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By Dexter Kimball

THE ease and promptness with which the public as a whole becomes accustomed to and takes advantage of the work of the engineer, using the term in a broad sense, is almost startling. Surprise at, and fear of radical innovations in transportation and private service quickly give way to blasé indifference, followed instantly by all manner of criticism that these things are not better constructed and managed. Does the street car stop a few minutes on a switch?-summon the State Commission. Is the Overland Express fifteen minutes late on a three thousand mile run?-Congress is memorialized to make the great railroad companies attend to their business. Does central not respond instantly when we take down the telephone receiver?-anathema!! Do the electric lights go out for a minute or so?-the darkness is illuminated by caustic sarcasm and other kinds of spoken English consigning all engineering and engineers to perdition; everyone apparently forgetting how steep the hills were before the days of street cars, how far away San Francisco was before the days of the locomotive, the telegraph and telephone, and how difficult it must have been to study by the light of a tallow candle.

Jan 9, 1922

By Young C. Kim, Francis Martino, Ish Chopra

For the past two and one-half years, various emission control strategies were jointly developed by the University of Arizona and the Homer City Owners to com- ply with the clean air requirements at its Homer City Power Plant. Some of the available options for the SO2 emission control by the Homer City Owners were:l)cleaning of run-of-mine coal,2) scheduling of mining operations at its captive mines, 3) blending the captive mine coal with externally purchased low sulfur coa1,and 4) placing a partial FGD system. This paper describes two specific emission control strategies developed and implemented. These are: 1) production scheduling at the mining face to minimize sulfur variability, and 2) external purchasing of low sulfur coal for further blending. The main objective of this paper is to share our experiences on implementing the developed strategies. This paper emphasizesthe need for proper mine planning on a short-term basis, if the power plant is to meet the desired objective.

Jan 1, 1983

By R. M. Hudson

A study has been made of the decarburization of low-carbon sheet steels at temperatures from 1100" to 1475°F in mixtures containing hydrogen, nitrogen, water vapor, and in some instances carbon monoxide. Decarburization occurs principally by the reaction C (in steel) + H20 = CO + H2 and follows a first-order rate law. The decarburization rate appreciably increases with an increase in temperature up to about 1325°F, but the increase in rate is small with fur- Use of a dry hydrogen atmosphere results in a relatively slow decarburization of steel and use of a wet hydrogen atmosphere results in relatively rapid decarburization. It is now generally recognized' that the reaction C (in steel) + H2O = H2 + CO [l] accounts for most of the decarburization that occurs in wet hydrogen-containing atmospheres. The present article is concerned with the decarburization of low-carbon sheet steel in H2-N2 atmospheres ther increase in temperature. The limiting rate of decarburization can be predicted from a knowledge of the solid solubility and diffusivity of carbon and this rate is approached as the water-vapor content of an atmosphere is increased. Hydrogen contents above about 8 pct are beneficial only in that they permit higher levels of water vapor to be used without oxidation of the steel. A buildup of CO in the atmosphere lowers the rate of decarburization. containing various amounts of water vapor and carbon monoxide. The effectiveness of these atmospheres and the influence of temperature on decarburization rate will be considered. EXPERIMENTAL WORK The chemical compositions of the three steels used in decarburization-rate studies are listed in Table I. Steel A was a commercially hot-rolled rimmed steel that was cold-reduced at the Laboratory to furnish specimens 0.025, 0.041, and 0.059 in. thick. Most of the experiments in which this steel was used were made on the 0.041-in.-thick material. Steel B and Steel C were cut from 0.010-in.-thick commercially cold-reduced coils that were

