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By G. Sachs, G. Espey

SIMPLE methods can be used for the determination of the residual stresses in thin-walled tubing if the stresses consist of high tensile stresses at the one surface and high compressive stresses at the other surface Such a stress distribution is approximated in sunk tubing and in deep-drawn shells It is possible to cut sections from such articles in such a manner that a major part of the residual stress is relieved by a bending of the part that is separated from the adjacent metal The circumferential stress is evaluated from the change in diameter D, occurring on splitting a length of tubing (Fig Ib),1-5 or from deflection resulting from the cutting out of a circumferential tongue (Fig Ia) G The bending moment M released by such a flexure is [ ] The release of this bending moment corresponds to the release of stresses, which, in a thin section, vary linearly from one surface to the other, and have the following value in a particular fiber a certain distance (zx from the surface [ ] where C is the section modulus and d is the thickness of the section, the ratio AI C being d 2 for a rectangular section* The maximum stress values at the surfaces are [ ] For most purposes the simpler equations [ ] will be satisfactory, where Dm is the average of the mean diameters of the tubing

Jan 1, 1941

Jan 1, 1923

By Frank Calvin Roberts

An examination of the various devices employed for operating blast-furnace charging-bells has led me to design the arrangement slrown in the accompanying figure. In order to contribute to the even distribution of stock, the movement of the bell should be in a vertical line, since any tendency to side-thrust which may be in-

Jan 1, 1888

During the year this Committee has had the benefit of the services of 75 Committee members, resident in the various States of the Union and in foreign countries, 10 of them representing us abroad. A number of plans for awakening the interest of possible new members have been carried out and the results have been very gratifying. The comparative results for 1913 and 1914 are as shown in the following table: 1913 1914 Applied for membership 630 946 Elected 450 1,006 Accepted election 433 921 When it is remembered that the depression following the outbreak of war in Europe has had more serious effect on the mining industry than almost any other, these results cannot be regarded as anything other than very encouraging. Because of the unsatisfactory conditions still prevailing it will doubtless be difficult to make even as good a showing next year. It is considered, however, that the function of this Committee is not merely to secure new members, having no regard for other than numbers; its true function is to exercise a proper supervision over the growth of the Institute, building it up in those fields in which it is weak, and directing its growth in such a way as to make it most effective in fulfilling its proper function as the national organization representative of the mining profession. The plan of inviting the alumni of the leading mining schools to apply for membership, which was initiated last year, was completed this year, with the exception of one or two schools, notably the University of California, from which we have not been able to obtain a list of alumni. With these exceptions we have now extended to the graduates of all the important mining schools of this country, and several of those abroad, an invitation to apply for membership in the Institute. It. is not thought desirable to repeat this invitation too frequently, and it is therefore suggested that this field be left alone for a year or two, when, if the mining industry experiences a marked revival of interest, it will be well to send out a second letter to the same men.

Jan 4, 1915

Jan 1, 1923

By William Klement

THIS note reports the results of some attempts to metastably extend the primary solid solubilities of tin, antimony, and silicon in silver by rapidly quenching these binary alloys from the melt. The procedures employed for alloy preparation, quenching, and Debye-Scherrer X-ray diffraction measurements have been described elsewhere. The lattice parameters obtained for the fcc structures in Ag-Sn and Ag-Sb alloys are presented in Fig. 1, together with the results of Owen and Roberts.4 Alloy compositions are believed to be within ± 0.2 at. pct on the basis of negligible weight losses during preparation and reproducibility of the lattice spacings. Diffraction lines from hcp phases were also detected: the relative visual intensities of the fcc (200) and hcp (10.2) lines were estimated as shown in Table I. The intensities were m for the (200) and w for the (10.2) in a quenched 13.6 at. pct Sn alloy: a lattice spacing for the fcc structure could not be reliably obtained, however. As seen from Fig. 1, the lattice parameters vary linearly with composition up to 8., at. pct Sb and 13." at. pct Sn, respectively, which may be compared with the maximum equilibrium solid solubilities5 of 7.2 at. pct Sb and 11.5 at. pct Sn, respectively. The presence of the hcp phases, which were found together with the fcc phases, is a consequence of the competition1,3 in the nucleation and growth processes during solidification. Both the fcc and hcp phases must be of the same composition for those alloys in the range where lattice parameters increase linearly with solute concentration. Despite much effort with quenched alloys of several silicon concentrations, it has not been possible to obtain lattice spacings of sufficient precision to establish the variation of lattice parameter with composition or the maximum metastable solid solubility: the equilibrium data5 suggest little primary solid solubility of silicon in silver. For alloys containing less than 16 at. pct Si, the Si (111) diffraction line was not observed. For alloys containing 10 to 25 at. pct Si, faint low-angle lines were detected and these could be indexed as the (10.0), (00.2). and (10.1) reflections of an hcp structure with a = 2.87 + 3A. c = 4.52 ± 3A, and c/a = 1.57 ± 2. The 16 at. pct Si alloy was quenched to, and examined at. liquid nitrogen temperatures without any change observed in the proportion of the hcp phase. These experiments were jointly supported by the Atomic Energy Commission and Office of Naval Research under a program directed by Professor P. Duwez. The assistance of H.-L. Luo and A. Abu-Shumays is acknowledged. as is the support afforded

