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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) or from deflection resulting from the cutting out of a circumferential tongue (Fig. Ia) .6 The bending moment M released by such a flexure is. M - EI (I-I) = EI R1-R0 I - u2(R0-R1) I -V2 R0XR1 where E = modulus of elasticity, v = Poisson's ratio, I = moment of inertia of the section, R0 =. mean radius before splitting, R1 = mean radius after splitting. 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 (x) from the surface: S = c d I - V2 x c x d 2 2 RI - R0____E (d ) R1 - R0 X R0 X R1 ~ i - u2 (2 x) Ro X R1 where C is the section modulus and d is the thickness of the section, the ratio M:C being d: 2 for a rectallgular section.* The maximum stress values at the surfaces are. Smax = +E X d X R1-R0 I — u2- 2 R0 X R1 For most purposes the simpler equations: EXd AD1 = ± I - u2 x dm2 and will be satisfactory, where D,, is the aver. age of the mean diameters of the tubing

Jan 1, 1942

By Biswas AK, Hayes P

During the reduction of iron oxide pellets in the blast furnace it has been found that catastrophic swelling (up to 300% volume increase) can occur. Although the burden preparation conditions can be designed to avoid this phenomenon the exact reason and mechanism of the swelling has yet to be clearly identified. Swelling of the burden is undesirable since it reduces the interparticulate voidage in the blast furnace thus reducing gas flow through the stack resulting in low production rates of iron. The present study differs significantly from previous experiments in that reduction is carried out on single crystals of wustite thus the problems of control of gas composition and specimen preparation are minimised. The microstructures formed on reduction have been examined by optical and scanning microscopy. Pure wustite and wustite doped with various levels of CaO have been examined after reduction in controlled CO-CO 2 gas mixtures at 968¦C. The catastrophic swelling on reduction coincides with the formation of an unusually open iron structure in which the iron appears as whiskers or needles as previously reported. The spacing and thickness of the needles are shown to vary with impurity content and gas composition. Metallographic examination has shown in addition, however, that the whiskers do not necessarily constitute the only product form of the iron produced and in CaO containing wustites with less than - 2% CaO there is a transition from needle growth to porous growth of iron. Thus the % swelling of the oxide particles is dependent on the initial size of the oxide grains. Samples of FeO - 10% CaO exhibited a previously unreported product inorphology associated with the nucleation of 2CaO.Fe203.

Jan 1, 1980

By L. E. Garner

Aggregate resources should be considered primary factors in urban development. Resource planning is essential because land values, previous construction, or zoning restrictions often preempt exploitation of aggregate deposits within an urban area. Sequential land use practices allow development of area prior to urban development population and aggregate consumption trends in Austin, TX, indicate that substantial quantities of reserves will be lost to future development. Aggregate materials are present in nearby areas. However, a comparison of transportation and reclamation costs indicates that reclaiming land after mineral extraction can be significantly cheaper than transporting materials longer distances.

Jan 1, 1982

By P. R. A. Andrews

"The sillimanite group minerals, kyanite, sillimanite and andalusite are identified as alumino-silicate minerals with the common chemical composition AIP3.Si02' so that each possesses similar physical properties. Kyanite is the most abundant mineral and mainly occurs in Quebec, Ontario and British Columbia; sillimanite occurs in Ontario and Manitoba; and andalusite in Nova Scotia. The main use for the sillimanite-group minerals is in refractory applications for the production of refractory bricks and shapes. In refractory applications, the main performance criterion is the relative percentage of mullite formed within the material during firing. This phase gives a greater degree of resistance to creep deformation and slag attack, and improves the ability of the refractory to withstand high temperatures under load. The beneficiation of refractory silicate minerals has been the subject of many investigations at CANMET, and the former Mines Branch. Eighteen kyanite, two sillimanite, and three andalusite evaluation studies were conducted between 1933 and 1987. A review of some of the more important studies is presented, which includes information concerning mineralogy, beneficiation methods and flotation data."