Jan 1, 1963

By Arthur B. Foote

Ore production from the property of the Miami Copper Co. began early in 1911. Until 1925 this ore came from the so-called high-grade orebodies, which contained a little over 2 per cent. copper. This ore was mined by the following methods: 1. Top slicing after mining the peaks by square setting, which produced 4,524,347 tons, including ore from square setting. 2. Shrinkage stoping with sublevel caving of the pillars, which produced 2,230,577 tons. 3. Undercut caving with hand tramming, which produced 15,427,672 tons. Estimating December tonnage, the total ore mined to the end of 1929 will amount to slightly more than 43,000,000 tons. The first method was described by E. G. Deane' and the second by D. B. Scott,' and the third, together with a general description of the mine, by J. H. Hensley, Jr.' The geology of the district has been worked out by Dr. F. L. Ransome.2 The author acknowledges also the assistance of R. W. Hughes, assistant mine superintendent, E. V. Graybeal, chief mine engineer, A. J. McDermid and S. R. Burdick, engineers of Miami Copper Co., Miami, Arizona. Factors Influencing Selection of Mining Methods The mining method described herein was selected primarily with a low mining cost in view and was developed to avoid as far as possible dilution of the already very low-grade ore. In 1924, with the exhaustion of the high-grade orebodies in sight, it was decided to develop the low-grade orebody, which at that time contained 36,000,000 tons of ore assaying 1.06 per cent. copper, and had an area of 50 acres with an average thickness of 206 ft. overlain by an average thickness of 320 ft. of barren capping.

Jan 1, 1930

By Brahm Prakash, R. Schuhmann

Maurice Rey—It may be interesting to note that depressing effects can also be obtained from cyclic compounds other than dyes. One such compound which is a dispersing agent for carbon, pigments and other compounds is known in France by the trade name "dispergine" and in the United States by the name of Lomar P W (Jacques Wolf & Co.) Dr. Rey admits that the compound is not very selective and is similar in its action to starch and dextrin.

Jan 1, 1951

By Brahm Prakash, R. Schuhmann

Maurice Rey—It may be interesting to note that depressing effects can also be obtained from cyclic compounds other than dyes. One such compound which is a dispersing agent for carbon, pigments and other compounds is known in France by the trade name "dispergine" and in the United States by the name of Lomar P W (Jacques Wolf & Co.) Dr. Rey admits that the compound is not very selective and is similar in its action to starch and dextrin.

Jan 1, 1951

By C. D. Williams, C. E. Ells

The susceptibility of quenched and aged Zr-2.5 wt pct Nb alloy to embritt2ement during irradiation has been examined for a number of solution temperatures and aging times. Material quenched from temperatures approximately 40°C below the transus has high tensile ductility, and this ductility is insensitive to aging at 500°C or to irradiation. If, however, the material is quenched from temperatures above the transus it becomes highly susceptible to loss of ductility either from aging at 500 or from irradiation. Inter granular failure is characteristic of the materials having low ductility. The distribution of the equilibrium phase is found to control the susceptibility to embrittlement by restricting 6 grain growth during heat treatment and thus influencing crack propagation. IN zirconium, as in titanium, -stabilizing alloy additions are used to obtain high strengths via quench and age heat treatments, and the Zr-2.5 pct Nb alloy has been developed1 because of its strength advantage over the Zircaloys. Early in the development of the Zr-2.5 pct Nb alloy the problem of 13 embrittlement was appreciated, and for this reason the solution temperature was chosen below the p transus.' In the course of irradiation studies on quenched and aged Zr-2.5 wt pct Nb alloy it was found' that irradiation introduced an important aspect of p embrittlement, riz., material quenched from the phase and aged 24 hr at 500°C was severely embrittled by moderate doses of neutron irradiation. This effect had not been studied in titanium alloys. In titanium the metallurgical features leading to 0 ernbrittlement were found to be structures with: a) coarse a platelets at the grain bondaries, b) finely dispersed a uniformly distributed throughout the (0) matrix,6 c) Widmanstatten a-13 with more than 50 pct P, d) the presence of some metastable p transformation products,3 and e) large prior -phase grain size.5 Alternatively, the presence of a uniform distribution of coarse a was conducive to high ductility and a structure largely of equiaxed a was very dctile. The detailed mechanisms of the embrittlement have not been worked out for all of these conditions, although weakness at either a-matrix boundaries or prior p grain boundaries have been prominent in the eculation. It was proposed that acicular a might act as a mild notch, and low ductility has been associated with easy fracture along its boundary.' There have been two opposing suggestions for the source of the high ductility associated with equiaxed a phase. JaffeeB proposed that this a would accept a large por- tion of the oxygen, thus increasing the ductility of the matrix, whereas after study of a Zr-Nb-Cu alloy Weinstein and oltz proposed that the a phase, softer than the martensitic matrix, acted to blunt cracks formed in the matrix. In the present work we have studied the effect of neutron irradiation on the ductility, particularly the P embrittlement, of the Zr-2.5 wt pct Nb alloy. By a variation of solution temperature and aging time a variety of metallurgical conditions have been examined, and a range of resultant ductilities obtained. The ductility has been related to the material microstructure and mode of fracture. EXPERIMENTAL The alloy used in the present work came from two separate ingots fabricated into rod of 3/8 or i in. diam, Table I. For both batches the P transus temperature was approximately 890° C. Most of the heat treatments were done directly on lengths of the j} in. diam rod, after which the tensile test specimens were machined. Quenching was achieved by dropping rods from a dynamic vacuum into water, the cooling rate estimated to be 2 100°C per sec. For aging the rods were encapsulated in evacuated silica tubes. Round tensile test specimens, with gage diam and length 0.160 and 1.0 in., respectively, were used throughout and pulled at room temperature or 300°C on Instron tensile machines, at a crosshead speed of 0.05 ipm. Specimens were irradiated in the NRX and NRU reactors, in facilities described in previous publications.'0 The metallurgical conditions examined have been: All tensile test specimens were machined with axes in the axial direction of the swaged rod. Although the specimen had a degree of preferred crystallo-graphic orientation with basal plane normals both parallel with and perpendicular to the tensile axis, the material was comparatively isotropic." The techniques of thin foil examination in the electron micro-