Jan 1, 1965

St. Joe Minerals Corp. opened a new $30 million mine and mill at its Balmat-Edwards division in September. It will be the largest single zinc mining operation in the United States. St. Joe expects to produce more than 200,000 tons of zinc concentrates from its combined Balmat-Edwards mines and mills in 1972, equivalent to more than 100,000 tons of zinc metal-20% of U.S. mine production. The company has operated in Northern New York since 1926, having commenced zinc mining with its Edwards mine and mill, 12 miles from Balmat. They will continue to operate at a rate of 31,000 tons of concentrate per year. St. Joe started the Balmat facility in 1930 with two mine shafts and a mill, with a capacity of 2300 tpd.

Jan 1, 1971

By Roy Lindgren

SINCE the year 1643, when the first blast furnace in America for treating iron ore was built at Saugus, Mass., out of mica schist quarried in the neighboring district, the procurement of a suitable refractory for furnace lining has been a problem of concern to the operators of furnaces. The stacks built of mica schist continued to smelt iron ore until about 1836, when, according to F. H. Norton, the first firebrick were produced1, at Queens Run, Pa. Other writers speak of brick having been molded and burned in Massachusetts about the year 1834. In 1841, Andrew Russell began to produce medium refractory plastic clay brick near East Liverpool, Ohio, that were used for lining blast furnaces1. The well-known Kentucky clay-producing district was not opened up until the year 1871, but since then it has produced a large percentage of the linings for iron blast furnaces. While some strides have been made by the refractories industry during the 100 years that have passed since the first firebrick were produced, it has been only during the last two decades that any real progress has been made towards bettering the product, even though the method of production had improved. Perhaps the fault lies with the user of the brick rather than with the producer, for not sooner demanding a supe-rior product. During the past 15 years the tonnage produced per lining has increased from 500,000 gross tons to 1,000,000 gross tons, and now some furnaces are producing 1,600,000 gross tons and better on a single lining. It is true that enlarged capacity of furnaces and improved practice have accounted for some of this increase in tonnage, nevertheless better quality in firebrick must be given credit for its share. However, we are not yet ready to say that we have reached a maximum life of furnace lining. We believe that a better product can be produced and that the refractories industries of America will, through their extensive research depart-

