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By W. A. Tiller, J. P. McHugh

HE majority of liquidus and solidus surfaces in phase diagrams have been determined by the conventional cooling- and heating-curve techniques.' These techniques have two main shortcomings: 1) the solidus may be in considerable error due to the difficulty involved in completely homogenizing the solid and 2) the determination of liquidus and solidus in more than a two-component system does not enable one to determine tie-lines connecting the specific equilibrium solid and liquid compositions. However, in a recent paper by one of the authors,' a method was suggested whereby the liquidus and solidus surfaces plus tie-lines in an n-component system may be determined. This method utilizes a controlled solidification technique and assumes that interface equilibrium exists during freezing. The present work was undertaken with a twofold purpose; first, to determine the liquidus and solidus lines in the pseudo-binary system Bi2Te3-Bi2Se3 by heating- and cooling-curve techniques and, second, to determine the partition coefficients of Te and Se in the BizTe3-,Sex system by controlled solidifica- tion techniques. The two sets of results can be compared to test the accuracy of the controlled solidification method. EXPERIMENTAL I—The starting materials for this study were 997999 pct Bi, Te, and Se, obtained from the American Smelting and Refining Co. The compounds BizTe, and Bi2Se3 were each prepared by melting together stoichiometric amounts of the elements, followed by twelve zone-refining passes. This produced homogeneous bars of the compounds for use in the phase-diagram studies. The apparatus used to obtain heating and cooling curves is illustrated schematically in Fig. 1. The alloy samples were located in a graphite crucible placed in a stainless steel canister. The canister was supported in a heavily lagged pit furnace by a device which oscillated the canister about its vertical axis at a frequency of about 3 cycles per sec during heating and cooling-curve runs. The graphite crucible was designed to minimize the thermal coupling of the sample to the furnace. A thin graphite sleeve separated the alloy sample from the stainless steel tube that housed the thermo-

Jan 1, 1960

By OWEN H. PERRY

One of man's primary tools is the ordinary screen. Whether of mesh or punched plate, it is fundamental in principle, primitive in its origin, and common in its application through all the world; and yet the screen goes only a part of the way toward the completion of its job of separating materials according to size. It will give a practical and continuous separation according to "size," as generally understood (accurate according to the breadth), but the accurate and continuous separation as to thickness is not a practical function of the screen. Still, all through history, the thickness of particles of material must have been important to many people; therefore, one would expect that some standard method of sizing for thickness would long since have been evolved and that equipment applying that method would be readily available to any in¬dustry. This, however, seems not to be so.

Jan 1, 1949

Jan 1, 1884

By Goodman, Richard E.

A complete rational analysis for design of excavation slopes and loaded rock masses is a desirable but perhaps unattainable goal. Irregular external and internal boundary conditions, poor understanding of failure criteria for large masses of rock, capricious material properties, and the importance of indeterminate forces and inaccessible and virtually un- sampleable rock defects emphasize the importance of experience in this aspect of rock engineering. The experience must be correlated with geological factors. In certain regions the accumulation of such experience through the observation of existing rock slopes in various formations constitutes an important aspect of studies for design of rock excavations.

Jan 1, 1969

By Y. Nakada, E. J. Fasiska, A. S. Keh, L. Zwell

DURING an investigation of solid-solution hardening of nickel by carbon,' we found that there were no reliable data on the dilating effect of dissolved carbon on the unit cell of nickel. Bernier2 reported an increase in lattice parameter of nickel (3.523A) when an unknown amount of carbon was introduced into solid solution (3.536A). Similarly KG, Tsien, and Misek3 found an increase from 3.523 to 3.531A when nickel was carburized. strong4 studied the variation of nickel lattice constant as a function of dissolved carbon. However, in his case carbon was introduced into nickel by solidifying the melt at 65 kbar. Therefore, his carbon concentrations were much above the highest equilibrium solubility limit5 (2.7 at. pct C at 1 atm). Knowledge of the lattice mismatch between solute and solvent is essential in understanding the mechanism of solid-solution hardening. Therefore, we decided to determine the dilation of the nickel lattice by carbon under the more usual conditions of atmospheric pressure. The material used was Inco Electrolytic Nickel of 99.95 pct purity, as specified by the supplier. The impurity contents in wt pct were: Fe, 0.01; Cu, 0.01; Co, 0.03; 0, 0.005; C, Si, S, N, trace. To this base material various amounts of AUC-grade high-purity carbon were added during vacuum induction casting. Ingots, 2 in. in diam, were heated in a muffle furnace at 1000°C for i hr., hot-rolled to 1/2-in. thickness, and quenched into brine. All ingots with carbon concentration greater than 0.98 at. pct were enclosed in a cast iron box during the heating to minimize decar-burization. Small pieces were then either swaged down to 0.028-in.-diam wire or cold-rolled to 0.010-in.-thick sheets. After the final cold reduction in area of 50 pct, the specimens were recrystallized by heating in evacuated capsules at 1100°C for 60 to 80 sec and then quenched into brine. The final grain size was 50 to 100 µ. The carbon contents of the alloys, Table I, were determined by a combustion method

