the dithionate ion, S2O6, as one of the reaction products. Since then, the reaction has become a standard method of preparing dithionates in the laboratory and one of the more promising methods of leaching manganese from low-grade ores. In the "dithionate process" developed by the U.S. Bureau of Mines2,3, manganese-dioxide ore is suspended in a solution of calcium dithionate and leached with gas containing sulfur dioxide. The manganese is dissolved and the sulfur dioxide is oxidized according to the reactions:

Jan 1, 1965

By P. T. Gallagher, W. A. Oates

THE partial excess entropy of interstitial solutes in metals, SXS , has usually been interpreted as being principally vibrational ever since the initial statistical treatment of hydrogen in metals by Fowler and Smith-ells. The vibrational entropy is considered being due to the optical modes of the light interstitial atom. Little attention has been given to the magnitudes of the values of SXS'. Leiser and Witte2 and Ebisuzaki and O'Keeffe3 have noted that for hydrogen in metals Si is approximately constant for different metals. On the other hand if it is assumed that the interstitial solute is an isotopic defect then, as shown by McLellan, SXS should vary from metal to metal as follows: where S is the standard entropy of the solvent and Mi, M, are the masses of the interstitial and solvent atoms. respectively. Fair agreement with this equation was found for oxygen in silver and nitrogen in iron4 and for carbon in iron.= Ln a subsequent analysis of metal- hdrogen systems McLellan' found a variation of $' from metal to metal but not in a manner expected from the isotopic impurity equation. However, a possible correlation between the energy of solution, Ei, and sf was noted. Similar correlations have been noted for certain dilute substitutional solid Solutions 7, 8 and recently Kubaschewski 9 has demonstrated a correlation between integral heats and ex-

Jan 1, 1970

By D. R. George, J. R. Ross, J. D. Prater

In the United States nearly 200,000 tons of copper per year are being produced, by leaching waste rock and oxidized copper ore with dilute sulfuric acid-ferric sulfate solutions and precipitating the copper on scrap iron. The flow of solutions is in excess of 80 million gpd. A survey conducted by the U.S. Bureau of Mines in late 1965 at 14 mines in Arizona, Utah and Nevada, showed that with a few exceptions, the solutions contain from two to a maximum of 15 ppm U3O8, and there is strong evidence that these represent equilibrium concentration and not merely an accumulated in-process inventory resulting from recycling the solutions for many years. Consequently, it is believed that uranium could be recovered at a constant rate as long as mining and leaching operations continue. Preliminary surveys and estimates by the USBM indicate a production potential of possibly 1000 tons of U3O8 per year at a cost of less than $8 per lb if the major process streams from most of the large copper mines in the western United States were to be treated. Laboratory research by the USBM showed that the uranium could be efficiently recovered as a specification-grade uranium concentrate by a combination of ion exchange resin and solvent extraction of liquid ion exchange techniques. A joint pilot plant investigation by Kennecott Copper Corp. and the USBM was conducted on solutions from the Bingham Canyon mine to evaluate a new system of countercurrent ion exchange developed during the laboratory studies. In subsequent small-scale continuous tests, recovery of uranium from the pregnant eluate by solvent extraction and chemical precipitation techniques was investigated.