Jan 1, 1937

By John C. Gifford, Charles L. Thomas

A unique and reproducible method is presented for the determination of water vapor in tough pitch wire bar copper. The procedure involves reduction of the water vapor with molten aluminum to form hydrogen, which is subsequently measured by mass spectroscopy. Average water vapor pressures within the porosities of the wire bar samples are calculated. Correlation is to exist between the specific gravities of the samples and their measured water vapor contents. The method should find application as a very sensitive means of detecting hydrogen embrittlement in copper. The nature and quantity of gases evolved and retained during the horizontal casting of tough pitch wire bar copper have long been of interest to the metallurgist. Considerable work has been done at this laboratory on the determination of these gases. The work has involved not only qualitative but also quantitative analysis, so as to provide a basis for a total accounting of the porosity which is associated with the cast product. From a knowledge of the gas-forming elements within the copper, and the practice of melting and protecting it with a reducing flame followed by contact with a charcoal cover in the casting ladle, the gases which one might expect to find in the pores of the cast product are sulfur dioxide, carbon monoxide, carbon dioxide, hydrogen, and water vapor. Hydrogen sulfide, nitrogen, and hydrocarbons would be other possibilities; however vacuum fusion-mass spectroscopy techniques employed at this laboratory have shown that no hydrogen sulfide and only traces of nitrogen and methane are present. It is highly improbable according to phillipsl that any sulfur dioxide could be evolved in wire bar copper with 10 ppm or less sulfur under normal freezing conditions. Mackay and smith2 have noted that porosity due to sulfur dioxide only becomes noticeable at concentrations above 20 ppm S. Investigation of carbon monoxide and carbon dioxide by a variation in the method of Bever and Floe showed that these two gases could only account, at 760 mm and 1064°C (Cu-Cua eutectic temperature), for a maximum of about 25 pct of the total porosity in a wire bar having a specific gravity of 8.40 g per cu cm. phillips' has noted that no normal furnace atmosphere is ever sufficiently rich in hydrogen to cause porosity in copper from hydrogen alone. In addition, using a hot vacuum extraction technique for hydrogen,4 values have never been observed in excess of 10 ppb in tough pitch wire bar. On the basis of the preceding considerations of gases in tough pitch wire bar, only water vapor is left to account for the major portion of the porosity. Direct determinations of water vapor are virtually impossible at low concentrations by any presently known technique, due to adsorption and desorption within the walls of the apparatus used.5 The present investigation deals with a method for the determination of water vapor by an indirect procedure, using molten aluminum as a reducing agent to form hydrogen according to the reaction: 2A1 + 3H2O — A12O3 + 3H2 The evolved hydrogen can then be measured quantitatively by mass spectroscopy. EXPERIMENTAL A 10-g piece of 99.9+ pct A1 was charged into a porous alumina crucible (Laboratory Equipment Co., No. 528-30). Fig. 1 shows the crucible in place at the bottom of an 8-in.-long quartz thimble. A funnel tube with two l1/8-in.-OD sidearms extending at a 90-deg angle from each other was attached to the top of the thimble. One of the sidearms was joined to the inlet system of the mass spectrometer (Consolidated Electrodynamics Corp. Model 21-620A) via a mercury diffusion pump situated between two dry-ice traps. The copper samples were placed in the other sidearm, followed by a glass-enclosed magnetic stirring bar for pushing the samples into the crucible. All ground joints were sealed with vacuum-grade wax. The entire system was evacuated and the aluminum was heated with a T-2.5 Lepel High Frequency Induction Furnace for 21/2 hr at a temperature visually estimated to be 900°C. The temperature was then lowered and the hydrogen was monitored on the mass spectrometer until it was given off at a constant rate of about 4 to 5 1 per hr. This rate corresponded to a slope of 2 to 3 divisions per min on the X3 attenuation of a 10-mv recorder at a hydrogen sensitivity of approximately 100 divisions per 1. A micromanometer (Consolidated Electrodynamics Corp. Model 23-105)

Jan 1, 1969

By Roy Lindgren

SINCE the year 1643, when the first blast furnace in America for treating iron ore was built at Saugus, Mass., out of mica schist quarried in the neighboring district, the procurement of a suitable refractory for furnace lining has been a problem of concern to the operators of furnaces. The stacks built of mica schist continued to smelt iron ore until about 1836, when, according to F. H. Norton, the first firebrick were produced1, at Queens Run, Pa. Other writers speak of brick having been molded and burned in Massachusetts about the year 1834. In 1841, Andrew Russell began to produce medium refractory plastic clay brick near East Liverpool, Ohio, that were used for lining blast furnaces1. The well-known Kentucky clay-producing district was not opened up until the year 1871, but since then it has produced a large percentage of the linings for iron blast furnaces. While some strides have been made by the refractories industry during the 100 years that have passed since the first firebrick were produced, it has been only during the last two decades that any real progress has been made towards bettering the product, even though the method of production had improved. Perhaps the fault lies with the user of the brick rather than with the producer, for not sooner demanding a supe-rior product. During the past 15 years the tonnage produced per lining has increased from 500,000 gross tons to 1,000,000 gross tons, and now some furnaces are producing 1,600,000 gross tons and better on a single lining. It is true that enlarged capacity of furnaces and improved practice have accounted for some of this increase in tonnage, nevertheless better quality in firebrick must be given credit for its share. However, we are not yet ready to say that we have reached a maximum life of furnace lining. We believe that a better product can be produced and that the refractories industries of America will, through their extensive research depart-