Jan 1, 1970

(Members are urged to send in for this column any notes of interest concerning themselves or their fellow-members.) Members and guests who registered at Institute headquarters during the first half of March: James C. H. Ferguson, San Francisco, Cal. Capt. A. F. Lucas, Washington, D.C. Henry Adams, Stamford, Conn. Dexter P. Cooper, New York, N. Y. H. A. Wheeler, St. Louis, Mo. L. D. Moore, Chatham, N. J. John M. Sherrerd, Easton, Pa. Hennen Jennings, Washington, D. C. R. T. White, formerly General Manager of the Braden Copper Co., Chile, is to take charge of a copper company in Caucasus, South Russia.

Jan 4, 1914

By A. B. Kinzel

SINCE the exposition of the behavior of certain iron alloys by Sykes1 involving the existence of an austenite loop and the discovery of such a loop in the chrome iron system by Bain,2 there has been much conjecture both on his part and on the part of metallurgists in general as to the exact shape and location of this loop. In previous work commercial steel has been used and the microscope has been employed to locate the critical points so that the position of the loop has been quite approximate. Numerous attempts have been made to measure the critical points of the carbon-free alloys but all of these for one reason or another have failed. A satisfactory method for studying these phenomena is presented here. MATERIAL The first difficulty in this study was to obtain pure chromium-iron alloys. This has been overcome by melting in a vacuum electrolytic Eton and chromium analyzing 99.84 Cr, Fe and C. A pure magnesite crucible was used and the melt allowed to solidify in the crucible. A typical analysis is chromium, 10.10 per cent., carbon, 0.006 per cent., silicon and manganese nil. To overcome the problem presented by segregation, ingots were made into wire 0.04 in, in diameter. This was accomplished by hand-forging the ingots into rods, using an oxyhydrogen flame for heating, in order to avoid carbon. Subsequently the rods were swaged to wire, the heating being carried out in hydrogen. Thus local segregation was eliminated although differences in analysis between portions 50 ft. apart were noted. An electric-resistance method was first tried to determine the critical points, but due to the physical defects in the wire this failed. Bain had previously shown the presence or absence of critical points in a qualitative way by observing the sag in a catenary. The author has devised the following method which gives an accurate determination of the critical points from expansion-temperature curves of suspended wire, a special telescopic dilatometer being used for the purpose.

Jan 1, 1928

By Lewis M. Haupt

IT has given me great pleasure to read, in the papers recently published by this Society, the discussions on the subject of Technical Education, which were developed at the joint meeting held at the Franklin Institute in June, 1876; and since it was impossible for me to be present, I desire to improve this my first opportunity of adding the weight of my testimony and experience to what has been so ably presented by others. It is a subject about which the people need to be kept agitated, that their views may expand with the demands made for a higher and more thorough education. It is the public at large, the capitalist, the manufacturer, and the laborer, who are to be benefited more or less by this elevation of the standard of our professional schools, and it is but just, therefore, that the schools should look to them for the means with which to accomplish so desirable an object. It is no doubt to the interest of a metallurgist to employ a skilled laborer who will prevent waste by properly proportioning his materials ; by regulating the supplies of air and fuel ; by arranging his plant in the most economical manner, and by disposing of his products to the greatest advantage. The engineer is benefited by selecting for an assistant a person able to determine the values of his factors of safety for the same materials in different forms and positions, avoiding expensive suits for damages and cost of reconstruction; he should be able to so locate a road as best to fulfil the requirements of a through traffic, and yet develop local industries. But I need not multiply instances to show what all will readily concede, viz.: the advantages of a theoretical education ; that was fully demonstrated at the previous special meeting, but it is still an open question whether the practical instruction should precede, accompany, or follow the theory.