Jan 1, 1968

By Gaudin. A. M., S. C. Sun

THIS paper presents the results of a study of the relationship of the electrokinetic or zeta potential to flotation phenomena. The relationship is established on the experimental evidence that mineral behavior in flotation and in cataphoresis is generally governed by the chemical properties and amount of the reagents adsorbed at mineral surfaces. Cataphoresis1-5 or electrophoresis is the name given to the movement of a charged particle in a liquid medium under the influence of an applied electric field. Mineral behavior in cataphoresis, as indicated by the magnitude and sign of its ionic charge, can be represented by the term zeta potential. In this paper, the zeta potential represents the difference in potential between the immovable liquid layer attached to the surface of a solid particle and the movable liquid layer in the body of the liquid, and is the result of the tendency of ions on the surface of the particle and within the liquid boundary layer to establish a condition of equilibrium. A high positive zeta potential means that the mineral surface is dominated by cations, a high negative zeta potential indicates domination by anions, and a low zeta potential indicates that the surface is influenced almost equally by cations and anions. In terms of observed quantities the zeta potential is given by the relation [z = 47ruu(300)$ Kx] in which z is the zeta potential expressed in in volts, u the viscosity of the solution in poises, u the velocity of particles in centimeters per second, x the impressed potential gradient in volts per centimeter, and k the dielectric constant of the solution in c.g.s. units. A convenient source for the derivation of the equation is the book by Thomas,6 The term zeta coefficient is an expression coined to denote the difference between the magnitude of the zeta potential of a mineral suspended in solution A, and that of the same mineral suspended in solution B, which consists of solution A and an additional chemical agent, but is at the same pH. For example, the difference between the zeta potential of galena particles in distilled water and that in any chemical solution at the same pH is a zeta coefficient. Or, when the zeta potential of a mineral particle is measured first in distilled water, then in a mixture of water and copper sulphate, and finally in a mix-

Jan 1, 1946

By K. Osseo-Asare

The DIAGRAM computer program has been used to develop stability diagrams such as Eh-pH, log [CNI-pH, and log [Me]-pH for the systems Me-CN-H 0 where Me = Au, Ag, Fe, Zn, Cu, Ni, Co. More complex 2 diagrams involving sulfur- and arsenic-containing species are also presented. With the aid of these diagrams, a discussion is presented of the solution conditions (e.g. pH, [CN], [CNS], Eh) vhich influence gold and silver extraction in cyanide solutions. Special emphasis is given to the effects of ore minerals or calcination products, such as pyrrhotite, pyrite, arsenopyrite and hematite on gold-silver dissolution. Application of the stability diagrams to solution treatment operations such as cementation is also indicated.

Jan 1, 1984

By William M. Courtis

While assaying some copper carbonate ore from the Frazer claims, Similakameen, B. C., I noticed that on parting the gold button a deep orange solution was formed. The button gave off pink bands in the nitric acid, which became deep orange at a short distance from it; and as it traveled over the surface of the porcelain dish, it left a deep orange track behind. As the button brightened in the cupel, it appeared to have a bronze color; but I have since found that when amarillium is in large excess of the gold, the button is a very dark gray. The button parted easily. To the orange solution I added a salt (NaCl) solution, shook in a silver testbottle, and filtered. With H2S I obtained a precipitate, which I supposed due to platinum. However, on further tests, it did

Jan 1, 1903

By Richard S. McCaffery, Morrison B. Yung

While assaying some copper carbonate ore from the Frazer claims, Similakameen, B. C., I noticed that on parting the gold button a deep orange solution was formed. The button gave off pink bands in the nitric acid, which became deep orange at a short distance from it; and as it traveled over the surface of the porcelain dish, it left a deep orange track behind. As the button brightened in the cupel, it appeared to have a bronze color; but I have since found that when amarillium is in large excess of the gold, the button is a very dark gray. The button parted easily. To the orange solution I added a salt (NaCl) solution, shook in a silver testbottle, and filtered. With H2S I obtained a precipitate, which I supposed due to platinum. However, on further tests, it did