Jan 1, 1936

By K. E. Starling

Phase equilibria data were used to develop an equation-of-state correlation for complex hydrocarbon mixtures, thereby circumventing difficulties associated with use of pressure-volume-temperature data. Equilibrium phase data for two condensate reservoir fluids were used to determine equation-of-state parameters for hydrocarbons as heavy as C22H46 in a modified form of the Benedict-Webb-Rubin equation of state. Comparative tests of K-values from the resultant correlation were made with data for condensate reservoir, separator and gas plant absorber mixtures. Generally, for temperatures above OF and computed liquid densities below 0.55 Ib-mole/cu ft, the modified BIVR equation predicted K-values in close agreement with the experimental data. INTRODUCTION Accurate predictions of thermodynamic behavior for complex hydrocarbon mixtures are necessary for many calculations in the petroleum industry. Because of the relatively high cost of extensive experimental data, many correlations for prediction of phase behavior have been developed. Some of these, such as the correlation of K-values presented in the NGAA Equilibrium Ratio Data Book, are totally empirical.l Others, such as the Benedict-Webb-Rubin (BWR) equation-of-state method, are semitheoretical.2-4 Unfortunately, published correlation methods often do not accurately predict the phase behavior of complex hydrocarbon mixtures, principally because of inadequate representation of the effects of components heavier than decane. This paper presents a new approach to this problem in which basic equation-of-state relations including heavy hydrocarbon effects are applied. Equilibrium phase data for two condensate reservoir fluids containing hydrocarbons as heavy as C22H46 are used to correlate component K-values. The BWR equation was chosen as the prototype equation of state for this study because of its proven capability for accurately predicting phase behavior and thermodynamic properties of light - hydrocarbon mixtures? Research was directed toward development of BWR parameters for the heavy hydrocarbons and modifications of the mathematical form of the BWR equation for application to complex hydrocarbon mixtures. The new equation-of-state approach presented differs considerably from previous methods in that phase equilibria rather than PVT data are used for determination of equation-of-state parameters. It is an explicit approach since the parameters are determined directly from mixture data. As such, it does not encounter problems inherent in the implicit method used by Benedict, Webb and Rubin 2-4 and numerous other investigators—one in which mixture parameters were postulated to be functions of the pure component parameters. The pure component BWR parameters, in turn, were determined from experimental PVT data. This method has been limited to mixtures containing components lighter than decane because of lack of vapor phase PVT data. Studies have been reported in which BWR parameters have been determined explicitly from PVT data for binary mixtures.6-8 However, since small concentrations of heavier components have only a minor effect on PVT behavior, it is doubtful that these explicit methods would yield useful results for condensate systems. Ellington and Eakin9 have shown that the accuracy of K-values predicted by an equation of state developed from mixture PVT data probably would be more than an order of magnitude lower than the accuracy of the PVT data. On the other hand, an equation of state utilizing parameters developed from phase equilibria data should predict K-values with accuracy comparable to the accuracy of the experimental phase compositions. This work applies this explicit approach with the objective of improving hydrocarbon mixture phase behavior predictions. Results are evaluated by comparing predicted and experimental K-values at reservoir, separator and gas plant

Jan 1, 1967

By A. C. Freeze

The first use of electric punched card accounting machines as an aid in calculating reserves at the Sullivan mine in Kimberly, B.C., was made in January, 1948. At that time their use was limited to totalling individual reserve blocks for the various reserve classes and for calculating total metal content. The immediate objective was to increase speed, improve accuracy, and to effect some savings in labor that could be employed more usefully elsewhere. It was recognized also that the potential for achieving even greater advantages was excellent. The initial experiment proved so successful that it was inevitable that the use of the method would expand. Thus, for the past nine years assay data from core hole and development headings have been processed by these machines and the results integrated with the program of calculating reserves. It was also learned that the machines could store and classify a large amount of other information concerning the mining characteristics of each reserve block in addition to tonnage and metal content. This has proven very useful for the preparation of monthly production reports as well as in long term planning, in forecasting production schedules, and in analysing the results achieved.