Jan 1, 1995

By J. C. Bayles

An obstacle to the more careful and satisfactory study of metals has been the difficulty in harmonizing the results of chemical and physical tests. These give us records of observations made from different and often widely separate points of view, and while it is true that they furnish bases for more or less accurate triangulations into the realm of speculation, it is doubtful if, with only the laboratory and the testing machine, our investigations would not move in parallel lines, leaving between them an unexplored field in which must probably be sought the information which shall connect the results of chemical and physical tests, and give to both a practical value which neither has yet been found to possess. The use of the microscope in the study of metals is not a new thing, but it is only lately that it has begun to attract the attention it merits or to show results of tangible value to the metallurgist. Among recent valuable contributions to the literature of this subject, I have been especially interested in the work of Mr. A. Martens, of

Jan 1, 1883

By Fernando Concha

"Thickening development and innovation in the 20th Century occurred in two decades periods. From 1900 to 1920, Dorr invented the continuous thickener and the first method of thickener design was proposed by Coe & Clevenger. From 1920 to 1940, the operating variables of continuous thickening were discovered by Comings at the University of Illinois. From 1940 to 1960, the first theory of sedimentation was proposed by Kynch and several authors, Talmage and Fitch, Ysioka and Hasset used this theory to develop new thickener design methods. From 1960 to 1980 Shannon and Tory demonstrated that this theory applied exactly for the sedimentation for small rigid spheres in water and Scott showed that it is not valid for flocculated suspensions. From 1970 to 1990 the phenomenological theory of thickening was developed based on the theory of mixtures. Papers by Kos, Bascur, Thacker and Lavelle, Concha and Bascur, Concha and Barrientos, Auzeris, Buscal and White, Landman, White and Buscal show the application of this theory to thickening and Adorjan presented the first thickener design method based on this theory. In 1980s the mathematical analysis and solutions of Kynch’s model for batch and continuous thickeners was obtained by Bustos. The new Century brought solution to the phenomenological thickening model which was applied to thickener design, simulation and control. The method of thickener parameter determination was improved by designing new laboratory and on-line instruments and advanced control strategies was designed and validated in plants. Structural thickener design produced improved feedwells and feed dilution mechanism, stronger raking mechanism and different thickener shapes according to new ambient requirements, such as high rate thickener and paste thickeners that increase the water recovery. New challenges include better flocculation and advanced control strategies."

Jan 1, 2014

Before commencing design of a coal prepar ation plant, it is essential to have detailed information of the raw coal to be treated to- gether with a clear understanding of the products required. Prediction of raw coal size distribution, particularly the amount of fine material, is difficult and the methods employed should be large scale pilot plant studies or techniques to simulate coal degradation and shale breakdown in water. A detailed knowledge of well proven coal preparation processes and new developments allows processes and process combinations to be compared to'obtain the maximum economic recovery when using lower cost, less efficient processes within acceptable limits. Equipment should be selected bearing in mind its precise application and the location where it is installed. Plant layout should be carefully studied to minimise equipment requirements and to simplify construction. Measurement, control and automation should be an integral part of plant design in order to obtain the optimum performance of the processing equipment.

Jan 1, 1974

By Gilles A. Tremblay

Acidic drainage has been long recognized to be the largest environmental liability facing the Canadian mining industry and to a lesser extent the public through abandoned mines. The Mine Environment Neutral Drainage (MEND) Program was the first initiative formed in 1989 to develop scientifically-based technologies to combat acidic drainage. This 9-year volunteer program reduced the liability by several hundreds of million dollars and established Canada as the recognized leader in research and development on acidic drainage for metal mines. MEND 2000 is a three-year program that started in 1998. The key to MEND 2000 is technology transfer- providing state-of-the-art information and technology developments to users. MEND-developed technologies are being verified by long-term monitoring of large-scale field tests. Maintaining linkages with a number of foreign government and industry-driven programs is also important to the successful completion of the program. Through these efforts a further reduction of the environmental liability associated with acidic drainage will be realized.