Jan 1, 1903

By J. R. Long, A. H. Roberson, T. R. Graham, R. S. Dean

EXPERIMENTAL work on the properties of high-purity alloys of the copper-manganese-zinc system has necessarily required extensive metallographic work to determine the equilibrium conditions in this system. Previous work on these alloys is fragmentary and, unfortunately, based on alloys made with impure grades of manganese, thus introducing significant amounts of iron, silicon, aluminum and carbon. Since these elements are known to affect equilibrium conditions, it became desirable to re-examine these alloys made from the pure metals. The alpha solid solution field was of particular interest and, therefore, was chosen for the initial work, which was outlined to determine the composition limits of this field. PREVIOUS WORK Heusler1 conducted an extensive survey of the liquid-solid regions of this system and also made an estimate of the solid-phase boundaries at 340°C. The pertinent part of his diagram is given in Fig. I, but it is of limited usefulness, since it applied to a single temperature only and is based on impure alloys under admittedly nonequilibrium conditions. Bauer and Hansen,2 likewise working with impure alloys, have determined the phase boundaries for alphabeta brasses containing small amounts of manganese and indicate an increase in the extent of the alpha field with increasing manganese. This is not in accordance with Heusler or with data obtained on pure alloys.3 They also described a third constituent precipitating in the alpha plus beta field below 350° to 400°C. but did not identify this constituent. Guillet4 and Heike and Ledibur5 have also noted this precipitate Each of these investigators recognized that impurities present in the manganese could and did have an effect on the structure and properties of their alloys. Corson6 in particular pointed out the hardening effects of silicon, aluminum, and carbon in copper-manganese alloys and Heusler reported that his alloys containing more than 25 per cent manganese were extremely brittle. In all probability this brittleness was due to the impurities present. This early work, therefore, should be taken as a general guide for preliminary studies only, and high-purity alloys may be expected to produce different results. The work of the Bureau of Mines laboratories with electrolytic manganese has been briefly summarized by Dean7 but includes only a short section on this system. Later work3 outlined a limited portion of the alpha field in the neighborhood of 65 per cent copper, 10 per cent manganese, and 25 per cent zinc. The present work was under-

Jan 1, 1945

By E. F. Bradley, R. I. Jaffee, H. R. Ogden, E. S. Bartlett, D. N. Williams

The mechanical properties of solid-solution-strengthened columbium alloys have been assessed as a function of alloying additions. Studies included the effects of tungsten, tantalum, molybdenum, and vanadium. Elevated temperature fabrication was required at alloying levels above about 15 pct W or 10 pct Mo. Tungsten, molybdenum, and vanadium additions increase tensile strength at room temperature and 2200°F, but tantalum additions exert little strengthening. Similarly, tungsten, molybdenum, and probably vanadium additions increase the ductile-to-brittle transition temperature, and tantalum additions decrease this parameter. The 2200°F stress-rupture strength is increased by tungsten and molybdenum additions; with 20 to 25 at. pct additions, 100-hr rupture strengths of 30,000 psi are obtainable. Small vanadium additions exhibit mild stress-rupture strengthening, and tantalum additions are innocuous. At 2500°F, tungsten additions retain stress-rutpure strengthening capability, but molybdenum additions are much less effective. Tantalum additions augment the stress-rupture strengthening of tungsten plus molybdenum additions at 2500°F. Of the refractory metals, columbium possesses specific potential for structural use in the temperature range from 2000" to about 2500°F. Desirable features of columbium are its good low-temperature ductility, ease of fabrication, oxidation mechanics (lack of a volatile oxide at moderate temperatures), good availability and reserves, and relatively low density. However, alloying is required to provide attractive strength at elevated temperatures. Published information concerning alloying be- havior of columbium relative to mechanical properties is sketchy, particularly in consideration for long-time applications at temperatures in excess of 2000°F. Only a few stress-rupture data at temperatures from 2000" to 2500°F have been reported;'-' these are too meager to allow rationalization of the effects of various alloying additions on creep or stress-rupture properties. Additional published data do, however, give some insight toward understanding of systematic alloying behavior for columbium relative to low-temperature strength4-' and ductility,' and elevated temperature tensile behavior.4,6 This paper is intended to augment previous knowledge, and to promote understanding of the alloying behavior of columbium for long-time structural service at elevated temperature. BASIC CONSIDERATIONS Solid-solution strengthening is recognized to be of prime importance in improving strength in columbium-base alloys. Other strengthening mechanisms may be (and are, in current alloys) used to augment solid-solution strengthening. As strengthening results primarily from lattice distortion, the strengthening effectiveness per atom depends upon atomic size mismatch between solvent and solute. Another factor in this regard is conformance to ideal solution behavior in the solid solution. Thus, for example, despite appreciable differences in the degree of mismatch between tungsten (5 pct), molybdenum (5 1/2 pct), and vanadium (7 1/2 pct) in solution in columbium, all are about equally effective in straining the columbium lattice at room temperature.'-' Similarly, tantalum additions do not strain the columbium lattice, and little strengthening is expected. Size effects being equal, maximum solution strengthening at high temperatures is anticipated to result from the addition of elements that increase the melting temperature of columbium. This expectation is based on an increase in the electronic bonding forces exhibited in the transition metal series as electronic structures approach those of the Group Vl metals. Of the metals that exhibit ex-