Jan 4, 1961

By A. D. Hodges

In 1874 my attention was called to what seemed to me an interesting and new nickel and cobalt combination found in Ludwig and Carter's copper mine, near Mason Valley, Esmeralda County, Nevada. With the assistance of Mr. A. Hebberling I made several partial analyses of the mineral or minerals. I also communicated with my friend, Professor H. B. Cornwall, of the John C. Green School of Science, College of New Jersey, who analyzed a couple of specimens which I forwarded to him. The copper ore occurs in the mine principally as carbonate and to a certain extent as silicate, the latter generally in connection with clay seams or bands. In some places, together with the copper silicate and clay, generally interstratified with them, there occurred a compact shining black mineral (a) containing nickel and cobalt. Occasionally, in cavities, in connection with (a) was found a black substance (b), either massive and in this case very similar to (a) but with driller lustre, or forming an incrustation with rough and botryoidal surface and radial-fibrous structure, or granular and earthy. A few specimens were found having on the surface very fragile black needles (c) sometimes 1/2-inch long, interspersed with needles of malachite. The mineral (a) seemed, according to the analyses, to be of nearly constant composition, and was considered by Professor Cornwall to be a chrysocolla containing nickel and cobalt—a new occurrence to

Jan 1, 1885

By S. Ramachandran, R. A. Walsh, J. C. Fulton

A method has been developed for calculating the oxygen content of commercially melted stainless steels. Application of thermodynamics to the de-oxidation reaction in straight chromium and Cr-Ni stainless steels has resulted in a set of equations DURING the past 30 years, many rewarding developments have resulted from the application of physical chemistry to steelmaking. A need still ex- which permits the calculation of oxygen contents. The model was programmed for computer calc~ilations. The validity of the method was demonstrated on routine oxygen samples from numerous commercially melted heats of stainless steel. ists for further progress in the use of thermodynamics to meet the more stringent requirements for cleaner steel. Current electric furnace practices have been developed around minimizing residual-oxygen content, one of the most important factors controlling the inclusion content of stainless steels. The residual oxygen is controlled by the use of deoxidizers during the finishing period and a number of empirical rules have been evolved. Although this feature of electric furnace practice has long been in use, only in recent years has funda-

Jan 1, 1963

By R. J. Blackwell, A. L. Pozzi

Scaled laboratory-model studies provide a powerful method for evaluation of a proposed oil-recovery process. In recent years, models have been used extensively to evaluate processes in which solvents displace oil, both for general cases and for specific reservoir conditions. Since the performance of a miscible flood in a horizontal reservoir can be significantly affected by transverse mixing between solvent and oil, this displacement mechanism must be accurately simulated in the scaled model studies. Unfortunately, precise scaling of transverse dispersion coupled with the requirement of geometric similarity requires impractically large laboratory models and long times for experiments. If scaling requirements for miscible displacements could be relaxed while accurate simulation of essential displacement mechanisms is maintained, the utility of model studies would be greatly enhanced. The purpose of the work reported herein was to evaluate the relative importance of various mechanisms affecting miscible displacement and to ascer tain whether the essential features of the displacement process can be simulated even though some scaling groups are not satisfied. These studies were performed with completely miscible systems in linear, horizontal models packed with unconsolidated media. From the experimental results, a set of relaxed scaling criteria was formulated which allows the requirements of geometric similarity and equality of the ratio of viscous to gravity forces to be omitted for specified conditions. The relaxed criteria are valid whether transverse mixing is by molecular diffusion or by convective dispersion. Correlations which permit prediction of vertical sweep efficiencies in linear, horizontal reservoirs were developed from the experimental data when transverse mixing is by molecular diffusion. These same correlations may be used when transverse mixing is by convective dispersion if an empirically defined, effective, transverse dispersion coefficient is used in the description of the mixing process. The effective transverse dispersion coefficient correlation essentially duplicates the dispersion coefficient correlation for equal-viscosity, equal-density fluid systems. Experimental values for the effective transverse dispersion coefficient can be measured readily. INTRODUCTION One of the most effective methods for evaluation of miscible-displacement oil-recovery processes is that of displacements in laboratory models scaled to simulate reservoir conditions. For these laboratory studies to be meaningful, however, the essential displacement mechanisms affecting reservoir performance must be accurately simulated. Since the performance of a miscible flood in horizontal reservoirs, or in dipping reservoirs at high rates, can be significantly affected by transverse mixing of solvent and oil, this mechanism must be considered in the design of laboratory experiments. Unfortunately, precise scaling of transverse dispersion coupled with the requirement of geometric similarity requires impractically large laboratory models and long experiment times. This difficulty seriously limits the utility of laboratory model studies. Craig,et al,1 demonstrated that geometric similarity is not required when mixing is unimportant. Their experimental data indicate, for the cases studied, that the displacement is sufficiently characterized by scaling the ratio of viscous-to-gravitational forces. This work suggests that relaxation of the requirement of geometric similarity and, possibly, other criteria might also be permissible when mixing is important, provided suitable groups describing the mixing process are scaled. The purpose of the work reported here was to evaluate the relative importance of various mechanisms affecting miscible displacement and to ascertain whether the essential features of the displacement process can be simulated even though some scaling groups are not satisfied. Consequently, laboratory investigations were made of the dependence of recovery on dispersion and other variables,