Jan 1, 1969

By E. I. Salkovitz, F. W. von Batchelder

AS Slawson1 and others have already shown, from a geometrical view twinning in the diamond structure may be considered as a reflection across a (111) plane or as a reflection across a (112) plane. An analysis by Ellis and Treuting2 showed that the twinning plane must be the (111) plane, but that a twin might have lateral boundaries along (112) planes. Earlier Slawson1 and Ellis3 had shown that only (111) twinning was present in diamond and germanium respectively. Since an ingot of silicon, 1 in. in diam and 1 1/2 in. long, prepared from Dupont silicon to which 0.2 pct Be had been added was available, it was examined for twinning. The ingot had been cooled slowly from the bottom. A section 1/16 in. thick was ground off from the bottom and then the ingot was sliced vertically through the center. Spectrographic analysis indicated only faint traces of iron and silver, in addition to the beryllium. The sample was first etched with a hot solution of 10 pct NaOH in water.and photographed. Back-reflection Laue patterns were made of the vertical and horizontal sections in the regions designated in Fig. 1. Orientations were obtained for each twin using the Greninger technique. Several regions of the same orientation were found; thus regions A and K were identical, similarly N and P, and C, G, J, and L. Knowing the angles between the traces of the twinning plane on the surface and the specimen axis, the indices of the twinning plane were deduced. In all cases the twinning plane was found to be (111); lateral boundaries, however, were found which were (112) such as the one indicated in Fig. 1. Therefore, as in the case of diamond1 and germanium' only (111) twinning occurs in silicon. We wish to thank Mr. Hino for the use of the ingot as well as for its metallographic preparation. References 1C. B. Slawson: American Mineralogist (1950) 35, p. 193. 2 W. C. Ellis and R. C. Treuting: Trans. AIME (1951) 191, p. 53; Journal of Metals (January 1951). 3W. C. Ellis: Trans. AIME (1950) 188, p. 886; Journal of Metals (June 1950).

Jan 1, 1953

Extractive Metallurgy Division Institute of Metals Division Iron and Steel Division OFFICERS AND COMMITTEES W R Hibbard, Jr , President J C Kinnear, Jr , Past President John Chipman, Vice-President T D Jones, Treasurer R W Shearman, Secretary AIME, 29 West 39th Street New York 18, N Y

Jan 1, 1958

By B. M. Burchfiel

CALIFORNIA possesses such an abundance of ceramic materials other than clays, that she is quite independent of other states and foreign countries so far as these materials are concerned. Certain users import some feldspar, silica, and allied minerals, but they do so from choice and not necessity. Production is largely for home consumption, so the total volume of ceramic materials produced is comparatively small. Many small deposits of the materials here under discussion are worked by individuals, and their output sold to individual grinding companies or users. The data given here shall be confined to the larger deposits and developments because they give a truer picture of typical deposits, operations, and materials.

Jan 1, 1936

University of Alabama University, Alabama Mining and Metallargical Society. FRED PISACAYNE. President JAMES REYNOLDS, Secretary (George T. BATOR. Faculty Sponsor RAY L. FARALEE. Counselor University of Arizona Tucson, Arizona Miners' Society J. POTTER TRAINER, President BLANCHE E. LIGHTOWLER, Secretary J. B. CUNNINGHAM, Faculty Sponsor BRENT N. RICKARD, Counselor

Jan 1, 1944

Established as a Division December 15, 1948 Evan Just, Chairman Richard J Lund, Past Chairman Granville S. Borden, Vice-Chairman J K Richardson, Vice-Chairman S H Williston, Vice-Chairman Allan Matthews, Secretary-Treasurer National Security Resources Board 17th and Pennsylvania Ave, N W Washington 25, D C