Jan 1, 1877

By Lewis M. Haupt

IT has given me great pleasure to read, in the papers recently pub lished by this Society, the discussions on the subject of Technical Education, which were developed at the joint meeting held at the Franklin Institute in June, 1876; and since it was impossible for me to be present, I desire to improve this my first opportunity of adding the weight of my testimony and experience to what has been so ably presented by others. It is a subject about which the people need to be kept agitated, that their views may expand with the demands made for a higher and more thorough education. It is the public at large, the capitalist, the manufacturer, and the laborer, who are to be benefited more or less by this elevation of the standard of our professional schools, and it is but just, therefore, that the schools should look to them for the means with which to accomplish so de sirable an object. It is no doubt to the interest of a metallurgist to employ a skilled laborer who will prevent waste by properly proportioning his ma terials ; by regulating the supplies of air and fuel; by arranging his plant in the most economical manner, arid by disposing of his products to the greatest advantage. The engineer is benefited by selecting for an assistant a person able to determine the values of his factors of safety for the same materials in different forms and positions, avoiding expensive suits for damages and cost of reconsiruction; he should be able to so locate a road as best to fulfil the requirements of a through traffic, arid yet develop local industries. But I need not multiply instances to show what all will readily concede, viz.: the advantages of a theoretical education ; that was fully demonstrated at the previous special meeting, but it is still an open question whether the practical instruction should precede, accompany, or follow the theory.

By Fred D. Wright, Philip B. Bucky

FOREWORD By E. D. Gardner[$] THE present known petroleum reserves are limited, and unless important new fields are discovered the Nation will be dependent, in the not too distant future, upon imports or upon synthetic liquid fuels to supplement domestic petroleum supplies. As a national defense measure, it would appear desirable to develop a substitute source of liquid fuels within the borders of the country if new discoveries of petroleum should prove disappointing. Congress undoubtedly had this in mind when it passed the Synthetic Liquid Fuels Act (78th Congress, approved April 5, 1944). The act directed the Bureau of Mines to construct and operate demonstration plants for producing synthetic liquid fuels from coal and oil shale, and from forestry and agricultural products. As a part of this program, the Bureau of Mines has built a demonstration plant at Anvil Points, near Rifle, Colo., for retorting the oil shale, and has developed a mine to supply the plant with oil shale. At the beginning of mining operations, the physical qualities of the oil shale, which would have a bearing upon the selection of mining methods and practices for exploiting the deposits, were largely unknown. A comprehensive mining-research program has been set up to determine the best methods and practices to follow to obtain the lowest overall practicable mining cost for producing the oil shale on a large scale. Unusually low mining costs will be necessary for shale oil to be produced commercially. Consideration now is being given to exploiting a series of flat-lying beds 70 ft thick by a room-and-pillar method of three benches with the advance heading at the top. This report is one of a series giving the results obtained in research on mining problems. INTRODUCTION The structure and physical qualities of the oil shale indicate that the 70-ft interval of the oil-shale measure can be safely mined in open stopes; studies indicate that this method would be the most economical one to use.1 As labor will be a major item of expense, the largest equipment that could be operated efficiently in the workings would be required to obtain the lowest practicable mining cost. It was therefore desirable to know the maximum safe span of unsupported rooms and the size of pillars necessary to support the overburden. This paper describes the work done at the Columbia School of Mines Barodynamic Laboratory in determining the maximum safe unsupported roof spans and the minimum safe pillar dimensions for the oil-shale mine at Rifle, Colo.