Jan 1, 2000

By R. Schuhmann

Available thermodynamic data applicable to copper smelting systems are collected and tabulated, and the important gaps are pointed out. A few examples are given of estimations which can be made from the available data. An experimental research program is proposed to supply the thermodynamic data that appear most essential to better quantitative understanding of the chemistry of copper smelting. The proposed program is designed also to shed specific light on the practical problems of slag losses and magnetite behavior. OPPER smelting, from flotation concentrates to V-/ blister copper, is conspicuous among the large scale chemical processes which are conducted with only relatively incomplete knowledge of the physical chemistry involved. For example, no common metallurgy text explains adequately why copper enters the matte phase while iron enters only to the extent that sulphur is left over after satisfying the copper. Explaining this important phenomenon as a manifestation of the greater affinity of sulphur for copper than for iron is unsound because the affinities of copper and iron for sulphur are about the same at smelting temperatures. As will be shown, other affinities are really decisive in the relatively clear-cut separation of copper in the matte. In contrast, thermodynamic studies have contributed much to our understanding of copper refining, zinc oxide reduction, magnesium production, steelmaking, etc. For each of these processes, the important reactions are clearly recognized, and fair to good quantitative values of the free-energy changes and equilibrium constants are available. Such data have proved to be of constantly increasing practical value in process development and improvement. Work in other fields has furnished much thermodynamic data applicable to copper smelting systems. In fact, several promising starts have been made in applying such data to specific smelting problems. Kelleyl made an appraisal of the possibilities of recovering elementary sulphur from low grade matte. His calculations and compilations of thermodynamic data have represented the starting point for much of the work in this field, including the present survey. Huang and Hayward2 nd Aksoy3 used thermodynamic methods in the study of copper losses in reverberatory slags. Peretti4 used thermodynamic data in explaining the chemistry of converting. The recent publications of Darken and Gurry"." and of Darken,' dealing with the iron-oxygen and iron-silicon-oxygen systems, respectively, present equilibrium data that are applicable to copper smelting systems. Also additional data were reported recently on the affinity of sulphur for copper, manganese, and iron8 and on the sulphur pressures of iron-sulphur melts." The survey presented in this paper was made as the basis for planning an experimental program on the thermodynamics of copper smelting. Few researches on the chemistry of copper smelting have been reported in recent years, so that a reappraisal and coordination of old and new data are essential if further work is to take the directions of maximum value. The experimental program is now in progress, and the plan of attack is outlined at the end of this paper. Progressive Oxidation and Desulphurization of Copper-bearing Liquid Phases: The chemical activities of sulphur and oxygen are two of the most important thermodynamic yardsticks to be applied to copper smelting processes. Virtually the entire smelting and refining sequence involves a series of systems characterized by decreasing sulphur activity and increasing oxygen activity. In this section, therefore, an attempt is made to define and explain these activities in terms of equilibrium partial pressures of SO2, s2, and O,. Also, estimates of these quantities are presented, the estimates being based largely on calculations presented in a later section of this paper. The sequence of steps from raw flotation concentrate to fully oxidized copper ready for poling involves progressive and controlled oxidation. Iron is oxidized and enters the slag. Sulphur is oxidized and leaves in the gas. Table I summarizes several important features of this oxidation and desulphurization sequence, starting at the beginning of the matte blow in the converter. The top line gives in order the principal smelting and refining stages up to fully oxidized copper, plus the additional step, not used commercially, of oxidizing all the way to Cu,O. In the second line are shown the principal copper-bearing liquid phases which characterize the process. Through most of the sequence the copper

Jan 1, 1951

In mid-1984, SAIMM reached an agreement with the South African Region of what is now the Institute of Metals to combine the physical-metallurgical activities of the two organizations. This was the outcome of several years of informal collaboration, and followed the recognition in 1982 by the SAIMM Council that applied physical metallurgy had grown in importance to South African industry and should have a place alongside the two areas already well-established for SAIMM commitment and support-mining and extractive metallurgy.