Jan 1, 1963

By James W. Burns

Thin, heavily doped n-type layers of GaSb have been grown on p-type GaSb substrates. Techniques have been developed for the growth of the n-type layers from a tellurium-doped gallium-rich solution. The solution used consists of 95 at. pct Ga and 5 at. pct Sb. The process consists of immersing the p-type wafer in the solution at a temperature slightly above the liquidus temperature, holding briefly to permit dissolution of the substrate surface, then decreasing the temperature to a value slightly below the liquidus to obtain 1 HE resistivity of n-type GaSb varies linearly with applied hydrostatic pressure, while the resistivity of p-type GaSb is insensitive to such pressure.1,2 The growth. Growth from a solution of GaSb in tin will also be described. In either case the substrate is clamped to a shelf at one end of a graphite boat, and immersion of the wafer and subsequent decanting of the solution is accomplished simply by tilting the furnace. The process is useful for the formation of p-n junctions in III-V compounds and has the advantage that the problems normally associated with diffusion of Group VI elements are not present. Layers up to 4.0 mils in thickness have been grown by the process. material therefore should be useful in a hydrostatic pressure-sensing device. A practical hydrostatic pressure sensor, however, requires the fabrication of GaSb sensing elements of several hundred ohms resistance. Attempts were made to prepare such elements by diffusion, taking advantage of the high sheet resistance of the thin diffused layers and depending upon the p-n junction to provide isolation from the base layer. Additionally, thin layers of conductivity type opposite from that of the base layer were pre-

Jan 1, 1969

By G. Purcell, S. C. Sun

In an attempt to determine the relative collecting ability of 18-carbon fatty acids, studies were performed on rutile in aqueous solutions of the fatty acid soaps. The preceding article reported the electro-kinetic properties; this article outlines the flotation behavior. Results of these flotation experiments are described and correlated with the electrokinetic results. Recent studies of the electrokinetic1-4 and the electrochemical5,6 properties of a few solid-liquid interfaces have provided a better understanding of the flotation process. A number of investigators have attempted to determine the relative collecting ability of 18-carbon fatty acids, but their published results (even for the same mineral) vary widely. Such lack of agreement indicated a need for further investigation. In an effort, therefore, to resolve the problem, electro-kinetic studies were made on rutile in aqueous solutions of the fatty acid soaps. Following the determination of the electrokinetic properties, the flotation behavior of rutile was studied. Results of these flotation experiments are described in this paper and are correlated with the electrokinetic results. MATERIALS AND EXPERIMENTAL PROCEDURE Materials: Pure -28, + 35-mesh rutile crystals were used for all flotation tests, and nitrogen-saturated conductivity water was used throughout. Sodium hydroxide and hydrochloric acid were added for pH regulation. The methods of purification for these materials and the preparation of the soaps have been described elsewhere. 7 Equipment: A Hallimond cell, constructed in a manner similar to that described by Fuerstenau, Metzger and Seele,8 was used for the flotation of mineral particles; however, a coarse pyrex frit was substituted for the capillary. Procedure: Purified nitrogen was led through a two- way stopcock into a graduated cylinder partly filled with water. The gas forced water from the cylinder back into a header tank until the water level in the cylinder coincided with a predetermined mark. Reversal of the stopcock then allowed water in the tank to force nitrogen into the cell until the water in the graduated cylinder rose to a second predetermined mark. In this way a constant volume of nitrogen under practically constant pressure was used for each flotation test. However, the flotation time varied, depending upon the amount of mineral floated and the pH of the solution. Rutile crystals were transferred under water from a storage bottle by a glass scoop holding 1.7 g. Consistency of the scoop samples was good, varying from a low value of 1.67 to a high of 1.74 g. The water added to the conditioning bottle during mineral transfer was drained off, and then 2 cu cm of either hydrochloric acid or sodium hydroxide were added. The concentration of pH regulator was adjusted to give approximately the final soap solution pH that was required. The order of addition of reagents did not affect the results within the limits of experimental error. Soap solution of the required concentration was added under nitrogen pressure to fill the bottles completely. Conditioning for 1 hr was carried out on rolls rotating at 35 rpm. After conditioning, 2.5 cu cm of solution were run off into the container of a Beckman (model G) glass electrode pH meter. The electrodes were rinsed in this solution, which was then discarded, and 2.5 cu cm more were added for pH determination. The remaining solution and the mineral were transferred to the cell; care was taken to ensure that all mineral was washed out of the bottle by the conditioning solution. With the cell back in its flotation position the liquid just reached the desired level, and the test was started immediately. The amount of agitation in the cell was kept constant, and flotation was carried out without the use of a frother. In each series of ten tests one was run with no collector added to ensure that the mineral had not become contaminated, and two were conditioned at the same pH to check reproducibility. After each test the cell was dismounted, soaked in cleaning solution, washed in hot water and then rinsed with distilled water.