Jan 1, 1947

By C. R. Fondersmith, John Chipman

In the manufacture of rimming steel—which constitutes the bulk of the world's production of mild steel—the factors that determine the quality of the product are very closely associated with the pouring and solidification of the steel in the ingot mold. The behavior of the metal in the mold is, on the one hand, the resultant of the complex processes through which the liquid metal has passed, and, on the other, it is an indication of the probable behavior of the ingot during subsequent rolling and finishing operations. A detailed study of the mechanism of solidification of rimming ingots ought to yield information that will be useful in controlling the structure of the ingot and the quality of the ultimate product. The first step in such a study is to determine the rate at which the solid shell of the ingot forms from the liquid metal in the mold. A knowledge of the rate of solidification will make it possible to correlate observations of rimming action and gas evolution with studies of the structure, porosity, and segregation within the ingot. Thus, if the metal in the mold is observed to fall, let us say one minute after pouring, the portion of the structure associated with this fall will be located in the part of the ingot that is solidifying at that particular moment. The knowledge that the ingot solidifies to a depth of 3/4 in. in the first minute enables us to locate in the ingot the structural features corresponding to the observed fall. Conversely, the blowhole condition associated with a rising or growing ingot will be found in the part of the ingot that is solidifying at the time the phenomenon occurs. The time required for the complete solidification of an ingot has long been a matter of speculation. It is of considerable practical importance in connection with charging and heating in the soaking pits. Too rapid handling of the ingot through heating and rolling processes has been thought to be associated with excessive pipe and other internal defects, so that a further object of this investigation was to attempt to estimate the time required for complete solidification, or the minimum practical time within which the subsequent operations can be performed with the minimum hazard.

Jan 1, 1937

By J. T. Norton, N. J. Grant, A. M. Gervais

An investigation of the creep deformation of coarse-grained high-purity aluminum at temperatures approaching the melting point permitted the formulation of a theory of subgrain formation. Subgrain boundaries were found to be formed by two different processes: kinking and polygonization. Polygonization is considered as the main factor in subgrain formation. SINCE "slipless flow" was first discussed in detail by Hanson and Wheeler,' many studies have been undertaken to determine how metals deform at high temperatures. Several types of observations have been reported. Jenkins and Mellor,² working on the creep of mild steels and various grades of commercial irons, found metallographic evidence of a kind of substructure within the grains after deformation at high temperatures. Homes" observed after creep deformation of steel at high temperatures that the original X-ray spots were sharply divided into several small ones. The same phenomenon was reported by Hirst4 from his studies on lead and later by Crussard5 from his work on aluminum. The works of these investigators demonstrated beyond any doubt that the splitting of the X-ray spots was due to the fact that the grains underwent a division into subgrains during deformation at high temperatures. Since then, numerous experiments have been undertaken on aluminum in order to determine the mechanism of formation of subgrains. Research workers can be divided, for the purpose of discussion, into two different groups as regards thinking on subgrain formation. On one hand, based on the work on polygonization by Cahn,6 Guinier and Lacombe,7 Greenough and Smith," Crussard,10,11 and Servi, Norton, and Grant," it was concluded that subgrain formation was a consequence of the simultaneous effects, first, of inhomogeneous deformation which produced bending of the lattice, and second, polygonization. On the other hand, Wood and coworkers13-16 based their work on the results of an earlier report" which dealt with crystallite size and a fragmentation theory. It is interesting to note that while Greenough and Smith8 and Wood et al. performed similar experiments, their conclusions were quite different. Wood et al. did not recognize polygonization as a fundamental mechanism and said that aluminum, at the beginning of the deformation, fragmented immedi- ately into subgrains in order to permit deformation of the metal, the number of these subgrains being a function of strain rate and temperature. They concluded that deformation of grains occurred by flow along the subgrain boundaries. In view of the contradictory conclusions, it would appear that the data were not explicit enough to provide an unambiguous conclusion. It appears that the techniques by which most of the results were obtained, namely, X-ray work, were not enough by themselves to solve the problem. Another approach was needed. In the present research, therefore, an extensive metallographic study was planned to supplement the X-ray work. The importance of revealing the subgrain boundaries metallographically was realized, and this will explain the extensive development and use of etching techniques. In order that subgrains would be considerably larger and therefore more readily visible under a microscope, the creep experiments were performed at very high temperatures approaching the melting point of aluminum. Development of Experimental Technique Creep tests were run at constant load on high purity (99.995 pct) aluminum specimens having a very coarse grain size. None of the specimens was run to fracture. The specimens were originally round (diameter, 0.187 in.; gage length, 1 in.) and had parallel flats milled in the gage section to permit

Jan 1, 1954

By A. W. Gauger

WITHOUT QUESTION the Commonwealth of Pennsylvania contains the most remarkable coal deposits of the whole world. Within its borders ,are to be found excellent coals ranging in rank from the high volatile bituminous of the western part of 'the state through the low volatile or semi-bituminous of central Pennsylvania to that aristocrat of solid fuels, anthracite, found in the East. . . . But while other states and even the Federa1 Government have recognized the needs of the coal industry, Pennsylvania has not. Though bituminous coal represents one of the most important industries in the state, far more important in annual productive wealth than agriculture, for example, hundreds, of thousands of dollars have been spent on agricultural research whereas little or nothing has been spent on coal investigation.