Jan 1, 1986

By Jun Li, Marc Le Vier, Rong Yu Wan, Jan D. Miller

The hydrometallurgical treatment of gold and silver ores by ammoniacal thiosulfate solutions in the presence of a copper catalyst has been actively studied in recent years. Such a process strategy is very attractive due to the low toxicity of the lixiviant and the efficient recovery of the precious metals from difficult-to-treat ores. Important features of the ammoniacal thiosulfate system for the recovery of precious metals from various sources are reviewed in this paper, including leaching, metal recovery, and system stability.

Jan 1, 1995

By A. R. Katti

The stone columns are widely used in the improving the bearing capacity of weak soils mostly for supporting flexible foundation systems. The load carrying capacity of a stone column is complex in nature. The load capacity is derived from the lateral stresses acting on the stone column due to load transmitted from the flexible structure due to deformation to soil mass and which in turn transmits lateral pressure in s3 direction. The load capacity is also function of the f value of the stone column, cohesion of the surrounding soil, K0 and Gb2 of surround­ing soil including passive resistance developed to lateral deformation of the stone column. The assessment of axial and radial deformation is much more complex. Recently Katti et.al. have developed a method based on a granular heap approach and computed with equivalent fe. which combines the effect of s3a and equivalent volume concept to estimate radial and axial strains. In this paper an attempt is made to put forward guidelines for design of stone column accounting for both stability with respect to shear and also with respect to settlement. The estimate of settlement are based on the internal properties of stone column and surrounding soil. It is considered thus the settlements computed are more realistic.

Jan 1, 1996

By E. V. Potter, H. C. Lukens

THE volume of hydrogen released from electrolytic manganese at various temperatures and pressures was determined in a previous investigation1 as part of a study to determine the most practical procedure for removing the hydrogen from electrolytic manganese metal. No attempt was made to determine the absolute volume of gas in the metal at any temperature and pressure; the volume of gas released showed only the variation in solubility with temperature and pressure. The results were very similar to those obtained by Sieverts and Moritz.2 Both sets of data show a minimum solubility between 500° and 700°C., but they differ in certain respects; on cooling from 500°C., our results showed an increase in solubility of about 7 C.C. as compared with an increase of 34 C.C. per 100 grams shown by Sieverts. Furthermore, the transition temperatures, as indicated by sharp breaks in the solubility curves, did not agree well with Sieverts' data. This information was of secondary importance in the earlier investigations, and the solubility at low temperatures and the transition temperatures were subject to considerable error. There- fore, a subsequent investigation, reported in this paper, was made to measure the absolute solubility at temperatures from room temperature through the melting point and make more accurate observations of the transition temperatures. APPARATUS AND METHOD The apparatus and method were essentially the same as those described in the previous work,1 as shown in Fig, I. At high temperatures, the small tube containing the thermocouple in the sample container A frequently broke off, so for some of this work the thermocouple was placed outside the sample container and protected by a quartz tube of about the same wall thickness as the sample container. No significant difference was found in the transition temperatures obtained in the two ways. The automatic temperature controller was used in these tests in the regions where there was little change in solubility with temperature. In the neighborhood of the transition points a continuously variable autotransformer was used instead of the automatic controller, and the power input to the furnace was adjusted so that the temperature increased or decreased at a very slow, uniform rate through the transition range. This procedure was followed because the temperature oscillations produced by the controller were too great compared with the transition range, and the transition points determined under such conditions were less accurate. ABSOLUTE SOLUBILITY Procedure and Results The absolute solubility of hydrogen in manganese could be determined most