Jan 1, 1952

Admissions: Joseph C. Gordon, Chairman K. F. Anderson Allen B. Gibson H. J. Gruy R. F. Madera Dan H.-McLendon K. W. Robbins Aurel E. Smith W. F. West Advertising: John. D. Wisenbaker, Chairman Bernard F. Klein Henry N. Lyle R. E. Howard Clark R. Edgecomb, Jr. [ ]

Jan 1, 1961

By G. M. Lee

SEVERAL improvements have been made in Granby smelting practice since the company abandoned the direct smelting of raw ore in the blast furnaces in June, 1927, in favor of sintered concentrate. These improvements have been made in several fields, but the most novel and outstanding change was the development of a process of concentrating most of the gold, and a somewhat smaller fraction of the silver present, in a small portion of the blister copper produced. The practice of making "copper bottoms" is usually associated with the reverberatory smelting of copper ores containing high percentages of impurities, or of copper matte high in precious metals. It has for its object, in the one case, the production of a major part of the copper relatively free from impurities and, in the other case, the production of a small per¬centage of the copper carrying the major part of the precious metals. Although the blister copper produced at the Anyox plant of the Granby company is remarkably free from deleterious impurities and normally contains no great amount of precious metals, certain economic considerations made it advisable to concentrate the existing precious metals into a relatively small percentage of the blister copper produced. The process devised took advantage of principles and reactions of the usual bottoms processes, but was carried out in the converters instead of in a reverberatory furnace.

Jan 1, 1935

By J. Chupak, D. J. Salley, G. L. Simard

Radiotracers were demonstrated to be of considerable value in a study of the interaction of dithiophosphate with galena. The interaction had characteristics of both chemisorption and chemical reaction, being complex because of the nature of the galena surface. Sorption was rapid and markedly reversible, and flotation occurred at relatively small amounts of dithiophosphate sorbed.

Jan 1, 1950

By S. LeFevre

, The solution of the housing and sanitation problem in mining communities, keeping in view both economic and humanitarian aspects, demands the best thought of the management of such enterprises. Upon the solution depend the health and comfort of the employee and his family, and as a consequence his contentment and efficiency. The following description covcrs briefly the methods installed for Witherbee, Sherman & Co. The operation of the system has been for about two years under the direct supervision of T. A. Hammond, Land Agent, and I am indebted to him for a compilation of the results. Sanitation The sanitary service covers 238 tenements. The installation cost was about $22 per tenement, as follows: Privy, $15; privy box, $3; proportion of incinerator cost, $2; garbage can, $2. The operating cost is $1 per month for each tenement. In considering the installation of an ordinary village system of water supply and sewerage two difficulties were encountered: First, lack of a sufficient quantity of water; there is no stream large enough, as Mineville is situated very close to the divide between the Lake Champlain and Hudson River watersheds. A storage reservoir was tried, but the only location available, among glacial hills, would not hold water. Second, the expense of digging ditches for the distribution of water and sewer pipes is so great as to be prohibitive; Mineville is built chiefly in a valley covered in the bottom with drift, in this case a combination of boulders and hard pan. Digging in this material costs 80c. to $1 per cubic yard, and pipes must be placed 41/2 ft. down to be below frost. The houses are scattered along 4 miles of streets, the oldest having been built in the original forest 65 years ago. The newer houses have gone up a few at a time wherevcr a clear space could be found and the slopes were not too steep. This has advantages, as it separates the dwellings into

Jan 1, 1915

By H. W. Morse

MANY of our largest copper deposits contain both sulfide and oxidized copper minerals. The large porphyry mines, with a total copper content of from 1.3 to 2.0 per cent., send to their mills ore with an oxide content of from 0.2 to 0.4 per cent. While the recoveries of the sulfide minerals are considered satisfactory, using modern flotation practice, the recovery of the oxi- dized portion of the copper is small; better recoveries of oxidized copper were made before flotation methods were adopted. Beside the ores containing copper mainly as sulfide, with a small amount of oxidized copper,, many of the large porphyry mines have oxide orebodies, in which the propor-tion of non-sulfide minerals is so high that 2 present methods of treatment are ineffi-cient. In some of the well-known ore-bodies in the Miami-Inspiration district the copper occurs about equally in sulfide and oxidized forms; and the mixing of minerals is complete throughout the ore-body. There is no possibility of mining the sulfides and the oxides selectively. At the New Cornelia mine, however, the oxide, and sulfide ores are sharply separated, per-haps by an ancient water level, so that the oxide ore may be mined and treated in a plant built for that purpose, and the under-lying sulfide ore may be left for treatment in another plant. If copper is to be made from an ore having a total content of 1.5 per cent., it must be concentrated or removed from the ore by some. hydrometallurgical method. Flotation is generally successful for the sulfide minerals and flotation after filming with sulfide seems to work in many cases on the pure carbonate minerals. Callow has given an extensive report on the results of "sulfidizing" flotation on the ores of the. Magma mine.1 Where such ?a 'method can be applied, it ?may be, the best