Jan 1, 1932

J. A. MATHEWS, * Syracuse, N. Y. (written discussion?).-The reagent described by Mr. Archer seems to be a selective reagent, useful in one particular field. Nevertheless, the field is one in which it is likely to prove of considerable value, because there is a great deal of alloy steel FIG. 1.-ETCHED 1 HR. IN ARCHER'S FIG. 2.-ETCHED 1 HR. IN ARCHER'S REAGENT. PLOD 60. X 188. REAGENT. IZOD 10. X 188. heat-treated to approximately the properties mentioned in the paper. If it is found, by further tests, to be applicable to a wider range of compositions than merely chrome-nickel steels, for the most part discussed by Mr. Archer, its value will be thereby increased to just the extent to which it can be applied. In view of the fact that certain of these chrome-nickel steels, very similar in physical properties and hardness, show very different results in the Izod or notch test, and in view of the fact that when such differences are noted in the fracture the brittle steels usually

Jan 5, 1919

By James E. McNulty

Coal reserve estimates are prepared using a simple equation: the product of area, bed thickness, density and recovery factors. Each of these elements involves a degree of risk based on certain assumptions. Reserve area, thickness and density rely on certain physical data whose accuracy, reliability and sufficiency may be problematical. Estimates of recovery factors for mining and coal preparation are often subjective. Most reserve estimates assume, sometimes incorrectly, that the subject reserves will be completely extracted. The principle that certain coal resources are reserves, if they can be considered economically recoverable at the time of determination, needs to be reexamined in the light of recent market cycles. Reserve estimating requires the exercise of judgments, the validity of which reflect the qualifications, experience and objectivity of the estimator.

Jan 1, 1985

By R. M. Asimow

Both smith1 and wells2 have shown that the dif-fusivity of carbon in austenite increases rapidly with increasing carbon concentration. Smith has shown, in addition, that part but not all of this increase can be attributed to the concentration dependence of the activity coefficient of carbon in austenite. From the work of Eshelby', it is known that, because of the image displacements, there is a uniform dilatation of the material in a body containing random centers of dilatation. It is thus tempting to explain the enhanced diffusivity as resulting from this apparent negative pressure caused by the interstitial carbon atoms.* That is, the activation free energy for diffusion is not directly a function of concentration if we consider that the alloy is subjected to a concentration-dependent pressure. To proceed with a quantitative solution, it is necessary to determine the activation volume AV for the diffusion process. An exact calculation of AV is quite a difficult problem and does not appear to have been solved as yet. A simpler procedure is to use the semiempirical, macroscopic theory of seyes' which relates the activation free energy AG to AV. Keyes has shown that for many types of diffusion processes the following relationship is valid Where p is the Gruneisen constant and x the compressibility. This relationship is based on the assumption that AG can be identified with strain-energy terms. In general there will also be contributions to AG due to a change in the energy of the valence electrons of the metal; thus the relation must be considered largely empirical. Surprisingly, for self-diffusion where it is well-known that the electronic contribution is quite important,' the Keyes relation works quite well for many systems. For interstitial diffusion where it might be expected that the relationship is on a firmer theoretical basis, the limited experimental data available is not in particularly good agreement as can be seen from Table I. However, it must be remembered that besides the uncertain basis of the Keyes formula there is considerable uncertainty in some of the experimental values of AV. The only real justification for using the Keyes formula in the present analysis is that it gives a result which satisfactorily solves the problem at hand and, further, there are no more reliable procedures for calculating AV available. The coefficient 3 in Eq. [I] is determined such that the room-temperature value for x is to be used. The activation entropy AS is estimated as 8.95 x 10"3 kcal per OK mole using the values in Table I1 and the Zener" relation AS = PAHIT, where p is a dimensionless thermal coefficient of Young's modulus which is to be evaluated at low values of T/T,, aH is the activation enthalpy, and T, is the melting temperature of the alloy. The resulting value of AG at 1000°C is 25.6 kcal per mole. The Gruneisen constant (p = 3cup/XC,), where p is the density, is evaluated from the room-temperature data in Table I1 after calculating C, from the relation. A value of p = 8.32 g per cu cm based on the value of a. in Table I is used. The result is C, = 5.0 x lo6 erg per g, H = 2.32, and AV = 3.41 cu cm per mole at 1000°C and infinite carbon dilution. It is assumed that the activation volume is not a function of carbon concentration. The theory could be refined to consider AV a function of concentration, but due to the uncertainties in the parameters there seems little justification for this. Carbon dissolved in austenite forms a nonideal solid solution, so that in writing an equation for. the diffusivity of carbon it is necessary to take into account the change in activity coefficient with concentration. The resulting equation is16