Jan 1, 1946

NEW MEMBERS The following list comprises the names of those persons who became members during the period Nov. 9, 1918, to Dec. 10, 1918. ALBERT, EDWARD J 235 E. Upsal St., Philadelphia, Pa. BARRY, D. A Supt. of. Mines, The Big Five Min. Co., Idaho Springs, Colo. BATON, GEORGE S., Cons. Min. Engr., Baton & Elliott, 2412 First National Bank Bldg., Pittsburgh, Pa. BAXTER, HAROLD ALEXANDER, Met. Engr. & Operation Supt., Tacony Ordnance Corpn., Philadelphia, Pa. BENNETT, JOHN S., Chem. and Min. Engr Copiap6, Chile, South America. BOWDEN, MALCOLM, Min. Engr.; Efficiency Engr., Elm Orlu Min. Co., Butte, Mont. BROWN, HAROLD C 2d Lieut., A. S. A. P. BROWN, THOMAS ALBERT, Min. and Met. Engr.; Supt., The Royal Tiger Mines Co., Breckenridge, Summit Co., Colo. BROWN, WALTER S., Investigator, New Jersey Zinc Co. (of Pa.), Palmerton, Pa. BURDETTE, R.. S Capt., Ord. Dept., U. S. A. CALLANDER, IRA C., Asst. Supt., Gauley Mountain Coal Co., Jodie P. 0., Fayette Co., W. Va. COLLINS, J. W., Foundryman, The Aluminum Casting's Co., "L" Plant, Cleveland, Ohio,

Jan 1, 1919

By R. W. Raymond

I HAVE the pleasure of exhibiting samples of the rock in which the South African diamonds are said to occur, for which I am in debted to Mr. Franz Groeger, of Vienna, formerly an assistant of the Royal Imperial Geological Institution, whose account of the general geology of Southern Africa was contained in a recent number of the proceedings of that Institution. The rock is apparently a sort of tufa, evidently of volcanic origin. Mr. Groeger assured me that it could be seen in situ, bounded by uplifted stratified rocks; and that diamonds had been mined from it, by means of shafts, some distance below the surface. Groeger calls it "greenstone-tufa," and says of it, in the proceedings of the Geological Institution, " it breaks through the younger members of Group III [lower Trias and Jura], . . .. and crops out in oval masses, filling fissures . . ..The occurrence of this tufa is not locally limited, but has been traced and proved already over a large territory." DR. HUNT remarked that the material looked like the trass of the Rhine region. He thought it a new occurrence for diamonds. He believed diamonds to belong to ancient crystalline rocks, although these materials might be brought tip by volcanic agency, and the diamonds remain unaltered. In the volcanic rocks of Auvergne, crystals of sapphire, zircon, and spinel are found; and yet no one supposes that these minerals have been generated by volcanic agency. He had had a conversation with Bertrand de Lom on this subject, who agreed with him that these minerals, being hard and resistant,

Jan 1, 1874

By F. D. DeVaney

[In the course of the investigation by the U. S. Bureau of Mines and the Missouri School of Mines and Metallurgy at the Mississippi Valley experiment Station at Rolla, Mo., on the beneficiation of the low-grade manganese ores of the country, some samples from the Cuyuna District, Minn., have been examined. The work was done under the direction of W. H. Coghill, supervising engineer of the Mississippi Valley Experiment Station. Josoph and Kinney5 in venting about the relative importance of Minnesota deposits of low-grade ore compared to the total reserves say:]