Jan 9, 1922

By David J. Dunn

GENERAL NOTES Liner Design for Comminution Liners in crushers and mills are the mechanical link between machine and ore. The way liners transfer energy to media and ore determines to large degree the production rate, liner wear rate, maintenance cost, energy use, and availability of the comminution process. Plant capacity and mineral recovery economics, and return on investment, are thus strongly dependent upon these simple, low cost metal shapes of which so much is demanded. The complexity of dynamic relationships between liner configuration, material properties, ore characteristics, and operating parameters defy simplistic generalization. Rules-of-thumb and axioms of years past fall into disuse almost daily as new analytical methods, assisted by computers and sophisticated control systems, are applied to crushing and grinding processes. Recent literature is well supplied with references citing production benefits that improved liner designs produce. This chapter is intended to review especially promising liner designs and material developments and presents cameo case studies showing the benefits derived from their application to comminution circuits (Tables 1,2,4,5,7). Complete discussions of liner design and wear materials are beyond the scope of this chapter. Norman's comprehensive studies in references (1) and (2) and Mclvor's analyses of mill speed/configuration effects (3) are especially useful reading for designers and operators of crushing and grinding circuits. Changing trends in ore, product value, and costs of wear materials, interest, labor, and energy, make ongoing evolution of liner design equally important for existing mines and for projects still on the drafter's board. Original designs supplied as new equipment must, of necessity, be best estimates. These can usually be improved as operating experience replaces engineering forecasts. Advent of new materials or design concepts such as the Angular Spiral Liners (Korpi (4) ) or Norman's Bimetallic design (2) offer improvement potential that must be evaluated if a given circuit is to be kept competitive versus others making similar products.

Jan 1, 1982

By W. H. Ode, W. A. Selvig

By plotting fixed carbon against British thermal units of coals free from mineral matter, and ranging in rank from anthracite to lignite, it is found that the coals of higher rank, from anthracite to the higher rank of the high-volatile bituminous coals, inclusive, can be separated into groups according to their degree of metamorphism by reference to their fixed carbon. Such charts show also that the coals lower in rank can be best separated into groups with respect to B.t.u., especially when plotted on the moist basis, that is, coal containing its natural bed moisture. A tentative scheme for coal classification was presented at the October, 1932, meeting of the Technical Committee on Scientific Classification, of the American Standards Association Sectional Committee on Coal Classification. This scheme was sponsored by Subcommittee IV on Tentative Classification of Coals, under the chairmanship of W. T. Thom, Jr. It proposed the grouping of coals according to rank by reference to fixed carbon and B.t.u., on the basis of coal containing its natural bed moisture but free from mineral matter. This scheme proposed classifying coals into four broad classes: (1) anthracitic, (2) bituminous, (3) subbituminous, (4) lignitic. The anthracitic class was divided into three groups designated as meta-anthracite, normal anthracite, and semianthracite. The bituminous class also was divided into three groups, low volatile, medium volatile, and high volatile. The high-volatile group was further subdivided into four subgroups according to moisture content, as fo1lows: (1) less than 5 per cent, (2) 5 to 10 per cent, (3) 10 to 15 per cent, and (4) 15 per cent and more. The subbituminous class was divided into two groups, group 1 including subbituminous coals having calorific values of 10,500 B.t.u. or more, and group 2 including those with less than 10,500 B.t.u. The lignitic class of coal was divided into two groups both below 8,000 B.t.u., the one group consisting of consolidated and the other of unconsolidated