By J. A. Danko, C. D. Pears, L. D. Schmidt, J. P. McGee

This paper describes a pilot plant built on the campus of West Virginia University by the Federal Bureau of Mines station at Morgantown, West Virginia, for gasifying pulverized coal in a mixture of oxygen and steam at pressures in the gasifier up to 450 psig. The work upon which this report is based was done under a cooperative agreement between the Bureau of Mines and the West Virginia University. The goal of Bureau of Mines work at Morgantown is development of a low-cost process for producing mixtures of carbon monoxide and hydrogen for the modified Fischer-Tropsch synthetic-fuel plants, which may be shifted to produce hydrogen for coal-hydrogenation plants. Gasification with oxygen offers the inducement that the gas may be generated at the pressure at which the gas will be utilized in a gas-synthesis plant. Since the optimum pressure for the synthesis appears to be about 400 psig, the gas should be produced at approximately 450 psig to take care of pressure drops in the purification train and control valves. If the gas is generated at the pressure of utilization, only the oxygen need be compressed, not the raw synthesis gas. This means a saving in power of 5 hp per hour per 1000 cu ft (CO + H2), which is approximately a saving of 4 cents per gallon of gasoline. For example, consider a commercial plant generating 18,000,000 standard cubic feet per hour of raw gas that would produce approximately 10,000bbl of liquid product per stream-day. Assume that this gas would be 85 pd CO + H2 and that the oxygen required would be 320 cu ft per 1000 cu ft of CO + H2. The following estimate is based on a commercial centrifugal compressor. If the 18,000,000 std cu ft per hour of synthesis gas is compressed to 450 psig with 74 pd efficiency, 107,000 hp is required for compression. If the synthesis gas is generated at 450 psig pressure, only

Jan 1, 1953

By S. W. Churchill

A digital computer was used to obtain an exact numerical solution for the transient behavior of the insulation and earth adjacent to an isothermal, submerged flat surface for a single set of parametric values. Comparison of the computed results with analytical solutions for limiting conditions revealed that a complete and general solution for all parametric values could be constructed from these limiting solutions. Complete and general solutions for insulated spheres and cylinders can also be constructed from limiting solutions. The procedure is illustrated in part for an insulated spherical tank. The heat flow was found to fall rapidly to a pseudo-steady state; after some time, it then decreased slowly to zero for a flat plate and cylinder, and to a low steady-state rate for a sphere. The accumulative heat flow during the initial falling-rate period may be a significant fraction of the heat flow during the entire first year. INTRODUCTION Underground storage of liquefied natural gas and liquefied petroleum gas has received considerable recent attention. The rate of heat flow from the earth to the storage cavity and the resulting temperature field in the earth are important factors in the technical and economic evaluation of such storage facilities. The objective of this paper is to indicate how complete solutions can be developed for the transient flux and temperature field for various geometrical configurations. The representative properties and dimensions, and the resulting parameters utilized in the illustrative results, are indicated in Table 1. The results presented herein are for dry earth. The effect of the latent heat of solidification of water in the soiI will be described in a subsequent paper. The temperature field in the insulation and earth is determined by energy balances, boundary conditions and initial conditions. The physical problem can be described mathematically with virtually no idealizations insofar as physical properties are known. It appears possible to solve the equations by numerical integration on a high-speed digital computer for any geometrical configuration and conditions. For complex situations, however, the computations are expensive and the results are highly specific. Analytical solutions have been developed for a few simple but important geometrical configurations and conditions, including one-dimensional heat transfer from (or to) earth at an initially uniform temperature to (or from) flat plates, spheres and circular cylinders. The solution for an insulated flat plate has also been derived but is in the form of a slowly converging series involving taklated functions. It was planned to use a computing machine to evaluate this series for a number of representative conditions. However, upon examination of the results of preliminary computations it was discovered that a complete, general and accurate solution could be developed by interpolation between several much simpler solutions for limiting conditions. This technique then was used to develop a a complete solution for an insulated sphere. The equations presented herein are derived in Carslaw and Jaegerl and other books on applied mathematics, or they are simple extensions of these previous results. Hence, all derivations are omitted. Emphasis is instead placed on the results and their