Jan 1, 1930

By Igor V. Nazarov

INTRODUCTION Tens of deposits in' coal basins of Western and Eastern Siberia are being open-mined with the technology of overburden rehandling into the mined out space of pits by excavators - draglines. This technology is preferred due to the high productive Russian equipment, comparatively low cost, and relatively small Influence exerted on the environment. The basic tendency of the last decades is the aspiration for enlarging the sphere of the' technology application for development of gentle and steeply dipping seams with the use of blast destruction of overburden and with combined winning of loose alluviums and rock partings. Complex technological schemes with multiple rehandling are widely used. In addition to it, stripping workings, intermediate storage of mineral resources, placing of transport dumps, and engineering construction can be realized with the use of draglines. More than ten of dragline faces are simultaneously exploited in some pits, and the rehandling coefficient ranks from 0.1 to 8. Here, conditions of winning and placing (position of a face and existing dump) are varying in space and time; this leads to the necessity of reconsidering the order for conduction of works (schemes) within the current designing. By now, in order to this, it is required to realize complex engineering calculations by graph-analytical methods and definite experience. The need is available for automatization of this process by creation of the corresponding software. The software is to: • Orient on the active pits and use information on the existing geology, equipment, and situation in mine. • Calculate the existing schemes more operative and on a higher qualitative level to model their development in a pit space with parameter optimization. • Predict situations demanding to change the existing technology for mining operations and recommend optimal technological schemes. METHODOLOGICAL FOUNDATIONS FOR MODELING The problem is not new, it has more than fifty year-old history of creating mathematical models algorithms, and programs in Russia, Ukraine, USA, Canada. Australia and other countries with the developed mining branch. Conventionally, all population of programs can be divided into three groups depending on goal and interval of prediction: • Long-term programs used in designing and intended for substantiation of the nine capacity, selection of mining system, establishment of limits for applying the technology of overburden rehandling. Mid-term programs used in current planning for calculation of technological schemes and certificates of face in active mines.INTRODUCTION Tens of deposits in' coal basins of Western and Eastern Siberia are being open-mined with the technology of overburden rehandling into the mined out space of pits by excavators - draglines. This technology is preferred due to the high productive Russian equipment, comparatively low cost, and relatively small Influence exerted on the environment. The basic tendency of the last decades is the aspiration for enlarging the sphere of the' technology application for development of gentle and steeply dipping seams with the use of blast destruction of overburden and with combined winning of loose alluviums and rock partings. Complex technological schemes with multiple rehandling are widely used. In addition to it, stripping workings, intermediate storage of mineral resources, placing of transport dumps, and engineering construction can be realized with the use of draglines. More than ten of dragline faces are simultaneously exploited in some pits, and the rehandling coefficient ranks from 0.1 to 8. Here, conditions of winning and placing (position of a face and existing dump) are varying in space and time; this leads to the necessity of reconsidering the order for conduction of works (schemes) within the current designing. By now, in order to this, it is required to realize complex engineering calculations by graph-analytical methods and definite experience. The need is available for automatization of this process by creation of the corresponding software. The software is to: • Orient on the active pits and use information on the existing geology, equipment, and situation in mine. • Calculate the existing schemes more operative and on a higher qualitative level to model their development in a pit space with parameter optimization. • Predict situations demanding to change the existing technology for mining operations and recommend optimal technological schemes. METHODOLOGICAL FOUNDATIONS FOR MODELING The problem is not new, it has more than fifty year-old history of creating mathematical models algorithms, and programs in Russia, Ukraine, USA, Canada. Australia and other countries with the developed mining branch. Conventionally, all population of programs can be divided into three groups depending on goal and interval of prediction: • Long-term programs used in designing and intended for substantiation of the nine capacity, selection of mining system, establishment of limits for applying the technology of overburden rehandling. • Mid-term programs used in current planning for calculation of technological schemes and certificates of face in active mines.

Jan 1, 2002

By T. A. Rickard

The province of Otago consists, roughly speaking, of the southern half of the South Island* of New Zealand. On three sides it is washed by the Pacific Ocean and on the north it abuts against Westland and Canterbury. It covers an area of over 20,000 square miles, and for the most part has an extremely broken surface; the narrow plains of the sea-board are bounded by the rounded foothills which in turn are overlooked by range after range of the snowy summits whose varied beauty has made the island known as the Switzerland of the southern hemisphere. The gold-fields are confined to the quartzose schists which, in a broad band, 70 to 75 miles wide, cross the district, extending in a northwesterly direction from the shore of the western ocean into the northern provinces. These quartzose schists are the characteristic rocks of Otago, and to their curious structure are due the interesting differences exhibited by the mining districts in the modes of occurrence of the gold. These rocks, which are almost unbroken over their full extent, have been divided by the Provincial Geologist, F. W. Hutton, into two series of beds, named respectively the Wanaka and Kakanui formations. The only reason given for this division is the desire " to divide such an enormous thickness of rocks in order that the map might display somewhat of the geological structure of the district." As Hutton and others have pointed out, there is in fact no dividing line. The changes noticeable in the ascending series of schists are very gradual, and are due to the slowly decreasing effects of metamorphism. Hutton estimates the thickness of the Wanaka series at as much as 50,000 feet, and the