Jan 1, 1934

By A. W. H. Morris, G. H. Laurie, J. N. Pratt

Using- galvanic cells of the form Sn(liq)/Sn" (LiCl-KC1-SnCl,)/Sn-Ag (alloy), measurements have been made of relative thermodynamic properties of the a, C, E, and liquid phases of the Ag-Sn alloy system. Partial heats of solution of the components in the liquid alloys lzave also been observed by direct cal-orimetric measurement in an isoperibol calorimeter. The thermodynanzic quantities are disczlssed in relation to structural and other properties and the existence of anomalous minor fluctuations in the partial heats and entropies of solution in liquid alloys is tentatively suggested. In the course of a recent electro motive-force study of the thermodynamic properties of Sn-Ag-Pd liquids,' some measurements were also performed on the Ag-Sn binary system. Most previous thermodynamic studies of this system have been concerned with the liquid state. Measurements confined to the limiting heat of solution of silver in liquid tin have been made by many calorimetric workers2 while high-temperature calorimetric measurements of the heats of formation of the full range of liquid alloys are reported in the early work of Kawakami~ (1323°K) and more recently by Wittig and Gehrin~(1248°K). Electromotive-force studies on liquid alloys have been made by Yanko, Drake, and Hovorka' (606" to 686°K; 86 to 99.4 at. pct Sn) and by Frantik and Mc Donald' (900°K; 30 to 90 at. pct Sn). The only known measurements on the solid state are of heats of formation of the a, £, and c phases; these values were obtained using tin-solution calorimetry, at 723"K, by Kleppa,~ whose investigation also yielded heats of formation of liquid alloys containing more than 64 at. pct Sn. The present experiments on the Ag-Sn alloys include a re-examination of the liquid phase and, because of the dearth of free-energy data for the solid state, attempted measurements on the a, c, and E phases. The principal new feature of electromotive-force results obtained for the liquid phase was an indication of anomalous fluctuations in the partial heats and entropies of solution of tin at certain compositions. However, since the values for these thermodynamic quantities were determined from the temperature coefficients of cell potentials, which are commonly subject to considerable error, confirmation by calorimetric measurements was considered desirable. A detailed investigation of the partial heats of solution of the components in the binary liquids was made using a liquid metal solution calorimeter. I) GALVANIC CELL STUDIES a) Experimental Details. Measurements were made, as a function of alloy composition and temperature, of the potentials of reversible galvanic cells of the form: ~n(liq)/~n++/~n-Ag (solid or liquid alloy) Details of the apparatus and experimental techniques have been given elsewhere.' so that a brief account will suffice here. Molten salt, 58 mole pct LiC1-42 mole pct KC1, containing small amounts (1 to 2 mole pct) of stannous chloride was used as the electrolyte. The salts were dehydrated by pre-electrolysis and vacuum -drying techniques. Cells were established under an argon atmosphere by immersing tin and alloy electrodes in the molten salt contained in a large silica tube, heated in a vertical resistance furnace. The tube was sealed at the top by a head plate provided with openings permitting the simultaneous insertion of six electrodes, a central thermocouple sheath, and connections to vacuum and argon lines. Temperatures were controlled to *0.2"C over prolonged periods, with maximum variation over the electrodes at any time of 0.l°C. Temperatures were measured with a standardized Pt/13 pct Rh-Pt couple. The electromotive force of this and the cell potentials were measured on a Cambridge Vernier potentiometer and short-period galvanometer. Alloys were prepared from Pass "S" tin (99.999 pct) and Johnson-Matthey high-purity silver (99.999 pct) by melting in evacuated silica capsules and quenching in cold water. For liquid phase experiments, pieces of the resulting alloys were remelted into prepared silica electrode units, while solid electrodes were prepared by remelting into 3-mm bore tubing, inserting a cleaned molybdenum lead wire, and quenching to produce uniform rods about 3 cm in length, with soundly attached leads. In all cases remelting was done under an argon atmosphere. The solid electrodes were subsequently annealed in evacu ated silica tubes for 14 days at about 20°C below the solidus and quenched. Analyses showed that these techniques produced uniform electrodes with no significant change from weighed out compositions. b) Results and Discussion. Measurements were made on about forty alloys in the solid and liquid states, over varying ranges of temperature between 550" and 1050°K. Stable, mutually consistent, and reproducible electromotive-force data were obtained with most liquid alloys and these are shown in Fig. 1. Investigations were extended below the liquidus tem-