Jan 1, 1963

CHEMICAL PRECIPITATION U.S. 4,067,789 - Removal of soluble manganous ions from a zinc sulfate solution formed by leaching roasted zinc sulfide ore with spent electrolyte. An excess of ammonium persulfate or like oxidant is added to the leach solution to convert manganese to insoluble, filterable gamma-manganese dioxide, and the precipitate separated from the solution by filtration. L. Harris and A. K. Hanson, Jr., assigned to Newmont Exploration Ltd. Jan. 10, 1978. 11 pp. (204-119). Filed: 5-3-76 (682.442). (Drawing on page 67.)

Jan 1, 1979

By Donald L. Ball

The equilibrium of boron nitride, gaseous nitrogen, and solute boron was investigated in Fe, Fe-C, and Fe-Si rnelts by the Sieverts technique. The free ellergy of dissociation of boron nitride, involving -the implied standard states, was evaluated in the range 1400" to 1600°C as: ?Fo = 38,000 - 23.5T, cal ber mole The solute-solute interaction coefficients eBB, ecB , and eg were determined as 0.058, 0.22, and 0.078, respectively. BORON is an important ingredient in some types of steel and cast iron. It was employed at a particularly high level, 0.01 wt pet, in the as-cast malleable iron "CentraSteel".1 In this material, the boron concentration was critical in order to assure graphite, and avoid primary cementite, in the as-cast structure. One possible function of the boron in this alloy was the nucleation of graphite through the agency of boron nitride, which, conceivably, precipitated from the melt during cooling. A research program was instituted to assess the validity of this proposed mechanism. The first undertaking, reported here, was a determination of the thermodynamic possibility of boron nitride precipitation. Data available in the literature on the activity coefficient of solute boron in iron-base melts are inadequate for the present purpose. They will be reviewed briefly, however, so that comparison can be made, when

Jan 1, 1968

By J. R. Sturgul

Two problems which are common to nearly every branch of applied physics, including geophysics, are the ‘Dirichlet Problem’ and the ‘Poisson Problem.’ A numerical method for their solution is derived and a problem of heat flow in a plate is solved using a high-speed digital computer. The solution to this problem is presented in a form which illustrates the versatility of computer output.

Jan 1, 1969

By Mehl, Robert F.