Jan 1, 1964

By H. H. Rachford, W. P. Schultz

The use of computing machines to solve physical problems has made it imperative to represent physical data in a form computing machines can use. Although curve-fitting is an old and well-practiced art, there still seems to be some interest in questions regarding what methods can be used and why. Even though there are many good references on this subject, it may be of some value to discuss a particular method which has been found to be useful, and to make available the associated tables for its use in the hope that there can be saved a few of the tedious hours necessary to reduce many of the suggested methods to practice. Although a very brief discussion of the mathematical background of the tables is included immediately below, those interested only in their use can skip directly to the section on Use of the Tables. Direct Fit of a Set of Points A frequently encountered problem is: Given data which can be represented by a smooth curve +(x), to find an easy-to-evaluate function F(x), with only a few coefficients, which is a good approximation of +(x) on the interval 0 5 x 5 x,,. Consider F(x) as a linear combination of m + 1 arbitrary, single-valued, continuous, linearly independent functions, f,(x), Ff.r) = a,f,,(x) + a,f,(x) + . . . -+ aifi(x) + If the value of Q(x) is known or can be read from the curve at the points xj: +(x,), +(x,), . . . +(xj) . . . +(x.), and if n = m, then all the coefficients of F(x) can be determined, and F(x,) — +(x,) = 0 for j =. 0, 1, . . . n. This follows from the solution of the set of linear simultaneous equations. +(x<.) = aofu(x,) + aJI(x0) + . . . + a,,f,,(x,) =a, = f,,(x,) + a,f,(x,) + . . . + a,f,,(x,) +(x,,) = a,,f,(x,,) + a,f,(x,) + ... + a,,f.,(x,,) ...........(2) for the coefficients ai. Although the set a, from the solutions of the set of Equations 2 yields an fix) which gives an exact value of $(x,) for the n + 1 points, there is no restraint on ~(xj in the interval xi < x < xj+,. Indeed, if the points +(x,) are not sufficiently smooth, very serious differences may arise between F(x) in the interval and the smooth curve +(x). Least-Squares Fit It has been suggested&apos; that if n is made to exceed m, and the set a, is found to minimize the function the function F(x) is much less sensitive to small errors in +(xi), and usually provides a much better fit to the smooth function +(x). This is known as the best fit in the sense of the least-squares error. To minimize $, set £ = 0,i = 0,1,... iTi,.....(3) The m + 1 equations from Equation 3 are k—n k=n a.^p /,,(a) f,(xt) + a, X A: = 0 k=O k = n k = n k=0 k=0 +(x.) f,(x,),............(4) one equation being obtained for each i = 0, 1, . . . m. Inasmuch as the arbitrary functions f(x) may be evaluated for x,, k = 0, 1, . . . n, and the +(x,) are known values of the curve to be fitted, the simultaneous Equations 4 may be solved for the set a,. Particular Functions Given the functions fi(x) and the set +(xj), the solutions for require evaluating a number of sums of products as well as the solution of an m + 1 order set

Jan 1, 1956

By Richard Akerman

(Translated by FREDERICK PRIME, JR., Professor of Metallurgy in Lafayette College, Easton, Pa.) [THE attention now being paid both in this country and Europe to the greatest economy in the working of the blast furnace, and the eagerness with which all thoughtful men in the iron business look for any new information which will tend to throw light on this sub¬ject, is a quite sufficient excuse for presenting this paper to the Amer¬ican Institute of Mining Engineers.] I. It must be borne in mind that when two bodies unite to form a chemical compound, heat is almost always evolved. In order to

Jan 1, 1873