Jan 1, 1967

By E. P. Klier, Volker Weiss, George Sachs

IT has been shown that the isothermal transformation of austenite in a special steel can be modified by isothermal holding in the high subcritical transformation range.' Since this treatment potentially leads to increased hardenability, limited testing has been completed to determine if the stabilization effects observed with this treatment can be used to advantage in the heat-treating of 4340 steel. As an index of the effects of the several austenitizing treatments on the hardenability of the steel, Jominy-type hardenability tests were completed for specimens 2.5 in. in diameter and 8 in. long. Since the steel studied is to be used at strength levels where notch sensitivity is of major concern, notch sensitivity after selected austenitizing treatments has been evaluated by notch tensile tests for several specimen sizes. The steel composition and the austenitizing treatments are given in Table I. The test specimens are presented in Fig. 1. The hardenability data are given in Fig. 2 and the notch tensile properties are presented in Fig. 3. The hardenability of the steel investigated when determined by use of the standard Jominy test specimen2 as high and remained essentially unchanged for the different austenitizing treatments. For the larger test specimen, as has been shown by other investigations," the characteristic hardenability indexes are changed and it becomes possible to isolate austenitizing treatments which promote maximum hardenability. The stepped austenitizing treatment promotes higher hardenability as is indicated in Fig. 2. The evaluation of notch sensitivity for very high strength steels is best accomplished by means of the notch tensile test. The experimental conditions of the test, however, modify the notch strengths measured, and in the present experimentation an effort was made to achieve a limiting notch condition by fixing the notch root radius at 0.001 in. while the specimen diameter was allowed to increase from 0.3 to 1.1 in.* For this root radius the notch strength, 0.3-in.-diam specimen, and this trend differs from that for the larger specimens. At the highest tempering temperatures the 1.1-ip.-diam specimens yield comparable results for the austenitizing treatments compared. However, as the tempering temperature is progressively lowered below 800°F, em-

Jan 1, 1958

By M. R. Tek, K. H. Coats, D. L. Katz

A large number of boundary value problems encountcred in unsteady-state heat transfer, fluid flow through porous media, neutron diffusion and mass transfer involve the solution of a linear, parabolic partial differential equation commonly refcrred to as the diffusivity equation, where U is the dependent potential variable. K is the diffusivity (hydraulic, thermal, neutron, etc.) and 1 is the time variablc. Solutions to Eq. I are available in the literature for a wide variety of initial and houndary conditions. The great majority of these solutions are ohtained for geometric boundaries corresponding to linear. cylindrical or spherical flow models. A typical engineering application where the solution to Eq. 1 is required is the calculation of underground water encroachment across the boundaries of oil or natural gas reservoirs, In this particular area of application, the reservoir boundary is invariably approximated by circular geometry. However. the areal shape of many reservoirs can be better approximated by elliptic rather than circular boundaries. Thus the need for a general method of solving the diffusivity equation in elliptic coordinates arises in this problem as well as in other engineering applications involving elliptic boundaries. The solution to the diffusivity equation usually in volves the Error Function for the linear flow model, Bessel functions for the radial flow model and trigonometric or Legendre functions for the spherical flow model. It is well known that the general solution to the diffusivity equation in elliptic coordinates involves Mathieu functions. The significance of Mathieu functions in the analytical treatment of the diffusivity equation in elliptic coordinates is discussed in the literature However, these references do not providc analytical solutions useful in practical engineering problems. The objectives of this papcr are the development of the equations describing the unsteady-state liquid flow through a porous medium with an elliptic inner boun- dary, the development of a numerical method of solving these equations and, finally, a comparison of the water encroachment quantities calculated from the elliptic flow equation with those calculated from the radial flow equation. While the specific problem treated in this paper relates to unsteady-state liquid flow through a porous medium, the basic equations and computational techniques devcloped will apply equally well to problems occurring in the other areas of engincering interest mentioned previously. The solution given here is limited to a single case in which thc outer boundary encloses an area 100 times that of the inner boundary. DESCRIPTION OF THE FLOW MODEL Fig. 1 shows the flow model upon which the calcu lations presented in this paper are based. The inncr and outer houndaries of the flow model are represented by two confocal ellipses with major and minor axes, respectively, equal to 2a1, 2b1, and 2a, and 26,. The height of the elliptic cylinder flow model is denoted by 17. The following assumptions are employed in the development 01 the equations governing the unsteady-state liquid flow through the described flow model. 1. Uniform porosity and permeability throughout the flow model