By C. H. Ault, D. D. Carr

Four counties in Indiana- LaPorte, Vigo, Vanderburgh, and Switzerland-have potential for deep underground limestone mining because they are in or near high population areas and have no surface-mineable limestone deposits. The principal markets are Gary-South Bend, Terre Haute, Evansville, and Cincinnati. Mineable seams suitable for aggregate are 120-150 m (400-500 ft) below the surface in LaPorte and Vigo Counties, about 90 m (300 ft) below the surface in Switzerland County, and about 600 m (2,000 ft) below the surface in Vanderburgh County. Some deposits are also suitable for high-purity uses or for cement raw materials, which enhances their potential for exploitation.

Jan 1, 1983

By D. V. Carter, F. M. Hackbusch

Beginning the year 1938, the East and East Central Texas district comprised 48 counties, which is equivalent to the Texas Railroad Commission districts 5 and 6. At the close of the year there were 46 oil and gas fields in this district. Eight other fields, seven oil and one gas, have been abandoned. Exploratory Drilling During the year, 113 exploratory wells were drilled. Nine discoveries were made, five of which proved to be oil fields, three distillate, and one gas. Completions for the district were 2043 oil wells (distillate wells included), 36 gas wells and 163 dry holes. Exclusive of the East Texas field, the Marion County extension of the Rodessa field led the district in the number of completions during the year. Production and Proration All fields in the district produced a total of 182,369,484 bbl. of oil, a decrease of 12.57 per cent compared with the 208,594,453 bbl. produced during 1937. The East Texas field produced 148,189,913 bbl., which was 81.6 per cent of the district's production for 1938. November daily average oil production for the East and East Central district was 469,102 bbl. The estimated cumulative production to Jan. 1, 1939, for this district was 1,753,894,802 bbl. It is estimated that the East and East Central district produced 38.9 per cent of the state's total production for the year, which was 468,781,632 barrels. The decrease in 1938 production, as compared to that of 1937, in this district was partly due to the Saturday and Sunday shutdowns, 71 days for the year, which is equivalent to 19.45 per cent of the year. All fields in this district were affected by shutdowns except the Texas portion of the Rodessa field, which was shut in only during January and February. Certain wells were exempt from these shutdowns because of special pro-

Jan 1, 1939

By D. V. Carter, F. M. Hackbusch

Beginning the year 1938, the East and East Central Texas district comprised 48 counties, which is equivalent to the Texas Railroad Commission districts 5 and 6. At the close of the year there were 46 oil and gas fields in this district. Eight other fields, seven oil and one gas, have been abandoned. Exploratory Drilling During the year, 113 exploratory wells were drilled. Nine discoveries were made, five of which proved to be oil fields, three distillate, and one gas. Completions for the district were 2043 oil wells (distillate wells included), 36 gas wells and 163 dry holes. Exclusive of the East Texas field, the Marion County extension of the Rodessa field led the district in the number of completions during the year. Production and Proration All fields in the district produced a total of 182,369,484 bbl. of oil, a decrease of 12.57 per cent compared with the 208,594,453 bbl. produced during 1937. The East Texas field produced 148,189,913 bbl., which was 81.6 per cent of the district's production for 1938. November daily average oil production for the East and East Central district was 469,102 bbl. The estimated cumulative production to Jan. 1, 1939, for this district was 1,753,894,802 bbl. It is estimated that the East and East Central district produced 38.9 per cent of the state's total production for the year, which was 468,781,632 barrels. The decrease in 1938 production, as compared to that of 1937, in this district was partly due to the Saturday and Sunday shutdowns, 71 days for the year, which is equivalent to 19.45 per cent of the year. All fields in this district were affected by shutdowns except the Texas portion of the Rodessa field, which was shut in only during January and February. Certain wells were exempt from these shutdowns because of special pro-

Jan 1, 1939