Jan 1, 1893

By J. W. Matousek

"Computer modeling of smelting processes requires internally consistent equations for calculating the compositions of mattes and slags. That is, the sum of the calculated assays must total 100%. One set of equations that satisfies this requirement for copper produced under oxidizing conditions (pSO2>one atmosphere pressure) is given by the following:%[Fe] = 62.0 – 0.775%[Cu]%[S] = 28.0 – 0.00125%[Cu]2%[O] = 10.0 – 0.225%[Cu] + 0.00125 %[Cu]2Mattes containing nickel in appreciable quantities do not have the defined “white metal” end point of approximately 80 percent copper and 20 percent sulphur that is found in the copper system during the converting process. The above equations, however, are readily extended to nickel and nickel/copper mattes for any desired end product composition."

Jan 1, 1996

By Leonard B. Lipson

Boyer, Morgan and Muskat,' with improvements by Morgan, McDowell, and Doty,l and Laird and Putnam,' have described a scheme for the determination of fluid saturatic in porous media by measuring the x-ray linear absorbing power of particular fluids in the media. This method is one of several which depend on the linear absorbing power of the fluids in the porous medium. Other examples of linear absorption methods involve measurement of dielectric constant, gamma ray absorption, and ultrasonic attenuation. It is the purpose of this note to demonstrate by theortical considerations that the absorption versus saturation curve for a linear absorption method is not necessarily a single valued function of the saturation. Such non-unique behavior must be considered and evaluated before suitable saturation determinations can be made by a linear absorption method. To illustrate the discussion, examples will be given only for the simplest cases of combinations of two different dielectrics. The dielectric constant method was chosen for illustration because it was thought to demonstrate most graphically the point in question. According to Argue and Maass,4 the resultant dielectric constant of a combination of two different dielectrics depends on the orientation of the dielectrics in the electric field of the test condenser used to measure the dielectric constant. One ease involves alternate slabs of dielectrics E1 and E2 perpendicular to the electric field of the test condenser, as shown in Fig. 1A. For this case: l/'E, = A/E, + B/E,.......(1) where E,,, is the dielectric constant of the combination, A is the ratio of the path length through dielectric E, to the distance between the plates of the condenser (assuming the dielectrics have the same cross sectional area as the condenser), and B is the ratio of the path length through dielectric E2 to the distance between the plates of the condenser. It will be noted that the constants A and B are numerically equal to the fractional "saturation" of the region between the test plates of the condenser by the two dielectrics E1 and E2, respectively. Another case involves alternate columns of the two dielectrics parallel to the electric field and forming a continuous path between the condenser plates, as shown in Fig. 1B. For this case: E., = AE1 + BE2.........(2) where E., is the dielectric constant of the combination, A is the ratio of the cross sectional area of dielectric E, to the cross sectional area of the condenser plates (assuming the lengths of the dielectrics equal the distance between the condenser plates) and B is the ratio of the cross sectional area of dielectric E2 to the cross sectional area of the condenser plates. As before the constants A and B are the effective "saturation" of the condenser by the two dielectrics. Still another case is described by Lichtenecker5 where dielectric E2 is shown in the form of small particles distributed at random in dielectric E1. This is shown in Fig. 1C. For this case: log Em = A log E1 + B log E2.....(3) where Em is the dielectric constant of the combination. A is the ratio of the volume of dielectric E1 to the volume of the condenser, i.e., the effective "saturation" of the condenser by dielectric E,. B is the ratio of the volume of dielectric E2 to the volume of the condenser, i.e., "saturation" of dielectric El. Equations (l), (2) and (3) are plotted in Fig. 2 for E1 = 2.5 (oil) and E2 = 80 (water). Equations (1) and (2) may he thought of as representing the limiting cases of the configuration of two fluids which might be expected to exist in a porous medium. Equation (3),

Jan 1, 1951