IT has been shown by numerous studies that the orientations of new metal crystals are determined by the orientations of the crystals in the original matrix, whether these new crystals are formed by recrystalliza-tion, by precipitation from solid solutions, or by transitions in the solid state. The orientations of crystals formed by recrystallization of cold-worked worked metals that bear preferred orientations are occasionally simply related to the initial preferred orientation; often, however, the relation-ship is not simple, but complicated and obscure in origin.1 The orientations of crystals formed by precipitation from solid solu-tions have been shown by many studies in this and other countries to be determined by the orientation of the crystals of the solid solution stable at the higher temperatures, though here again complicated cases have been found and no general theory is available .2 Related to this latter class

Jan 1, 1934

By I. Javandel, P. A. Witherspoon

The finite element method was originally developed in the aircraft industry to handle problems of stress distribution in complex airframe configurations. This paper describes how the method can be extended to problems of transient flow in porous media. In this approach, the continuum is replaced by a system of finite elements. By employing the variational principle, one can obtain time dependent solutions for the potential at every point in the system by minimizing a potential energy functional. The theory of the method is reviewed. To demonstrate its validity, nonsteady-state results obtained by the finite clement method are compared with those of typical boundary value problems for which rigorous analytical solutions are available. To demonstrate the power of this approach, solutions for the more complex problem of transient flow in layered systems with crossflow are also presented. The generality of this approach with respect to arbitrary boundary conditions and changes in rock properties provides a new method of handling problems of fluid flow in complex systems. INTRODUCTION Problems of transient flow in porous media often can be handled by the methods of analytical mathematics as long as the geometry or properties of the flow system do not become too complex. When the analytical approach becomes intractable, it is customary to resort to numerical methods, and a great variety of problems have been handled in this manner. One such method relies on the finite difference approach wherein the system is divided into a network of elements, and a finite difference equation for the flow into and out of each element is developed. The solution of the resulting set of equations usually requires a high speed computer. When heterogeneous systems of arbitrary geometry must be considered, however, this approach is sometimes difficult to apply and may require large amounts of computer time. The finite element method is a new approach that avoids these difficulties. It was developed originally in the aircraft industry to provide a refined solution for stress distributions in extremely complex airframe configurations. 27 Clough has recently reviewed the application of the finite element method in the field of structural mechanics.6 The technique has been applied successfully in the stress analysis of many complex structures.l, 27, 28 Recognition that this procedure can be interpreted in terms of variational procedures involving minimizing a potential energy functional7 leads naturally to its extension to other boundary value problems. In the field of heat flow, there recently have been introduced several approximate methods of solution that are based on variational principles.2-4, 17 By employing the variational principle in conjunction with the finite element idealization, a powerful solution technique is now available for determining the potential distribution within complex bodies of arbitrary geometry. In the finite element approximation of solids, the continuum is replaced by a system of elements. An approximate solution for the potential field within each element is assumed, and flux equilibrium equations are developed at a discrete number of points within the network of finite elements. For the case of steady-state heat flow, the technique is completely described by Zienkiewicz and Cheung.33 Since the flow of fluids in porous media is analogous to the flow of heat, Zienkiewicz et al. have employed the finite element method in obtaining steady-state solutions to heterogeneous and anisotropic seepage problems. 34 Taylor and Brown have used this method to investigate steady-state flow problems involving a free surface.25 The work of Gurtin has been instrumental in laying the groundwork for the application of finite element methods to linear initial-value problems.12 As a result, Wilson and Nickell have recently

Jan 1, 1969

By Charles V. Jenkins

The structure of steel, when rendered coarse by over-heating, is made fine by re-heating to a certain temperature, the determination of which has received much attention from eminent metallurgical authorities. Among these, I may particularly mention Prof. D. Tschernoff' [Chernoff], who, about thirty years ago, studied this question in connection with his investigations on the structure of steel in genera1. † Some years later, Mr. J. A. Brinell took up the inquiry, and arrived at many important conclusions, stated in his well-known rules on the treatment of steel. ‡ These two gentlemen, however, based their reasoning chiefly upon the aspect of fractures—a method which, though it affords valuable information, does not readily reveal the different steps by which a change in structure takes place. For further light on the subject, we owe much to more recent microscopic investigations, which have made us better acquainted with the internal structure of metals. Such an investigation, closely connected with the present subject, and made by Mr. John E. Stead a few years ago, was first published in 1898.6

Jan 1, 1903